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Working mathematically
Working mathematically

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1.2 Describing learning

Activity 3  Describing learning

Complete one or more of the following prompts.

  • Learning mathematics is like …
  • I enjoy learning mathematics when …
  • I dislike learning mathematics when …


Many teachers offer their personal metaphors and images such as:

Learning mathematics is like …

  • using common sense
  • learning the rules of the game
  • opening curtains
  • a voyage of discovery.

Some have commented that it seems like different things at different times and that their responses vary. The changes might depend on the kind of mathematics being worked on or on how well things were going. So, for one teacher learning mathematics was like ‘climbing a wall: sometimes easy, sometimes very hard’.

Personal images are also invoked when teachers try to say what they like or dislike about learning mathematics. Here are some examples.

I enjoy learning mathematics when …

  • I reach the light at the end of the tunnel.
  • I seem to be discovering the truth, unravelling a mystery.
  • I get completely absorbed and forget about the time.
  • Somebody says something about a topic I thought I knew and it gives me a new way of looking at it.

Responses to ‘I dislike learning mathematics when …’ are sometimes related to the mathematics itself:

  • I can’t see why anybody might be interested in ‘the answer’;

sometimes to the social context of learning:

  • I’m in a group and everyone around seems to be better at it than I am;

and sometimes to both:

  • I get completely stuck and there is no one around to ask.

Often memories of a change from a positive state to a negative one – or negative to positive – are reported, and some learners have found that this change of state can happen several times in a lesson or study session.

One minute you are jogging along happily thinking you can see just what is going on and then you grind to a halt and decide that you must be really stupid. When you are on a high it’s very difficult to remember what it’s like to be low, and vice versa. I am just beginning to realise that this happens to almost everyone – and that must include the children!

Clarifying what has worked well or badly for you in helping learners to learn mathematics successfully can all be a useful starting point in planning effective activities that you offer learners. Meanwhile it could be very useful to your planning and teaching to ask your learners (or friends or colleagues) what their responses are to the prompts about learning mathematics given in Activity 3.