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University Using visualisation in maths teaching
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Using visualisation in maths teaching

About this free course

Find out more about studying with The Open University by visiting our online prospectus.

This version of the content may include video, images and interactive content that may not be optimised for your device.

You can experience this free course as it was originally designed on OpenLearn, the home of free learning from The Open University: http://www.open.edu/openlearn/education/using-visualisation-maths-teaching/content-section-0.

There youll also be able to track your progress via your activity record, which you can use to demonstrate your learning.

The Open University, Walton Hall, Milton Keynes, MK7 6AA

Copyright 2016 The Open University

Intellectual property

Unless otherwise stated, this resource is released under the terms of the Creative Commons Licence v4.0 http://creativecommons.org/licenses/by-nc-sa/4.0/deed.en_GB. Within that The Open University interprets this licence in the following way: www.open.edu/openlearn/about-openlearn/frequently-asked-questions-on-openlearn. Copyright and rights falling outside the terms of the Creative Commons Licence are retained or controlled by The Open University. Please read the full text before using any of the content.

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978-1-4730-1461-9 (.kdl)
978-1-4730-0693-5 (.epub)

Contents
Introduction

This course looks at visualisation as it relates to mathematics, focusing upon how it can be used to improve learning. It will also identify ways in which to make more use of visualisation within the classroom.

Find out more about studying with The Open University by visiting our online prospectus.

Learning outcomes

After studying this course, you should be able to:

  • demonstrate an engagement in a number of activities that involve visualisation and learning from personal experiences what it means
  • understand the views of a well-known mathematics educator talking about visualisation and find out how personal views compare with those of some other secondary-school mathematics teachers
  • identify some ways that visualising could be incorporated into a classroom and consider a number of resources that might be useful.
1. A powerful force for perception and understanding

Imagery is a powerful force for perception and understanding. Being able to see something mentally is a common metaphor for understanding it. An image may be of some geometrical shape, or of a graph or diagram, or it may be some set of symbols or some procedure.

(Open University, 1988, p. 10)

This course uses the word visualisation synonymously with mental imagery. It happens as we articulate our thoughts and as we understand what we are doing.

Each of the four sections in this course should further develop your thinking on visualisation.

Starters

The main purpose of this course is to encourage you to form images and be aware of your experiences of visualisation.

What does visualisation mean?

In What does visualisation mean?, you will find quotes and readings about visualisation, followed by an opportunity to compare your views with those of some other secondary-school mathematics teachers. By the end of this section you should be confident that you know what visualisation means.

In the classroom

In the classroom describes a lesson in which visualising provides an introduction for the students, another worthwhile and interesting activity, and some ways to use resources to promote and stimulate visualisation.

Conclusion

The conclusion points to some recommended books that will be useful if you want to think a little more seriously about visualisation, as well as highlighting where visualisation is incorporated into the framework for mathematics school teaching.

2. Starters

We all have pictures in our heads but some people use them more than others.

Doing can often be the most powerful way to learn. Before discussing other people's thoughts on visualisation, it is probably worthwhile to spend some time exploring some visualisation activities with your colleagues. This should enable you to consider the next section from an experiential perspective.

Activity 1

Please click on the view document links below to explore a range of visualisation activities. Try at least two of these.

Click 'view document' below to download Arithmetic

View document

Click 'view document' below to download Circles

View document

Click 'view document' below to download Cutting paper

View document

Click 'view document' below to download Locus

View document

Click 'view document' below to download Multiples on grids

View document

Click 'view document' below to download Nets

View document

Click 'view document' below to download TV

View document

  1. For each activity you attempt:

    • Try to do them in your heads before you look at anything.

    • Shut your eyes if it helps.

    • Try them individually and then talk in a group, but do not give any answers away help others to see what you can see.

    • No drawing, only talking.

    • No gesticulating either.

  2. When you have experienced a number of visualisation activities, write down some of your own thoughts about visualisation and what it means.

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