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Working mathematically
Working mathematically

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1.3  Describing teaching

Activity 4  Describing teaching

Now try to write down some of your beliefs about teaching mathematics.

Complete the following prompts.

  • Teaching mathematics is like …
  • What I like most about teaching mathematics is …
  • What I like least about teaching mathematics is …


As with learning, metaphors for teaching may be very personal and may vary, even for an individual at different times. Some of these that have been reported include the following.

Teaching mathematics is like …

  • pushing water uphill (sometimes downhill)
  • learning something new every day
  • banging one’s head against a wall
  • juggling balls in the air
  • opening up new vistas for learners
  • a roller coaster
  • helping learners to climb a hill – sometimes a steep one.

Ways of completing the prompt ‘What I like most about teaching mathematics is …’ often mention enjoyment and achievement, the latter especially after a struggle. Thus, responses from teachers include:

  • the ‘aha’ factor
  • a sense of achievement
  • trying to make the subject enjoyable
  • watching the penny drop and seeing learners’ pleasure at mastering a new skill
  • when someone has been struggling and they suddenly discover they can understand and they can do it
  • when I’ve taught a difficult subject and learners think it is easy
  • seeing learners enjoy themselves
  • I’ve always enjoyed doing mathematics
  • the sense of fulfilment when a problem clicks for a learner.

Dislikes with respect to mathematics teaching are frequently related to pressures: sometimes from external sources, and sometimes intrinsic to any mathematics teaching situation. Thus:

What I like least about teaching mathematics is …

  • having to deal with large classes that lack motivation
  • lack of time needed to present the subject in such a way that even the weakest learners can appreciate some of the fun, pattern and power
  • heavy marking load
  • record-keeping
  • having to teach learners who spoil, or attempt to spoil, the learning experience for others in the class
  • when too much pressure is put on learners (often from parents) to excel, and as a result they achieve less.

It is worth remembering that much of what teachers do is adapted, consciously or unconsciously, from what they have seen other teachers do. Your sense of yourself as a teacher may be coloured by how closely you come to achieving what you have admired or responded to in others – or it may depend on the extent to which you have found the ‘better way’ you were sure must exist.

You have now examined some of your beliefs about learning and teaching mathematics. But what are your beliefs about the nature of mathematics itself? One of the key ways in which your perception of the nature of mathematics has developed is through your own experience of learning and doing mathematics. This experience will also have a bearing on your notions of how mathematics is learned and on your perceptions of the roles of teachers and learners in mathematics classrooms. You may also experience strong feelings and emotions relating to your own work on mathematical activities. Don’t be afraid to consider your feelings as you reflect on the nature of mathematics and its role in schools.