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Introduction
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection0
Tue, 12 Apr 2016 23:00:00 GMT
<p>This course explores reasons for studying mathematics, practical applications of mathematical ideas and aims to help you to recognize mathematics when you come across it. It introduces the you to the graphics calculator, and takes you through a series of exercises from the <i>Calculator Book</i>, <i>Tapping into Mathematics With the TI83 Graphics Calculator</i>. The course ends by asking you to reflect on the process of studying mathematics.</p><p>
<b>In order to complete this course you will need to have obtained a Texas Instruments TI83 calculator and the book <i>Tapping into Mathematics With the TI83 Graphics Calculator</i> by Barrie Galpin and Alan Graham (eds), Addison Wesley, 1997 (ISBN 0201175479)</b>.</p><p></p><p>This OpenLearn course provides a sample of level 1 study in <span class="oucontentlinkwithtip"><a class="oucontenthyperlink" href="http://www.open.ac.uk/courses/find/mathematics?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">Mathematics</a></span>.</p>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection0
IntroductionMU120_1<p>This course explores reasons for studying mathematics, practical applications of mathematical ideas and aims to help you to recognize mathematics when you come across it. It introduces the you to the graphics calculator, and takes you through a series of exercises from the <i>Calculator Book</i>, <i>Tapping into Mathematics With the TI83 Graphics Calculator</i>. The course ends by asking you to reflect on the process of studying mathematics.</p><p>
<b>In order to complete this course you will need to have obtained a Texas Instruments TI83 calculator and the book <i>Tapping into Mathematics With the TI83 Graphics Calculator</i> by Barrie Galpin and Alan Graham (eds), Addison Wesley, 1997 (ISBN 0201175479)</b>.</p><p></p><p>This OpenLearn course provides a sample of level 1 study in <span class="oucontentlinkwithtip"><a class="oucontenthyperlink" href="http://www.open.ac.uk/courses/find/mathematics?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">Mathematics</a></span>.</p>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

Learning outcomes
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsectionlearningoutcomes
Tue, 12 Apr 2016 23:00:00 GMT
<p>After studying this course, you should be able to:</p><ul><li><p>Give an opinion of what mathematics is</p></li><li><p>recognise different types of written mathematics</p></li><li><p>tackle mathematical problems using a calculator , demonstrating an understanding for basic arithmetic, percentages, square roots, reciprocals and powers</p></li><li><p>express and interpret numbers in scientific notation, both in writing and with the use of a calculator</p></li><li><p>give some examples of common mathematical ‘doing–undoing’ pairs of operations.</p></li></ul>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsectionlearningoutcomes
Learning outcomesMU120_1<p>After studying this course, you should be able to:</p><ul><li><p>Give an opinion of what mathematics is</p></li><li><p>recognise different types of written mathematics</p></li><li><p>tackle mathematical problems using a calculator , demonstrating an understanding for basic arithmetic, percentages, square roots, reciprocals and powers</p></li><li><p>express and interpret numbers in scientific notation, both in writing and with the use of a calculator</p></li><li><p>give some examples of common mathematical ‘doing–undoing’ pairs of operations.</p></li></ul>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

Why study mathematics?
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection1
Tue, 12 Apr 2016 23:00:00 GMT
<div class="oucontentfigure" style="width:371px;" id="fig001_002"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/3b7cb50d/mu120_1_002i.jpg" alt="Figure 1.2" width="371" height="493" style="maxwidth:371px;" class="oucontentfigureimage"/><div class="oucontentfiguretext"><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Having set out on her mathematical journey, Dawn suddenly remembered that she had forgotten to pack any sandwiches</span></div></div></div><p>There are many reasons why people study mathematics and they gain a range of different benefits from doing so. For some, it provides a means of achieving greater understanding and insight into the physical world around them. For others, it is the social world of people and their concerns that is most in focus and of greatest interest. For some, doing mathematics is about sharing in an ageold human activity. For others again, it is curiosity about the inner, individual worlds of imagination and possibility.</p><p>You, of course, will have your own interests and enthusiasms. As your mathematical thinking develops, both while you are studying this course and afterwards, you will be able to bring your enhanced mathematical understanding and skill to bear on different aspects of your life.</p>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection1
Why study mathematics?MU120_1<div class="oucontentfigure" style="width:371px;" id="fig001_002"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/3b7cb50d/mu120_1_002i.jpg" alt="Figure 1.2" width="371" height="493" style="maxwidth:371px;" class="oucontentfigureimage"/><div class="oucontentfiguretext"><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Having set out on her mathematical journey, Dawn suddenly remembered that she had forgotten to pack any sandwiches</span></div></div></div><p>There are many reasons why people study mathematics and they gain a range of different benefits from doing so. For some, it provides a means of achieving greater understanding and insight into the physical world around them. For others, it is the social world of people and their concerns that is most in focus and of greatest interest. For some, doing mathematics is about sharing in an ageold human activity. For others again, it is curiosity about the inner, individual worlds of imagination and possibility.</p><p>You, of course, will have your own interests and enthusiasms. As your mathematical thinking develops, both while you are studying this course and afterwards, you will be able to bring your enhanced mathematical understanding and skill to bear on different aspects of your life.</p>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

1 Aims
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.1
Tue, 12 Apr 2016 23:00:00 GMT
<p>The aims of this section are to:</p><ul class="oucontentbulleted"><li>
<p>help you clarify your own ideas of what mathematics is;</p>
</li><li>
<p>give you experience of reading different types of written mathematics;</p>
</li><li>
<p>give you an initial feel of how a mathematician views the world.</p>
</li></ul><p>You have chosen to study a course entitled ‘Mathematics everywhere’, but what exactly is mathematics? It sounds a simple enough question but, in fact, mathematics is not easy to define.</p><p>The Concise Oxford Dictionary defines mathematics like this:</p><div class="oucontentquote oucontentsbox" id="quo001_001"><blockquote><p>
<b>mathematics</b>
<i>n. pl</i>. (also treated as <i>sing</i>.) (pure) ∼, abstract science of space, number, and quantity; (applied) ∼, this applied to branches of physics, astronomy, etc.; (as <i>pl</i>.) use of mathematics in calculation etc.; so <b>mathemati’</b>cian <i>n</i>.</p></blockquote></div><p>While Pears Cyclopaedia describes it like this:</p><div class="oucontentquote oucontentsbox" id="quo001_002"><blockquote><p>
<b>Mathematics</b> is a body of knowledge expressed in a language of symbols. <i>Pure</i> mathematics studies the propositions that can be deduced in this language by applying definite rules of reasoning to sets of axioms. In <i>Applied</i> mathematics, the mathematical language is used, often with great effect to discuss problems of the real world, such as mechanics, statistics and science generally. In range, subtlety, complexity and depth mathematics is unsurpassed among the intellectual disciplines and its study has attracted some of the most brilliant men (<i>sic</i>) in history.</p></blockquote></div><p>One of these ‘brilliant’ individuals, Jacob Bronowski, under the heading <i>The Music of the Spheres</i> wrote:</p><div class="oucontentquote oucontentsbox" id="quo001_003"><blockquote><p>Mathematics is in many ways the most elaborated and sophisticated of the sciences—or so it seems to me, as a mathematician. So I find both a special pleasure and constraint in describing the progress of mathematics, because it has been part of so much human speculation: a ladder for mystical as well as rational thought in the intellectual ascent of man.</p></blockquote></div><p>However, not all scientists share the same enthusiasm for the subject. Carl Jung, the eminent Swiss psychiatrist, described his ‘downright fear of the mathematics class’ and went on:</p><div class="oucontentquote oucontentsbox" id="quo001_004"><blockquote><p>All my life it remained a puzzle to me why it was that I never managed to get my bearings in mathematics when there was no doubt that I could calculate properly.</p></blockquote></div>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.1
1 AimsMU120_1<p>The aims of this section are to:</p><ul class="oucontentbulleted"><li>
<p>help you clarify your own ideas of what mathematics is;</p>
</li><li>
<p>give you experience of reading different types of written mathematics;</p>
</li><li>
<p>give you an initial feel of how a mathematician views the world.</p>
</li></ul><p>You have chosen to study a course entitled ‘Mathematics everywhere’, but what exactly is mathematics? It sounds a simple enough question but, in fact, mathematics is not easy to define.</p><p>The Concise Oxford Dictionary defines mathematics like this:</p><div class="oucontentquote oucontentsbox" id="quo001_001"><blockquote><p>
<b>mathematics</b>
<i>n. pl</i>. (also treated as <i>sing</i>.) (pure) ∼, abstract science of space, number, and quantity; (applied) ∼, this applied to branches of physics, astronomy, etc.; (as <i>pl</i>.) use of mathematics in calculation etc.; so <b>mathemati’</b>cian <i>n</i>.</p></blockquote></div><p>While Pears Cyclopaedia describes it like this:</p><div class="oucontentquote oucontentsbox" id="quo001_002"><blockquote><p>
<b>Mathematics</b> is a body of knowledge expressed in a language of symbols. <i>Pure</i> mathematics studies the propositions that can be deduced in this language by applying definite rules of reasoning to sets of axioms. In <i>Applied</i> mathematics, the mathematical language is used, often with great effect to discuss problems of the real world, such as mechanics, statistics and science generally. In range, subtlety, complexity and depth mathematics is unsurpassed among the intellectual disciplines and its study has attracted some of the most brilliant men (<i>sic</i>) in history.</p></blockquote></div><p>One of these ‘brilliant’ individuals, Jacob Bronowski, under the heading <i>The Music of the Spheres</i> wrote:</p><div class="oucontentquote oucontentsbox" id="quo001_003"><blockquote><p>Mathematics is in many ways the most elaborated and sophisticated of the sciences—or so it seems to me, as a mathematician. So I find both a special pleasure and constraint in describing the progress of mathematics, because it has been part of so much human speculation: a ladder for mystical as well as rational thought in the intellectual ascent of man.</p></blockquote></div><p>However, not all scientists share the same enthusiasm for the subject. Carl Jung, the eminent Swiss psychiatrist, described his ‘downright fear of the mathematics class’ and went on:</p><div class="oucontentquote oucontentsbox" id="quo001_004"><blockquote><p>All my life it remained a puzzle to me why it was that I never managed to get my bearings in mathematics when there was no doubt that I could calculate properly.</p></blockquote></div>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

1.1 Mathematics and you
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.2
Tue, 12 Apr 2016 23:00:00 GMT
<p>Many people's ideas about what mathematics actually is are based upon their early experiences at school. The first two activities aim to help you recall formative experiences from childhood.</p><div class=" oucontentactivity oucontentsheavybox1 oucontentsbox " id="act001_001"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 1 Carl Jung's school days</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Read carefully the article below, <i>School Years</i>. As you read, look out for and make a note of any sentences which resonate particularly with your own experience of learning mathematics at school. It may be that you remember similar feelings or situations. Alternatively, Jung's words may spark off much more positive memories for you.</p><p>Click on the link below to read Carl Jung on 'School Years'</p><p><span class="oucontentlinkwithtip"><a class="oucontenthyperlink" href="https://www.open.edu/openlearn/ocw/mod/resource/view.php?id=26497">School Years</a></span></p></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><p>Of course, there is no single right answer to this activity as your response will depend entirely on your memories of your own experience at school.</p><p>Some people might have marked the following sentence as one with which they agreed:</p><div class="oucontentquote oucontentsbox" id="quo001_007"><blockquote><p>The teacher pretended that algebra was a perfectly natural affair, to be taken for granted, whereas I didn't even know what numbers were.</p></blockquote></div><p>However, one person reading this underlined the word ‘pretended’, and wrote in the margin ‘The teacher wasn't pretending! I expect for him, as for me, algebra did seem a perfectly natural affair.’</p><p>Here are some other parts of the article which have particular significance for some people.</p><div class="oucontentquote oucontentsbox" id="quo001_008"><blockquote><p>Oddly enough my class mates could handle these things …</p><p>I finally grasped that what was aimed at was a kind of system of abbreviation, with which many quantities could be put into a short formula.</p><p>Equations I could comprehend only by inserting specific numerical values in place of the letters …</p><p>I was so intimidated by my incomprehension that I did not dare to ask any questions.</p></blockquote></div></div></div></div></div><p>Notice that this was an activity: and so you were expected to be active. You were asked to read and to make notes.</p><div class=" oucontentactivity oucontentsheavybox1 oucontentsbox " id="act001_002"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 2 Back to school</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Spend a couple of minutes thinking about your experiences of mathematics at the schools you have attended. Try to picture the classrooms, the teachers, or any of the individual lessons. Are there particular emotions linked to mathematics? Did any of your teachers affect the way you felt about the subject? Do you think you were ‘good at maths’?</p><p>Summarize your thinking by completing the following sentence: ‘During my school years, I came to see that mathematics was…’.</p></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><p>Again, this activity has no right or wrong answers. You were asked to do two things: some thinking (mainly using your memory) and some writing. You will know whether you responded to both these requests as thoroughly as possible.</p><p>In this case you might have found it useful to do the writing on a separate sheet of paper, or perhaps you squeezed it into the margin beside the main text in the course.</p><p>Here are some contrasting ways in which people have completed the sentence: ‘During my school years, I came to see that mathematics was …’</p><ul class="oucontentbulleted"><li>
<p>a subject which I found intriguing, challenging and sometimes confusing.</p>
</li><li>
<p>to be avoided as much as possible.</p>
</li><li>
<p>fun!</p>
</li><li>
<p>going to be useful in my work as a nurse.</p>
</li></ul></div></div></div></div><p>Outside school, you will have moved on from <i>learning</i> mathematics to <i>using</i> it, perhaps consciously but, probably more frequently, unconsciously. For example, you may have looked at a statistical chart in a newspaper or on TV and subconsciously used mathematics in interpreting the meaning. You may have had to prepare a report which used numerical data. You will certainly have used mathematics when handling money, comparing prices, estimating the length of a journey (both time and distance), doing DIY jobs, following recipes, and so on.</p><div class=" oucontentactivity oucontentsheavybox1 oucontentsbox " id="act001_003"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 3 Everyday maths</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><ol class="oucontentnumbered"><li>
<p>Think back over the last day or two and try to identify as many occasions as possible when you have been using mathematics. How would you describe your level of competence with the mathematics that you were using?</p>
</li><li>
<p>When was the last time you noticed that you were consciously thinking about mathematics? Did you do so with confidence?</p>
</li></ol></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><p>In this activity you were not asked to write anything—the activity required here was simply to think. Of course, there is no reason why you should not have made some notes or answered the questions in writing, and indeed this may have helped you to ensure that you really engaged with the questions asked. It is all too easy to give such questions only cursory thought, whereas the discipline of writing ensures that your thinking is active and purposeful.</p><p>An alternative way of ensuring that you engage fully is to speak your answers out loud. If there is a friend or member of the family who is willing to listen it can be very helpful, but otherwise many OU students have found that household pets make good listeners! Either way, writing or speaking your answers will certainly help you maintain an active learning style.</p><p>One person discussed this activity with their partner and together they came up with the following list of occasions when they had been subconsciously using mathematics during one weekend spent visiting parents.</p><ul class="oucontentbulleted"><li>
<p>Estimating what time to leave home in order to arrive in time for lunch.</p>
</li><li>
<p>Comparing petrol prices.</p>
</li><li>
<p>Calculating (roughly) the cost of coffees when they stopped at the service station–did they have enough cash?</p>
</li><li>
<p>Working out how long it had been since we saw a distant member of the family.</p>
</li><li>
<p>Estimating how much water to put in an unfamiliar teapot.</p>
</li><li>
<p>Discussing with parents ways of increasing the interest they get on their savings.</p>
</li><li>
<p>Working out whether there was enough wood of the right size in the garage to put up extra shelves.</p>
</li><li>
<p>Sharing the cost of a meal in a restaurant.</p>
</li><li>
<p>Planning an alternative route home in order to avoid roadworks on the motorway.</p>
</li></ul></div></div></div></div>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.2
1.1 Mathematics and youMU120_1<p>Many people's ideas about what mathematics actually is are based upon their early experiences at school. The first two activities aim to help you recall formative experiences from childhood.</p><div class="
oucontentactivity
oucontentsheavybox1 oucontentsbox " id="act001_001"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 1 Carl Jung's school days</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Read carefully the article below, <i>School Years</i>. As you read, look out for and make a note of any sentences which resonate particularly with your own experience of learning mathematics at school. It may be that you remember similar feelings or situations. Alternatively, Jung's words may spark off much more positive memories for you.</p><p>Click on the link below to read Carl Jung on 'School Years'</p><p><span class="oucontentlinkwithtip"><a class="oucontenthyperlink" href="https://www.open.edu/openlearn/ocw/mod/resource/view.php?id=26497">School Years</a></span></p></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><p>Of course, there is no single right answer to this activity as your response will depend entirely on your memories of your own experience at school.</p><p>Some people might have marked the following sentence as one with which they agreed:</p><div class="oucontentquote oucontentsbox" id="quo001_007"><blockquote><p>The teacher pretended that algebra was a perfectly natural affair, to be taken for granted, whereas I didn't even know what numbers were.</p></blockquote></div><p>However, one person reading this underlined the word ‘pretended’, and wrote in the margin ‘The teacher wasn't pretending! I expect for him, as for me, algebra did seem a perfectly natural affair.’</p><p>Here are some other parts of the article which have particular significance for some people.</p><div class="oucontentquote oucontentsbox" id="quo001_008"><blockquote><p>Oddly enough my class mates could handle these things …</p><p>I finally grasped that what was aimed at was a kind of system of abbreviation, with which many quantities could be put into a short formula.</p><p>Equations I could comprehend only by inserting specific numerical values in place of the letters …</p><p>I was so intimidated by my incomprehension that I did not dare to ask any questions.</p></blockquote></div></div></div></div></div><p>Notice that this was an activity: and so you were expected to be active. You were asked to read and to make notes.</p><div class="
oucontentactivity
oucontentsheavybox1 oucontentsbox " id="act001_002"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 2 Back to school</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Spend a couple of minutes thinking about your experiences of mathematics at the schools you have attended. Try to picture the classrooms, the teachers, or any of the individual lessons. Are there particular emotions linked to mathematics? Did any of your teachers affect the way you felt about the subject? Do you think you were ‘good at maths’?</p><p>Summarize your thinking by completing the following sentence: ‘During my school years, I came to see that mathematics was…’.</p></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><p>Again, this activity has no right or wrong answers. You were asked to do two things: some thinking (mainly using your memory) and some writing. You will know whether you responded to both these requests as thoroughly as possible.</p><p>In this case you might have found it useful to do the writing on a separate sheet of paper, or perhaps you squeezed it into the margin beside the main text in the course.</p><p>Here are some contrasting ways in which people have completed the sentence: ‘During my school years, I came to see that mathematics was …’</p><ul class="oucontentbulleted"><li>
<p>a subject which I found intriguing, challenging and sometimes confusing.</p>
</li><li>
<p>to be avoided as much as possible.</p>
</li><li>
<p>fun!</p>
</li><li>
<p>going to be useful in my work as a nurse.</p>
</li></ul></div></div></div></div><p>Outside school, you will have moved on from <i>learning</i> mathematics to <i>using</i> it, perhaps consciously but, probably more frequently, unconsciously. For example, you may have looked at a statistical chart in a newspaper or on TV and subconsciously used mathematics in interpreting the meaning. You may have had to prepare a report which used numerical data. You will certainly have used mathematics when handling money, comparing prices, estimating the length of a journey (both time and distance), doing DIY jobs, following recipes, and so on.</p><div class="
oucontentactivity
oucontentsheavybox1 oucontentsbox " id="act001_003"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 3 Everyday maths</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><ol class="oucontentnumbered"><li>
<p>Think back over the last day or two and try to identify as many occasions as possible when you have been using mathematics. How would you describe your level of competence with the mathematics that you were using?</p>
</li><li>
<p>When was the last time you noticed that you were consciously thinking about mathematics? Did you do so with confidence?</p>
</li></ol></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><p>In this activity you were not asked to write anything—the activity required here was simply to think. Of course, there is no reason why you should not have made some notes or answered the questions in writing, and indeed this may have helped you to ensure that you really engaged with the questions asked. It is all too easy to give such questions only cursory thought, whereas the discipline of writing ensures that your thinking is active and purposeful.</p><p>An alternative way of ensuring that you engage fully is to speak your answers out loud. If there is a friend or member of the family who is willing to listen it can be very helpful, but otherwise many OU students have found that household pets make good listeners! Either way, writing or speaking your answers will certainly help you maintain an active learning style.</p><p>One person discussed this activity with their partner and together they came up with the following list of occasions when they had been subconsciously using mathematics during one weekend spent visiting parents.</p><ul class="oucontentbulleted"><li>
<p>Estimating what time to leave home in order to arrive in time for lunch.</p>
</li><li>
<p>Comparing petrol prices.</p>
</li><li>
<p>Calculating (roughly) the cost of coffees when they stopped at the service station–did they have enough cash?</p>
</li><li>
<p>Working out how long it had been since we saw a distant member of the family.</p>
</li><li>
<p>Estimating how much water to put in an unfamiliar teapot.</p>
</li><li>
<p>Discussing with parents ways of increasing the interest they get on their savings.</p>
</li><li>
<p>Working out whether there was enough wood of the right size in the garage to put up extra shelves.</p>
</li><li>
<p>Sharing the cost of a meal in a restaurant.</p>
</li><li>
<p>Planning an alternative route home in order to avoid roadworks on the motorway.</p>
</li></ul></div></div></div></div>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

Learning through video clips
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.3
Tue, 12 Apr 2016 23:00:00 GMT
<p>The aim of the first three activities was to help you to answer the question ‘What does the term <i>mathematics</i> mean to you?’ Soon you will be asked to view a short video sequence that shows a collection of other people's responses to this question and others that you are trying to answer in this course.</p><p>Video clips are used in many OpenLearn units when it is the most suitable way of introducing some aspect of the topic being studied. Here are some of the reasons why video is used here:</p><ul class="oucontentbulleted"><li>
<p>to show events and places that cannot be easily experienced at first hand;</p>
</li><li>
<p>to save time: for example, in presenting statistical evidence of a study that took over a year to complete;</p>
</li><li>
<p>to provide dynamic visual images that aid learning;</p>
</li><li>
<p>to allow you to collect otherwise inaccessible data;</p>
</li><li>
<p>to provide motivation or trigger curiosity to help you work through a difficult topic;</p>
</li><li>
<p>to add variety to topics by giving alternative viewpoints or approaches.</p>
</li></ul><p>Viewing video for learning purposes requires its own set of skills. Video material is often intensive and needs to be worked on actively and not merely passively ‘watched’. It is not a television programme for entertainment purposes. It is not ‘moving wallpaper’.</p><p>Although watching a video or television programme may well be an excellent aid to memory, a video clip for learning should not be used in isolation. Before watching, complete any preparatory work and find out what the video has been designed to do. As you watch and listen, try to think about the key points that are being made and how they relate to your understanding of the topic. Stop the clip whenever you need time to think about a point that has been made. One strength of video is that you can watch different parts again as often as you like.</p><p>In some video clips, concepts are built up by the rapid intercutting of visual images and such pictures can provides a powerful impact. However, the material being presented may represent just one of a number of possible viewpoints. Try to be critical—question and evaluate what you are viewing. Think about what may have been left out in creating the story, and whether this helps you to understand what is there</p><p>So, to the practicalities of viewing video clips.</p><ul class="oucontentbulleted"><li>
<p>Make sure that you can watch the video in comfort but that you are also in a position where you can make notes. Have a pencil and paper to hand.</p>
</li><li>
<p>Try to ensure that you have enough time to view the clip and respond to the sequence completely. For example, this first sequence itself lasts less than 15 minutes but you may find that you will need a clear halfhour to be able to view parts of it a second time and to do some writing.</p>
</li></ul>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.3
Learning through video clipsMU120_1<p>The aim of the first three activities was to help you to answer the question ‘What does the term <i>mathematics</i> mean to you?’ Soon you will be asked to view a short video sequence that shows a collection of other people's responses to this question and others that you are trying to answer in this course.</p><p>Video clips are used in many OpenLearn units when it is the most suitable way of introducing some aspect of the topic being studied. Here are some of the reasons why video is used here:</p><ul class="oucontentbulleted"><li>
<p>to show events and places that cannot be easily experienced at first hand;</p>
</li><li>
<p>to save time: for example, in presenting statistical evidence of a study that took over a year to complete;</p>
</li><li>
<p>to provide dynamic visual images that aid learning;</p>
</li><li>
<p>to allow you to collect otherwise inaccessible data;</p>
</li><li>
<p>to provide motivation or trigger curiosity to help you work through a difficult topic;</p>
</li><li>
<p>to add variety to topics by giving alternative viewpoints or approaches.</p>
</li></ul><p>Viewing video for learning purposes requires its own set of skills. Video material is often intensive and needs to be worked on actively and not merely passively ‘watched’. It is not a television programme for entertainment purposes. It is not ‘moving wallpaper’.</p><p>Although watching a video or television programme may well be an excellent aid to memory, a video clip for learning should not be used in isolation. Before watching, complete any preparatory work and find out what the video has been designed to do. As you watch and listen, try to think about the key points that are being made and how they relate to your understanding of the topic. Stop the clip whenever you need time to think about a point that has been made. One strength of video is that you can watch different parts again as often as you like.</p><p>In some video clips, concepts are built up by the rapid intercutting of visual images and such pictures can provides a powerful impact. However, the material being presented may represent just one of a number of possible viewpoints. Try to be critical—question and evaluate what you are viewing. Think about what may have been left out in creating the story, and whether this helps you to understand what is there</p><p>So, to the practicalities of viewing video clips.</p><ul class="oucontentbulleted"><li>
<p>Make sure that you can watch the video in comfort but that you are also in a position where you can make notes. Have a pencil and paper to hand.</p>
</li><li>
<p>Try to ensure that you have enough time to view the clip and respond to the sequence completely. For example, this first sequence itself lasts less than 15 minutes but you may find that you will need a clear halfhour to be able to view parts of it a second time and to do some writing.</p>
</li></ul>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

