Experiences of learning mathematics
Experiences of learning mathematics

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1.2.3 Process

Mathematical processes are different from content in that they overarch the subject and are not thought of as hierarchical. A list of processes could contain:

  • problem-solving (including investigating);

  • mathematical modelling;

  • reasoning;

  • communicating;

  • making connections (including applying mathematics); and

  • using tools.

Each of the six processes listed here represents a wide range of component skills that usefully contribute to a pupil's mathematical thinking as well as to their general thinking skills. In the task that follows, you are invited first to spend some time thinking of examples of the different processes. You will then be able to consider in more detail what the component skills for each process might be.

Task 6 Putting processes under the microscope

  1. For each of the six processes listed above, write down two or three examples.

  2. Click on the 'View document' link below to open ‘Processes uncovered’ and read a detailed listing of the possible components for these processes provided by Andy Begg (Begg, 1994).

Click on the link below to open 'Processes uncovered'. With thanks to Begg, A. (1994/1996) in Neyland, J. (ed) Mathematics Education: A Handbook for Teachers, Volume 1, Masterton nz: Wairarapa Education Resource Centre / Reston va: National Council of Teachers of Mathematics,(pp. 183–1920)

Processes uncovered [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]


One teacher found part 1 of this task difficult to do (he was particularly stuck on the ‘modelling’ process) until it was suggested that he might find it helpful to think about classroom situations where his pupils were engaged in modelling. He was then able to come up with several graphical examples of modelling based on a recent data handling investigation that his pupils had carried out.

There is no unique or universal set of processes in mathematics. The following five mathematical processes have been mentioned in various reports (for example, NCTM, 1989). They partially overlap with the six you have just been thinking about in Task 6, and the general educational skills listed in the Key Stage 3 National Strategy framework document for England and Wales (DfEE, 2001)

  • information processing skills;

  • enquiry skills;

  • creative thinking skills;

  • reasoning skills; and

  • evaluation skills.

As you will see in the next section, these general skills can be cross-matched with the mathematical content normally taught in school. Indeed, it should be possible, for each mathematical topic that you teach, and for each of the six processes considered in Task 6, to identify an example of that process in which that mathematical topic is applied.

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