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Working mathematically
Working mathematically

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2.2  Process

Mathematical processes are different from content in that they overarch the subject and are not thought of as hierarchical. You may find that once you have identified and clarified in your mind the key mathematical processes, you are then ready to make the shift from mathematical content to mathematical thinking. A list of processes could contain:

  • problem solving (including investigating)
  • mathematical modelling
  • reasoning
  • communicating
  • making connections (including applying mathematics)
  • using tools.

Each of the six processes listed here represents a wide range of component skills that usefully contribute to a learner’s mathematical thinking as well as to their general thinking skills. In the activity 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.

Activity 7  Putting processes under the microscope

  1. For each of the six processes listed above, write down two or three examples.
  2. Turn to the Appendix: processes uncovered and read a detailed listing of the possible components for these processes provided by Andy Begg (Begg, 1994).


One teacher found part 1 of this activity 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 learners 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 learners 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 Activity 7, and are similar to the key processes listed in the National Curriculum in England (Qualifications and Curriculum Authority, 2007):

  • information processing skills
  • enquiry skills
  • creative thinking skills
  • reasoning skills
  • 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 and this is something that you are asked to do in Section 4.