The pros and cons of using contexts in the ... - mei.org.uk

The pros and cons of using contexts in the teaching of mathematics Steve Gough & Sue Hough Manchester Metropolitan University [email protected] [email protected]

Session Overview Consider how we generally use context in the UK Compare with how context is used in Holland. In particular, we will look in detail at how area is taught using context.

Briefly look at the results of trials in the UK Extreme examples Less Extreme 1. Jasons study is a cuboid. The floor is 3.2m by 2.5m, and

it is 2.1m high. Find its volume. 2. The top of a desk is a piece of wood 80cm high, 50cm deep and 15mm thick. Find its volume. Source: GCSE Foundation textbook

The use of context in maths Why do we use contexts? When do we use contexts? Use of Context under MIC Traditionally context is mainly used

As a motivator at the start of a topic To add an extra layer of complexity towards the end of a topic As an application of the mathematics

Under RME, context is used To help pupils to make sense of the topic To keep the maths

close to pupils reality As a source of the mathematics Making Sense of Area

Stained glass windows from houses built in the 1920s and 1890s 6 Stained Glass A company uses

rectangular sheets of coloured glass (4 by 6). They cut pieces from these to make a window. Find the prices of the

coloured pieces. 18 4 2

4 4 4

2 4 2 3

4 4 4

4 3 2 4

2 4 4 4

4 2 3

3 2 3 3

2 4 4 2 2

4 5 4 1

2 4 2 4

2 4 4 4

2 Finding Areas Find the area in square units of each of the

shaded pieces Chris works for a window cleaning firm who charge by the pane of glass How many windowpanes are there in this office block?

Touching the rectangle Touching the trapezium This is Toms attempt to find the area of the trapezium. Describe what you think Tom has done.

This is Kylies attempt to find the area of the trapezium. Describe what you think Kylie has done. Pupil Responses (1) Control Students None RME

classes Pupil Responses (2) Project Students RME classes Counting How many

bottles in a full crate of: a) Schweppes Lemonade? b)Damm beer? How many packs of Anchor butter are there on the shelf at the moment?

The packs of butter in the photo below can be packed 5 deep and 4 high. How many packs can fit on the shelf altogether? How many cubes? This block of cheese is 4cm high. How many

1 cm cubes can be made? A stitch in time Lin has her own company making designer t-shirts. Her latest design includes contrasting circles of

fabric which are to be hand stitched in sequins. In order to think about pricing the t-shirts Lin wishes to estimate how long it will take her to sew the sequins on each badge

by hand. In the case of the smallest badge it took Lin 2 minutes and 20 seconds to sew the line of sequins across the middle.

The Use of Context Context is a route into the mathematics. It is crucial that pupils engage with the context. Moving between the context and the mathematics enables pupils to make sense

of mathematics. Context provides a route through the mathematics.