Using visualisation in maths teaching

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4. In the classroom

There are many possible strategies for making more use of visualisation within the mathematics classroom. There are several visualisation activities for you to experiment with in Activity 3. One teacher's approach to incorporating visualisation is given in the following case study and three-part video clip.

Case study

In a secondary-school classroom, the teacher, Peter Gates, is working with fourteen-year-old students on a topic in which they are exploring aspects of circles. This particular activity involves working out distances around a race-track.

The school is Brindley Hall, at Stantonbury Campus, Milton Keynes. Peter has a class of 27 mixed-ability students. They are his own class for pastoral purposes and he teaches them mathematics. They work on an individualised scheme, the Kent Mathematics Project (KMP) for roughly half of their mathematics lessons and participate in whole-class projects, such as the one on circles, for the other lessons. These projects help to prepare students for their GCSE coursework that they will have to undertake in subsequent years.

The video clip has a three-part structure; view the three parts now by clicking on the links in the list below.

• Introducing the problem.

Click on the 'play' button below to view the video

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Transcript: Video 1

Peter
You're in the outside lane. What do you think about the person who's in lane number 1?
Boy
They're gonna be, 'cos they've got a shorter end line than you.
Peter
They've got a shorter run, haven't they?
Boy
They've got to run right round the outside.
Peter
Right. Is that what you were going to say? Now when I was doing that I was thinking, 'Hang on, this person next to me hasn't got as far to run as I have. I've got to run faster, it's not fair'. On the outside of the track, it's a lot longer. How can we make a race that goes right the way round the track fair? Now put your hands down, I want you to think about that, and that's the problem we're going to work on for the rest of this session.
Now that's a mock-up. It tells you where the finish is. What they haven't yet put on is the start line. Where can I put the starting line for the 400 metres?
End transcript: Video 1
Video 1
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• Two groups of students working on the problem.

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Transcript: Video 2

Peter
Which track are you doing, tell me.
Boy (out of shot)
The inside, the inside one.
Peter
So you’re measuring the whole length of the inside track?
Boy 1
Inside...
Boy 2
Inside.
Boy 3
That looks straight.
Boy 1
Yeah, that’s straight.
Boy 2
Yeah, that’s fine.
Boy 3
So how much have we got spare?
Boy 2
48, yeah.
Boy 3
47½.
Boy 2
Yeah, but make it... Alright, 47½.
End transcript: Video 2
Video 2
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• Reporting back.

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Transcript: Video 3

Peter
Lucy.
Lucy
First, we measured what – each lane with a piece of string. First we measured the outside lane and found that that was 50 centimetres, then the third lane which was 49, and so on, and each time it went down a centimetre. So we decided that we would stagger them out a centimetre behind each other.
Peter
So on your diagram they're a centimetre behind?
Lucy
Yeah.
Peter
Can I just have a look at that? Either one will do. Right, have a look at this then.
That was Lucy, Anita's and Marsha's solution to the problem. Anything you notice, any comments, any questions you want to ask? Robert?
Robert
What's the rectangle for?
Lucy
We just wanted to see what the em – if we had a rectangle, how big the whole thing would be if it was like that. It was 62 centimetres but it – we found it had nothing to do with the track.
End transcript: Video 3
Video 3
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The students are encouraged to devise their own approaches to problems and to follow their own ideas and questions. Peter is concerned to involve the students in the mathematics they encounter, so that it becomes as meaningful as possible for them. He uses a number of devices in order to achieve this, one of which invokes their mental imagery to help them ‘see’ into a problem. Use of practical apparatus and calculators is also important to their way of working.

Activity 3

Visualisation is an important facet in all areas of the curriculum. Many people argue that we visualise what we have seen, but all our senses may be important. There are many resources that actively promote visualisation in the classroom.

Figure 3

In the classroom activity illustrated here the students design a solid from a few coloured cubes and then describe it. The others in the group then try to visualise the configuration and make their own.

You might like to try this activity in your classroom.

Further classroom activities for visualisation are available by clicking on the ‘view document’ and website links below. Explore some of these with colleagues and identify two or three to try out in class.

Click 'view document' below to download Diagrams.

View document [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]

Click 'view document' below to download The feely box.

Click 'view document' below to download The hundred square.

Click 'view document' below to download Number lines.

Click 'view document' below to download People activities.

Click 'view document' below to download Photographs.

Click 'view document' below to download Tracing paper.

The Key Stage 3 National Strategy website.

Multiples and factors: assessing pupils' work website.

TL_MATHT9

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