# Recognizing mathematics, continued

In Example 1 it is the use of many **numbers** that identifies it as mathematics and suggest the area of mathematics called *arithmetic*. Example 2 has numbers but also **graphs and diagrams**, suggesting *statistics*. The **shapes** in Example 3 suggest that the *geometrical* part of mathematics is being used whereas Example 4, with all the **alphabetic symbols**, is clearly drawing upon *algebra*.

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^{−3}.

It is clearly mathematical writing. There are numbers all over the page, along with other well-known mathematical symbols such as =, × and ÷ Notice also the use of powers, the small digits written slightly above and to the right of the usual-sized digits. For example, 7^{−3} is read as ‘seven to the power minus three’.

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^{−3} represents and how it matches what the writer already knows about powers.

The writing in Example 1 is an example of a mathematical **investigation**. The writer is not setting out to answer a well-defined question to which there is a single right answer. Rather she was working at an open-ended series of questions and aiming to increase her own understanding. Notice how she works from *what she knows* towards *what she want* 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).

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.