Maths everywhere

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# Maths everywhere

Many people see calculators only as a way of producing answers—indeed some people see them almost as a means of cheating, of short-cutting 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!

After studying this course and related units you should know how to use many, but not all, of the mathematical features available on the calculator. Much more importantly, you should understand the mathematics associated with those features and know when it is appropriate to use them. For example, it is one thing to know how to work out the square root of a number using the calculator. It is quite another thing to understand what a square root is and when it is sensible to use it.

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 Calculator Book, 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.

Work through the first four chapters of the Calculator Book before going on to the next activity.

## Activity 12 Glancing back

Take a very quick look through Sections 1.1 to 1.4 of the Calculator Book and any notes you made when you studied the sections in your preparation. Ask yourself the following questions:

1. What calculator skills were covered?

2. What learning or revision of mathematical ideas was covered? Make notes on what you find.

You may have included all or some of these and you might have a few extra ones.

1. Calculator skills

• Turning on/off and resetting memory;

• Using the main and second function keys;

• Very basic arithmetic: +, −, × and ÷; Editing an expression and use of the cursor keys;

• Inputting negative numbers;

• Setting the number of decimal places: Being aware of calculator conventions and the use of brackets;

• Interpreting error messages;

• Use of the MODE menu;

• Use of square and power keys.

2. Mathematical ideas covered

• Inverse operations;

• Decimal places;

• Negative numbers;

• Order of operations;

• Sequences and converging to a limit (see Brain stretcher in Section 3);

• Squares, square roots and other powers.

In order to answer the questions in Activity 12, you may have used some or all of the following:

• the main headings in the text of the Calculator Book; for example, ‘1.2 Using the calculator for basic arithmetic’;

• the sub-headings in the text, for example, ‘Some calculator conventions’;

• the diagrams—the representations both of the keyboard and of the calculator's screen (or ‘screendumps’);

• the single words in bold type in the margins, for example operation keys inverse, and so on;

• any highlighting, underlining or extra notes which you added to the text;

• any separate pages of notes which you may have made.

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.

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?

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