Maths as others see it
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.4
Tue, 12 Apr 2016 23:00:00 GMT
<p>Video: Click to view clip on Whittington Hospital in north London</p><div id="vid001_001" class="oucontentmedia oucontentaudiovideo ompversion1" style="width:400px;"><div class="oucontentdefaultfilter "><span class="oumediafilter"><a href="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/89d3cb0c/ee025aa4/mu120_1_001v.mp4?forcedownload=1" class="oumedialinknoscript ompspacer">Download this video clip.</a><span class="accesshide">Video player: Whittington Hospital</span><a href="#" class="ompentermedia ompaccesshide" tabindex="1">
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</span></div><div class="filter_transcript" id="transcript_ad4a21922"><div><a href="#skip_transcript_ad4a21922" class="accesshide">Skip transcript: Whittington Hospital</a><h4 class="accesshide">Transcript: Whittington Hospital</h4></div><div class="filter_transcript_box" tabindex="0" id="content_transcript_ad4a21922"><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MARK HANSON</div><div class="oucontentdialogueremark">Just nine minutes to go now until the news on the hour. We’ll be back straight after the break with two more records to take us to the news.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">EMMA PRESCOTT</div><div class="oucontentdialogueremark">… but she’s a different girl.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">PATIENT</div><div class="oucontentdialogueremark">She looks good.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">EMMA PRESCOTT</div><div class="oucontentdialogueremark">It’s very important that we use the machine to ensure that the flow rate is correct – so that you get exactly the right amount of drug per hour.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">TREVOR ARNOLD</div><div class="oucontentdialogueremark">My porters and domestics are responsible for cleaning the whole of the hospital – the theatres, the wards, the corridors … This corridor is about 75 metres long, but it’s not that simple. It’s full of little nooks and crannies that have to be accounted for. We measure them separately and come up with the total figure. I know how long it takes.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">RECEPTIONIST</div><div class="oucontentdialogueremark">Hello, Porters.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">TREVOR ARNOLD</div><div class="oucontentdialogueremark">We’ve got porters that look after the routine. Regular collection and deliveries of things like linen, refuse, medical records, the pharmacy. People that carry out those type of duties are our Logistics Team.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">DOMINIC AMOS</div><div class="oucontentdialogueremark">There’s a lot of judgement you’ve got to do in this work, because you’ve got to judge, like, where are you going to go to first, second, third, fourth and so on, and if you can’t get that right, you can’t do the job. Another role that our porters carry out is the Rapid Response Team. These people are responsible for responding quickly to calls for moving patients from A to B, occasionally for equipment as well. And also, importantly, we’ve got to maintain the cleanliness of the hospital, and that falls to our FSAs, the Facility Service Assistants. A ward area is an awkward shape – lots of nooks and crannies. It’s almost impossible to know how long it’s going to take to clean. So what I do instead is I break it down into manageable chunks. Look at each of the areas in turn and break them down as well. Hi Carlos, how’s it going?</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">CARLOGERO MARZIANO</div><div class="oucontentdialogueremark">I’m all right …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">TREVOR ARNOLD</div><div class="oucontentdialogueremark">I used to have to calculate, in long hand, masses and masses of paperwork – sheets of A4. Now, I use a simple spreadsheet on a computer. The spreadsheet calculates for me the square area. At the top you can see the circulation area; that’s the corridor. That particular piece of the corridor, it’s two by two point six metres. I’ve told the computer that it takes point one seven three minutes to clean a square metre of floor area. Times the frequency – it’s cleaned seven times a week. It already knows the dimensions of the room from these two boxes. In this box I’ve put a formula that looks at all of those factors and calculates the time to clean the floor for me – just under six point three minutes. The whole thing I can put in there, and once it’s on that system it’s there for as long as I want it, and it’ll do the calculation for me every time.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">VOX POPS</div><div class="oucontentdialogueremark">Mathematics means to me numbers, figures, adding up, taking
away … … Numbers, figures, graphs …
… Working things out, financial things …
… Numbers, numbers …
… Basics …
… Sums, maths, figures …
… It means numbers and figures and calculations and
headaches …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">EMMA PRESCOTT</div><div class="oucontentdialogueremark">In my job the sort of maths I would be using are things like estimate the probability of drops in haemoglobins, calculation of drug dosages, calculation of volumes to be infused intravenously… This is the patient’s haemoglobin, measured in grams, and these are the weekly periods. So if this patient, after one week posttransfusion, starts at eleven grams, we can estimate that within a week it will drop one and half grams. So, for this particular patient, after the second week, they would have dropped to nine point five grams. So we can estimate that around this time is when we need to actually transfuse some blood into them, and then we would see the rise up again. Why don’t I send off the sample to the blood bank, we can hold it to store it, and then give me a call next week and tell me how you feel …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">PATIENT</div><div class="oucontentdialogueremark">Yeah, alright.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">EMMA PRESCOTT</div><div class="oucontentdialogueremark">… and if need be we can order a couple of pints of blood for you … Thalassaemia is a genetic disorder, which means that these patients are actually born with the disorder. From about the age of six months they don’t produce enough, or any at all, adult haemoglobin, which is essential for life. Haemoglobin carries oxygen to the body tissues, so therefore we have to replace this haemoglobin in the form of blood transfusions. And that usually means that they come to the hospital every three weeks for six to eight hours. Well, we don’t want to overtransfuse these patients, because that in itself would produce problems, so we have to estimate how the haemoglobin will drop, and ideally we’d like to transfuse when the haemoglobin is around nine point five to ten grams.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">EMMA PRESCOTT</div><div class="oucontentdialogueremark">… OK, cos I can’t add the extra to this small bag …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">PATIENT</div><div class="oucontentdialogueremark">Right you are.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">EMMA PRESCOTT</div><div class="oucontentdialogueremark">… so we’ll have to give you a little bit more.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">PATIENT</div><div class="oucontentdialogueremark">Will it be at the same time or …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">EMMA PRESCOTT</div><div class="oucontentdialogueremark">It will be extended, I’m afraid. I’ll put this over the same time as the … The probability of any of your children being born with thalassaemia major is one in four, right. I’ll just illustrate it by showing you on a diagram. So, if we say that this is you – one normal gene and one thalassaemia gene and you’re perfectly normal. And then this is your wife, and likewise she is the same as you, she’s inherited just the trait. OK? So, we can work out the probability of each child being born, on whether they have a normal, a carrier, or have thalassaemia. So, if you pass on this gene, and your wife passes on this gene, then again this baby will be born like yourself as a carrier.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">VOX POPS</div><div class="oucontentdialogueremark">… when I was at school it was add and take away and that was
it …
… arithmetic and algebra and all that sort of thing, and
geometry …
… I liked mathematics at University …
… I wasn’t very good at maths so – and I had a bad teacher so I
didn’t enjoy it very much …
… I saw it as something that was necessary …
… it was probably one of the better things that I did …
… at primary school and secondary school I did not like it at
all …
… one of the number one subjects, along with history and other
things …
… I didn’t like maths, because I wasn’t very good at it …
… well I think it was good in school, when I was in school many,
many moons ago …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">EMMA PRESCOTT</div><div class="oucontentdialogueremark">… I found it quite an intense subject and a rather boring subject, I have to say …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MARK HANSON</div><div class="oucontentdialogueremark">I’ve got two hours to play with each week, and while it’s down to myself what goes into those two hours, you have obviously got to be quite disciplined with how you distribute your time. We’ve got certain reference points within those two hours, those being the news on the hour, which we can’t change, it’s always on the hour, and we’ve also got the advertising as well. Adverts pay the bills, so we can’t move them around. So they’re always at quarter past and quarter to. So, really, we’re trying to organise the music, which is the core of the programme, around those reference points. And in terms of going towards the news and hitting those reference points that I’ve got, you want to be going with a track which you pretty much know how long it’s going to last for. It’s not going to be too short and it’s going to have a sort of ending which is quite a long run out, we call it. And that basically means I’ve got the flexibility that if I’m sort of twenty seconds over I can fade it out, it doesn’t make a lot of difference – I’m losing no vocals. Or if I’ve got to spin some more time out I’ll just leave it running. So that helps us out quite a lot. And that’s for Helen on Mercer Ward. She’s due out today. She’s looking forward to getting home and seeing her cat. So, Helen, nice to have you with us. Hope we don’t see you again, but I really do hope you enjoyed your stay.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">VOX POPS</div><div class="oucontentdialogueremark">… I use maths as part of my everyday life, in work, at home …
… I’m using maths in the way of measurements, I suppose
everyday …
… A lot of the work we do involves figures. You know, even
your cost of living, working out how much mortgage you’ve got
to pay and the rest of it …
… I’ve got two children so when they’re at school they bring
their homework home and I have to help them with that …
… It’s more of the domestic side of my life where mathematics
comes in …
… If you’re talking about measurements, estimating, quantifying,
then I suppose I would say I use maths …
… Every single hour probably. Maths is part of life …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MARK HANSON</div><div class="oucontentdialogueremark">The term ‘mathematician’ means to me a mathematics professional, so somebody who actually maybe teaches maths or studies maths at university or whatever. So I wouldn’t consider myself to be a mathematician. But, on reflection, I probably am somebody who uses maths day to day, and if that’s a mathematician then I think we’re a nation of mathematicians …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">EMMA PRESCOTT</div><div class="oucontentdialogueremark">Yes, I do use mathematics in my daily life, and if that’s how you would perceive mathematics, then yes I suppose I am a mathematician …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">TREVOR ARNOLD</div><div class="oucontentdialogueremark">Well, if you say that what I’m doing makes me a mathematician, then I’ll take that as a compliment. Thanks very much.</div><div class="clearer"></div></div></div><span class="accesshide" id="skip_transcript_ad4a21922">End transcript: Whittington Hospital</span></div><div class="filter_transcript_output" id="output_transcript_ad4a21922"><div class="filter_transcript_copy"><a href="#" id="action_link5d2f3803c36513" class="actionicon" ><img class="icon iconsmall" alt="Copy this transcript to the clipboard" title="Copy this transcript to the clipboard" src="https://www.open.edu/openlearn/ocw/theme/image.php/_s/openlearnng/core/1563274092/t/copy" /></a></div><div class="filter_transcript_print"><a href="#" id="action_link5d2f3803c36514" class="actionicon" ><img class="icon iconsmall" alt="Print this transcript" title="Print this transcript" src="https://www.open.edu/openlearn/ocw/theme/image.php/_s/openlearnng/core/1563274092/t/print" /></a></div></div><div class="oucontentfiguretext"><div class="oucontenttranscriptlink"><span class="filter_transcript_button" id="button_transcript_ad4a21922">Show transcriptHide transcript</span></div><div class="oucontentmediadownload"><a href="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/89d3cb0c/ee025aa4/mu120_1_001v.mp4?forcedownload=1" title="Download this video clip">Download</a></div><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Whittington Hospital</span></div></div></div><div class="oucontentinteractionprint"><div class="oucontentinteractionunavailable">Interactive feature not available in single page view (<a class="oucontentcrossref" href="https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.4#vid001001">see it in standard view</a>).</div></div><div class=" oucontentactivity oucontentsheavybox1 oucontentsbox " id="act001_004"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 4</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>This video clip was recorded in the Whittington Hospital in north London. You will see a series of short sequences in which people respond to questions concerning their own views of mathematics. However, the clip also shows extended sequences in which three people (pictured below) talk about their work in the hospital.</p><div class="oucontentfigure" style="width:373px;" id="fig001_005"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/0c0a0e4a/mu120_1_005i.jpg" alt="Figure 1.5" width="373" height="277" style="maxwidth:373px;" class="oucontentfigureimage"/><div class="oucontentfiguretext"><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Trevor Arnold, hotel services manager</span></div></div></div><div class="oucontentfigure" style="width:389px;" id="fig001_006"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/4970e1d4/mu120_1_006i.jpg" alt="Emma Prescott, Thalassaemia nurse specialist" width="389" height="290" style="maxwidth:389px;" class="oucontentfigureimage" longdesc="view.php?id=4199&extra=longdesc_idp5940352"/><div class="oucontentfiguretext"><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Emma Prescott, Thalassaemia nurse specialist</span></div></div><div class="oucontentlongdesclink oucontentlongdesconly"><a href="https://www.open.edu/openlearn/ocw/mod/oucontent/view.php?id=4199&extra=longdesc_idp5940352&clicked=1">Long description</a></div><a id="back_longdesc_idp5940352"></a></div><div class="oucontentfigure" style="width:390px;" id="fig001_007"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/7781ad76/mu120_1_007i.jpg" alt="Figure 1.7" width="390" height="288" style="maxwidth:390px;" class="oucontentfigureimage"/><div class="oucontentfiguretext"><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Mark Hanson, hospital radio DJ</span></div></div></div><ol class="oucontentnumbered"><li>
<p>As you watch and listen to Trevor, Emma and Mark, make a note of mathematical ideas to which they refer.</p>
<ul class="oucontentbulleted"><li>
<p>What mathematical skills and ideas do they use?</p>
</li><li>
<p>Do you think they are consciously using mathematics?</p>
</li></ul>
</li><li>
<p>As you listen, make a note of any responses about people's view of mathematics which strike you as unusual or particularly interesting.</p>
<ul class="oucontentbulleted"><li>
<p>Are the responses similar to your own?</p>
</li><li>
<p>Do these responses seem to you typical of the population as a whole?</p>
</li></ul>
</li><li>
<p>When the clip has finished look back over the notes you have made and check to see whether you have answered the questions above. If necessary view any parts of the video band again and add to your notes. Also think about the pros and cons of using video in this way.</p>
</li></ol></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><ol class="oucontentnumbered"><li>
<p>Trevor Arnold talks about the need to estimate and measure distances, areas and times. The spreadsheet he created uses hidden formulas which instruct the computer to carry out the routine calculations that he previously did by hand.</p>
<p>Emma Prescott uses mathematics to help her estimate the drop of haemoglobin levels in her patients. By recording how far levels have fallen, she is able to predict when the next blood transfusion will be necessary. She also calculates necessary drug dosages and volumes of intravenous infusions. She uses probability when explaining the likelihood of passing on the disease to a patient's offspring. You will have seen her twice using simple diagrams to convey mathematical ideas—an important theme of this course.</p>
<p>Although Mark Hanson is not consciously using mathematics, he is using a range of mathematical skills as he schedules the time he has available, estimates the lengths of record tracks, subtracts them from the time available, and so on.</p>
</li><li>
<p>When first asked about their attitudes to mathematics, the responses were fairly varied; some people had positive memories of school mathematics while others disliked it or found it boring. You may also have noticed that at the beginning of the videotape most people viewed maths in a rather narrow way—in fact, they tended to see it simply as basic arithmetic applied to everyday situations. As the video unfolds, these perceptions of mathematics became extended. Indeed, all the hospital workers interviewed were prepared, by the end, to think of their jobs more mathematically than they had at the beginning of the video.</p>
<p>Whether or not the views expressed are similar to yours, they may well seem to be typical of the population as a whole. However, this is just a small selection of people and it was not chosen as a representative sample of the whole population. They all came from one particular hospital in one particular area in London. Can you be sure that people's views of mathematics are not influenced by the circumstances of the interview or the nature of their job or the area in which they live?</p>
</li><li>
<p>You may care to read again the comments about using video that were given before Activity 4.</p>
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https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.4
Maths as others see itMU120_1<p>Video: Click to view clip on Whittington Hospital in north London</p><div id="vid001_001" class="oucontentmedia oucontentaudiovideo ompversion1" style="width:400px;"><div class="oucontentdefaultfilter "><span class="oumediafilter"><a href="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/89d3cb0c/ee025aa4/mu120_1_001v.mp4?forcedownload=1" class="oumedialinknoscript ompspacer">Download this video clip.</a><span class="accesshide">Video player: Whittington Hospital</span><a href="#" class="ompentermedia ompaccesshide" tabindex="1">
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</span></div><div class="filter_transcript" id="transcript_ad4a21922"><div><a href="#skip_transcript_ad4a21922" class="accesshide">Skip transcript: Whittington Hospital</a><h4 class="accesshide">Transcript: Whittington Hospital</h4></div><div class="filter_transcript_box" tabindex="0" id="content_transcript_ad4a21922"><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MARK HANSON</div><div class="oucontentdialogueremark">Just nine minutes to go now until the news on the hour. We’ll be back straight after the break with two more records to take us to the news.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">EMMA PRESCOTT</div><div class="oucontentdialogueremark">… but she’s a different girl.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">PATIENT</div><div class="oucontentdialogueremark">She looks good.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">EMMA PRESCOTT</div><div class="oucontentdialogueremark">It’s very important that we use the machine to ensure that the flow rate is correct – so that you get exactly the right amount of drug per hour.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">TREVOR ARNOLD</div><div class="oucontentdialogueremark">My porters and domestics are responsible for cleaning the whole of the hospital – the theatres, the wards, the corridors … This corridor is about 75 metres long, but it’s not that simple. It’s full of little nooks and crannies that have to be accounted for. We measure them separately and come up with the total figure. I know how long it takes.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">RECEPTIONIST</div><div class="oucontentdialogueremark">Hello, Porters.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">TREVOR ARNOLD</div><div class="oucontentdialogueremark">We’ve got porters that look after the routine. Regular collection and deliveries of things like linen, refuse, medical records, the pharmacy. People that carry out those type of duties are our Logistics Team.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">DOMINIC AMOS</div><div class="oucontentdialogueremark">There’s a lot of judgement you’ve got to do in this work, because you’ve got to judge, like, where are you going to go to first, second, third, fourth and so on, and if you can’t get that right, you can’t do the job. Another role that our porters carry out is the Rapid Response Team. These people are responsible for responding quickly to calls for moving patients from A to B, occasionally for equipment as well. And also, importantly, we’ve got to maintain the cleanliness of the hospital, and that falls to our FSAs, the Facility Service Assistants. A ward area is an awkward shape – lots of nooks and crannies. It’s almost impossible to know how long it’s going to take to clean. So what I do instead is I break it down into manageable chunks. Look at each of the areas in turn and break them down as well. Hi Carlos, how’s it going?</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">CARLOGERO MARZIANO</div><div class="oucontentdialogueremark">I’m all right …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">TREVOR ARNOLD</div><div class="oucontentdialogueremark">I used to have to calculate, in long hand, masses and masses of paperwork – sheets of A4. Now, I use a simple spreadsheet on a computer. The spreadsheet calculates for me the square area. At the top you can see the circulation area; that’s the corridor. That particular piece of the corridor, it’s two by two point six metres. I’ve told the computer that it takes point one seven three minutes to clean a square metre of floor area. Times the frequency – it’s cleaned seven times a week. It already knows the dimensions of the room from these two boxes. In this box I’ve put a formula that looks at all of those factors and calculates the time to clean the floor for me – just under six point three minutes. The whole thing I can put in there, and once it’s on that system it’s there for as long as I want it, and it’ll do the calculation for me every time.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">VOX POPS</div><div class="oucontentdialogueremark">Mathematics means to me numbers, figures, adding up, taking
away … … Numbers, figures, graphs …
… Working things out, financial things …
… Numbers, numbers …
… Basics …
… Sums, maths, figures …
… It means numbers and figures and calculations and
headaches …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">EMMA PRESCOTT</div><div class="oucontentdialogueremark">In my job the sort of maths I would be using are things like estimate the probability of drops in haemoglobins, calculation of drug dosages, calculation of volumes to be infused intravenously… This is the patient’s haemoglobin, measured in grams, and these are the weekly periods. So if this patient, after one week posttransfusion, starts at eleven grams, we can estimate that within a week it will drop one and half grams. So, for this particular patient, after the second week, they would have dropped to nine point five grams. So we can estimate that around this time is when we need to actually transfuse some blood into them, and then we would see the rise up again. Why don’t I send off the sample to the blood bank, we can hold it to store it, and then give me a call next week and tell me how you feel …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">PATIENT</div><div class="oucontentdialogueremark">Yeah, alright.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">EMMA PRESCOTT</div><div class="oucontentdialogueremark">… and if need be we can order a couple of pints of blood for you … Thalassaemia is a genetic disorder, which means that these patients are actually born with the disorder. From about the age of six months they don’t produce enough, or any at all, adult haemoglobin, which is essential for life. Haemoglobin carries oxygen to the body tissues, so therefore we have to replace this haemoglobin in the form of blood transfusions. And that usually means that they come to the hospital every three weeks for six to eight hours. Well, we don’t want to overtransfuse these patients, because that in itself would produce problems, so we have to estimate how the haemoglobin will drop, and ideally we’d like to transfuse when the haemoglobin is around nine point five to ten grams.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">EMMA PRESCOTT</div><div class="oucontentdialogueremark">… OK, cos I can’t add the extra to this small bag …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">PATIENT</div><div class="oucontentdialogueremark">Right you are.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">EMMA PRESCOTT</div><div class="oucontentdialogueremark">… so we’ll have to give you a little bit more.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">PATIENT</div><div class="oucontentdialogueremark">Will it be at the same time or …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">EMMA PRESCOTT</div><div class="oucontentdialogueremark">It will be extended, I’m afraid. I’ll put this over the same time as the … The probability of any of your children being born with thalassaemia major is one in four, right. I’ll just illustrate it by showing you on a diagram. So, if we say that this is you – one normal gene and one thalassaemia gene and you’re perfectly normal. And then this is your wife, and likewise she is the same as you, she’s inherited just the trait. OK? So, we can work out the probability of each child being born, on whether they have a normal, a carrier, or have thalassaemia. So, if you pass on this gene, and your wife passes on this gene, then again this baby will be born like yourself as a carrier.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">VOX POPS</div><div class="oucontentdialogueremark">… when I was at school it was add and take away and that was
it …
… arithmetic and algebra and all that sort of thing, and
geometry …
… I liked mathematics at University …
… I wasn’t very good at maths so – and I had a bad teacher so I
didn’t enjoy it very much …
… I saw it as something that was necessary …
… it was probably one of the better things that I did …
… at primary school and secondary school I did not like it at
all …
… one of the number one subjects, along with history and other
things …
… I didn’t like maths, because I wasn’t very good at it …
… well I think it was good in school, when I was in school many,
many moons ago …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">EMMA PRESCOTT</div><div class="oucontentdialogueremark">… I found it quite an intense subject and a rather boring subject, I have to say …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MARK HANSON</div><div class="oucontentdialogueremark">I’ve got two hours to play with each week, and while it’s down to myself what goes into those two hours, you have obviously got to be quite disciplined with how you distribute your time. We’ve got certain reference points within those two hours, those being the news on the hour, which we can’t change, it’s always on the hour, and we’ve also got the advertising as well. Adverts pay the bills, so we can’t move them around. So they’re always at quarter past and quarter to. So, really, we’re trying to organise the music, which is the core of the programme, around those reference points. And in terms of going towards the news and hitting those reference points that I’ve got, you want to be going with a track which you pretty much know how long it’s going to last for. It’s not going to be too short and it’s going to have a sort of ending which is quite a long run out, we call it. And that basically means I’ve got the flexibility that if I’m sort of twenty seconds over I can fade it out, it doesn’t make a lot of difference – I’m losing no vocals. Or if I’ve got to spin some more time out I’ll just leave it running. So that helps us out quite a lot. And that’s for Helen on Mercer Ward. She’s due out today. She’s looking forward to getting home and seeing her cat. So, Helen, nice to have you with us. Hope we don’t see you again, but I really do hope you enjoyed your stay.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">VOX POPS</div><div class="oucontentdialogueremark">… I use maths as part of my everyday life, in work, at home …
… I’m using maths in the way of measurements, I suppose
everyday …
… A lot of the work we do involves figures. You know, even
your cost of living, working out how much mortgage you’ve got
to pay and the rest of it …
… I’ve got two children so when they’re at school they bring
their homework home and I have to help them with that …
… It’s more of the domestic side of my life where mathematics
comes in …
… If you’re talking about measurements, estimating, quantifying,
then I suppose I would say I use maths …
… Every single hour probably. Maths is part of life …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MARK HANSON</div><div class="oucontentdialogueremark">The term ‘mathematician’ means to me a mathematics professional, so somebody who actually maybe teaches maths or studies maths at university or whatever. So I wouldn’t consider myself to be a mathematician. But, on reflection, I probably am somebody who uses maths day to day, and if that’s a mathematician then I think we’re a nation of mathematicians …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">EMMA PRESCOTT</div><div class="oucontentdialogueremark">Yes, I do use mathematics in my daily life, and if that’s how you would perceive mathematics, then yes I suppose I am a mathematician …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">TREVOR ARNOLD</div><div class="oucontentdialogueremark">Well, if you say that what I’m doing makes me a mathematician, then I’ll take that as a compliment. Thanks very much.</div><div class="clearer"></div></div></div><span class="accesshide" id="skip_transcript_ad4a21922">End transcript: Whittington Hospital</span></div><div class="filter_transcript_output" id="output_transcript_ad4a21922"><div class="filter_transcript_copy"><a href="#" id="action_link5d2f3803c36513" class="actionicon" ><img class="icon iconsmall" alt="Copy this transcript to the clipboard" title="Copy this transcript to the clipboard" src="https://www.open.edu/openlearn/ocw/theme/image.php/_s/openlearnng/core/1563274092/t/copy" /></a></div><div class="filter_transcript_print"><a href="#" id="action_link5d2f3803c36514" class="actionicon" ><img class="icon iconsmall" alt="Print this transcript" title="Print this transcript" src="https://www.open.edu/openlearn/ocw/theme/image.php/_s/openlearnng/core/1563274092/t/print" /></a></div></div><div class="oucontentfiguretext"><div class="oucontenttranscriptlink"><span class="filter_transcript_button" id="button_transcript_ad4a21922">Show transcriptHide transcript</span></div><div class="oucontentmediadownload"><a href="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/89d3cb0c/ee025aa4/mu120_1_001v.mp4?forcedownload=1" title="Download this video clip">Download</a></div><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Whittington Hospital</span></div></div></div><div class="oucontentinteractionprint"><div class="oucontentinteractionunavailable">Interactive feature not available in single page view (<a class="oucontentcrossref" href="https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.4#vid001001">see it in standard view</a>).</div></div><div class="
oucontentactivity
oucontentsheavybox1 oucontentsbox " id="act001_004"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 4</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>This video clip was recorded in the Whittington Hospital in north London. You will see a series of short sequences in which people respond to questions concerning their own views of mathematics. However, the clip also shows extended sequences in which three people (pictured below) talk about their work in the hospital.</p><div class="oucontentfigure" style="width:373px;" id="fig001_005"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/0c0a0e4a/mu120_1_005i.jpg" alt="Figure 1.5" width="373" height="277" style="maxwidth:373px;" class="oucontentfigureimage"/><div class="oucontentfiguretext"><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Trevor Arnold, hotel services manager</span></div></div></div><div class="oucontentfigure" style="width:389px;" id="fig001_006"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/4970e1d4/mu120_1_006i.jpg" alt="Emma Prescott, Thalassaemia nurse specialist" width="389" height="290" style="maxwidth:389px;" class="oucontentfigureimage" longdesc="view.php?id=4199&extra=longdesc_idp5940352"/><div class="oucontentfiguretext"><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Emma Prescott, Thalassaemia nurse specialist</span></div></div><div class="oucontentlongdesclink oucontentlongdesconly"><a href="https://www.open.edu/openlearn/ocw/mod/oucontent/view.php?id=4199&extra=longdesc_idp5940352&clicked=1">Long description</a></div><a id="back_longdesc_idp5940352"></a></div><div class="oucontentfigure" style="width:390px;" id="fig001_007"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/7781ad76/mu120_1_007i.jpg" alt="Figure 1.7" width="390" height="288" style="maxwidth:390px;" class="oucontentfigureimage"/><div class="oucontentfiguretext"><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Mark Hanson, hospital radio DJ</span></div></div></div><ol class="oucontentnumbered"><li>
<p>As you watch and listen to Trevor, Emma and Mark, make a note of mathematical ideas to which they refer.</p>
<ul class="oucontentbulleted"><li>
<p>What mathematical skills and ideas do they use?</p>
</li><li>
<p>Do you think they are consciously using mathematics?</p>
</li></ul>
</li><li>
<p>As you listen, make a note of any responses about people's view of mathematics which strike you as unusual or particularly interesting.</p>
<ul class="oucontentbulleted"><li>
<p>Are the responses similar to your own?</p>
</li><li>
<p>Do these responses seem to you typical of the population as a whole?</p>
</li></ul>
</li><li>
<p>When the clip has finished look back over the notes you have made and check to see whether you have answered the questions above. If necessary view any parts of the video band again and add to your notes. Also think about the pros and cons of using video in this way.</p>
</li></ol></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><ol class="oucontentnumbered"><li>
<p>Trevor Arnold talks about the need to estimate and measure distances, areas and times. The spreadsheet he created uses hidden formulas which instruct the computer to carry out the routine calculations that he previously did by hand.</p>
<p>Emma Prescott uses mathematics to help her estimate the drop of haemoglobin levels in her patients. By recording how far levels have fallen, she is able to predict when the next blood transfusion will be necessary. She also calculates necessary drug dosages and volumes of intravenous infusions. She uses probability when explaining the likelihood of passing on the disease to a patient's offspring. You will have seen her twice using simple diagrams to convey mathematical ideas—an important theme of this course.</p>
<p>Although Mark Hanson is not consciously using mathematics, he is using a range of mathematical skills as he schedules the time he has available, estimates the lengths of record tracks, subtracts them from the time available, and so on.</p>
</li><li>
<p>When first asked about their attitudes to mathematics, the responses were fairly varied; some people had positive memories of school mathematics while others disliked it or found it boring. You may also have noticed that at the beginning of the videotape most people viewed maths in a rather narrow way—in fact, they tended to see it simply as basic arithmetic applied to everyday situations. As the video unfolds, these perceptions of mathematics became extended. Indeed, all the hospital workers interviewed were prepared, by the end, to think of their jobs more mathematically than they had at the beginning of the video.</p>
<p>Whether or not the views expressed are similar to yours, they may well seem to be typical of the population as a whole. However, this is just a small selection of people and it was not chosen as a representative sample of the whole population. They all came from one particular hospital in one particular area in London. Can you be sure that people's views of mathematics are not influenced by the circumstances of the interview or the nature of their job or the area in which they live?</p>
</li><li>
<p>You may care to read again the comments about using video that were given before Activity 4.</p>
</li></ol></div></div></div></div> <script>
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</script>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

