3.1 Spotlight on study
As you have been working through this course, have you thought about how 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.
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. Long-lasting learning comes about from reflecting on experience and integrating it into what you already know.
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:
express numbers in scientific notation, and understand how this notation is displayed by the calculator.
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 clear-cut. 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.
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 Calculator Book 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.
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 theory) and doing (the practice).
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.
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.
Activity 16 Studying study
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.
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 pre-planned times.
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.
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.
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?
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.
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.