When looking into any aspect of mathematics it is essential to know what you are required to do by the National Curriculum and what is suggested in the National Numeracy Strategy. In the National Curriculum practical work seems to be more important in Key Stage One:
‘During key stage 1… they learn about shape and space through practical activity which builds on their understanding of their immediate environment.’(DFEE. 2000 p.62)
In Key Stage Two the emphasis has changed to abstract thinking and concepts:
‘During key stage 2 … they always try to tackle a problem with mental methods before using any other approach’ (DFEE 2000 p.67)
In the National Numeracy Strategy practical work is only mentioned in the reception learning objectives. We assume that it is an innate part of teaching but the emphasis is on young children. However practical work is teamed with discussion in other areas of mathematics in the NNS:
‘In practical activities and discussion, begin to use the vocabulary involved in adding and subtracting’ (DFEE 1999 p.2 key learning objectives)
In the NNS shape and space examples, ‘making models’ is repeated throughout the years. This hands on experimenting is also suggested by Merttens in ‘Teaching primary maths’:
‘Sorting boxes, cartons, rolls, etc. to make junk models. Which ones will roll?… this type of question concentrates the children’s attention on the properties of these shapes in relation to the task in hand’ (Merttens 1991 p.115)
This brings shape and space out of the Numeracy Hour and back where it started, in every day life, just with more awareness of ideas and properties of shapes:
‘Some children develop spatial awareness by playing with construction toys and the like outside school’ (Merttens 1991 p.117)
I like the idea of bringing maths out into the real world and away from the scary world of mathematics in the classroom. The ideas I have learnt and remembered from school are based on experiences I enjoyed and found interesting. Therefore in my experience concepts are more likely to be learnt and remembered if they are linked with practical activities.
In primary mathematics by Williams and Shurard they devote most of a chapter to ‘variety of activities which help children become aware of many shape and some of their important properties’ most of which involve starting from a practical activity or having experience in some way. They use practical activities as a catalyst for thinking about ideas. Practical activities don’t just stop when the objects are put down they can generate discussion and ideas as Mertten suggests:
‘Doing this activity together provides an excellent opportunity for the children to discuss the shapes that they are using and the language they use often generates as much learning as the actual handling of the shapes’ (Merttens 1991 p.119)
Mertten seems to agree with the National Curriculum and says how as children get older it becomes important to move away from practical work and on to mental maths such as visualising. But after further reading I discovered he also says that practical work is important because as concepts get harder it is more important to make them as real as possible for the children:
‘The importance of practical activities does not diminish as the children get older’ (Mertten 1991 p.129)
The difference in age just means that younger children may not grasp the idea formed after the practical not that older children can do without the practical.
Ashew and Wiliam in ‘Recent research in mathematics education 5-16’, show evidence that for pupils with more mathematical knowledge practical work can be a waste of time:
‘For those pupils who already had access to the formal mathematics, the time spent on practical work, from which they were expected to abstract the ideas, was probably unnecessary. The time might have been better been used for these pupils to explore the justification of results’ (Askew & Wiliam 1998 p.10)
They also stress that practical work is essential to start the mathematical process and is therefore very useful when used in he correct way:
‘The main message from such research is that while practical work and ‘real’ contexts can be useful, they need to be chosen carefully, and accompanied by careful dialogue’ (Ashew & Wiliam 1998 p.11)
For example a trip to a mosque to look at tiling would not be beneficial in shape and space terms unless accompanied by discussion about the shapes and repetition etc. This work would then need to be followed up in the classroom if I was to become useful.
In a Key Stage Two class I saw children being given the task of making different triangles on a pin board and recording the different types and their names. Although this got the children physically involved and classifying the shapes they were not discussing things like area, or properties which could of come out from this practical activity. The importance of teacher questioning along side practical work is evident if the children are to grasp shape and space to its full extent.
In conclusion I agree with the above statement. In shape and space practical work is an essential tool. It allows children to experience the ideas and then move on to develop them. It however needs to be considered and planning:
‘practical work is a valuable vehicle for assisting pupils to construct meaning, but success cannot be guaranteed, and the teacher must also expect to have to work hard in trying to move the pupils forward in their mathematical thinking.’(Orton & Frobisher 1996 p.19)
Bibliography
Askew, M & Wiliam, D. (199t8) Recent research in mathematics education 5-16. Ofstead & stationary office.
DFEE (2000) National Curriculum. DFEE.
DFEE (1991) National numeracy Strategy. DFEE
Fisher, R. (1995) Teaching children to learn. Stanley Thornes
Merttens, R. (1991) Teaching primary maths. London: Hodder and Stoughton
Orton, A & Frobisher, L. (1996) Insights into mathematics. London: Cassell.
Williams, E & Shuard, H. (1982) Primary mathematics today 3rd edition. Essex: Longman