1.2 Recognizing mathematics
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.5
Tue, 12 Apr 2016 23:00:00 GMT
<p>You were asked to consider what mathematics means to you as you study this course. Should you continue your studies your ideas about mathematics will develop and change. In this subsection, you will continue to think about the nature of mathematics as you look at four very different pieces of mathematical writing.</p><p>All four pieces of writing are instantly recognizable as mathematics. Some can be easily understood but others are much more difficult. Please do not worry about that for the moment. The four pieces of writing have been chosen with some care in order to make particular points about the nature of mathematics.</p><div class=" oucontentactivity oucontentsheavybox1 oucontentsbox " id="act001_005"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 5 Yes, but is it maths?</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>On the next few screens you will see four pieces of writing labelled Examples 1, 2, 3 and 4.</p><p>In later activities you will be asked to read each of them in detail but for now spend no more than a minute looking at each one. Identify what it is that indicates that this is mathematical writing and decide what sort of mathematics is being used.</p></div></div></div></div>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.5
1.2 Recognizing mathematicsMU120_1<p>You were asked to consider what mathematics means to you as you study this course. Should you continue your studies your ideas about mathematics will develop and change. In this subsection, you will continue to think about the nature of mathematics as you look at four very different pieces of mathematical writing.</p><p>All four pieces of writing are instantly recognizable as mathematics. Some can be easily understood but others are much more difficult. Please do not worry about that for the moment. The four pieces of writing have been chosen with some care in order to make particular points about the nature of mathematics.</p><div class="
oucontentactivity
oucontentsheavybox1 oucontentsbox " id="act001_005"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 5 Yes, but is it maths?</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>On the next few screens you will see four pieces of writing labelled Examples 1, 2, 3 and 4.</p><p>In later activities you will be asked to read each of them in detail but for now spend no more than a minute looking at each one. Identify what it is that indicates that this is mathematical writing and decide what sort of mathematics is being used.</p></div></div></div></div>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

Examples 1 and 2
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.6
Tue, 12 Apr 2016 23:00:00 GMT
<div class="oucontentexample oucontentsheavybox1 oucontentsbox " id="exm001_001"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Example 1</h2><div class="oucontentinnerbox"><div class="oucontentfigure" style="width:511px;" id="fig001_00827"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/155be0d1/mu120_1_008i.jpg" alt="Example 1" width="511" height="692" style="maxwidth:511px;" class="oucontentfigureimage oucontentmediawide"/></div></div></div></div><div class="oucontentexample oucontentsheavybox1 oucontentsbox " id="exm001_002"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Example 2</h2><div class="oucontentinnerbox"><div class="oucontentfigure" style="width:511px;" id="fig001_00929"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/07380184/mu120_1_009i.jpg" alt="Example 2" width="511" height="702" style="maxwidth:511px;" class="oucontentfigureimage oucontentmediawide"/></div></div></div></div>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.6
Examples 1 and 2MU120_1<div class="oucontentexample oucontentsheavybox1 oucontentsbox " id="exm001_001"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Example 1</h2><div class="oucontentinnerbox"><div class="oucontentfigure" style="width:511px;" id="fig001_00827"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/155be0d1/mu120_1_008i.jpg" alt="Example 1" width="511" height="692" style="maxwidth:511px;" class="oucontentfigureimage oucontentmediawide"/></div></div></div></div><div class="oucontentexample oucontentsheavybox1 oucontentsbox " id="exm001_002"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Example 2</h2><div class="oucontentinnerbox"><div class="oucontentfigure" style="width:511px;" id="fig001_00929"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/07380184/mu120_1_009i.jpg" alt="Example 2" width="511" height="702" style="maxwidth:511px;" class="oucontentfigureimage oucontentmediawide"/></div></div></div></div>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

Examples 3 and 4
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.7
Tue, 12 Apr 2016 23:00:00 GMT
<div class="oucontentexample oucontentsheavybox1 oucontentsbox " id="exm001_003"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Example 3</h2><div class="oucontentinnerbox"><div class="oucontentfigure" style="width:511px;" id="fig001_01532"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/7b897475/mu120_1_015i.jpg" alt="Example 3" width="511" height="718" style="maxwidth:511px;" class="oucontentfigureimage oucontentmediawide"/></div></div></div></div><div class="oucontentexample oucontentsheavybox1 oucontentsbox " id="exm001_004"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Example 4</h2><div class="oucontentinnerbox"><div class="oucontentfigure" style="width:511px;" id="fig001_01634"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/a8829806/mu120_1_016i.jpg" alt="Example 4" width="511" height="720" style="maxwidth:511px;" class="oucontentfigureimage oucontentmediawide"/></div></div></div></div>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.7
Examples 3 and 4MU120_1<div class="oucontentexample oucontentsheavybox1 oucontentsbox " id="exm001_003"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Example 3</h2><div class="oucontentinnerbox"><div class="oucontentfigure" style="width:511px;" id="fig001_01532"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/7b897475/mu120_1_015i.jpg" alt="Example 3" width="511" height="718" style="maxwidth:511px;" class="oucontentfigureimage oucontentmediawide"/></div></div></div></div><div class="oucontentexample oucontentsheavybox1 oucontentsbox " id="exm001_004"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Example 4</h2><div class="oucontentinnerbox"><div class="oucontentfigure" style="width:511px;" id="fig001_01634"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/a8829806/mu120_1_016i.jpg" alt="Example 4" width="511" height="720" style="maxwidth:511px;" class="oucontentfigureimage oucontentmediawide"/></div></div></div></div>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

Recognizing mathematics, continued
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.8
Tue, 12 Apr 2016 23:00:00 GMT
<p>In Example 1 it is the use of many <b>numbers</b> that identifies it as mathematics and suggest the area of mathematics called <i>arithmetic</i>. Example 2 has numbers but also <b>graphs and diagrams</b>, suggesting <i>statistics</i>. The <b>shapes</b> in Example 3 suggest that the <i>geometrical</i> part of mathematics is being used whereas Example 4, with all the <b>alphabetic symbols</b>, is clearly drawing upon <i>algebra</i>.</p><p>In the next activity you will be asked to look in more detail at Example 1. The question here is to investigate what meaning would be attached to the symbols 7<sup>−3</sup>.</p><p>It is clearly mathematical writing. There are numbers all over the page, along with other wellknown mathematical symbols such as =, × and ÷ Notice also the use of powers, the small digits written slightly above and to the right of the usualsized digits. For example, 7<sup>−3</sup> is read as ‘seven to the power minus three’.</p><p>It is one thing to know how to read the symbols and quite another to know what they mean. What is shown here is an attempt to work out what 7<sup>−3</sup> represents and how it matches what the writer already knows about powers.</p><p>The writing in Example 1 is an example of a mathematical <b>investigation</b>. The writer is not setting out to answer a welldefined question to which there is a single right answer. Rather she was working at an openended series of questions and aiming to increase her own understanding. Notice how she works from <i>what she knows</i> towards <i>what she want</i> and writes relevant words alongside her working. There are indications of where she is stuck (look for the question marks) and where she gets flashes of insight (look for exclamation marks).</p><p>For whom do you think the author of Example 1 was writing? It is likely that she was writing a response to the investigation mainly for her own benefit. She may well want to come back to look at this writing later and it is important that she will be able to follow her own thinking through again. Notice the way she has highlighted her conclusion. This is the thing that she wants to remember, the thing that, hopefully, she has learned.</p>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.8
Recognizing mathematics, continuedMU120_1<p>In Example 1 it is the use of many <b>numbers</b> that identifies it as mathematics and suggest the area of mathematics called <i>arithmetic</i>. Example 2 has numbers but also <b>graphs and diagrams</b>, suggesting <i>statistics</i>. The <b>shapes</b> in Example 3 suggest that the <i>geometrical</i> part of mathematics is being used whereas Example 4, with all the <b>alphabetic symbols</b>, is clearly drawing upon <i>algebra</i>.</p><p>In the next activity you will be asked to look in more detail at Example 1. The question here is to investigate what meaning would be attached to the symbols 7<sup>−3</sup>.</p><p>It is clearly mathematical writing. There are numbers all over the page, along with other wellknown mathematical symbols such as =, × and ÷ Notice also the use of powers, the small digits written slightly above and to the right of the usualsized digits. For example, 7<sup>−3</sup> is read as ‘seven to the power minus three’.</p><p>It is one thing to know how to read the symbols and quite another to know what they mean. What is shown here is an attempt to work out what 7<sup>−3</sup> represents and how it matches what the writer already knows about powers.</p><p>The writing in Example 1 is an example of a mathematical <b>investigation</b>. The writer is not setting out to answer a welldefined question to which there is a single right answer. Rather she was working at an openended series of questions and aiming to increase her own understanding. Notice how she works from <i>what she knows</i> towards <i>what she want</i> and writes relevant words alongside her working. There are indications of where she is stuck (look for the question marks) and where she gets flashes of insight (look for exclamation marks).</p><p>For whom do you think the author of Example 1 was writing? It is likely that she was writing a response to the investigation mainly for her own benefit. She may well want to come back to look at this writing later and it is important that she will be able to follow her own thinking through again. Notice the way she has highlighted her conclusion. This is the thing that she wants to remember, the thing that, hopefully, she has learned.</p>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

Investigating the investigation
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.9
Tue, 12 Apr 2016 23:00:00 GMT
<p>Look again at example 1.</p><div class="oucontentfigure" style="width:511px;" id="fig001_008i"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/155be0d1/mu120_1_008i.jpg" alt="" width="511" height="692" style="maxwidth:511px;" class="oucontentfigureimage oucontentmediawide"/></div><div class=" oucontentactivity oucontentsheavybox1 oucontentsbox " id="act001_006"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 6</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>As you read through Example 1 again, take your time and read very carefully, bearing in mind the points made above. Work through the mathematics, thinking about each line of the argument.</p><p>Keep asking yourself these questions:</p><ul class="oucontentbulleted"><li>
<p>Do I agree with that?</p>
</li><li>
<p>Would I have expressed that differently?</p>
</li><li>
<p>Could I explain that to someone else in my own words?</p>
</li></ul></div></div></div></div><p>Example 1 was a piece of socalled <i>pure mathematics</i>. Recall the definitions of pure mathematics given at the beginning of this course.</p><div class="oucontentquote oucontentsbox" id="quo001_005"><blockquote><p>Pure mathematics: abstract science of space, number, and quantity.</p><p>Pure mathematics studies the propositions that can be deduced in this language by applying definite rules of reasoning to sets of axioms.</p></blockquote></div><p>In Example 1, there was no link to the real world. However, Example 2 is a very different type of mathematical writing. It is taken from a newspaper and uses mathematics to convey information to a general readership. It is therefore an example of mathematics being applied to handling data that arise in the real world. This particular branch of mathematics is known as statistics.</p>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.9
Investigating the investigationMU120_1<p>Look again at example 1.</p><div class="oucontentfigure" style="width:511px;" id="fig001_008i"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/155be0d1/mu120_1_008i.jpg" alt="" width="511" height="692" style="maxwidth:511px;" class="oucontentfigureimage oucontentmediawide"/></div><div class="
oucontentactivity
oucontentsheavybox1 oucontentsbox " id="act001_006"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 6</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>As you read through Example 1 again, take your time and read very carefully, bearing in mind the points made above. Work through the mathematics, thinking about each line of the argument.</p><p>Keep asking yourself these questions:</p><ul class="oucontentbulleted"><li>
<p>Do I agree with that?</p>
</li><li>
<p>Would I have expressed that differently?</p>
</li><li>
<p>Could I explain that to someone else in my own words?</p>
</li></ul></div></div></div></div><p>Example 1 was a piece of socalled <i>pure mathematics</i>. Recall the definitions of pure mathematics given at the beginning of this course.</p><div class="oucontentquote oucontentsbox" id="quo001_005"><blockquote><p>Pure mathematics: abstract science of space, number, and quantity.</p><p>Pure mathematics studies the propositions that can be deduced in this language by applying definite rules of reasoning to sets of axioms.</p></blockquote></div><p>In Example 1, there was no link to the real world. However, Example 2 is a very different type of mathematical writing. It is taken from a newspaper and uses mathematics to convey information to a general readership. It is therefore an example of mathematics being applied to handling data that arise in the real world. This particular branch of mathematics is known as statistics.</p>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

Packaging the pictures
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.10
Tue, 12 Apr 2016 23:00:00 GMT
<p>Here's Example 2 again.</p><div class="oucontentfigure" style="width:511px;" id="fig001_009i"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/07380184/mu120_1_009i.jpg" alt="" width="511" height="702" style="maxwidth:511px;" class="oucontentfigureimage oucontentmediawide"/></div><div class=" oucontentactivity oucontentsheavybox1 oucontentsbox " id="act001_007"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 7</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Study each of the five statistical diagrams that make up Example 2. Write down, in one or two sentences, your interpretation of the information that each diagram displays.</p></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><p>What's in your dustbin’ (the pie chart) shows the percentage of packaging materials in an average UK dustbin: 7.5% glass, 5% paper, and so on. It also shows that 75.25% is nonpackaging.</p><p>‘How much is recycled’ (the line graph) shows that the percentage of materials recycled is increasing. It is highest for glass, at 60%, and lowest for plastics and paper (about 10%). Notice, however, that the horizontal scale is not evenly spaced. Does this distort the graph unreasonably?</p><p>‘German ambition’ (a bar chart) shows Germany's aim to collect and recycle different materials. Although comparisons between the different materials are shown, it does not make clear what the percentages are part of. For example, 60% of what glass is collected?</p><p>‘How much’ (a bar chart) shows the quantity of packaging materials used in the UK (in millions of tons); paper (industrial) is the largest.</p><p>‘Could do better’ (a bar chart) compares the percentage of glass recycled in different Western European countries in 1992. The Netherlands is highest at about 75%; the UK and Greece are low with about 20%.</p></div></div></div></div><p>Graphs and diagrams offer thoughtprovoking ways of displaying quantitative information. Often the most effective way of describing and summarizing a set of numbers is to use images related to those numbers. Of course, the newspaper could have chosen to represent the information about packaging using tables of numbers, but the diagrams are certainly more eyecatching and make patterns more obvious. For example, the UK's low percentage of recycled glass in ‘Could do better’ is shown much more clearly than it would be if only the numerical percentages were displayed.</p><p>However, like numbers, graphs and diagrams are abstract representations that summarize certain aspects of the world in a very condensed form. Unlike photographs which provide a ‘true’ likeness, their interpretation requires a degree of mental effort on the part of the reader. Although a picture may sometimes be worth a thousand words, a poorly designed one merely obscures the underlying message.</p>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.10
Packaging the picturesMU120_1<p>Here's Example 2 again.</p><div class="oucontentfigure" style="width:511px;" id="fig001_009i"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/07380184/mu120_1_009i.jpg" alt="" width="511" height="702" style="maxwidth:511px;" class="oucontentfigureimage oucontentmediawide"/></div><div class="
oucontentactivity
oucontentsheavybox1 oucontentsbox " id="act001_007"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 7</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Study each of the five statistical diagrams that make up Example 2. Write down, in one or two sentences, your interpretation of the information that each diagram displays.</p></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><p>What's in your dustbin’ (the pie chart) shows the percentage of packaging materials in an average UK dustbin: 7.5% glass, 5% paper, and so on. It also shows that 75.25% is nonpackaging.</p><p>‘How much is recycled’ (the line graph) shows that the percentage of materials recycled is increasing. It is highest for glass, at 60%, and lowest for plastics and paper (about 10%). Notice, however, that the horizontal scale is not evenly spaced. Does this distort the graph unreasonably?</p><p>‘German ambition’ (a bar chart) shows Germany's aim to collect and recycle different materials. Although comparisons between the different materials are shown, it does not make clear what the percentages are part of. For example, 60% of what glass is collected?</p><p>‘How much’ (a bar chart) shows the quantity of packaging materials used in the UK (in millions of tons); paper (industrial) is the largest.</p><p>‘Could do better’ (a bar chart) compares the percentage of glass recycled in different Western European countries in 1992. The Netherlands is highest at about 75%; the UK and Greece are low with about 20%.</p></div></div></div></div><p>Graphs and diagrams offer thoughtprovoking ways of displaying quantitative information. Often the most effective way of describing and summarizing a set of numbers is to use images related to those numbers. Of course, the newspaper could have chosen to represent the information about packaging using tables of numbers, but the diagrams are certainly more eyecatching and make patterns more obvious. For example, the UK's low percentage of recycled glass in ‘Could do better’ is shown much more clearly than it would be if only the numerical percentages were displayed.</p><p>However, like numbers, graphs and diagrams are abstract representations that summarize certain aspects of the world in a very condensed form. Unlike photographs which provide a ‘true’ likeness, their interpretation requires a degree of mental effort on the part of the reader. Although a picture may sometimes be worth a thousand words, a poorly designed one merely obscures the underlying message.</p>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

Puzzling out the Soma cube
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.11
Tue, 12 Apr 2016 23:00:00 GMT
<p>The mathematical writing in Example 3 also uses diagrams but for a very different purpose. It arises from a particular threedimensional puzzle, sometimes called a Soma cube, pictured below.</p><div class="oucontentfigure oucontentmediamini" id="fig001_010"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/0d5ab57b/mu120_1_010i.jpg" alt="Figure 1.10" width="313" height="220" style="maxwidth:313px;" class="oucontentfigureimage" longdesc="view.php?id=4199&extra=longdesc_idp6021568"/><div class="oucontentlongdesclink oucontentlongdesconly"><a href="https://www.open.edu/openlearn/ocw/mod/oucontent/view.php?id=4199&extra=longdesc_idp6021568&clicked=1">Long description</a></div><a id="back_longdesc_idp6021568"></a></div><div class="oucontentfigure oucontentmediamini" id="fig001_011"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/de48d688/mu120_1_011i.jpg" alt="Figure 1.11" width="313" height="210" style="maxwidth:313px;" class="oucontentfigureimage" longdesc="view.php?id=4199&extra=longdesc_idp6025680"/><div class="oucontentfiguretext"><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Piecing together a Soma cube</span></div></div><div class="oucontentlongdesclink oucontentlongdesconly"><a href="https://www.open.edu/openlearn/ocw/mod/oucontent/view.php?id=4199&extra=longdesc_idp6025680&clicked=1">Long description</a></div><a id="back_longdesc_idp6025680"></a></div><p>There are seven wooden pieces, which can be assembled to form a solid cube. The manufacturer of the puzzle claimed that there are over 16,000 ways of assembling the cube. The writer of Example 3 had found, by trial and error, several different solutions but was beginning to doubt the claim that there were as many as 16,000. The example shows the notes that he made as ideas crossed his mind about how to make sense of the manufacturer's claim.</p><p>There were two particular problems faced by the writer. First, what precisely is meant by a ‘solution’: what makes one solution different from another? Second, what is the best way of recording a particular solution: what notation is best to use?</p>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.11
Puzzling out the Soma cubeMU120_1<p>The mathematical writing in Example 3 also uses diagrams but for a very different purpose. It arises from a particular threedimensional puzzle, sometimes called a Soma cube, pictured below.</p><div class="oucontentfigure oucontentmediamini" id="fig001_010"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/0d5ab57b/mu120_1_010i.jpg" alt="Figure 1.10" width="313" height="220" style="maxwidth:313px;" class="oucontentfigureimage" longdesc="view.php?id=4199&extra=longdesc_idp6021568"/><div class="oucontentlongdesclink oucontentlongdesconly"><a href="https://www.open.edu/openlearn/ocw/mod/oucontent/view.php?id=4199&extra=longdesc_idp6021568&clicked=1">Long description</a></div><a id="back_longdesc_idp6021568"></a></div><div class="oucontentfigure oucontentmediamini" id="fig001_011"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/de48d688/mu120_1_011i.jpg" alt="Figure 1.11" width="313" height="210" style="maxwidth:313px;" class="oucontentfigureimage" longdesc="view.php?id=4199&extra=longdesc_idp6025680"/><div class="oucontentfiguretext"><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Piecing together a Soma cube</span></div></div><div class="oucontentlongdesclink oucontentlongdesconly"><a href="https://www.open.edu/openlearn/ocw/mod/oucontent/view.php?id=4199&extra=longdesc_idp6025680&clicked=1">Long description</a></div><a id="back_longdesc_idp6025680"></a></div><p>There are seven wooden pieces, which can be assembled to form a solid cube. The manufacturer of the puzzle claimed that there are over 16,000 ways of assembling the cube. The writer of Example 3 had found, by trial and error, several different solutions but was beginning to doubt the claim that there were as many as 16,000. The example shows the notes that he made as ideas crossed his mind about how to make sense of the manufacturer's claim.</p><p>There were two particular problems faced by the writer. First, what precisely is meant by a ‘solution’: what makes one solution different from another? Second, what is the best way of recording a particular solution: what notation is best to use?</p>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

