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Working mathematically
Working mathematically

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Working mathematically


In this course you will explore a number of major issues in mathematics education. For example, when you think about mathematics, do you see it mainly as a collection of topics (mathematical content) or as a way of thinking (mathematical process)? Later in the course you will be asked to consider further the distinction between content and process in mathematics. You will also be asked to consider a particular organising framework for thinking about your teaching. It is referred to as the do–talk–record (DTR) framework. You will also be asked to work on some mathematics yourself and then reflect on what you have done. The mathematical context used in this course is Möbius strips. This context has been chosen to give you the opportunity to work on some mathematics at your own level. After you have completed several mathematical activities relating to Möbius strips, you will be expected to select parts of these activities, adapting them as necessary, to try out with your learners (or others). This work with learners will give you the opportunity to apply the DTR framework to your own teaching.

But first, take a little time to reflect on your own feelings about your aims for this course. What do you want to work on with regard to the learning and teaching of mathematics and what is of most concern to you? Activity 1 will help you engage with these and related questions.

Activity 1  Hopes and fears

In your notebook, complete the following sentences. You may have one overwhelming response to each prompt or it may be appropriate to list three or four responses to each.

  • I expect this course to include work on …
  • I personally would like to work on …
  • An anxiety that I have about the course is …


Clearly the degree of flexibility of this course is limited by the fixed nature of the course materials. It is important to stress that what you bring to the course is at least as important as the course materials. Awareness of your needs and hopes will help you choose which activities to focus on and which personal examples of your own to stress as you progress through the units.

This OpenLearn course is an adapted extract from the Open University course ME620 Mathematical thinking in schools [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .