Mathagony Aunt

16th September 2005 at 01:00
Let's change the shape of lessons


Have we forgotten that there are ways of teaching maths without using high-tech equipment? Surely, to keep our pupils stimulated we should be encouraged to use a diversity of materials and not just depend on information and communication technology? As a newly-qualified teacher I feel woefully ill-equipped in this area.


Wouldn't life be boring if all we did was watch television and all learning was done via it? So much learning happens through discussion in maths and this also enriches the language that's available.

Interactive materials don't have to be ICT-based to stimulate discussion.

For example, I have created a stack of interactive cards to aid understanding of notation and order of operations, where students work together to find the solutions. This picture shows part of the set.

Each card has an expression and the students have to decide (working with their calculator, if they wish), which of the expressions represents a value of 1. This does lead to discussion about how the solutions are arrived at. One of the nice things about this is that there is no writing either.

Following this exercise I encourage students to create their own cards and the collection can be added to as you come across examples during lessons.

This then addresses the problems that your students are likely to have.

Another useful technique is to write problems on sheets of A3 paper and get pupils to work together to find the solutions in any way they want, coming together to discuss their answers.

An activity you might like to try is looking at what happens to the shadows of shapes when a shape is moved. I once saw an activity like this at a conference. It doesn't require anything particularly high-tech, in fact a light bulb will do, but it is easier if you have an overhead projector.

Place a large sheet of paper on the wall. Take, for instance, an equilateral triangle and hold it up between the OHP and the wall, casting the shape's shadow. Invite a student to come up and trace the shape on the paper. Now move the shape to show that moving the triangle creates a different kind of triangle. Invite someone else to trace the new shape.

Ask the pupils if they can guess how many different shapes the shadows of an equilateral triangle could make. They could try drawing the shapes they think will occur. Then get them to come up and move the triangle to try and make the shape they think the shadow will make. You can then have a look at other triangles, quadrilaterals, pentagons, hexagons and so forth. Here, the square becomes a rhombus:

This could be a discussion at the start of a lesson on shapes or you could look at these over a series of lessons. Is there a non-regular shape that through movement enables the creation of the regular version with its shadow?

Here, a scalene triangle's shadow becomes an equilateral triangle.

The next step would be to investigate the shadows of 3D shapes. Can the students guess the 3D shape from seeing the shadow of each face, for example. What new 3D shapes are made by moving the 3D shape?

Playing with these shapes inspired me to write a poem.

Shapes' shadows

Shapes' shadows created with light fall.

Shapes' shadows appearing on the wall.

Shapes' shadows taking new direction.

Shapes' shadows changing my reflection.

You might like to refer students to Flatland: A Romance of Many Dimensions by Edwin A Abbott (Penguin pound;6.99). The story is based around a central character called A. Square, who tells the story of his life in the 2D world of Flatland.

In the first half of the book, Square explains the practicalities of a 2D world. In the second half, Square becomes aware of other worlds - 1D and 3D.

A website devoted to Flatland, which describes the maths behind it,is available by visiting

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