Does it make sense?
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.12
Tue, 12 Apr 2016 23:00:00 GMT
<div class="oucontentexample oucontentsheavybox1 oucontentsbox " id="exm001_003a"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Example 3</h2><div class="oucontentinnerbox"><div class="oucontentfigure" style="width:511px;" id="fig001_015i"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/7b897475/mu120_1_015i.jpg" alt="" width="511" height="718" style="maxwidth:511px;" class="oucontentfigureimage oucontentmediawide"/></div></div></div></div><div class=" oucontentactivity oucontentsheavybox1 oucontentsbox " id="act001_008"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 8</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Look carefully at Example 3 and try to make some sense of it. Notice that there are four bullet points: try understanding each of these points separately, but don't worry if you find it difficult to follow. However, do make a note of the point when it becomes very difficult to understand.</p></div></div></div></div><p>No doubt you will have found parts of this mathematical writing puzzling. In some places, the writer does not make clear exactly what he means, so as a piece of mathematical communication it does not work. However, the author was not intending to communicate with anyone other than himself. It was a means for him to record his solution to a problem he had set himself and as such it may have been useful and successful.</p><p>An explanation of the mathematics goes as follows:</p><p>The first bullet point tackles the problem of what is meant by a ‘solution’. Imagine all seven pieces have been combined to make a cube. Now imagine taking a single piece out and seeing whether that piece can be reinserted in any different ways. The first piece pictured can be positioned in only one way, whereas the piece next to it could be turned round and put back upside down. This is to do with the symmetry of the piece (see ‘<i>Preparatory Resource Book B</i>’, Module 7). The number of ways each piece can be inserted in any cube has been noted: 1, 2, 2, 2, 2, 2 and 3. These numbers are then multiplied to give 96, the total number of different ways of putting the pieces together to form any single cubic arrangement.</p><p>The second bullet point tackles the problem of how to record a particular cubic arrangement. The threedimensional picture of the cube is easy to visualize but difficult to draw. It also does not record the position of pieces on the far side of the cube. The author is experimenting with a notation where the three horizontal layers of the cube are drawn side by side but there are then problems visualizing the individual pieces.</p><p>In the third bullet point the author realizes that any complete cubic arrangement of the seven pieces can be turned around in various ways (because of the symmetry of the cube). He reckons there are 24 ways of positioning each complete cubic arrangement.</p><p>Finally he begins to record some of what he thought originally were different solutions. Alongside the drawings he has written ×4, ×2, ×1, ×2, presumably indicating that he thinks there are 4, 2, 1 and 2 similar cubic arrangements to those illustrated but it is not clear from the writing what these are. The 1+4+2+2+1=10 may be the total of these cubic arrangements (including 1 from the second bullet point). He then combines the 96 ways of putting the pieces together, with the 24 ways of positioning each complete cubic arrangement and multiplies by 10 the number of cubic arrangements. Counting like this, he seems to have found about 2,400 ways of completing the Soma Cube. Only another 14,000 or so to go!</p>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.12
Does it make sense?MU120_1<div class="oucontentexample oucontentsheavybox1 oucontentsbox " id="exm001_003a"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Example 3</h2><div class="oucontentinnerbox"><div class="oucontentfigure" style="width:511px;" id="fig001_015i"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/7b897475/mu120_1_015i.jpg" alt="" width="511" height="718" style="maxwidth:511px;" class="oucontentfigureimage oucontentmediawide"/></div></div></div></div><div class="
oucontentactivity
oucontentsheavybox1 oucontentsbox " id="act001_008"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 8</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Look carefully at Example 3 and try to make some sense of it. Notice that there are four bullet points: try understanding each of these points separately, but don't worry if you find it difficult to follow. However, do make a note of the point when it becomes very difficult to understand.</p></div></div></div></div><p>No doubt you will have found parts of this mathematical writing puzzling. In some places, the writer does not make clear exactly what he means, so as a piece of mathematical communication it does not work. However, the author was not intending to communicate with anyone other than himself. It was a means for him to record his solution to a problem he had set himself and as such it may have been useful and successful.</p><p>An explanation of the mathematics goes as follows:</p><p>The first bullet point tackles the problem of what is meant by a ‘solution’. Imagine all seven pieces have been combined to make a cube. Now imagine taking a single piece out and seeing whether that piece can be reinserted in any different ways. The first piece pictured can be positioned in only one way, whereas the piece next to it could be turned round and put back upside down. This is to do with the symmetry of the piece (see ‘<i>Preparatory Resource Book B</i>’, Module 7). The number of ways each piece can be inserted in any cube has been noted: 1, 2, 2, 2, 2, 2 and 3. These numbers are then multiplied to give 96, the total number of different ways of putting the pieces together to form any single cubic arrangement.</p><p>The second bullet point tackles the problem of how to record a particular cubic arrangement. The threedimensional picture of the cube is easy to visualize but difficult to draw. It also does not record the position of pieces on the far side of the cube. The author is experimenting with a notation where the three horizontal layers of the cube are drawn side by side but there are then problems visualizing the individual pieces.</p><p>In the third bullet point the author realizes that any complete cubic arrangement of the seven pieces can be turned around in various ways (because of the symmetry of the cube). He reckons there are 24 ways of positioning each complete cubic arrangement.</p><p>Finally he begins to record some of what he thought originally were different solutions. Alongside the drawings he has written ×4, ×2, ×1, ×2, presumably indicating that he thinks there are 4, 2, 1 and 2 similar cubic arrangements to those illustrated but it is not clear from the writing what these are. The 1+4+2+2+1=10 may be the total of these cubic arrangements (including 1 from the second bullet point). He then combines the 96 ways of putting the pieces together, with the 24 ways of positioning each complete cubic arrangement and multiplies by 10 the number of cubic arrangements. Counting like this, he seems to have found about 2,400 ways of completing the Soma Cube. Only another 14,000 or so to go!</p>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

When it doesn't make sense …
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.13
Tue, 12 Apr 2016 23:00:00 GMT
<p>Why were you asked to try to understand some mathematics which was not clearly written? There will be times (hopefully not too many!) in the course of your mathematical studies when you will not immediately be able to follow a mathematical argument. In such circumstances it is very easy for your mind to boggle at the complexity of it all and to give up, feeling that you cannot understand any of it.</p><p>In Activity 8 you were asked to ‘make a note of the point when it becomes very difficult to understand’. Identifying precisely the actual cause of the misunderstanding is often a means of overcoming the difficulty. One technique that you might like to try in some circumstances is to go through the text, ticking line by line as you are able to follow an argument and marking clearly the point at which it is no longer clear. Then skip on a bit and see if there are lines further down the page where it is possible to follow the argument and tick those too. Then go back up the text and gradually you should be able to whittle away at the lines where there is lack of clarity. Eventually, the light may dawn completely, or you will have located a particular point which can subsequently be raised in the course Forum.</p><p>You may be wondering why anyone would want to spend time trying to solve a problem like the one in Example 3. Often, in the real world, problems arise that need to be solved—but this is not the case here. Rather it is one of a class of realworld problems that are provoked by curiosity rather than necessity. As your mathematical confidence grows, you may experience a greater curiosity about the world and a willingness to apply newfound mathematical skills to problems that you have posed for yourself. In <a class="oucontentcrossref" href="https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection3.1">Section 1.3</a>, you will return to this theme, as you listen to some mathematical musings in which curiosity about the world plays an important part.</p><p>In Example 3, as has been already pointed out, one aspect of the problem was finding a suitable way of recording solutions on paper or, in other words, of developing a suitable notation. The author chose an essentially geometrical representation in which the different twodimensional drawings represented various threedimensional arrangements. It is possible to conceive all sorts of different recording systems; for example, labelling each of the seven pieces of the puzzle with a different letter or using some kind of threedimensional coordinate system. The general point here is that often in mathematical problem solving the problem solver has to decide which symbols will be most appropriate. Frequently it is algebraic symbols that are used, as with the formidablelooking Example 4!</p>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.13
When it doesn't make sense …MU120_1<p>Why were you asked to try to understand some mathematics which was not clearly written? There will be times (hopefully not too many!) in the course of your mathematical studies when you will not immediately be able to follow a mathematical argument. In such circumstances it is very easy for your mind to boggle at the complexity of it all and to give up, feeling that you cannot understand any of it.</p><p>In Activity 8 you were asked to ‘make a note of the point when it becomes very difficult to understand’. Identifying precisely the actual cause of the misunderstanding is often a means of overcoming the difficulty. One technique that you might like to try in some circumstances is to go through the text, ticking line by line as you are able to follow an argument and marking clearly the point at which it is no longer clear. Then skip on a bit and see if there are lines further down the page where it is possible to follow the argument and tick those too. Then go back up the text and gradually you should be able to whittle away at the lines where there is lack of clarity. Eventually, the light may dawn completely, or you will have located a particular point which can subsequently be raised in the course Forum.</p><p>You may be wondering why anyone would want to spend time trying to solve a problem like the one in Example 3. Often, in the real world, problems arise that need to be solved—but this is not the case here. Rather it is one of a class of realworld problems that are provoked by curiosity rather than necessity. As your mathematical confidence grows, you may experience a greater curiosity about the world and a willingness to apply newfound mathematical skills to problems that you have posed for yourself. In <a class="oucontentcrossref" href="https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection3.1">Section 1.3</a>, you will return to this theme, as you listen to some mathematical musings in which curiosity about the world plays an important part.</p><p>In Example 3, as has been already pointed out, one aspect of the problem was finding a suitable way of recording solutions on paper or, in other words, of developing a suitable notation. The author chose an essentially geometrical representation in which the different twodimensional drawings represented various threedimensional arrangements. It is possible to conceive all sorts of different recording systems; for example, labelling each of the seven pieces of the puzzle with a different letter or using some kind of threedimensional coordinate system. The general point here is that often in mathematical problem solving the problem solver has to decide which symbols will be most appropriate. Frequently it is algebraic symbols that are used, as with the formidablelooking Example 4!</p>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

Introducing algebra
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.14
Tue, 12 Apr 2016 23:00:00 GMT
<div class="oucontentexample oucontentsheavybox1 oucontentsbox " id="exm001_004a"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Example 4</h2><div class="oucontentinnerbox"><div class="oucontentfigure" style="width:511px;" id="fig001_016i"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/a8829806/mu120_1_016i.jpg" alt="" width="511" height="720" style="maxwidth:511px;" class="oucontentfigureimage oucontentmediawide"/></div></div></div></div><p>Trying to understand this example is like trying to understand something written in a foreign language. You need to be familiar with the many symbols and signs in the same sort of way as you need to be familiar with the basic words of a language.</p><p>In this example there are symbols and signs, many of which you may not understand at present. Here are explanations of some of the symbols used in Example 4. Don't worry if you are unable to understand all the details.</p><ul class="oucontentunnumbered"><li>
<p>The letters <i>d</i>, <i>h</i> and <i>x</i> are being used to stand for the lengths of the sides of a triangle. Each one can take any sensible value—the letters are known as <b>variables</b>.</p>
</li><li>
<p>The Greek letter <i>θ</i> (theta) is also being used as a <b>variable</b>, representing the size of one of the angles of the triangle—Greek letters are often used to stand for angles.</p>
</li><li>
<p>Subscripts are used to indicate two different but related values: for example <i>g</i>
<sub>1</sub> and <i>g</i>
<sub>2</sub> (say <i>g</i>one <i>g</i>two) represent two different gradients.</p>
</li><li>
<p>Superscripts are used to represent powersߞin particular here <i>d</i>
<sup>2</sup> means <i>d</i> to the power of 2 or <i>d</i> squared.</p>
</li></ul><div class="oucontentequation oucontentequationequation oucontentnocaption" id="ueq001"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/c65e9288/mu120_1_ie001i.jpg" alt=""/></div><p>means <i>h</i> divided by <i>x</i>, just as the fraction </p><div class="oucontentequation oucontentequationequation oucontentnocaption" id="ueq002"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/423df934/mu120_1_ie002i.jpg" alt=""/></div><p>is the same as 1 divided by 4.</p><ul class="oucontentunnumbered"><li>
<p>Where two letters are written together it means their values are to be multiplied. For example <i>xg</i>
<sub>1</sub> is shorthand for <i>x</i> times <i>g</i>
<sub>1</sub>.</p>
</li><li>
<p>tan and sin (say sine) stand for the trigonometric ratios, tangent and sine. Notice sin is not shorthand for <i>s</i> times <i>i</i> times <i>n</i>.</p>
</li><li>
<p>= is used to denote equality. Where it occurs at the beginning of a line it means the expression that follows is the equivalent of the one above.</p>
</li><li>
<p>Brackets have been used, along with the superscript 2, to indicate that everything in the bracket has been squared. for example,</p>
<div class="oucontentequation oucontentequationequation oucontentnocaption" id="ueqn003"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/a6c8f9bb/mu120_1_ie003i.jpg" alt=""/></div>
<p>is read as ‘<i>h</i> divided by <i>g</i> all squared’.</p>
</li><li>
<p>Several equations have been labelled ((1), (2), and so on) so that they can be referred to later.</p>
</li></ul><div class=" oucontentactivity oucontentsheavybox1 oucontentsbox " id="act001_009"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 9 A good read</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Even though you will have little idea of what the symbols represent at the moment, it is still useful to practise reading them. Read Example 4 aloud to yourself, or impress someone else by reading it to them. Remember that what you are doing is similar to reading a passage from a foreign language. As you read, try to appreciate the patterns in the symbols and begin to appreciate the underlying story. Try to read with confidence—pretend that you speak mathematics like a native!</p></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><p>You may have begun like this:</p><p>Let the map gradient be <i>g</i>one which equals <i>h</i> divided by <i>x</i> (Equation 1)…</p><p>About halfway down comes the more difficult line:</p><p>Substitute into Equation 5 to give.</p><p>‘<i>h</i> divided by <i>g</i>two all squared equals <i>h</i>squared plus <i>h</i> divided by <i>g</i>one all squared’.</p></div></div></div></div><p>Now that you have read this formidable page of algebra you may feel a little more comfortable with the ‘look’ of symbols.</p>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.14
Introducing algebraMU120_1<div class="oucontentexample oucontentsheavybox1 oucontentsbox " id="exm001_004a"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Example 4</h2><div class="oucontentinnerbox"><div class="oucontentfigure" style="width:511px;" id="fig001_016i"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/a8829806/mu120_1_016i.jpg" alt="" width="511" height="720" style="maxwidth:511px;" class="oucontentfigureimage oucontentmediawide"/></div></div></div></div><p>Trying to understand this example is like trying to understand something written in a foreign language. You need to be familiar with the many symbols and signs in the same sort of way as you need to be familiar with the basic words of a language.</p><p>In this example there are symbols and signs, many of which you may not understand at present. Here are explanations of some of the symbols used in Example 4. Don't worry if you are unable to understand all the details.</p><ul class="oucontentunnumbered"><li>
<p>The letters <i>d</i>, <i>h</i> and <i>x</i> are being used to stand for the lengths of the sides of a triangle. Each one can take any sensible value—the letters are known as <b>variables</b>.</p>
</li><li>
<p>The Greek letter <i>θ</i> (theta) is also being used as a <b>variable</b>, representing the size of one of the angles of the triangle—Greek letters are often used to stand for angles.</p>
</li><li>
<p>Subscripts are used to indicate two different but related values: for example <i>g</i>
<sub>1</sub> and <i>g</i>
<sub>2</sub> (say <i>g</i>one <i>g</i>two) represent two different gradients.</p>
</li><li>
<p>Superscripts are used to represent powersߞin particular here <i>d</i>
<sup>2</sup> means <i>d</i> to the power of 2 or <i>d</i> squared.</p>
</li></ul><div class="oucontentequation oucontentequationequation oucontentnocaption" id="ueq001"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/c65e9288/mu120_1_ie001i.jpg" alt=""/></div><p>means <i>h</i> divided by <i>x</i>, just as the fraction </p><div class="oucontentequation oucontentequationequation oucontentnocaption" id="ueq002"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/423df934/mu120_1_ie002i.jpg" alt=""/></div><p>is the same as 1 divided by 4.</p><ul class="oucontentunnumbered"><li>
<p>Where two letters are written together it means their values are to be multiplied. For example <i>xg</i>
<sub>1</sub> is shorthand for <i>x</i> times <i>g</i>
<sub>1</sub>.</p>
</li><li>
<p>tan and sin (say sine) stand for the trigonometric ratios, tangent and sine. Notice sin is not shorthand for <i>s</i> times <i>i</i> times <i>n</i>.</p>
</li><li>
<p>= is used to denote equality. Where it occurs at the beginning of a line it means the expression that follows is the equivalent of the one above.</p>
</li><li>
<p>Brackets have been used, along with the superscript 2, to indicate that everything in the bracket has been squared. for example,</p>
<div class="oucontentequation oucontentequationequation oucontentnocaption" id="ueqn003"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/a6c8f9bb/mu120_1_ie003i.jpg" alt=""/></div>
<p>is read as ‘<i>h</i> divided by <i>g</i> all squared’.</p>
</li><li>
<p>Several equations have been labelled ((1), (2), and so on) so that they can be referred to later.</p>
</li></ul><div class="
oucontentactivity
oucontentsheavybox1 oucontentsbox " id="act001_009"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 9 A good read</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Even though you will have little idea of what the symbols represent at the moment, it is still useful to practise reading them. Read Example 4 aloud to yourself, or impress someone else by reading it to them. Remember that what you are doing is similar to reading a passage from a foreign language. As you read, try to appreciate the patterns in the symbols and begin to appreciate the underlying story. Try to read with confidence—pretend that you speak mathematics like a native!</p></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><p>You may have begun like this:</p><p>Let the map gradient be <i>g</i>one which equals <i>h</i> divided by <i>x</i> (Equation 1)…</p><p>About halfway down comes the more difficult line:</p><p>Substitute into Equation 5 to give.</p><p>‘<i>h</i> divided by <i>g</i>two all squared equals <i>h</i>squared plus <i>h</i> divided by <i>g</i>one all squared’.</p></div></div></div></div><p>Now that you have read this formidable page of algebra you may feel a little more comfortable with the ‘look’ of symbols.</p>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

1.3 What is a mathematician?
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.15
Tue, 12 Apr 2016 23:00:00 GMT
<p>In Section 1.2 you looked in detail at four pieces of very different mathematical writing:</p><ul class="oucontentunnumbered"><li>
<p>an investigation of patterns within our system of numbers;</p>
</li><li>
<p>mathematical diagrams being used to convey statistical information about the real world;</p>
</li><li>
<p>a solution of a geometrical problem which arose from someone's curiosity;</p>
</li><li>
<p>use of algebraic symbols.</p>
</li></ul><p>The aim was to broaden your experience of the sorts of situations where mathematics is used to help you develop your own understanding of what mathematics is. The examples were drawn from different areas of mathematics (arithmetic, statistics, geometry, algebra) and introduced ideas that will be developed further throughout the course.</p><p>Now you are asked to turn your attention to the question of what it means to be a mathematician. Recall the responses made to this question by the people you saw in the Whittington Hospital on the video clip. Does it simply mean someone who does mathematics? Or is it someone who uses it? Or is there more to it? How does a mathematician ‘see’ the world?</p>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.15
1.3 What is a mathematician?MU120_1<p>In Section 1.2 you looked in detail at four pieces of very different mathematical writing:</p><ul class="oucontentunnumbered"><li>
<p>an investigation of patterns within our system of numbers;</p>
</li><li>
<p>mathematical diagrams being used to convey statistical information about the real world;</p>
</li><li>
<p>a solution of a geometrical problem which arose from someone's curiosity;</p>
</li><li>
<p>use of algebraic symbols.</p>
</li></ul><p>The aim was to broaden your experience of the sorts of situations where mathematics is used to help you develop your own understanding of what mathematics is. The examples were drawn from different areas of mathematics (arithmetic, statistics, geometry, algebra) and introduced ideas that will be developed further throughout the course.</p><p>Now you are asked to turn your attention to the question of what it means to be a mathematician. Recall the responses made to this question by the people you saw in the Whittington Hospital on the video clip. Does it simply mean someone who does mathematics? Or is it someone who uses it? Or is there more to it? How does a mathematician ‘see’ the world?</p>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

Stressing and ignoring
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.16
Tue, 12 Apr 2016 23:00:00 GMT
<p>Click on the link below to read William Boyd on 'Cabbages are not spheres'.</p><p><span class="oucontentlinkwithtip"><a class="oucontenthyperlink" href="https://www.open.edu/openlearn/ocw/mod/resource/view.php?id=26498">Cabbages are not spheres</a></span></p><div class=" oucontentactivity oucontentsheavybox1 oucontentsbox " id="act001_010"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 10</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Click on the link to read the article ‘Cabbages are not spheres’ which is taken from a novel by William Boyd. Part of the conversation between the two characters, John and Hope, concerns how humans can look at one thing and see it in terms of something else.</p><p>Mark or make a note of any sentences or ideas which strike you as illustrating a mathematician's view of the world.</p></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><p>A key sentence comes towards the end of the excerpt.</p><div class="oucontentquote oucontentsbox" id="quo001_009"><blockquote><p>The natural world is full of irregularity and random alteration, but in the antiseptic, dustfree, shadowless, brightly lit, abstract realm of the mathematicians they like their cabbages spherical, please.</p></blockquote></div></div></div></div></div><p>The extract draws a distinction between the objects of the physical world around us and the ‘objects’ of mathematics: for instance, cones, spheres and straight lines. Yet for mathematics to be of use in solving problems in the physical world, it must also be possible to see these physical and mathematical objects as being the same thing under certain circumstances. Instead of <i>stressing</i> the differences, it can be important at times to <i>ignore</i> the differences; to be able to see cabbages as spheres, mountains as triangles, and rivers as flowing in straight lines. Thus particular features of the physical objects are <i>stressed</i> while others are <i>ignored</i>—with a cabbage, in some situations, its near spherical shape can be stressed while features like its colour, its stalk and its taste can be ignored. Seeing what to stress and what to ignore in particular circumstances is a key part of being a mathematician.</p><div class="oucontentfigure" style="width:450px;" id="fig001_017"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/49aefa94/mu120_1_017i.jpg" alt="" width="450" height="435" style="maxwidth:450px;" class="oucontentfigureimage oucontentmediawide"/><div class="oucontentfiguretext"><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Mrs Johnson began to regret introducing the ‘cabbages as spheres’ metaphor to the rest of the family</span></div></div></div><p>Another necessary component of developing a mathematical view of the world is being able to recognize mathematical ‘things’—shapes, curves, numbers, graphs, equations, and so on. Yet another element is developing a curious, questioning attitude towards the world around you. Why is that the way it is? Could it be different? If so, how? What if it were slightly different? Why isn't it different? What are the forces operating to make it the way it is? How can I describe the relationships I see?</p><p>Do people who study mathematics view the world and think about things any differently from other people? To find out whether there is a distinctively mathematical outlook on life, a member of the unit team noted down things that set off a train of thought which could be described (in a broad sense) as mathematical. You can hear the result in the audio clip on the next screen.</p>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.16
Stressing and ignoringMU120_1<p>Click on the link below to read William Boyd on 'Cabbages are not spheres'.</p><p><span class="oucontentlinkwithtip"><a class="oucontenthyperlink" href="https://www.open.edu/openlearn/ocw/mod/resource/view.php?id=26498">Cabbages are not spheres</a></span></p><div class="
oucontentactivity
oucontentsheavybox1 oucontentsbox " id="act001_010"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 10</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Click on the link to read the article ‘Cabbages are not spheres’ which is taken from a novel by William Boyd. Part of the conversation between the two characters, John and Hope, concerns how humans can look at one thing and see it in terms of something else.</p><p>Mark or make a note of any sentences or ideas which strike you as illustrating a mathematician's view of the world.</p></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><p>A key sentence comes towards the end of the excerpt.</p><div class="oucontentquote oucontentsbox" id="quo001_009"><blockquote><p>The natural world is full of irregularity and random alteration, but in the antiseptic, dustfree, shadowless, brightly lit, abstract realm of the mathematicians they like their cabbages spherical, please.</p></blockquote></div></div></div></div></div><p>The extract draws a distinction between the objects of the physical world around us and the ‘objects’ of mathematics: for instance, cones, spheres and straight lines. Yet for mathematics to be of use in solving problems in the physical world, it must also be possible to see these physical and mathematical objects as being the same thing under certain circumstances. Instead of <i>stressing</i> the differences, it can be important at times to <i>ignore</i> the differences; to be able to see cabbages as spheres, mountains as triangles, and rivers as flowing in straight lines. Thus particular features of the physical objects are <i>stressed</i> while others are <i>ignored</i>—with a cabbage, in some situations, its near spherical shape can be stressed while features like its colour, its stalk and its taste can be ignored. Seeing what to stress and what to ignore in particular circumstances is a key part of being a mathematician.</p><div class="oucontentfigure" style="width:450px;" id="fig001_017"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/49aefa94/mu120_1_017i.jpg" alt="" width="450" height="435" style="maxwidth:450px;" class="oucontentfigureimage oucontentmediawide"/><div class="oucontentfiguretext"><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Mrs Johnson began to regret introducing the ‘cabbages as spheres’ metaphor to the rest of the family</span></div></div></div><p>Another necessary component of developing a mathematical view of the world is being able to recognize mathematical ‘things’—shapes, curves, numbers, graphs, equations, and so on. Yet another element is developing a curious, questioning attitude towards the world around you. Why is that the way it is? Could it be different? If so, how? What if it were slightly different? Why isn't it different? What are the forces operating to make it the way it is? How can I describe the relationships I see?</p><p>Do people who study mathematics view the world and think about things any differently from other people? To find out whether there is a distinctively mathematical outlook on life, a member of the unit team noted down things that set off a train of thought which could be described (in a broad sense) as mathematical. You can hear the result in the audio clip on the next screen.</p>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

