The pros and cons of using contexts in
- Slides: 34
The pros and cons of using contexts in the teaching of mathematics Steve Gough & Sue Hough Manchester Metropolitan University s. j. gough@mmu. ac. uk s. hough@mmu. ac. uk
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. Jason’s study is a cuboid. The floor is 3. 2 m by 2. 5 m, and it is 2. 1 m high. Find its volume. 2. The top of a desk is a piece of wood 80 cm high, 50 cm deep and 15 mm 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 1920 s and 1890 s
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.
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 Tom’s attempt to find the area of the trapezium. Describe what you think Tom has done.
This is Kylie’s 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 4 cm 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.
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