Slide 1

The pros and cons of using contexts in the teaching of mathematicsSteve Gough & Sue HoughManchester Metropolitan University

s.j.gough@mmu.ac.uks.hough@mmu.ac.uk1Session OverviewConsider how we generally use context in the UKCompare 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 UKExtreme examples

5Less ExtremeJasons study is a cuboid. The floor is 3.2m by 2.5m, and it is 2.1m high. Find its volume.

The top of a desk is a piece of wood 80cm high, 50cm deep and 15mm thick. Find its volume.

Source: GCSE Foundation textbookThe use of context in mathsWhy do we use contexts?

When do we use contexts?7Use of Context under MICTraditionally context is mainly usedAs a motivator at the start of a topicTo add an extra layer of complexity towards the end of a topicAs an application of the mathematics

Under RME, context is usedTo help pupils to make sense of the topicTo keep the maths close to pupils realityAs a source of the mathematics

Making Sense of Area

Stained glass windows from houses built in the 1920s and 1890s

Stained GlassA 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.

Finding AreasFind 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

A Year 7 control pupil making no sense of the problem, but simply attempting to do something with the numbers

21

A Year 11 control pupil attempting two different multiplication approaches, with no attempt to make sense of the problem from an area perspective.

22Pupil Responses (2)Project Students RME classes

A Year 8 project pupil attempting a sense making strategy24

A Year 11 project pupil using a reallocating strategy to correctly solve the problem

25

A lower ability Year 7 project pupil making sense of the problem despite achieving an incorrect answer

26

CountingHow many bottles in a full crate of:Schweppes Lemonade?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 timeLin 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 ContextContext 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.34