A mathematical muse
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.17
Tue, 12 Apr 2016 23:00:00 GMT
<p>Audio: Click to listen to the audio clip entitled 'Mathematical Musings'</p><div id="mp3001_001" class="oucontentmedia oucontentaudiovideo ompversion1" style="width:342px;"><div class="oucontentdefaultfilter"><span class="oumediafilter"><a href="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/1b2503fd/mu120_1_001s.mp3?forcedownload=1" class="oumedialinknoscript ompspacer">Download this audio clip.</a><span class="accesshide">Audio player: Mathematical musings</span><a href="#" class="ompentermedia ompaccesshide" tabindex="1">
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</span></div><div class="filter_transcript" id="transcript_9c42f2f74"><div><a href="#skip_transcript_9c42f2f74" class="accesshide">Skip transcript: Mathematical musings</a><h4 class="accesshide">Transcript: Mathematical musings</h4></div><div class="filter_transcript_box" tabindex="0" id="content_transcript_9c42f2f74"><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">FRANCESCA HUNT</div><div class="oucontentdialogueremark">Saturday today. I went to the City Centre in the morning – window shopping. I looked in a music shop. Looking at the guitars, I was struck by how small the gaps between the frets get. I wonder how the makers know where to put them?
Went to see friends this evening. I amused Sarah, their daughter, with my ‘think of a number’ routine. It’s the one that goes, ‘Think of a number without telling me which one; double it; add five; multiply by three; add nine; divide by six; take away the number you first thought of; and the answer’s four’. She thought it was magic that I already knew she’d got four as the answer. But the thing is, the answer will always be four. In fact, it doesn’t depend on the number she thought of at all! I suppose I could try to explain it to Sarah using algebra. But I didn’t want to destroy the spell for her.
I left rather late – about one a.m. We’d got there about eight p.m. – so we’d stayed five hours. But eight and five aren’t one! And neither is one minus five, eight! Funny arithmetic clocks use.
A lovely sunny Sunday afternoon. I took the dog for a walk in the park. Tried to find the age of the oak and the silver birch. I read somewhere that if you measured the circumference of a tree in centimetres, it gives roughly the tree’s age in years. I used the dog’s lead to try it out – although I had to estimate the length of the lead. I got the answer that the silver birch is 25 years old and the oak a hundred years. The oak was quite big, so maybe 100 years is about right. On the way back I met Pat, my nextdoor neighbour, who remarked that it’s getting lighter in the evenings now. It’s funny how in the spring the days do seem to lengthen rapidly. Of course, it’s the other way round in the autumn: the days shorten rapidly. But in June and December, there seems to be very little variation in the length of the days. I wonder how exactly the length of the day does vary throughout the year.
Phew! A busy Monday. I went to the supermarket on the way home from work. Decided to buy some things to make a cauliflower cheese. Funny things cauliflowers. Each little floret (caulifloret?!) looks just like a little cauliflower. And a piece of the floret looks like an even smaller cauliflower. I suppose I could keep on going with this idea for ever, in theory. When part of something looks like the whole thing but on a smaller scale, it’s called ‘selfsimilarity’ – and that’s something to do with fractals, I think. Perhaps cauliflower cheese should be called ‘fractal cheese’.
Tuesday. I glanced through the paper this morning – had at least half a dozen graphs and charts in it relating to various news stories. How the Prime Minster’s popularity has waned compared with that of the Leader of the Opposition. A comparison of inflation rates and interest rates over the last 20 years. Unemployment figures. Even isobars on the weather chart.
I wonder how fairly and accurately represented much of the data we get in the newspapers and on TV really is. How true is the phrase ‘lies, damned lies, and statistics’? Watched the evening news on Wednesday. More discussion about the consequences of increasing the size of the European Union. Apparently, the aim is for at least 22 member nations – which would mean a lot of different languages.
I suppose it’s not really surprising that a third of all the EU employees in Brussels are translators! Think of all the different translators you’d need. English to French – and French to English. French to Dutch and vice versa. Dutch to German, to Italian, and to Spanish … Mind you, at least some member nations use the same language for EU purposes. I think the total number of different languages is only ten. So what happens when a new nation, with a new language, joins? It’d add another language. But how many more translators? Think I’d need to draw a diagram to get my head round this.
Thursday already! Decided I really must pay my enormous phone bill. When I rang Molly later in Vancouver, she told me about a friend being sent a telephone bill for 32 300 dollars instead of 32 dollars 30. Wonder how long I could talk to Molly for 32 000 dollars continuously? It’s hard enough anyway trying to work out when it’s best to call her – Vancouver’s eight hours behind the UK. And when I went to see her last year, as we flew over the different places I found myself wondering what the ‘real’ time was – on the ground – in Greenland and Baffin Bay. Is there a map somewhere showing the different time zones around the world?
Friday. It’s Saturday again tomorrow. Sitting at my desk today, trying to write a letter, I found myself distracted by the OU logo. It’s a very simple design really – just a square, a semicircle and a circle. But it’s not really that straightforward. The relative sizes of the three shapes create the overall effect – which is somehow pleasing to the eye. I suppose this is deliberate. I wonder if the logo would look less satisfying if the relative sizes of the shapes were different?
There was a thunderstorm in the afternoon – then brilliant sunshine and a rainbow. Why do rainbows happen? Had a discussion with Mike about rainbows, and what the raindrops do to the sunlight to make the colours. We decided between us that reflection of the sun’s rays came into it somehow. But what happens to the light? I know what happens with reflections in a flat mirror, but raindrops aren’t flat. I wonder if it’s the shape of the drops that produces the different colours of the rainbow – or what?
Thinking back over this week, there’s been mathematics of some kind everywhere I look. I suppose if you start to think of it like that, maths is just part of everyday life.</div><div class="clearer"></div></div></div><span class="accesshide" id="skip_transcript_9c42f2f74">End transcript: Mathematical musings</span></div><div class="filter_transcript_output" id="output_transcript_9c42f2f74"><div class="filter_transcript_copy"><a href="#" id="action_link5d2f3803c36517" class="actionicon" ><img class="icon iconsmall" alt="Copy this transcript to the clipboard" title="Copy this transcript to the clipboard" src="https://www.open.edu/openlearn/ocw/theme/image.php/_s/openlearnng/core/1563274092/t/copy" /></a></div><div class="filter_transcript_print"><a href="#" id="action_link5d2f3803c36518" class="actionicon" ><img class="icon iconsmall" alt="Print this transcript" title="Print this transcript" src="https://www.open.edu/openlearn/ocw/theme/image.php/_s/openlearnng/core/1563274092/t/print" /></a></div></div><div class="oucontentfiguretext"><div class="oucontenttranscriptlink"><span class="filter_transcript_button" id="button_transcript_9c42f2f74">Show transcriptHide transcript</span></div><div class="oucontentmediadownload"><a href="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/1b2503fd/mu120_1_001s.mp3?forcedownload=1" title="Download this audio clip">Download</a></div><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Mathematical musings</span></div></div></div><div class="oucontentinteractionprint"><div class="oucontentinteractionunavailable">Interactive feature not available in single page view (<a class="oucontentcrossref" href="https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.17#mp3001001">see it in standard view</a>).</div></div><div class=" oucontentactivity oucontentsheavybox1 oucontentsbox " id="act001_011"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 11</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Click on the link above to hear the audio clip called ‘Mathematical musings’.</p><p>The speaker describes a number of everyday things and occurrences which she sees as having interesting mathematical features. Make a note of the subjects described and any questions that interest you. Which elements mentioned do you find easy to see as mathematical and which are harder to see that way?</p><div class="oucontentfigure" style="width:511px;" id="fig001_018"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/c3b46df4/mu120_1_018i.jpg" alt="" width="511" height="295" style="maxwidth:511px;" class="oucontentfigureimage oucontentmediawide"/></div></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><p>Below is a list of the topics referred to in the audio clip.</p><div class="oucontenttable oucontentsnormal noborder oucontentsbox" id="tbl001"><div class="oucontenttablewrapper"><table><tr><td>Saturday:</td><td>Guitar frets, thinkofanumber games, clock arithmetic.</td></tr><tr><td>Sunday:</td><td>Formula for the age of a tree, daylight length.</td></tr><tr><td>Monday:</td><td>Cauliflorets (self similarity*).</td></tr><tr><td>Tuesday:</td><td>Graphs in a newspaper.</td></tr><tr><td>Wednesday:</td><td>How many translators?</td></tr><tr><td>Thursday:</td><td>Phone bill, Time zones, Types of maps.</td></tr><tr><td>Friday:</td><td>OU Logo, rainbows.</td></tr></table></div><div class="oucontentsourcereference"></div></div></div></div></div></div><p>Over the coming week, try to cultivate your own ‘mathematical eye and ear’, looking out for ways in which mathematics permeates the various things you do, see and hear.</p><p>So, what is mathematics? And what is a mathematician? An aim of this course was to help you begin to answer these questions. However, as you gain more experience of doing mathematics, your own understanding of the words will probably change. So press on with your studies and see how your understanding develops.</p><div class="oucontentbox oucontentsheavybox1 oucontentsbox " id="box001_001"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Outcomes</h2><div class="oucontentinnerbox"><p>Now that you have completed your work on this section, you should have:</p><ul class="oucontentbulleted"><li>
<p>clarified your own ideas of what mathematics is and what it is to be a mathematician (Activities 1–5, 10 and 11);</p>
</li><li>
<p>gained experience in working from videotape and audiotape as part of your mathematical learning (Activities 4 and 11);</p>
</li><li>
<p>begun to recognize different types of written mathematics (Activities 6–9);</p>
</li><li>
<p>developed your skill at reading mathematics (Activity 9);</p>
</li><li>
<p>become more attuned to noticing mathematical questions arising from the world around you (Activities 3, 4, 10 and 11).</p>
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https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.17
A mathematical museMU120_1<p>Audio: Click to listen to the audio clip entitled 'Mathematical Musings'</p><div id="mp3001_001" class="oucontentmedia oucontentaudiovideo ompversion1" style="width:342px;"><div class="oucontentdefaultfilter"><span class="oumediafilter"><a href="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/1b2503fd/mu120_1_001s.mp3?forcedownload=1" class="oumedialinknoscript ompspacer">Download this audio clip.</a><span class="accesshide">Audio player: Mathematical musings</span><a href="#" class="ompentermedia ompaccesshide" tabindex="1">
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</span></div><div class="filter_transcript" id="transcript_9c42f2f74"><div><a href="#skip_transcript_9c42f2f74" class="accesshide">Skip transcript: Mathematical musings</a><h4 class="accesshide">Transcript: Mathematical musings</h4></div><div class="filter_transcript_box" tabindex="0" id="content_transcript_9c42f2f74"><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">FRANCESCA HUNT</div><div class="oucontentdialogueremark">Saturday today. I went to the City Centre in the morning – window shopping. I looked in a music shop. Looking at the guitars, I was struck by how small the gaps between the frets get. I wonder how the makers know where to put them?
Went to see friends this evening. I amused Sarah, their daughter, with my ‘think of a number’ routine. It’s the one that goes, ‘Think of a number without telling me which one; double it; add five; multiply by three; add nine; divide by six; take away the number you first thought of; and the answer’s four’. She thought it was magic that I already knew she’d got four as the answer. But the thing is, the answer will always be four. In fact, it doesn’t depend on the number she thought of at all! I suppose I could try to explain it to Sarah using algebra. But I didn’t want to destroy the spell for her.
I left rather late – about one a.m. We’d got there about eight p.m. – so we’d stayed five hours. But eight and five aren’t one! And neither is one minus five, eight! Funny arithmetic clocks use.
A lovely sunny Sunday afternoon. I took the dog for a walk in the park. Tried to find the age of the oak and the silver birch. I read somewhere that if you measured the circumference of a tree in centimetres, it gives roughly the tree’s age in years. I used the dog’s lead to try it out – although I had to estimate the length of the lead. I got the answer that the silver birch is 25 years old and the oak a hundred years. The oak was quite big, so maybe 100 years is about right. On the way back I met Pat, my nextdoor neighbour, who remarked that it’s getting lighter in the evenings now. It’s funny how in the spring the days do seem to lengthen rapidly. Of course, it’s the other way round in the autumn: the days shorten rapidly. But in June and December, there seems to be very little variation in the length of the days. I wonder how exactly the length of the day does vary throughout the year.
Phew! A busy Monday. I went to the supermarket on the way home from work. Decided to buy some things to make a cauliflower cheese. Funny things cauliflowers. Each little floret (caulifloret?!) looks just like a little cauliflower. And a piece of the floret looks like an even smaller cauliflower. I suppose I could keep on going with this idea for ever, in theory. When part of something looks like the whole thing but on a smaller scale, it’s called ‘selfsimilarity’ – and that’s something to do with fractals, I think. Perhaps cauliflower cheese should be called ‘fractal cheese’.
Tuesday. I glanced through the paper this morning – had at least half a dozen graphs and charts in it relating to various news stories. How the Prime Minster’s popularity has waned compared with that of the Leader of the Opposition. A comparison of inflation rates and interest rates over the last 20 years. Unemployment figures. Even isobars on the weather chart.
I wonder how fairly and accurately represented much of the data we get in the newspapers and on TV really is. How true is the phrase ‘lies, damned lies, and statistics’? Watched the evening news on Wednesday. More discussion about the consequences of increasing the size of the European Union. Apparently, the aim is for at least 22 member nations – which would mean a lot of different languages.
I suppose it’s not really surprising that a third of all the EU employees in Brussels are translators! Think of all the different translators you’d need. English to French – and French to English. French to Dutch and vice versa. Dutch to German, to Italian, and to Spanish … Mind you, at least some member nations use the same language for EU purposes. I think the total number of different languages is only ten. So what happens when a new nation, with a new language, joins? It’d add another language. But how many more translators? Think I’d need to draw a diagram to get my head round this.
Thursday already! Decided I really must pay my enormous phone bill. When I rang Molly later in Vancouver, she told me about a friend being sent a telephone bill for 32 300 dollars instead of 32 dollars 30. Wonder how long I could talk to Molly for 32 000 dollars continuously? It’s hard enough anyway trying to work out when it’s best to call her – Vancouver’s eight hours behind the UK. And when I went to see her last year, as we flew over the different places I found myself wondering what the ‘real’ time was – on the ground – in Greenland and Baffin Bay. Is there a map somewhere showing the different time zones around the world?
Friday. It’s Saturday again tomorrow. Sitting at my desk today, trying to write a letter, I found myself distracted by the OU logo. It’s a very simple design really – just a square, a semicircle and a circle. But it’s not really that straightforward. The relative sizes of the three shapes create the overall effect – which is somehow pleasing to the eye. I suppose this is deliberate. I wonder if the logo would look less satisfying if the relative sizes of the shapes were different?
There was a thunderstorm in the afternoon – then brilliant sunshine and a rainbow. Why do rainbows happen? Had a discussion with Mike about rainbows, and what the raindrops do to the sunlight to make the colours. We decided between us that reflection of the sun’s rays came into it somehow. But what happens to the light? I know what happens with reflections in a flat mirror, but raindrops aren’t flat. I wonder if it’s the shape of the drops that produces the different colours of the rainbow – or what?
Thinking back over this week, there’s been mathematics of some kind everywhere I look. I suppose if you start to think of it like that, maths is just part of everyday life.</div><div class="clearer"></div></div></div><span class="accesshide" id="skip_transcript_9c42f2f74">End transcript: Mathematical musings</span></div><div class="filter_transcript_output" id="output_transcript_9c42f2f74"><div class="filter_transcript_copy"><a href="#" id="action_link5d2f3803c36517" class="actionicon" ><img class="icon iconsmall" alt="Copy this transcript to the clipboard" title="Copy this transcript to the clipboard" src="https://www.open.edu/openlearn/ocw/theme/image.php/_s/openlearnng/core/1563274092/t/copy" /></a></div><div class="filter_transcript_print"><a href="#" id="action_link5d2f3803c36518" class="actionicon" ><img class="icon iconsmall" alt="Print this transcript" title="Print this transcript" src="https://www.open.edu/openlearn/ocw/theme/image.php/_s/openlearnng/core/1563274092/t/print" /></a></div></div><div class="oucontentfiguretext"><div class="oucontenttranscriptlink"><span class="filter_transcript_button" id="button_transcript_9c42f2f74">Show transcriptHide transcript</span></div><div class="oucontentmediadownload"><a href="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/1b2503fd/mu120_1_001s.mp3?forcedownload=1" title="Download this audio clip">Download</a></div><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Mathematical musings</span></div></div></div><div class="oucontentinteractionprint"><div class="oucontentinteractionunavailable">Interactive feature not available in single page view (<a class="oucontentcrossref" href="https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection2.17#mp3001001">see it in standard view</a>).</div></div><div class="
oucontentactivity
oucontentsheavybox1 oucontentsbox " id="act001_011"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 11</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Click on the link above to hear the audio clip called ‘Mathematical musings’.</p><p>The speaker describes a number of everyday things and occurrences which she sees as having interesting mathematical features. Make a note of the subjects described and any questions that interest you. Which elements mentioned do you find easy to see as mathematical and which are harder to see that way?</p><div class="oucontentfigure" style="width:511px;" id="fig001_018"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/c3b46df4/mu120_1_018i.jpg" alt="" width="511" height="295" style="maxwidth:511px;" class="oucontentfigureimage oucontentmediawide"/></div></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><p>Below is a list of the topics referred to in the audio clip.</p><div class="oucontenttable oucontentsnormal noborder oucontentsbox" id="tbl001"><div class="oucontenttablewrapper"><table><tr><td>Saturday:</td><td>Guitar frets, thinkofanumber games, clock arithmetic.</td></tr><tr><td>Sunday:</td><td>Formula for the age of a tree, daylight length.</td></tr><tr><td>Monday:</td><td>Cauliflorets (self similarity*).</td></tr><tr><td>Tuesday:</td><td>Graphs in a newspaper.</td></tr><tr><td>Wednesday:</td><td>How many translators?</td></tr><tr><td>Thursday:</td><td>Phone bill, Time zones, Types of maps.</td></tr><tr><td>Friday:</td><td>OU Logo, rainbows.</td></tr></table></div><div class="oucontentsourcereference"></div></div></div></div></div></div><p>Over the coming week, try to cultivate your own ‘mathematical eye and ear’, looking out for ways in which mathematics permeates the various things you do, see and hear.</p><p>So, what is mathematics? And what is a mathematician? An aim of this course was to help you begin to answer these questions. However, as you gain more experience of doing mathematics, your own understanding of the words will probably change. So press on with your studies and see how your understanding develops.</p><div class="oucontentbox oucontentsheavybox1 oucontentsbox " id="box001_001"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Outcomes</h2><div class="oucontentinnerbox"><p>Now that you have completed your work on this section, you should have:</p><ul class="oucontentbulleted"><li>
<p>clarified your own ideas of what mathematics is and what it is to be a mathematician (Activities 1–5, 10 and 11);</p>
</li><li>
<p>gained experience in working from videotape and audiotape as part of your mathematical learning (Activities 4 and 11);</p>
</li><li>
<p>begun to recognize different types of written mathematics (Activities 6–9);</p>
</li><li>
<p>developed your skill at reading mathematics (Activity 9);</p>
</li><li>
<p>become more attuned to noticing mathematical questions arising from the world around you (Activities 3, 4, 10 and 11).</p>
</li></ul></div></div></div> <script>
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</script>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

2 Aims
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection3.1
Tue, 12 Apr 2016 23:00:00 GMT
<p>The aims of this section are for you to:</p><ul class="oucontentbulleted"><li>
<p>gain greater fluency, confidence and skill in using your calculator;</p>
</li><li>
<p>begin to appreciate how the calculator can be used as a tool for learning mathematics;</p>
</li><li>
<p>develop an effective means of working from the <i>Calculator Book</i>.</p>
</li></ul><p>
<b>In order to complete this section you will need to have obtained a Texas Instruments TI83 calculator and the book <i>Tapping into Mathematics With the TI83 Graphics Calculator</i> (ISBN 0201175479)</b>, referred to in the section as the <i>Calculator Book</i>.</p>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection3.1
2 AimsMU120_1<p>The aims of this section are for you to:</p><ul class="oucontentbulleted"><li>
<p>gain greater fluency, confidence and skill in using your calculator;</p>
</li><li>
<p>begin to appreciate how the calculator can be used as a tool for learning mathematics;</p>
</li><li>
<p>develop an effective means of working from the <i>Calculator Book</i>.</p>
</li></ul><p>
<b>In order to complete this section you will need to have obtained a Texas Instruments TI83 calculator and the book <i>Tapping into Mathematics With the TI83 Graphics Calculator</i> (ISBN 0201175479)</b>, referred to in the section as the <i>Calculator Book</i>.</p>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

The history of the calculator
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection3.2
Tue, 12 Apr 2016 23:00:00 GMT
<p>Ever since recorded mathematics began, people have been making use of mathematical aids. Four thousand years ago, Babylonian scribes were consulting mathematical tables which included multiplication tables, tables of squares and square roots, and tables of reciprocals of numbers. These values were recorded as marks on clay tablets that were then baked hard in the sun—and some have survived to the present day. (There are several originals to be seen in the British Museum.)</p><div class="oucontentfigure" style="width:400px;" id="fig001_019"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/32a1a6d2/mu120_1_019i.jpg" alt="Figure 1.19" width="400" height="545" style="maxwidth:400px;" class="oucontentfigureimage" longdesc="view.php?id=4199&extra=longdesc_idp6153392"/><div class="oucontentfiguretext"><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Figure 1.19</span></div></div><div class="oucontentlongdesclink oucontentlongdesconly"><a href="https://www.open.edu/openlearn/ocw/mod/oucontent/view.php?id=4199&extra=longdesc_idp6153392&clicked=1">Long description</a></div><a id="back_longdesc_idp6153392"></a></div><p>Your calculator is one of the latest in a long and distinguished history of devices that have been invented to assist with the <i>doing</i> of mathematics. The list includes mathematical tables (stored on clay, papyrus, vellum and paper), the abacus and counting board, the slide rule, mechanical adding machines, and basic fourfunction electronic calculators. Some students will recall using a slide rule themselves (or seeing others working with them); others may remember using logarithm tables at school or work; still others may have had no exposure to either of them. Mathematical devices and calculating aids come and go.</p><div class="oucontentfigure" style="width:472px;" id="fig001_020"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/eb8546fd/mu120_1_020i.jpg" alt="Figure 1.20" width="472" height="318" style="maxwidth:472px;" class="oucontentfigureimage oucontentmediawide" longdesc="view.php?id=4199&extra=longdesc_idp6159376"/><div class="oucontentfiguretext"><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Figure 1.20</span></div></div><div class="oucontentlongdesclink oucontentlongdesconly"><a href="https://www.open.edu/openlearn/ocw/mod/oucontent/view.php?id=4199&extra=longdesc_idp6159376&clicked=1">Long description</a></div><a id="back_longdesc_idp6159376"></a></div><p>In this course you will be using an electronic device known as a <i>graphics calculator</i>. It is capable not only of carrying out calculations but also of drawing graphs and other diagrams, of processing large amounts of statistical data and of carrying out preprogrammed sequences of instructions. There is a great deal of history in your calculator. Hundreds of years of mathematical activity and past thoughts of many people in different cultures have gone into producing and refining the ideas that are coded within this device. And all those human resources are available to you.</p>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection3.2
The history of the calculatorMU120_1<p>Ever since recorded mathematics began, people have been making use of mathematical aids. Four thousand years ago, Babylonian scribes were consulting mathematical tables which included multiplication tables, tables of squares and square roots, and tables of reciprocals of numbers. These values were recorded as marks on clay tablets that were then baked hard in the sun—and some have survived to the present day. (There are several originals to be seen in the British Museum.)</p><div class="oucontentfigure" style="width:400px;" id="fig001_019"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/32a1a6d2/mu120_1_019i.jpg" alt="Figure 1.19" width="400" height="545" style="maxwidth:400px;" class="oucontentfigureimage" longdesc="view.php?id=4199&extra=longdesc_idp6153392"/><div class="oucontentfiguretext"><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Figure 1.19</span></div></div><div class="oucontentlongdesclink oucontentlongdesconly"><a href="https://www.open.edu/openlearn/ocw/mod/oucontent/view.php?id=4199&extra=longdesc_idp6153392&clicked=1">Long description</a></div><a id="back_longdesc_idp6153392"></a></div><p>Your calculator is one of the latest in a long and distinguished history of devices that have been invented to assist with the <i>doing</i> of mathematics. The list includes mathematical tables (stored on clay, papyrus, vellum and paper), the abacus and counting board, the slide rule, mechanical adding machines, and basic fourfunction electronic calculators. Some students will recall using a slide rule themselves (or seeing others working with them); others may remember using logarithm tables at school or work; still others may have had no exposure to either of them. Mathematical devices and calculating aids come and go.</p><div class="oucontentfigure" style="width:472px;" id="fig001_020"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/eb8546fd/mu120_1_020i.jpg" alt="Figure 1.20" width="472" height="318" style="maxwidth:472px;" class="oucontentfigureimage oucontentmediawide" longdesc="view.php?id=4199&extra=longdesc_idp6159376"/><div class="oucontentfiguretext"><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Figure 1.20</span></div></div><div class="oucontentlongdesclink oucontentlongdesconly"><a href="https://www.open.edu/openlearn/ocw/mod/oucontent/view.php?id=4199&extra=longdesc_idp6159376&clicked=1">Long description</a></div><a id="back_longdesc_idp6159376"></a></div><p>In this course you will be using an electronic device known as a <i>graphics calculator</i>. It is capable not only of carrying out calculations but also of drawing graphs and other diagrams, of processing large amounts of statistical data and of carrying out preprogrammed sequences of instructions. There is a great deal of history in your calculator. Hundreds of years of mathematical activity and past thoughts of many people in different cultures have gone into producing and refining the ideas that are coded within this device. And all those human resources are available to you.</p>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

Using your calculator
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection3.3
Tue, 12 Apr 2016 23:00:00 GMT
<p>Many people see calculators only as a way of producing answers—indeed some people see them almost as a means of cheating, of shortcutting procedures that can and should be carried out in one's head or on paper. However, the calculator can also be a means of learning mathematics more effectively, something you will come to appreciate more. Many previous mathematics students have found that their graphics calculator, used with understanding and intelligence, has become a most effective aid to their learning. Many also say that using the calculator has been great fun!</p><p>After studying this course and related units you should know <i>how</i> to use many, but not all, of the mathematical features available on the calculator. Much more importantly, you should <i>understand</i> the mathematics associated with those features and know <i>when</i> it is appropriate to use them. For example, it is one thing to know <i>how</i> to work out the square root of a number using the calculator. It is quite another thing to <i>understand</i> what a square root is and <i>when</i> it is sensible to use it.</p><p>You should by now have acquired your calculator along with the manufacturer's manual which describes how to use the various functions of the calculator. You also should have got a copy of the <i>Calculator Book</i>, which was specially written for the Open University. It serves two functions: to show you how to use the calculator and also to teach you the associated mathematics.</p><p>Work through the first four chapters of the <i>Calculator Book</i> before going on to the next activity.</p><div class=" oucontentactivity oucontentsheavybox1 oucontentsbox " id="act001_012"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 12 Glancing back</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Take a very quick look through Sections 1.1 to 1.4 of the <i>Calculator Book</i> and any notes you made when you studied the sections in your preparation. Ask yourself the following questions:</p><ol class="oucontentnumbered"><li>
<p>What calculator skills were covered?</p>
</li><li>
<p>What learning or revision of mathematical ideas was covered? Make notes on what you find.</p>
</li></ol></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><p>You may have included all or some of these and you might have a few extra ones.</p><ol class="oucontentnumbered"><li>
<p>Calculator skills</p>
<ul class="oucontentunnumbered"><li>
<p>Adjusting display contrast;</p>
</li><li>
<p>Turning on/off and resetting memory;</p>
</li><li>
<p>Using the main and second function keys;</p>
</li><li>
<p>Very basic arithmetic: +, −, × and ÷; Editing an expression and use of the cursor keys;</p>
</li><li>
<p>Inputting negative numbers;</p>
</li><li>
<p>Setting the number of decimal places: Being aware of calculator conventions and the use of brackets;</p>
</li><li>
<p>Interpreting error messages;</p>
</li><li>
<p>Use of the MODE menu;</p>
</li><li>
<p>Use of square and power keys.</p>
</li></ul>
</li><li>
<p>Mathematical ideas covered</p>
<ul class="oucontentunnumbered"><li>
<p>Inverse operations;</p>
</li><li>
<p>Decimal places;</p>
</li><li>
<p>Negative numbers;</p>
</li><li>
<p>Order of operations;</p>
</li><li>
<p>Sequences and converging to a limit (see Brain stretcher in Section 3);</p>
</li><li>
<p>Squares, square roots and other powers.</p>
</li></ul>
</li></ol><p>There are further comments about this activity in the main text.</p></div></div></div></div><p>In order to answer the questions in Activity 12, you may have used some or all of the following:</p><ul class="oucontentbulleted"><li>
<p>the main headings in the text of the Calculator Book; for example, ‘1.2 Using the calculator for basic arithmetic’;</p>
</li><li>
<p>the subheadings in the text, for example, ‘Some calculator conventions’;</p>
</li><li>
<p>the diagrams—the representations both of the keyboard and of the calculator's screen (or ‘screendumps’);</p>
</li><li>
<p>the single words in bold type in the margins, for example <b>operation keys inverse</b>, and so on;</p>
</li><li>
<p>any highlighting, underlining or extra notes which you added to the text;</p>
</li><li>
<p>any separate pages of notes which you may have made.</p>
</li></ul><p>Why bother to point this out to you? The reason is that it is important to develop efficient and effective methods of studying (from a very early stage). Certainly you need to ‘do the mathematics’ but there is also much to be gained from putting your own study methods and mathematical learning under the spotlight from time to time.</p><p>You were recommended to look back over, to see again or revise, work you had completed before. How useful were the notes you made? Were they too detailed or too sparse?</p>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection3.3
Using your calculatorMU120_1<p>Many people see calculators only as a way of producing answers—indeed some people see them almost as a means of cheating, of shortcutting procedures that can and should be carried out in one's head or on paper. However, the calculator can also be a means of learning mathematics more effectively, something you will come to appreciate more. Many previous mathematics students have found that their graphics calculator, used with understanding and intelligence, has become a most effective aid to their learning. Many also say that using the calculator has been great fun!</p><p>After studying this course and related units you should know <i>how</i> to use many, but not all, of the mathematical features available on the calculator. Much more importantly, you should <i>understand</i> the mathematics associated with those features and know <i>when</i> it is appropriate to use them. For example, it is one thing to know <i>how</i> to work out the square root of a number using the calculator. It is quite another thing to <i>understand</i> what a square root is and <i>when</i> it is sensible to use it.</p><p>You should by now have acquired your calculator along with the manufacturer's manual which describes how to use the various functions of the calculator. You also should have got a copy of the <i>Calculator Book</i>, which was specially written for the Open University. It serves two functions: to show you how to use the calculator and also to teach you the associated mathematics.</p><p>Work through the first four chapters of the <i>Calculator Book</i> before going on to the next activity.</p><div class="
oucontentactivity
oucontentsheavybox1 oucontentsbox " id="act001_012"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 12 Glancing back</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Take a very quick look through Sections 1.1 to 1.4 of the <i>Calculator Book</i> and any notes you made when you studied the sections in your preparation. Ask yourself the following questions:</p><ol class="oucontentnumbered"><li>
<p>What calculator skills were covered?</p>
</li><li>
<p>What learning or revision of mathematical ideas was covered? Make notes on what you find.</p>
</li></ol></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><p>You may have included all or some of these and you might have a few extra ones.</p><ol class="oucontentnumbered"><li>
<p>Calculator skills</p>
<ul class="oucontentunnumbered"><li>
<p>Adjusting display contrast;</p>
</li><li>
<p>Turning on/off and resetting memory;</p>
</li><li>
<p>Using the main and second function keys;</p>
</li><li>
<p>Very basic arithmetic: +, −, × and ÷; Editing an expression and use of the cursor keys;</p>
</li><li>
<p>Inputting negative numbers;</p>
</li><li>
<p>Setting the number of decimal places: Being aware of calculator conventions and the use of brackets;</p>
</li><li>
<p>Interpreting error messages;</p>
</li><li>
<p>Use of the MODE menu;</p>
</li><li>
<p>Use of square and power keys.</p>
</li></ul>
</li><li>
<p>Mathematical ideas covered</p>
<ul class="oucontentunnumbered"><li>
<p>Inverse operations;</p>
</li><li>
<p>Decimal places;</p>
</li><li>
<p>Negative numbers;</p>
</li><li>
<p>Order of operations;</p>
</li><li>
<p>Sequences and converging to a limit (see Brain stretcher in Section 3);</p>
</li><li>
<p>Squares, square roots and other powers.</p>
</li></ul>
</li></ol><p>There are further comments about this activity in the main text.</p></div></div></div></div><p>In order to answer the questions in Activity 12, you may have used some or all of the following:</p><ul class="oucontentbulleted"><li>
<p>the main headings in the text of the Calculator Book; for example, ‘1.2 Using the calculator for basic arithmetic’;</p>
</li><li>
<p>the subheadings in the text, for example, ‘Some calculator conventions’;</p>
</li><li>
<p>the diagrams—the representations both of the keyboard and of the calculator's screen (or ‘screendumps’);</p>
</li><li>
<p>the single words in bold type in the margins, for example <b>operation keys inverse</b>, and so on;</p>
</li><li>
<p>any highlighting, underlining or extra notes which you added to the text;</p>
</li><li>
<p>any separate pages of notes which you may have made.</p>
</li></ul><p>Why bother to point this out to you? The reason is that it is important to develop efficient and effective methods of studying (from a very early stage). Certainly you need to ‘do the mathematics’ but there is also much to be gained from putting your own study methods and mathematical learning under the spotlight from time to time.</p><p>You were recommended to look back over, to see again or revise, work you had completed before. How useful were the notes you made? Were they too detailed or too sparse?</p>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

Glancing ahead
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection3.4
Tue, 12 Apr 2016 23:00:00 GMT
<div class=" oucontentactivity oucontentsheavybox1 oucontentsbox " id="act001_013"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 13</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Take a very quick look through Section 1.5 of the <i>Calculator Book</i>, entitled ‘Everyday calculations’. Do not read it all yet!</p><p>Use the headings, subheadings, diagrams, and so on to give yourself an overview of what the section is about. In particular, ask yourself the following questions.</p><ol class="oucontentnumbered"><li>
<p>Are there many new calculator skills?</p>
</li><li>
<p>What new mathematical ideas are covered?</p>
</li><li>
<p>What sorts of activities are required of me?</p>
</li><li>
<p>How long will it take me?</p>
</li></ol></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><ol class="oucontentnumbered"><li>
<p>There are only two new calculator skills: storing numbers and entering alphabetic characters.</p>
</li><li>
<p>Percentage increases and decreases, including working with VAT;</p>
<p>Comparing price rises;</p>
<p>Conducting an investigation;</p>
<p>Estimation.</p>
</li><li>
<p>
<i>Calculating</i> using the calculator and <i>checking</i> calculations;</p>
<p>
<i>Following instructions</i>, especially those involving key sequences;</p>
<p>
<i>Recalling</i> earlier skills;</p>
<p>
<i>Comparing</i> different values and methods; for example, with <i>practising</i> methods just introduced;</p>
<p>
<i>Making notes</i> and <i>reflecting</i> on methods; <i>Investigating</i>, which might involve some research;</p>
<p>
<i>Predicting</i> and <i>estimating</i> to get a rough idea of the solution to a problem; <i>Interpreting</i> results.</p>
<p>These activities can be divided roughly into ‘doing exercises’, ‘using skills to work on a problem’ and ‘making notes’.</p>
</li><li>
<p>The answer will vary from student to student, but it will clearly depend on how familiar you are with the use of percentages.</p>
</li></ol></div></div></div></div><p>Just as glancing back is a very useful study skill, so too is glancing ahead as it sets the ensuing work into context. It may take only a few seconds to complete but you need to be quite disciplined in order to do it—there's usually an almost overwhelming urge to press on with the actual study.</p><p>So, now that you have glanced ahead,… press on!</p>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection3.4
Glancing aheadMU120_1<div class="
oucontentactivity
oucontentsheavybox1 oucontentsbox " id="act001_013"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 13</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Take a very quick look through Section 1.5 of the <i>Calculator Book</i>, entitled ‘Everyday calculations’. Do not read it all yet!</p><p>Use the headings, subheadings, diagrams, and so on to give yourself an overview of what the section is about. In particular, ask yourself the following questions.</p><ol class="oucontentnumbered"><li>
<p>Are there many new calculator skills?</p>
</li><li>
<p>What new mathematical ideas are covered?</p>
</li><li>
<p>What sorts of activities are required of me?</p>
</li><li>
<p>How long will it take me?</p>
</li></ol></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><ol class="oucontentnumbered"><li>
<p>There are only two new calculator skills: storing numbers and entering alphabetic characters.</p>
</li><li>
<p>Percentage increases and decreases, including working with VAT;</p>
<p>Comparing price rises;</p>
<p>Conducting an investigation;</p>
<p>Estimation.</p>
</li><li>
<p>
<i>Calculating</i> using the calculator and <i>checking</i> calculations;</p>
<p>
<i>Following instructions</i>, especially those involving key sequences;</p>
<p>
<i>Recalling</i> earlier skills;</p>
<p>
<i>Comparing</i> different values and methods; for example, with <i>practising</i> methods just introduced;</p>
<p>
<i>Making notes</i> and <i>reflecting</i> on methods; <i>Investigating</i>, which might involve some research;</p>
<p>
<i>Predicting</i> and <i>estimating</i> to get a rough idea of the solution to a problem; <i>Interpreting</i> results.</p>
<p>These activities can be divided roughly into ‘doing exercises’, ‘using skills to work on a problem’ and ‘making notes’.</p>
</li><li>
<p>The answer will vary from student to student, but it will clearly depend on how familiar you are with the use of percentages.</p>
</li></ol></div></div></div></div><p>Just as glancing back is a very useful study skill, so too is glancing ahead as it sets the ensuing work into context. It may take only a few seconds to complete but you need to be quite disciplined in order to do it—there's usually an almost overwhelming urge to press on with the actual study.</p><p>So, now that you have glanced ahead,… press on!</p>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

A pressing engagement
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection3.5
Tue, 12 Apr 2016 23:00:00 GMT
<div class=" oucontentactivity oucontentsheavybox1 oucontentsbox " id="act001_014"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 14</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Work through Section 1.5 of the <i>Calculator Book</i>. As you do so, bear in mind what you decided about the notes you made for the earlier sections—will you annotate the text itself in the margin, or do you need fuller, separate notes?</p><p>In Section 1.5 you are asked to complete four exercises. Do you need to write down the answers? If so, where and in how much detail? At what point should you check your answers with those at the back of the <i>Calculator Book</i>? When you have completed the section, glance back over the text and your notes, asking yourself what calculator skills and mathematical ideas were covered.</p></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><p>Some students like to see notes in the original context and so choose to annotate the text. Others like to make notes on cards so that they can be easily referenced—there are many alternatives. You need to decide on a method that will work well for you.</p><p>If you feel that the question requires a written answer then do not throw your solution away, but keep it for reference later. Remember that most of this writing will be seen only by you, so do not waste too much precious time on presentation.</p><p>When you have completed the section and glanced back to see what calculator skills and mathematical ideas were covered, you may like to compare the list of points in the comment to Activity 13(a) and (b), above with your points.</p></div></div></div></div><p>This section of the course involves quite a lot of work from the <i>Calculator Book</i> and you may well not be able to complete it all in one study session. This may be a good point at which to assess how much time you have spent so far and how much work lies ahead. If you have not had a break since starting Section 2, why not take one now before you press on with the calculator?</p>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection3.5
A pressing engagementMU120_1<div class="
oucontentactivity
oucontentsheavybox1 oucontentsbox " id="act001_014"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 14</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Work through Section 1.5 of the <i>Calculator Book</i>. As you do so, bear in mind what you decided about the notes you made for the earlier sections—will you annotate the text itself in the margin, or do you need fuller, separate notes?</p><p>In Section 1.5 you are asked to complete four exercises. Do you need to write down the answers? If so, where and in how much detail? At what point should you check your answers with those at the back of the <i>Calculator Book</i>? When you have completed the section, glance back over the text and your notes, asking yourself what calculator skills and mathematical ideas were covered.</p></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><p>Some students like to see notes in the original context and so choose to annotate the text. Others like to make notes on cards so that they can be easily referenced—there are many alternatives. You need to decide on a method that will work well for you.</p><p>If you feel that the question requires a written answer then do not throw your solution away, but keep it for reference later. Remember that most of this writing will be seen only by you, so do not waste too much precious time on presentation.</p><p>When you have completed the section and glanced back to see what calculator skills and mathematical ideas were covered, you may like to compare the list of points in the comment to Activity 13(a) and (b), above with your points.</p></div></div></div></div><p>This section of the course involves quite a lot of work from the <i>Calculator Book</i> and you may well not be able to complete it all in one study session. This may be a good point at which to assess how much time you have spent so far and how much work lies ahead. If you have not had a break since starting Section 2, why not take one now before you press on with the calculator?</p>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

Pressing onwards
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection3.6
Tue, 12 Apr 2016 23:00:00 GMT
<div class=" oucontentactivity oucontentsheavybox1 oucontentsbox " id="act001_015"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 15</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><ol class="oucontentnumbered"><li>
<p>Work through Sections 1.6 and 1.7 of the <i>Calculator Book</i>, using the method suggested above of glancing aheadpressing onglancing back, if you find it useful.</p>
</li><li>
<p>A number of important mathematical terms were introduced in Chapter 1 of the <i>Calculator Book</i>; for example, square, square root, reciprocal, and so on. Make notes on each new term mentioned (check back in the <i>Calculator Book</i> if you need to).</p>
</li></ol></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><ol class="oucontentnumbered"><li>
<p>There are many answers and comments relating to the exercises at the back of the Calculator Book.</p>
</li></ol></div></div></div></div><div class="oucontentfigure" style="width:438px;" id="fig001_021"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/0db815db/mu120_1_021i.jpg" alt="" width="438" height="374" style="maxwidth:438px;" class="oucontentfigureimage oucontentmediawide"/></div><div class="oucontentbox oucontentsheavybox1 oucontentsbox " id="box001_002"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Outcomes</h2><div class="oucontentinnerbox"><p>Now that you have completed your work on this section, you should be able to:</p><ul class="oucontentbulleted"><li>
<p>use the calculator for everyday calculations involving addition, subtraction, multiplication, division, and percentages (<i>CalculatorBook</i>, 1.2 and 1.5);</p>
</li><li>
<p>express numbers in scientific notation and understand how this notation is displayed by the calculator (<i>Calculator Book</i>, 1.6);</p>
</li><li>
<p>understand the effect on a number entered on the calculator of the <i>x</i>squared, square root, reciprocal and power keys (<i>CalculatorBook</i>, 1.4 and 1.7);</p>
</li><li>
<p>read simple mathematical expressions containing symbols such as +, −, ×, ÷, √ and positive and negative powers (<i>CalculatorBook</i>, 1.2 and 1.6);</p>
</li><li>
<p>appreciate the idea of ‘doing’ and ‘undoing’ associated with pairs of specific keys on the calculator, and give some examples of common mathematical ‘doing–undoing’ pairs of operations (<i>Calculator Book</i>, 1.7).</p>
</li></ul></div></div></div>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection3.6
Pressing onwardsMU120_1<div class="
oucontentactivity
oucontentsheavybox1 oucontentsbox " id="act001_015"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 15</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><ol class="oucontentnumbered"><li>
<p>Work through Sections 1.6 and 1.7 of the <i>Calculator Book</i>, using the method suggested above of glancing aheadpressing onglancing back, if you find it useful.</p>
</li><li>
<p>A number of important mathematical terms were introduced in Chapter 1 of the <i>Calculator Book</i>; for example, square, square root, reciprocal, and so on. Make notes on each new term mentioned (check back in the <i>Calculator Book</i> if you need to).</p>
</li></ol></div>
<div class="oucontentsaqanswer" datashowtext="Reveal answer" datahidetext="Hide answer"><h3 class="oucontenth4">Answer</h3><ol class="oucontentnumbered"><li>
<p>There are many answers and comments relating to the exercises at the back of the Calculator Book.</p>
</li></ol></div></div></div></div><div class="oucontentfigure" style="width:438px;" id="fig001_021"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/0db815db/mu120_1_021i.jpg" alt="" width="438" height="374" style="maxwidth:438px;" class="oucontentfigureimage oucontentmediawide"/></div><div class="oucontentbox oucontentsheavybox1 oucontentsbox " id="box001_002"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Outcomes</h2><div class="oucontentinnerbox"><p>Now that you have completed your work on this section, you should be able to:</p><ul class="oucontentbulleted"><li>
<p>use the calculator for everyday calculations involving addition, subtraction, multiplication, division, and percentages (<i>CalculatorBook</i>, 1.2 and 1.5);</p>
</li><li>
<p>express numbers in scientific notation and understand how this notation is displayed by the calculator (<i>Calculator Book</i>, 1.6);</p>
</li><li>
<p>understand the effect on a number entered on the calculator of the <i>x</i>squared, square root, reciprocal and power keys (<i>CalculatorBook</i>, 1.4 and 1.7);</p>
</li><li>
<p>read simple mathematical expressions containing symbols such as +, −, ×, ÷, √ and positive and negative powers (<i>CalculatorBook</i>, 1.2 and 1.6);</p>
</li><li>
<p>appreciate the idea of ‘doing’ and ‘undoing’ associated with pairs of specific keys on the calculator, and give some examples of common mathematical ‘doing–undoing’ pairs of operations (<i>Calculator Book</i>, 1.7).</p>
</li></ul></div></div></div>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

3 Aims
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection4.1
Tue, 12 Apr 2016 23:00:00 GMT
<p>The aim of this section is to help you to think about how you study mathematics and consider ways in which you can make your study more effective.</p>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection4.1
3 AimsMU120_1<p>The aim of this section is to help you to think about how you study mathematics and consider ways in which you can make your study more effective.</p>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

3.1 Spotlight on study
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection4.2
Tue, 12 Apr 2016 23:00:00 GMT
<p>As you have been working through this course, have you thought about <i>how</i> you are studying, and what this process involves? Do you feel confident or concerned about whether you will be able to learn mathematics and use it in the future? Put your study methods under the spotlight now, before moving on with your studies.</p><p>Learning rarely happens passively. A number of aspects of this course have been designed to encourage your more active participation and involvement. However, even that active experience may not be sufficient. There is a dangerous myth about ‘learning from experience’. Of course, experience is necessary and important but it is seldom enough. Longlasting learning comes about from <i>reflecting</i> on experience and integrating it into what you already know.</p><p>Think about how your own knowledge has developed on the course so far, in particular by concentrating on what you did in Section 2 of this course. At the end of that section, like every section of the course, there was a list of ‘outcomes’. One example of what you should have been able to do when you reached the end of that section was:</p><div class="oucontentquote oucontentsbox" id="quo001_006"><blockquote><p>express numbers in scientific notation, and understand how this notation is displayed by the calculator.</p></blockquote></div><p>Such outcomes should provide you with a stimulus to reflect on what you have done—to think, for example, ‘Am I sure what that means? How confident am I about doing that?’ Sometimes your response will not be totally clearcut. For example, you may think ‘I am pretty confident about using scientific notation, at least for big numbers’ or ‘I think I understand what the calculator notation looks like’. The key point is to use the lists of outcomes to help you put your understanding under the spotlight.</p><div class="oucontentfigure" style="width:469px;" id="fig001_022"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/1b5f58be/mu120_1_022i.jpg" alt="" width="469" height="445" style="maxwidth:469px;" class="oucontentfigureimage oucontentmediawide"/></div><p>Some activities in the course require a written response to some task or question. For example, in the last exercise in Chapter 1 of the <i>Calculator Book</i> you were asked to write down an explanation of some mathematical terms for somebody else. It is one thing to have some vague understanding of a particular mathematical concept and quite another to be able to describe it in words. Activities like this are designed to help you deepen your understanding and, although not everyone finds this sort of writing easy, it can be a valuable tool and is a skill well worth developing. Such written explanations will also be useful as reference for you later in your studies.</p><div class="oucontentfigure" style="width:511px;" id="fig001_023"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/115bbef4/mu120_1_023i.jpg" alt="" width="511" height="312" style="maxwidth:511px;" class="oucontentfigureimage oucontentmediawide"/><div class="oucontentfiguretext"><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Timothy's love letters took a new turn when he started studying mathematics</span></div></div></div><p>Most of the learning that takes place in everyday life happens through a combination of theory and practice. For example, learning to make bread involves some theory (such as knowing what activates the yeast) and some practice (knowing when the dough has been kneaded sufficiently). So, learning involves making a connection between knowing (the <i>theory</i>) and doing (the <i>practice</i>).</p><div class="oucontentfigure oucontentmediamini" id="fig001_024"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/db9310fe/mu120_1_024i.jpg" alt="" width="324" height="347" style="maxwidth:324px;" class="oucontentfigureimage"/></div><p>Similarly, learning in this course requires both theory and practice to be present. The theory on its own is not sufficient. The ideas or theories have to be practised in real situations to see how they work. Similarly the practice—that is, mathematical activities and exercises—is not sufficient on its own. Without reflection or critical thinking, thorough learning will not result. It is when you think carefully about the activities and exercises that you can start to form general rules or theories.</p><p>Writing about your own experience can be a very powerful way of learning from it because it helps you to stand back and move from the practice to the theory. The next activity asks you to do some more reflective writing, not this time about a particular mathematical topic but rather about your experience of study so far. Here you are putting your study methods under the spotlight.</p><div class=" oucontentactivity oucontentsheavybox1 oucontentsbox " id="act001_016"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 16 Studying study</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Describe your experience of study on this course so far. Make brief notes under each of the headings which are also listed below. Don't spend more than 10 minutes on this activity.</p><ul class="oucontentbulleted"><li>
<p>How did you get started? For example, at one extreme you may have just sat down, logged on to the website and got on with it, or at the opposite extreme you may have organized your working space carefully and sat down at preplanned times.</p>
</li><li>
<p>What have you enjoyed? For example, it may be the calculator work, or the chance to stretch your mind again, or it may be the different approach to mathematics.</p>
</li><li>
<p>What practical problems have you faced so far? For example, you may have found it hard to concentrate; you may have suddenly realized that you needed to get the calculator.</p>
</li><li>
<p>What have you learned from this? For example, is it best to plan study sessions at particular times of day? Is it best to organize the study resources you need in advance, and so on?</p>
</li></ul></div></div></div></div><p>Becoming more aware of how you go about studying allows you to monitor and improve your approach and study methods. If you discuss Activity 17 with other students, friends or family members, you may see that individuals differ enormously in how they go about studying.</p><p>To be effective, study must be organized so that it suits both your own life style and your own preferred learning methods. People differ in how they learn, how they approach solving problems and how they process information. Try to become more aware of the learning methods and study skills that suit you.</p>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection4.2
3.1 Spotlight on studyMU120_1<p>As you have been working through this course, have you thought about <i>how</i> you are studying, and what this process involves? Do you feel confident or concerned about whether you will be able to learn mathematics and use it in the future? Put your study methods under the spotlight now, before moving on with your studies.</p><p>Learning rarely happens passively. A number of aspects of this course have been designed to encourage your more active participation and involvement. However, even that active experience may not be sufficient. There is a dangerous myth about ‘learning from experience’. Of course, experience is necessary and important but it is seldom enough. Longlasting learning comes about from <i>reflecting</i> on experience and integrating it into what you already know.</p><p>Think about how your own knowledge has developed on the course so far, in particular by concentrating on what you did in Section 2 of this course. At the end of that section, like every section of the course, there was a list of ‘outcomes’. One example of what you should have been able to do when you reached the end of that section was:</p><div class="oucontentquote oucontentsbox" id="quo001_006"><blockquote><p>express numbers in scientific notation, and understand how this notation is displayed by the calculator.</p></blockquote></div><p>Such outcomes should provide you with a stimulus to reflect on what you have done—to think, for example, ‘Am I sure what that means? How confident am I about doing that?’ Sometimes your response will not be totally clearcut. For example, you may think ‘I am pretty confident about using scientific notation, at least for big numbers’ or ‘I think I understand what the calculator notation looks like’. The key point is to use the lists of outcomes to help you put your understanding under the spotlight.</p><div class="oucontentfigure" style="width:469px;" id="fig001_022"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/1b5f58be/mu120_1_022i.jpg" alt="" width="469" height="445" style="maxwidth:469px;" class="oucontentfigureimage oucontentmediawide"/></div><p>Some activities in the course require a written response to some task or question. For example, in the last exercise in Chapter 1 of the <i>Calculator Book</i> you were asked to write down an explanation of some mathematical terms for somebody else. It is one thing to have some vague understanding of a particular mathematical concept and quite another to be able to describe it in words. Activities like this are designed to help you deepen your understanding and, although not everyone finds this sort of writing easy, it can be a valuable tool and is a skill well worth developing. Such written explanations will also be useful as reference for you later in your studies.</p><div class="oucontentfigure" style="width:511px;" id="fig001_023"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/115bbef4/mu120_1_023i.jpg" alt="" width="511" height="312" style="maxwidth:511px;" class="oucontentfigureimage oucontentmediawide"/><div class="oucontentfiguretext"><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Timothy's love letters took a new turn when he started studying mathematics</span></div></div></div><p>Most of the learning that takes place in everyday life happens through a combination of theory and practice. For example, learning to make bread involves some theory (such as knowing what activates the yeast) and some practice (knowing when the dough has been kneaded sufficiently). So, learning involves making a connection between knowing (the <i>theory</i>) and doing (the <i>practice</i>).</p><div class="oucontentfigure oucontentmediamini" id="fig001_024"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/db9310fe/mu120_1_024i.jpg" alt="" width="324" height="347" style="maxwidth:324px;" class="oucontentfigureimage"/></div><p>Similarly, learning in this course requires both theory and practice to be present. The theory on its own is not sufficient. The ideas or theories have to be practised in real situations to see how they work. Similarly the practice—that is, mathematical activities and exercises—is not sufficient on its own. Without reflection or critical thinking, thorough learning will not result. It is when you think carefully about the activities and exercises that you can start to form general rules or theories.</p><p>Writing about your own experience can be a very powerful way of learning from it because it helps you to stand back and move from the practice to the theory. The next activity asks you to do some more reflective writing, not this time about a particular mathematical topic but rather about your experience of study so far. Here you are putting your study methods under the spotlight.</p><div class="
oucontentactivity
oucontentsheavybox1 oucontentsbox " id="act001_016"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 16 Studying study</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Describe your experience of study on this course so far. Make brief notes under each of the headings which are also listed below. Don't spend more than 10 minutes on this activity.</p><ul class="oucontentbulleted"><li>
<p>How did you get started? For example, at one extreme you may have just sat down, logged on to the website and got on with it, or at the opposite extreme you may have organized your working space carefully and sat down at preplanned times.</p>
</li><li>
<p>What have you enjoyed? For example, it may be the calculator work, or the chance to stretch your mind again, or it may be the different approach to mathematics.</p>
</li><li>
<p>What practical problems have you faced so far? For example, you may have found it hard to concentrate; you may have suddenly realized that you needed to get the calculator.</p>
</li><li>
<p>What have you learned from this? For example, is it best to plan study sessions at particular times of day? Is it best to organize the study resources you need in advance, and so on?</p>
</li></ul></div></div></div></div><p>Becoming more aware of how you go about studying allows you to monitor and improve your approach and study methods. If you discuss Activity 17 with other students, friends or family members, you may see that individuals differ enormously in how they go about studying.</p><p>To be effective, study must be organized so that it suits both your own life style and your own preferred learning methods. People differ in how they learn, how they approach solving problems and how they process information. Try to become more aware of the learning methods and study skills that suit you.</p>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

3.2 Keeping a record: a learning file
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection4.3
Tue, 12 Apr 2016 23:00:00 GMT
<p>The term <i>learning file</i> is used to mean a record of your work in some sort of filing system. This may consist of a file, a box, note books, a filing cabinet, files on your computer or something else that suits you. Whatever the content, you will certainly need some way of organizing your written notes so that they stay together and in order.</p><div class="oucontentfigure" style="width:500px;" id="fig001_025i"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/b43c46df/mu120_1_025i.jpg" alt="" width="500" height="340" style="maxwidth:500px;" class="oucontentfigureimage oucontentmediawide"/><div class="oucontentfiguretext"><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Gradually, Snowy began to develop a taste for algebra</span></div></div></div><div class=" oucontentactivity oucontentsheavybox1 oucontentsbox " id="act001_017"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 17 Organizing your learning file</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>If you have not already done so, collect together all the written work you have produced so far, like the pages of answers to exercises and investigations.</p><p>Decide what your learning file should consist of. Organize it in a way that is useful and easy for you to use.</p></div></div></div></div>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection4.3
3.2 Keeping a record: a learning fileMU120_1<p>The term <i>learning file</i> is used to mean a record of your work in some sort of filing system. This may consist of a file, a box, note books, a filing cabinet, files on your computer or something else that suits you. Whatever the content, you will certainly need some way of organizing your written notes so that they stay together and in order.</p><div class="oucontentfigure" style="width:500px;" id="fig001_025i"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/b43c46df/mu120_1_025i.jpg" alt="" width="500" height="340" style="maxwidth:500px;" class="oucontentfigureimage oucontentmediawide"/><div class="oucontentfiguretext"><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Gradually, Snowy began to develop a taste for algebra</span></div></div></div><div class="
oucontentactivity
oucontentsheavybox1 oucontentsbox " id="act001_017"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 17 Organizing your learning file</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>If you have not already done so, collect together all the written work you have produced so far, like the pages of answers to exercises and investigations.</p><p>Decide what your learning file should consist of. Organize it in a way that is useful and easy for you to use.</p></div></div></div></div>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

3.3 Skills in learning mathematics
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection4.4
Tue, 12 Apr 2016 23:00:00 GMT
<p>A great deal has already been said about the study skills that you will be developing as you work. But how might these help you in your future study, in the workplace or in any voluntary work that you do? This is the subject of the second band of the audiotape.</p><p>Audio: Click to listen to the audio clip entitled 'Skills in Learning Mathmatics'</p><div id="mp3001_002" class="oucontentmedia oucontentaudiovideo ompversion1" style="width:342px;"><div class="oucontentdefaultfilter"><span class="oumediafilter"><a href="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/e0bff34a/mu120_1_002s.mp3?forcedownload=1" class="oumedialinknoscript ompspacer">Download this audio clip.</a><span class="accesshide">Audio player: Skills in Learning Mathematics</span><a href="#" class="ompentermedia ompaccesshide" tabindex="1">
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</span></div><div class="filter_transcript" id="transcript_8133a9f16"><div><a href="#skip_transcript_8133a9f16" class="accesshide">Skip transcript: Skills in Learning Mathematics</a><h4 class="accesshide">Transcript: Skills in Learning Mathematics</h4></div><div class="filter_transcript_box" tabindex="0" id="content_transcript_8133a9f16"><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">You may have thought that in studying MU120 you’d only be learning mathematics, but has it actually turned out like that? I expect you found that you are actually doing many other things as well as mathematics. It’s often the case, isn’t it, that when we embark on a journey we pick up lots of new things, but we also use our own personal skills and experiences to help us along the way.
Starting MU120 is like beginning a journey. The main aim, clearly, is to get involved with doing and learning about mathematics, so that you can improve – for whatever reason. But in getting involved in learning mathematics you need to be able to do other things as well. And often, the better you are at doing these, the easier the journey. That’s what we’ll be exploring on this band. We’ll be looking at some of the skills you’ll be using and developing while doing MU120. We’ll be talking about how they can be described and assessed, and how useful they are. So, first of all, let’s try to identify some of these learning skills. In fact you’ve been using them already while working on the course. You’ve certainly had to get things done on time, learn by yourself, grapple with the calculator and wonder what to do when you got stuck – and, of course, sort out all the paper from the OU.
Try to make a list of all the different skills you’ve been using since you started the course. Stop while you do this.
Track 3
I’ve asked lots of OU students to do a similar exercise, and every time they come up with a long list, and each time it’s slightly different. Here’s some of the skills that other students have included:
• time management
• numeracy
• evaluation of information
• presentation
• analysis
• specialised reading skills
• summarising
• decision making
• discussion
• and using and interacting with different media.
Now take a look at your list. Do you notice that many of these skills are in fact things you do all the time – at home or at work – in all sorts of situations and not just in studying. In fact, these skills are so useful that employers have identified many of them as being crucial in the world of work. So much so that when companies are recruiting, they’re not just looking for knowledge in a particular area – they need these other things as well. Pick up any paper with job adverts and have a look at them. You’ll find phrases like:</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">FEMALE EMPLOYER (ROSEMARY HILL)</div><div class="oucontentdialogueremark">Good presentation skills a must.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MALE EMPLOYER (JOHN JAWORSKI)</div><div class="oucontentdialogueremark">Must be motivated and proactive.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">FEMALE EMPLOYER</div><div class="oucontentdialogueremark">Must have good numeracy skills.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MALE EMPLOYER</div><div class="oucontentdialogueremark">We need someone who has a good balance of interpersonal skills
and business skills.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">FEMALE EMPLOYER</div><div class="oucontentdialogueremark">You will need to organise and make strategic decisions in a
changing environment.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MALE EMPLOYER</div><div class="oucontentdialogueremark">We are not prescriptive about the subject qualifications, but, be
warned, you will need to demonstrate that you have the selfconfidence
and communication skills essential for the job.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">There are many ways of describing skills and competencies in the
workplace, and ideas of these are becoming more widespread.
So, you hear people talking about SNVQs or transferable skills,
based on what people actually do in the workplace. I spoke to
Dee Burkill, who’s a head of personnel for a Volkswagen
subsidiary, about the way that her organisation uses skills and
competencies with its staff.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">DEE BURKILL</div><div class="oucontentdialogueremark">We first started looking at competencies in the early ’90s, mainly
because the systems that we were using at that time had fallen
into disrepute, because of the recession, because of the limited
budgets that we had available for training, for salary increases.
So, we introduced a fully fledged competency programme, just
over three years ago now, for the whole of the group. So,
everybody now within this organisation fits into a job family.
The ‘job family’ is the generic term we use for people’s roles,
and we very much talk about roles now rather than jobs. Nobody
has a job description within the Volkswagen Group now. Nobody
at all. We have done away with job descriptions, and I will fight
vehemently to the end to maintain that, because I do not want to
go back to the days where we spent our lives rewriting these job
descriptions every time somebody’s job’s changed.
But the thing about our competencies, and the thing about
competencies that in most organisations that are different – they
are all focused on the softer issues. They’re all focused on the
‘how do you do’ things: ‘how do you behave?’ and ‘how do you
go about achieving your objectives?’
So, you will have objectives. You will have performancerelated
objectives, managerial objectives very, very focused. And, yes, I
am concerned about whether or not you have achieved this
objective, but I am more concerned about how you’ve gone about
doing it. And you will be rewarded for the ‘how you’ve done it’.
And if you’ve trampled on people, upset customers, been rude to
people or whatever, then you will not have achieved that
competence, and you will not get the tick towards it. And, as I
say, it does drive our salaries as well. So, without evidence of
achieving that competence, you will not get a salary increase, so
it does focus the mind somewhat.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">So, when you’re looking for, say, new graduates, what are you
looking for from them in terms of communication skills?</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">DEE BURKILL</div><div class="oucontentdialogueremark">We’re looking for people who’ve got a range of experiences.
We’re looking for people who are exhibiting, in the early stages,
the embryonic competencies, the embryonic skills,
communication skills, negotiating skills, ambassadorial skills that
we want for the future.
We will ask them to tell us about a specific project they were
given ownership for, that they were responsible for from
beginning to end. We will ask them to describe it to us, and how
they evaluated its success. And, in hindsight, what went well, and
what could have been done better.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">Privatesector companies like Volkswagen often use a set of
competencies that they’ve identified for themselves. Many of
these are common across organisations. For example,
communication skills and the management of people are often
part of this type of approach. These skills are equally sought after
in the voluntary sector.
Michael Murray, who used to be the Chief Executive of Milton
Keynes Borough Council, is now active in a number of voluntary
organisations. I first asked him what he looks for in recruiting
staff.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MICHAEL MURRAY</div><div class="oucontentdialogueremark">Obviously, you’re sometimes looking for a particular
professional or other skill – if you’re looking for somebody who
has an ability of marketing, for the sake of argument. But, most
importantly, I think you are probably looking for people who’ve
got an understanding of the community they’re going to be
dealing with or the particular area that they’re going to be dealing
with – if not understanding, at least an empathy with that,
because the ‘notforprofit sector’, or whatever they call it, is a
bit different in many ways to many other areas. There are some
changing conceptions about what people are or should be doing
in the voluntary sector. And the range of skills, then, that people
need to perform those roles is quite varied.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">Can you think of a specific example?</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MICHAEL MURRAY</div><div class="oucontentdialogueremark">The Living Archive Project. If you take the director who runs
that – there’s a very small team, four people or something of that
order altogether – and that person has to, one, understand about
the issues surrounding an oral archive. He has to understand
something about the immediate community in which he lives and
the opportunities which that community offers. He needs to
understand something about making bids for money. In fact he
needs to understand a lot about making bids for money. He needs
to, obviously, be able to identify opportunities and respond to
them very quickly. And he needs to be an extremely good
communicator – extremely good communicator – because he’s
dealing with a huge number of audiences.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">So when you say ‘a good communicator’, what sort of things do
you mean by that?</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MICHAEL MURRAY</div><div class="oucontentdialogueremark">First of all, a good communicator about the ideas which the
organisation is dealing in. Secondly, the range of people whom
he has to deal with is very varied, you know, from kind of
politicians and your local council, down to all kinds of fundraisers,
to staff you have to manage.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">And what about people who perhaps aren’t volunteering at the
board level, who are coming in perhaps to do a couple of hours a
week for an organisation in a very practical way …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MICHAEL MURRAY</div><div class="oucontentdialogueremark">Yes.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">…What sort of things do you look for there?</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MICHAEL MURRAY</div><div class="oucontentdialogueremark">I think you’re looking for enthusiasm and understanding what the
voluntary organisation is trying to achieve, their part in it, and,
because it – often the voluntary sector is quite informally
structured, an ability to be able to communicate with others
within the organisation, with minimal formal structures around
them.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">Both Michael Murray and Dee Burkill have emphasised the need
for flexibility and for a range of skills. Now have another look at
the list you drew up earlier with the skills you’ve used in MU120
so far. Of all the lists you and I might generate, none are right or
wrong. They simply represent different ways of talking about
skills. And another thing: no one set of descriptions will give us
watertight definitions. There’ll always be seepage from one
general descriptional category to another. In my list, for example,
notetaking, specialised reading skills and discussion are actually
all part of communicating. There’s no single set of descriptions which will work well in all
contexts. So one important reason for being able to describe
skills in a general sense is being able to be confident that
something that you’ve learned in one situation will help you in
another, different situation.
Just think about what you’ll need to be able to do as you progress
from this course. You’ll want to be confident that you can apply
mathematical techniques and solve problems using mathematics.
But you’ll also want to be sure that you can study independently
and meet deadlines. And like most students, I expect that you
also want to feel that you’re improving as you go on.
There’s some value for us then to be able to identify particular
skills. But if these skills are to be recognised and valued by
others, whether an employer, a voluntary organisation or
university, or for your own use, then it’s not sufficient to say, ‘I
can present my work well,’ or, ‘I can use this statistical technique
to sort this problem out.’ Other people, and organisations, will
want evidence of what your skills are so that they can judge the
level at which you’re operating.
Demonstrating your skills to an employer is not the end of the
story. Using and defining skills are all about helping people to
develop and improve, and that includes skills you use in learning.
So, finally, I spoke to Les Coupe, who successfully studied
MU120 in 1996, and has continued as a student with the OU ever
since. I was interested to find out how the skills that he
developed on MU120 helped him at the time, and what use
they’ve been to him since then. I started out by asking him about
his work.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">LES COUPE</div><div class="oucontentdialogueremark">My job is as a Road Safety Officer. I work for Hampshire County
Council. It basically involves education, training and publicity
issues for all classes of road users, from very young children all
the way through to older road users.
It looks a great deal at statistics: accident trends, where we have
to identify accident problems, whether they’re going up, or
they’re going down; the programmes that we implement, whether
they’re successful. So there’s a lot of statistical work involved in
that.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">MU120 is slightly unusual in the sense that students tend to
expect a course that develops their numeracy skills, and just their
numeracy skills. But obviously, as you’re aware, it develops
other things as well – communication skills and study skills and
reflective learning skills. Can you think of any examples where
this has been useful to you in practice?</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">LES COUPE</div><div class="oucontentdialogueremark">Yes. We deal with accident statistics, road accident statistics. But
generally we deal with members of the public, county
councillors, occasionally politicians, where they will ask
questions and you can give ball park figures – you can say,
‘Well, we’ve had an approximately 12 per cent reduction in the
number of accidents,’ or similar kinds of things, and you know in
your own mind that you’re about right. If anybody does actually
challenge you when it comes to writing the thing down on paper,
you know that you’re more or less right. And again it is just an
overall confidence in what you say will be about right. And it’s
really only going through MU120 that it’s given me the
confidence to do that.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">Have you found that to be useful elsewhere?</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">LES COUPE</div><div class="oucontentdialogueremark">Well, yes, I can; it was actually during ’96 as I was doing
MU120, I witnessed a road accident on the motorway, where a
car spun off in front of me. I did of course stop; I spoke to the
driver, who was completely unhurt – he was okay – but he told
me that a lorry had forced him off the motorway. There were
other drivers stopped; I just took his telephone number and said
I’ll catch this chap up. I know I was stopped for no longer than
three or four minutes. So I zoomed off after this lorry. I did
eventually catch him up after fifteen to twenty minutes,
something like that, and got the registration number of the lorry
and, later the same day, telephoned the chap back.
I was somewhat surprised a few weeks later to get a summons by
a court to go and give evidence about what I’d seen. And I
related my story to the court, and the defence solicitor questioned
me; he said there was absolutely no way I could catch this lorry
up in the time that I’d stated. And I was actually able to say to
him that ‘oh yes, I could quite easily do it,’ and I was able to
relate to him, really off the top of my head, that the length of time
I was waiting there, which was only three or four minutes, this
would put the lorry three to four miles down the road at 56 miles
an hour. And, at the speed I was travelling, 70 to 75 miles an
hour to catch him up – a speed differential of about 15, 20 miles
an hour – that I’d be able to catch him up at about a rate of a mile
every four minutes, and therefore 12 to 15 minutes later I would
catch him up. And of course, at that speed, would put me 15
miles away from the scene of the accident, which was on the
outskirts of Winchester, which was where I said I’d actually
caught the chap up. So it gave me the confidence to actually
question someone who I saw as an authoritative figure and to
actually contradict what he’d said, but, more importantly, be
actually right with it as well. Because that was the thing, I do
remember quite vividly whilst the court adjourned for a few
moments, while they got maps out and checked my figures, I can
remember scribbling all these notes down, working these little
calculations out to see how right I was. But it was never
questioned. My evidence was taken as correct. So, from a
communication point of view, it’s improved things tremendously
for me.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">The other thing that MU120 does is this idea about getting people
to reflect on the way that they’re learning. It takes a little while
for people to appreciate how that actually works. Can you think
of how it’s made a difference to you in the way that you study?</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">LES COUPE</div><div class="oucontentdialogueremark">I certainly can. You have to lay out a study schedule of the work
that you have to do, the timescale that you have to do it in. Now,
I’ve been able to use similar kinds of study schedules with
subsequent courses, not entirely completely successfully because
of work pressures, but generally I’ve found it to help in planning
my study time for the OU, because I can say that ‘yes, I’ll have a
couple of hours free here or there’ – or whatever, and because I
know that from the nature of my work – I don’t do work regular
hours – I have to slot study periods in whenever I can. And
planning it helps considerably towards that.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">Can you think of a time during MU120 when you suddenly
realised perhaps that this was useful?</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">LES COUPE</div><div class="oucontentdialogueremark">I think, if I’m honest, as far as planning my study time is
concerned, it was really during the final assessment, and if I were
to give any advice to new MU120 students, it would be to say, is:
plan your study time.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">As you can see, the skills that you’re developing on MU120 may
not be entirely those that you’re expecting. Most of us want to
get better at what we’re doing, but often we’re not quite sure
which skills to improve, and indeed how to go about it. This is
one reason why the course isn’t just about doing mathematics.
As you’ve seen, whenever you’re learning and doing new things,
you’re using many different skills. MU120 helps you to improve
those skills while you’re doing the mathematics.
That’s why you’re encouraged to complete a variety of activities,
review your progress and keep a record in your learning file.</div><div class="clearer"></div></div></div><span class="accesshide" id="skip_transcript_8133a9f16">End transcript: Skills in Learning Mathematics</span></div><div class="filter_transcript_output" id="output_transcript_8133a9f16"><div class="filter_transcript_copy"><a href="#" id="action_link5d2f3803c365111" class="actionicon" ><img class="icon iconsmall" alt="Copy this transcript to the clipboard" title="Copy this transcript to the clipboard" src="https://www.open.edu/openlearn/ocw/theme/image.php/_s/openlearnng/core/1563274092/t/copy" /></a></div><div class="filter_transcript_print"><a href="#" id="action_link5d2f3803c365112" class="actionicon" ><img class="icon iconsmall" alt="Print this transcript" title="Print this transcript" src="https://www.open.edu/openlearn/ocw/theme/image.php/_s/openlearnng/core/1563274092/t/print" /></a></div></div><div class="oucontentfiguretext"><div class="oucontenttranscriptlink"><span class="filter_transcript_button" id="button_transcript_8133a9f16">Show transcriptHide transcript</span></div><div class="oucontentmediadownload"><a href="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/e0bff34a/mu120_1_002s.mp3?forcedownload=1" title="Download this audio clip">Download</a></div><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Skills in Learning Mathematics</span></div></div></div><div class="oucontentinteractionprint"><div class="oucontentinteractionunavailable">Interactive feature not available in single page view (<a class="oucontentcrossref" href="https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection4.4#mp3001002">see it in standard view</a>).</div></div><div class=" oucontentactivity oucontentsheavybox1 oucontentsbox " id="act001_018"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 18 Identifying skills</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Listen to the audi clip above, entitled ‘Skills in learning mathematics’. As you listen you may wish to make some notes, and at one point you will be asked to stop the tape in order to draw up a list of skills that you have been using and developing in the course so far. In the last part of the tape, a former student of mathematics at the Open University speaks about some of the skills that he developed during his course of study and how he has been able to use them since.</p></div></div></div></div><p>Much of this section has involved looking at how you study and making learning more explicit. Many people can improve the effectiveness of their learning if they spend some time focusing not only on the content of what they are trying to learn, but also on the learning process itself. Even if you do not find any particular difficulties with studying, it is important to pause regularly to evaluate how well you are doing and whether you can learn more effectively by changing your approach. To this end, before you finish this course, there is one more studyskills activity to complete.</p><div class=" oucontentactivity oucontentsheavybox1 oucontentsbox " id="act001_019"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 19 On reflection</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Think about your first course of study and, if you feel it is helpful, briefly note down your thoughts. Consider how many hours you have studied, the pattern of your study periods, and where and when you have studied. Think about how you might like to change the way you work so that your study becomes more effective.</p></div></div></div></div><div class="oucontentbox oucontentsheavybox1 oucontentsbox " id="box001_003"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Outcome</h2><div class="oucontentinnerbox"><p>Now that you have completed your work on this section, you should have:</p><ul class="oucontentbulleted"><li>
<p>organized your learning file (Activity 18);</p>
</li><li>
<p>reviewed the way that you are studying the course so far and begun to think about improvements (Activities 17 and 19).</p>
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https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection4.4
3.3 Skills in learning mathematicsMU120_1<p>A great deal has already been said about the study skills that you will be developing as you work. But how might these help you in your future study, in the workplace or in any voluntary work that you do? This is the subject of the second band of the audiotape.</p><p>Audio: Click to listen to the audio clip entitled 'Skills in Learning Mathmatics'</p><div id="mp3001_002" class="oucontentmedia oucontentaudiovideo ompversion1" style="width:342px;"><div class="oucontentdefaultfilter"><span class="oumediafilter"><a href="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/e0bff34a/mu120_1_002s.mp3?forcedownload=1" class="oumedialinknoscript ompspacer">Download this audio clip.</a><span class="accesshide">Audio player: Skills in Learning Mathematics</span><a href="#" class="ompentermedia ompaccesshide" tabindex="1">
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</span></div><div class="filter_transcript" id="transcript_8133a9f16"><div><a href="#skip_transcript_8133a9f16" class="accesshide">Skip transcript: Skills in Learning Mathematics</a><h4 class="accesshide">Transcript: Skills in Learning Mathematics</h4></div><div class="filter_transcript_box" tabindex="0" id="content_transcript_8133a9f16"><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">You may have thought that in studying MU120 you’d only be learning mathematics, but has it actually turned out like that? I expect you found that you are actually doing many other things as well as mathematics. It’s often the case, isn’t it, that when we embark on a journey we pick up lots of new things, but we also use our own personal skills and experiences to help us along the way.
Starting MU120 is like beginning a journey. The main aim, clearly, is to get involved with doing and learning about mathematics, so that you can improve – for whatever reason. But in getting involved in learning mathematics you need to be able to do other things as well. And often, the better you are at doing these, the easier the journey. That’s what we’ll be exploring on this band. We’ll be looking at some of the skills you’ll be using and developing while doing MU120. We’ll be talking about how they can be described and assessed, and how useful they are. So, first of all, let’s try to identify some of these learning skills. In fact you’ve been using them already while working on the course. You’ve certainly had to get things done on time, learn by yourself, grapple with the calculator and wonder what to do when you got stuck – and, of course, sort out all the paper from the OU.
Try to make a list of all the different skills you’ve been using since you started the course. Stop while you do this.
Track 3
I’ve asked lots of OU students to do a similar exercise, and every time they come up with a long list, and each time it’s slightly different. Here’s some of the skills that other students have included:
• time management
• numeracy
• evaluation of information
• presentation
• analysis
• specialised reading skills
• summarising
• decision making
• discussion
• and using and interacting with different media.
Now take a look at your list. Do you notice that many of these skills are in fact things you do all the time – at home or at work – in all sorts of situations and not just in studying. In fact, these skills are so useful that employers have identified many of them as being crucial in the world of work. So much so that when companies are recruiting, they’re not just looking for knowledge in a particular area – they need these other things as well. Pick up any paper with job adverts and have a look at them. You’ll find phrases like:</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">FEMALE EMPLOYER (ROSEMARY HILL)</div><div class="oucontentdialogueremark">Good presentation skills a must.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MALE EMPLOYER (JOHN JAWORSKI)</div><div class="oucontentdialogueremark">Must be motivated and proactive.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">FEMALE EMPLOYER</div><div class="oucontentdialogueremark">Must have good numeracy skills.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MALE EMPLOYER</div><div class="oucontentdialogueremark">We need someone who has a good balance of interpersonal skills
and business skills.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">FEMALE EMPLOYER</div><div class="oucontentdialogueremark">You will need to organise and make strategic decisions in a
changing environment.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MALE EMPLOYER</div><div class="oucontentdialogueremark">We are not prescriptive about the subject qualifications, but, be
warned, you will need to demonstrate that you have the selfconfidence
and communication skills essential for the job.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">There are many ways of describing skills and competencies in the
workplace, and ideas of these are becoming more widespread.
So, you hear people talking about SNVQs or transferable skills,
based on what people actually do in the workplace. I spoke to
Dee Burkill, who’s a head of personnel for a Volkswagen
subsidiary, about the way that her organisation uses skills and
competencies with its staff.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">DEE BURKILL</div><div class="oucontentdialogueremark">We first started looking at competencies in the early ’90s, mainly
because the systems that we were using at that time had fallen
into disrepute, because of the recession, because of the limited
budgets that we had available for training, for salary increases.
So, we introduced a fully fledged competency programme, just
over three years ago now, for the whole of the group. So,
everybody now within this organisation fits into a job family.
The ‘job family’ is the generic term we use for people’s roles,
and we very much talk about roles now rather than jobs. Nobody
has a job description within the Volkswagen Group now. Nobody
at all. We have done away with job descriptions, and I will fight
vehemently to the end to maintain that, because I do not want to
go back to the days where we spent our lives rewriting these job
descriptions every time somebody’s job’s changed.
But the thing about our competencies, and the thing about
competencies that in most organisations that are different – they
are all focused on the softer issues. They’re all focused on the
‘how do you do’ things: ‘how do you behave?’ and ‘how do you
go about achieving your objectives?’
So, you will have objectives. You will have performancerelated
objectives, managerial objectives very, very focused. And, yes, I
am concerned about whether or not you have achieved this
objective, but I am more concerned about how you’ve gone about
doing it. And you will be rewarded for the ‘how you’ve done it’.
And if you’ve trampled on people, upset customers, been rude to
people or whatever, then you will not have achieved that
competence, and you will not get the tick towards it. And, as I
say, it does drive our salaries as well. So, without evidence of
achieving that competence, you will not get a salary increase, so
it does focus the mind somewhat.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">So, when you’re looking for, say, new graduates, what are you
looking for from them in terms of communication skills?</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">DEE BURKILL</div><div class="oucontentdialogueremark">We’re looking for people who’ve got a range of experiences.
We’re looking for people who are exhibiting, in the early stages,
the embryonic competencies, the embryonic skills,
communication skills, negotiating skills, ambassadorial skills that
we want for the future.
We will ask them to tell us about a specific project they were
given ownership for, that they were responsible for from
beginning to end. We will ask them to describe it to us, and how
they evaluated its success. And, in hindsight, what went well, and
what could have been done better.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">Privatesector companies like Volkswagen often use a set of
competencies that they’ve identified for themselves. Many of
these are common across organisations. For example,
communication skills and the management of people are often
part of this type of approach. These skills are equally sought after
in the voluntary sector.
Michael Murray, who used to be the Chief Executive of Milton
Keynes Borough Council, is now active in a number of voluntary
organisations. I first asked him what he looks for in recruiting
staff.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MICHAEL MURRAY</div><div class="oucontentdialogueremark">Obviously, you’re sometimes looking for a particular
professional or other skill – if you’re looking for somebody who
has an ability of marketing, for the sake of argument. But, most
importantly, I think you are probably looking for people who’ve
got an understanding of the community they’re going to be
dealing with or the particular area that they’re going to be dealing
with – if not understanding, at least an empathy with that,
because the ‘notforprofit sector’, or whatever they call it, is a
bit different in many ways to many other areas. There are some
changing conceptions about what people are or should be doing
in the voluntary sector. And the range of skills, then, that people
need to perform those roles is quite varied.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">Can you think of a specific example?</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MICHAEL MURRAY</div><div class="oucontentdialogueremark">The Living Archive Project. If you take the director who runs
that – there’s a very small team, four people or something of that
order altogether – and that person has to, one, understand about
the issues surrounding an oral archive. He has to understand
something about the immediate community in which he lives and
the opportunities which that community offers. He needs to
understand something about making bids for money. In fact he
needs to understand a lot about making bids for money. He needs
to, obviously, be able to identify opportunities and respond to
them very quickly. And he needs to be an extremely good
communicator – extremely good communicator – because he’s
dealing with a huge number of audiences.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">So when you say ‘a good communicator’, what sort of things do
you mean by that?</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MICHAEL MURRAY</div><div class="oucontentdialogueremark">First of all, a good communicator about the ideas which the
organisation is dealing in. Secondly, the range of people whom
he has to deal with is very varied, you know, from kind of
politicians and your local council, down to all kinds of fundraisers,
to staff you have to manage.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">And what about people who perhaps aren’t volunteering at the
board level, who are coming in perhaps to do a couple of hours a
week for an organisation in a very practical way …</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MICHAEL MURRAY</div><div class="oucontentdialogueremark">Yes.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">…What sort of things do you look for there?</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">MICHAEL MURRAY</div><div class="oucontentdialogueremark">I think you’re looking for enthusiasm and understanding what the
voluntary organisation is trying to achieve, their part in it, and,
because it – often the voluntary sector is quite informally
structured, an ability to be able to communicate with others
within the organisation, with minimal formal structures around
them.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">Both Michael Murray and Dee Burkill have emphasised the need
for flexibility and for a range of skills. Now have another look at
the list you drew up earlier with the skills you’ve used in MU120
so far. Of all the lists you and I might generate, none are right or
wrong. They simply represent different ways of talking about
skills. And another thing: no one set of descriptions will give us
watertight definitions. There’ll always be seepage from one
general descriptional category to another. In my list, for example,
notetaking, specialised reading skills and discussion are actually
all part of communicating. There’s no single set of descriptions which will work well in all
contexts. So one important reason for being able to describe
skills in a general sense is being able to be confident that
something that you’ve learned in one situation will help you in
another, different situation.
Just think about what you’ll need to be able to do as you progress
from this course. You’ll want to be confident that you can apply
mathematical techniques and solve problems using mathematics.
But you’ll also want to be sure that you can study independently
and meet deadlines. And like most students, I expect that you
also want to feel that you’re improving as you go on.
There’s some value for us then to be able to identify particular
skills. But if these skills are to be recognised and valued by
others, whether an employer, a voluntary organisation or
university, or for your own use, then it’s not sufficient to say, ‘I
can present my work well,’ or, ‘I can use this statistical technique
to sort this problem out.’ Other people, and organisations, will
want evidence of what your skills are so that they can judge the
level at which you’re operating.
Demonstrating your skills to an employer is not the end of the
story. Using and defining skills are all about helping people to
develop and improve, and that includes skills you use in learning.
So, finally, I spoke to Les Coupe, who successfully studied
MU120 in 1996, and has continued as a student with the OU ever
since. I was interested to find out how the skills that he
developed on MU120 helped him at the time, and what use
they’ve been to him since then. I started out by asking him about
his work.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">LES COUPE</div><div class="oucontentdialogueremark">My job is as a Road Safety Officer. I work for Hampshire County
Council. It basically involves education, training and publicity
issues for all classes of road users, from very young children all
the way through to older road users.
It looks a great deal at statistics: accident trends, where we have
to identify accident problems, whether they’re going up, or
they’re going down; the programmes that we implement, whether
they’re successful. So there’s a lot of statistical work involved in
that.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">MU120 is slightly unusual in the sense that students tend to
expect a course that develops their numeracy skills, and just their
numeracy skills. But obviously, as you’re aware, it develops
other things as well – communication skills and study skills and
reflective learning skills. Can you think of any examples where
this has been useful to you in practice?</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">LES COUPE</div><div class="oucontentdialogueremark">Yes. We deal with accident statistics, road accident statistics. But
generally we deal with members of the public, county
councillors, occasionally politicians, where they will ask
questions and you can give ball park figures – you can say,
‘Well, we’ve had an approximately 12 per cent reduction in the
number of accidents,’ or similar kinds of things, and you know in
your own mind that you’re about right. If anybody does actually
challenge you when it comes to writing the thing down on paper,
you know that you’re more or less right. And again it is just an
overall confidence in what you say will be about right. And it’s
really only going through MU120 that it’s given me the
confidence to do that.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">Have you found that to be useful elsewhere?</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">LES COUPE</div><div class="oucontentdialogueremark">Well, yes, I can; it was actually during ’96 as I was doing
MU120, I witnessed a road accident on the motorway, where a
car spun off in front of me. I did of course stop; I spoke to the
driver, who was completely unhurt – he was okay – but he told
me that a lorry had forced him off the motorway. There were
other drivers stopped; I just took his telephone number and said
I’ll catch this chap up. I know I was stopped for no longer than
three or four minutes. So I zoomed off after this lorry. I did
eventually catch him up after fifteen to twenty minutes,
something like that, and got the registration number of the lorry
and, later the same day, telephoned the chap back.
I was somewhat surprised a few weeks later to get a summons by
a court to go and give evidence about what I’d seen. And I
related my story to the court, and the defence solicitor questioned
me; he said there was absolutely no way I could catch this lorry
up in the time that I’d stated. And I was actually able to say to
him that ‘oh yes, I could quite easily do it,’ and I was able to
relate to him, really off the top of my head, that the length of time
I was waiting there, which was only three or four minutes, this
would put the lorry three to four miles down the road at 56 miles
an hour. And, at the speed I was travelling, 70 to 75 miles an
hour to catch him up – a speed differential of about 15, 20 miles
an hour – that I’d be able to catch him up at about a rate of a mile
every four minutes, and therefore 12 to 15 minutes later I would
catch him up. And of course, at that speed, would put me 15
miles away from the scene of the accident, which was on the
outskirts of Winchester, which was where I said I’d actually
caught the chap up. So it gave me the confidence to actually
question someone who I saw as an authoritative figure and to
actually contradict what he’d said, but, more importantly, be
actually right with it as well. Because that was the thing, I do
remember quite vividly whilst the court adjourned for a few
moments, while they got maps out and checked my figures, I can
remember scribbling all these notes down, working these little
calculations out to see how right I was. But it was never
questioned. My evidence was taken as correct. So, from a
communication point of view, it’s improved things tremendously
for me.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">The other thing that MU120 does is this idea about getting people
to reflect on the way that they’re learning. It takes a little while
for people to appreciate how that actually works. Can you think
of how it’s made a difference to you in the way that you study?</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">LES COUPE</div><div class="oucontentdialogueremark">I certainly can. You have to lay out a study schedule of the work
that you have to do, the timescale that you have to do it in. Now,
I’ve been able to use similar kinds of study schedules with
subsequent courses, not entirely completely successfully because
of work pressures, but generally I’ve found it to help in planning
my study time for the OU, because I can say that ‘yes, I’ll have a
couple of hours free here or there’ – or whatever, and because I
know that from the nature of my work – I don’t do work regular
hours – I have to slot study periods in whenever I can. And
planning it helps considerably towards that.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">Can you think of a time during MU120 when you suddenly
realised perhaps that this was useful?</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">LES COUPE</div><div class="oucontentdialogueremark">I think, if I’m honest, as far as planning my study time is
concerned, it was really during the final assessment, and if I were
to give any advice to new MU120 students, it would be to say, is:
plan your study time.</div><div class="clearer"></div></div><div class="oucontentdialogueline"><div class="oucontentdialoguespeaker">KAREN REX</div><div class="oucontentdialogueremark">As you can see, the skills that you’re developing on MU120 may
not be entirely those that you’re expecting. Most of us want to
get better at what we’re doing, but often we’re not quite sure
which skills to improve, and indeed how to go about it. This is
one reason why the course isn’t just about doing mathematics.
As you’ve seen, whenever you’re learning and doing new things,
you’re using many different skills. MU120 helps you to improve
those skills while you’re doing the mathematics.
That’s why you’re encouraged to complete a variety of activities,
review your progress and keep a record in your learning file.</div><div class="clearer"></div></div></div><span class="accesshide" id="skip_transcript_8133a9f16">End transcript: Skills in Learning Mathematics</span></div><div class="filter_transcript_output" id="output_transcript_8133a9f16"><div class="filter_transcript_copy"><a href="#" id="action_link5d2f3803c365111" class="actionicon" ><img class="icon iconsmall" alt="Copy this transcript to the clipboard" title="Copy this transcript to the clipboard" src="https://www.open.edu/openlearn/ocw/theme/image.php/_s/openlearnng/core/1563274092/t/copy" /></a></div><div class="filter_transcript_print"><a href="#" id="action_link5d2f3803c365112" class="actionicon" ><img class="icon iconsmall" alt="Print this transcript" title="Print this transcript" src="https://www.open.edu/openlearn/ocw/theme/image.php/_s/openlearnng/core/1563274092/t/print" /></a></div></div><div class="oucontentfiguretext"><div class="oucontenttranscriptlink"><span class="filter_transcript_button" id="button_transcript_8133a9f16">Show transcriptHide transcript</span></div><div class="oucontentmediadownload"><a href="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/028a959b/e0bff34a/mu120_1_002s.mp3?forcedownload=1" title="Download this audio clip">Download</a></div><div class="oucontentcaption oucontentnonumber"><span class="oucontentfigurecaption">Skills in Learning Mathematics</span></div></div></div><div class="oucontentinteractionprint"><div class="oucontentinteractionunavailable">Interactive feature not available in single page view (<a class="oucontentcrossref" href="https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection4.4#mp3001002">see it in standard view</a>).</div></div><div class="
oucontentactivity
oucontentsheavybox1 oucontentsbox " id="act001_018"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 18 Identifying skills</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Listen to the audi clip above, entitled ‘Skills in learning mathematics’. As you listen you may wish to make some notes, and at one point you will be asked to stop the tape in order to draw up a list of skills that you have been using and developing in the course so far. In the last part of the tape, a former student of mathematics at the Open University speaks about some of the skills that he developed during his course of study and how he has been able to use them since.</p></div></div></div></div><p>Much of this section has involved looking at how you study and making learning more explicit. Many people can improve the effectiveness of their learning if they spend some time focusing not only on the content of what they are trying to learn, but also on the learning process itself. Even if you do not find any particular difficulties with studying, it is important to pause regularly to evaluate how well you are doing and whether you can learn more effectively by changing your approach. To this end, before you finish this course, there is one more studyskills activity to complete.</p><div class="
oucontentactivity
oucontentsheavybox1 oucontentsbox " id="act001_019"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Activity 19 On reflection</h2><div class="oucontentinnerbox"><div class="oucontentsaqquestion"><p>Think about your first course of study and, if you feel it is helpful, briefly note down your thoughts. Consider how many hours you have studied, the pattern of your study periods, and where and when you have studied. Think about how you might like to change the way you work so that your study becomes more effective.</p></div></div></div></div><div class="oucontentbox oucontentsheavybox1 oucontentsbox " id="box001_003"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Outcome</h2><div class="oucontentinnerbox"><p>Now that you have completed your work on this section, you should have:</p><ul class="oucontentbulleted"><li>
<p>organized your learning file (Activity 18);</p>
</li><li>
<p>reviewed the way that you are studying the course so far and begun to think about improvements (Activities 17 and 19).</p>
</li></ul></div></div></div> <script>
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</script>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

Conclusion
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection5
Tue, 12 Apr 2016 23:00:00 GMT
<p>This course introduced the varied components that you will use to learn mathematics: a calculator, reader articles, audio and video clips. You have mainly been working from this course's text and the <i>Calculator Book</i>.</p><p>A number of activities involved communicating your ideas: the meaning of mathematical terms; where you can ‘see’ mathematics in everyday settings; reviewing how you have studied this material. Writing is one aspect of communication which is central to learning. So it makes sense for you to think about and develop your skills in this area.</p><p>Part of learning mathematics is to learn to speak and think like a mathematician: becoming more aware of and fluent with the language of mathematics.</p><p>As you have now completed this course of work, take a few minutes to go through the list of outcomes and think about what you have achieved.</p><div class="oucontentbox oucontentsheavybox1 oucontentsbox " id="box001_004"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Outcomes</h2><div class="oucontentinnerbox"><p>You should now:</p><ul class="oucontentbulleted"><li>
<p>be able to describe your view of what mathematics is (Section 1);</p>
</li><li>
<p>have begun to recognize different types of written mathematics and developed your skill at reading it (Activities 6–9);</p>
</li><li>
<p>be able to tackle mathematical problems using a calculator (<i>Calculator Book</i>, Chapter 1);</p>
</li><li>
<p>be able to use your calculator with understanding for basic arithmetic, percentages, square roots, reciprocals and powers (<i>Calculator Book</i>, Sections 1.2, 1.4, 1.5);</p>
</li><li>
<p>be able to express and interpret numbers in scientific notation, both in writing and on your calculator (<i>Calculator Book</i>, Section 1.6);</p>
</li><li>
<p>be able to give some examples of common mathematical ‘doing–undoing’ pairs of operations (<i>Calculator Book</i>, Section 1.7);</p>
</li><li>
<p>be more attuned to noticing mathematical questions arising from the world around you (Activities 3, 4, 10 and 11);</p>
</li><li>
<p>have increased experience in working from video and audiotape as part of your mathematical learning (Activities 4, 11 and 19);</p>
</li><li>
<p>have organized and planned your study (Activities 12–19).</p>
</li></ul></div></div></div>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection5
ConclusionMU120_1<p>This course introduced the varied components that you will use to learn mathematics: a calculator, reader articles, audio and video clips. You have mainly been working from this course's text and the <i>Calculator Book</i>.</p><p>A number of activities involved communicating your ideas: the meaning of mathematical terms; where you can ‘see’ mathematics in everyday settings; reviewing how you have studied this material. Writing is one aspect of communication which is central to learning. So it makes sense for you to think about and develop your skills in this area.</p><p>Part of learning mathematics is to learn to speak and think like a mathematician: becoming more aware of and fluent with the language of mathematics.</p><p>As you have now completed this course of work, take a few minutes to go through the list of outcomes and think about what you have achieved.</p><div class="oucontentbox oucontentsheavybox1 oucontentsbox " id="box001_004"><div class="oucontentouterbox"><h2 class="oucontenth3 oucontentheading oucontentnonumber">Outcomes</h2><div class="oucontentinnerbox"><p>You should now:</p><ul class="oucontentbulleted"><li>
<p>be able to describe your view of what mathematics is (Section 1);</p>
</li><li>
<p>have begun to recognize different types of written mathematics and developed your skill at reading it (Activities 6–9);</p>
</li><li>
<p>be able to tackle mathematical problems using a calculator (<i>Calculator Book</i>, Chapter 1);</p>
</li><li>
<p>be able to use your calculator with understanding for basic arithmetic, percentages, square roots, reciprocals and powers (<i>Calculator Book</i>, Sections 1.2, 1.4, 1.5);</p>
</li><li>
<p>be able to express and interpret numbers in scientific notation, both in writing and on your calculator (<i>Calculator Book</i>, Section 1.6);</p>
</li><li>
<p>be able to give some examples of common mathematical ‘doing–undoing’ pairs of operations (<i>Calculator Book</i>, Section 1.7);</p>
</li><li>
<p>be more attuned to noticing mathematical questions arising from the world around you (Activities 3, 4, 10 and 11);</p>
</li><li>
<p>have increased experience in working from video and audiotape as part of your mathematical learning (Activities 4, 11 and 19);</p>
</li><li>
<p>have organized and planned your study (Activities 12–19).</p>
</li></ul></div></div></div>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

Conclusion
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection6
Tue, 12 Apr 2016 23:00:00 GMT
<p>This free course provided an introduction to studying Mathematics. It took you through a series of exercises designed to develop your approach to study and learning at a distance and helped to improve your confidence as an independent learner.</p>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection6
ConclusionMU120_1<p>This free course provided an introduction to studying Mathematics. It took you through a series of exercises designed to develop your approach to study and learning at a distance and helped to improve your confidence as an independent learner.</p>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

Keep on learning
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection7
Tue, 12 Apr 2016 23:00:00 GMT
<div class="oucontentfigure oucontentmediamini"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/8ff4c822/d3c986e6/ol_skeleton_keeponlearning_image.jpg" alt="" width="300" height="200" style="maxwidth:300px;" class="oucontentfigureimage"/></div><p> </p><div class="oucontentinternalsection"><h2 class="oucontenth2 oucontentinternalsectionhead">Study another free course</h2><p>There are more than <b>800 courses on OpenLearn</b> for you to choose from on a range of subjects. </p><p>Find out more about all our <span class="oucontentlinkwithtip"><a class="oucontenthyperlink" href="http://www.open.edu/openlearn/freecourses?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">free courses</a></span>.</p><p> </p></div><div class="oucontentinternalsection"><h2 class="oucontenth2 oucontentinternalsectionhead">Take your studies further</h2><p>Find out more about studying with The Open University by <a class="oucontenthyperlink" href="http://www.open.ac.uk/courses?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">visiting our online prospectus</a>. </p><p>If you are new to university study, you may be interested in our <a class="oucontenthyperlink" href="http://www.open.ac.uk/courses/doit/access?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">Access Courses</a> or <a class="oucontenthyperlink" href="http://www.open.ac.uk/courses/certificateshe?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">Certificates</a>.</p><p> </p></div><div class="oucontentinternalsection"><h2 class="oucontenth2 oucontentinternalsectionhead">What’s new from OpenLearn?</h2><p>
<a class="oucontenthyperlink" href="http://www.open.edu/openlearn/aboutopenlearn/subscribetheopenlearnnewsletter?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">Sign up to our newsletter</a> or view a sample.</p><p> </p></div><div class="oucontentbox oucontentshollowbox2 oucontentsbox oucontentsnoheading "><div class="oucontentouterbox"><div class="oucontentinnerbox"><p>For reference, full URLs to pages listed above:</p><p>OpenLearn – <a class="oucontenthyperlink" href="http://www.open.edu/openlearn/freecourses?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">www.open.edu/<span class="oucontenthidespace"> </span>openlearn/<span class="oucontenthidespace"> </span>freecourses</a>
</p><p>Visiting our online prospectus – <a class="oucontenthyperlink" href="http://www.open.ac.uk/courses?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">www.open.ac.uk/<span class="oucontenthidespace"> </span>courses</a>
</p><p>Access Courses – <a class="oucontenthyperlink" href="http://www.open.ac.uk/courses/doit/access?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">www.open.ac.uk/<span class="oucontenthidespace"> </span>courses/<span class="oucontenthidespace"> </span>doit/<span class="oucontenthidespace"> </span>access</a>
</p><p>Certificates – <a class="oucontenthyperlink" href="http://www.open.ac.uk/courses/certificateshe?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">www.open.ac.uk/<span class="oucontenthidespace"> </span>courses/<span class="oucontenthidespace"> </span>certificateshe</a>
</p><p>Newsletter ­– <a class="oucontenthyperlink" href="http://www.open.edu/openlearn/aboutopenlearn/subscribetheopenlearnnewsletter?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">www.open.edu/<span class="oucontenthidespace"> </span>openlearn/<span class="oucontenthidespace"> </span>aboutopenlearn/<span class="oucontenthidespace"> </span>subscribetheopenlearnnewsletter</a>
</p></div></div></div>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsection7
Keep on learningMU120_1<div class="oucontentfigure oucontentmediamini"><img src="https://www.open.edu/openlearn/ocw/pluginfile.php/91788/mod_oucontent/oucontent/770/8ff4c822/d3c986e6/ol_skeleton_keeponlearning_image.jpg" alt="" width="300" height="200" style="maxwidth:300px;" class="oucontentfigureimage"/></div><p> </p><div class="oucontentinternalsection"><h2 class="oucontenth2 oucontentinternalsectionhead">Study another free course</h2><p>There are more than <b>800 courses on OpenLearn</b> for you to choose from on a range of subjects. </p><p>Find out more about all our <span class="oucontentlinkwithtip"><a class="oucontenthyperlink" href="http://www.open.edu/openlearn/freecourses?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">free courses</a></span>.</p><p> </p></div><div class="oucontentinternalsection"><h2 class="oucontenth2 oucontentinternalsectionhead">Take your studies further</h2><p>Find out more about studying with The Open University by <a class="oucontenthyperlink" href="http://www.open.ac.uk/courses?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">visiting our online prospectus</a>. </p><p>If you are new to university study, you may be interested in our <a class="oucontenthyperlink" href="http://www.open.ac.uk/courses/doit/access?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">Access Courses</a> or <a class="oucontenthyperlink" href="http://www.open.ac.uk/courses/certificateshe?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">Certificates</a>.</p><p> </p></div><div class="oucontentinternalsection"><h2 class="oucontenth2 oucontentinternalsectionhead">What’s new from OpenLearn?</h2><p>
<a class="oucontenthyperlink" href="http://www.open.edu/openlearn/aboutopenlearn/subscribetheopenlearnnewsletter?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">Sign up to our newsletter</a> or view a sample.</p><p> </p></div><div class="oucontentbox oucontentshollowbox2 oucontentsbox
oucontentsnoheading
"><div class="oucontentouterbox"><div class="oucontentinnerbox"><p>For reference, full URLs to pages listed above:</p><p>OpenLearn – <a class="oucontenthyperlink" href="http://www.open.edu/openlearn/freecourses?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">www.open.edu/<span class="oucontenthidespace"> </span>openlearn/<span class="oucontenthidespace"> </span>freecourses</a>
</p><p>Visiting our online prospectus – <a class="oucontenthyperlink" href="http://www.open.ac.uk/courses?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">www.open.ac.uk/<span class="oucontenthidespace"> </span>courses</a>
</p><p>Access Courses – <a class="oucontenthyperlink" href="http://www.open.ac.uk/courses/doit/access?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">www.open.ac.uk/<span class="oucontenthidespace"> </span>courses/<span class="oucontenthidespace"> </span>doit/<span class="oucontenthidespace"> </span>access</a>
</p><p>Certificates – <a class="oucontenthyperlink" href="http://www.open.ac.uk/courses/certificateshe?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">www.open.ac.uk/<span class="oucontenthidespace"> </span>courses/<span class="oucontenthidespace"> </span>certificateshe</a>
</p><p>Newsletter – <a class="oucontenthyperlink" href="http://www.open.edu/openlearn/aboutopenlearn/subscribetheopenlearnnewsletter?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">www.open.edu/<span class="oucontenthidespace"> </span>openlearn/<span class="oucontenthidespace"> </span>aboutopenlearn/<span class="oucontenthidespace"> </span>subscribetheopenlearnnewsletter</a>
</p></div></div></div>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University

Acknowledgements
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsectionacknowledgements
Tue, 12 Apr 2016 23:00:00 GMT
<p>The content acknowledged below is Proprietary (see terms and conditions) and is used under licence.</p><p>Grateful acknowledgement is made to the following sources for permission to reproduce material in this course:</p><p>Course image: <span class="oucontentlinkwithtip"><a class="oucontenthyperlink" href="https://www.flickr.com/photos/jsjgeology/">James St. John</a></span> in Flickr made available under <a class="oucontenthyperlink" href="https://creativecommons.org/licenses/by/2.0/">Creative Commons Attribution 2.0 Licence</a>.</p><p>Example 2: <i>Guardian</i>, 10 January, 1994. Copyright © 1994 The Guardian; The History of the Calculator: photograph of clay tablet by permission of The British Library (AC2692 p/20); photographs of calculating machines : Copyright © Science Museum/Science and Society Picture Library.</p><p><a class="oucontenthyperlink" href="http://www.flickr.com/photos/bgivens/12343640/">useful_fiction</a> </p><p><b>Don't miss out:</b></p><p>If reading this text has inspired you to learn more, you may be interested in joining the millions of people who discover our free learning resources and qualifications by visiting The Open University  <a class="oucontenthyperlink" href="http://www.open.edu/openlearn/freecourses?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">www.open.edu/<span class="oucontenthidespace"> </span>openlearn/<span class="oucontenthidespace"> </span>freecourses</a></p>
https://www.open.edu/openlearn/sciencemathstechnology/mathematicsandstatistics/mathematicseducation/mathseverywhere/contentsectionacknowledgements
AcknowledgementsMU120_1<p>The content acknowledged below is Proprietary (see terms and conditions) and is used under licence.</p><p>Grateful acknowledgement is made to the following sources for permission to reproduce material in this course:</p><p>Course image: <span class="oucontentlinkwithtip"><a class="oucontenthyperlink" href="https://www.flickr.com/photos/jsjgeology/">James St. John</a></span> in Flickr made available under <a class="oucontenthyperlink" href="https://creativecommons.org/licenses/by/2.0/">Creative Commons Attribution 2.0 Licence</a>.</p><p>Example 2: <i>Guardian</i>, 10 January, 1994. Copyright © 1994 The Guardian; The History of the Calculator: photograph of clay tablet by permission of The British Library (AC2692 p/20); photographs of calculating machines : Copyright © Science Museum/Science and Society Picture Library.</p><p><a class="oucontenthyperlink" href="http://www.flickr.com/photos/bgivens/12343640/">useful_fiction</a> </p><p><b>Don't miss out:</b></p><p>If reading this text has inspired you to learn more, you may be interested in joining the millions of people who discover our free learning resources and qualifications by visiting The Open University  <a class="oucontenthyperlink" href="http://www.open.edu/openlearn/freecourses?utm_source=openlearn&utm_campaign=ol&utm_medium=ebook">www.open.edu/<span class="oucontenthidespace"> </span>openlearn/<span class="oucontenthidespace"> </span>freecourses</a></p>The Open UniversityThe Open UniversityCoursetext/htmlenGBMaths everywhere  MU120_1Copyright © 2016 The Open University