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Choosing Resources for Primary MathematicsAuthor(s): Jenny HoussartSource: Mathematics in School, Vol. 30, No. 3 (May, 2001), pp. 10-11Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30212160 .
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CHOOIN RESOU RCES
FOR PRIMARY MATHEMATICS
by Jenny Houssart
Introduction
Choice of mathematics resources is likely to be a current issue in many primary schools. The advent of the numeracy strategy has meant that schools need to assess how their existing resources are likely to fit with the new approach. In addition there is an increasing number of new materials on the market with publishers making bold claims. How are teachers to choose, given the range of materials available and the claims made for them?
Choice of resources is just one of the many complex decisions which teachers have to make. Research on teacher knowledge (e.g. Shulman, 1986; Llinares, 2000) suggests that in making such decisions they call upon pedagogical content knowledge, including their understandings of how certain topics are best taught and what difficulties children are likely to experience. However, recent articles in practitioner journals suggest that teachers might make choices based more on the appearance of tasks or for organizational reasons and may indeed be encouraged to do so (Gold, 2000; Woodman, 1999).
The research reported below was designed to consider which aspects of commercial tasks teachers attended to when assessing their suitability. It has significant implications for teachers purchasing new resources.
The Research
The work described here forms part of a wider project concerning mathematics tasks at Key Stage 2. In this project segment, individual interviews were conducted with 26 Key Stage 2 teachers from seven schools. Teachers were shown a range of published mathematics tasks and asked whether they would be likely to use them with their current class or maths set, with or without amendments. The interviews were tape recorded and transcribed. The transcripts were analysed to establish how decisions were arrived at. Particular attention was paid to those factors which caused rejection. Various modes and styles of decision-taking were identified. Subsequently, a model of teacher decision making was developed, as outlined briefly below.
Findings
Findings suggest that some teachers made decisions based on the task's extrinsic features. These decisions tended to be taken rapidly. For example, some rejected a task from a widely-used scheme (Edwards et al., 1989, p. 44), on the grounds that they were critical of schemes per se. Others rejected a much more open task on the grounds that it did not contain enough guidance (Blinko, 1996, p. 23). Teachers making these judgements based on extrinsic features tended to be emphatic in their rejection. It was rare for them to look in detail at the task or to discuss the mathematics involved.
A second group rejected tasks because of level of difficulty. Teachers frequently felt tasks would be too hard for their pupils. Further analysis reveals that 'too hard' masks several meanings. On occasions, it meant that children had not yet reached a particular topic such as perimeter or two digit multiplication. On others, the level of reading rather than the mathematics, was seen as problematic. Sometimes teachers felt the children they taught could not cope with the openness of the task, or lacked the skills to organize their own work, overcome organizational problems or devise ways of recording. In many cases, problems with process skills or reasoning were associated with bottom sets; there was a tendency for more investigative activities to be seen as most suitable for top sets. Tasks were rarely rejected as 'too easy' as opposed to 'too hard'.
If tasks were not rejected due to extrinsic features or level of difficulty, they were generally accepted with only a few teachers rejecting tasks on mathematical grounds. However, teachers accepting tasks often reported that they would adapt them. In explaining how they would do this, teachers often explained how they usually taught the topic concerned. It was at this point that the teacher shifted towards the mathematical. Teachers talked, often in some detail, about how they approached certain topics, and which aspects children found difficult. Teachers frequently shifted to more general issues. For example when shown an activity on sequences (Bird, 1986, p. 47) many teachers referred to the importance of pattern, and how they might help children to detect patterns (Houssart, 1999). An investigative activity
10 Mathematics in School, May 2001 The MA web site www.m-a.org.uk
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which included a picture of a calculator (Kirkby, 1989, task 36) led many teachers to discuss their approach to calculator use (Houssart, 2000).
Conclusion
All the teachers interviewed demonstrated knowledge, sometimes detailed, of how to approach teaching various mathematical topics and the difficulties children might experience. Yet this knowledge was not always used in making decisions about task selection. Teachers were less likely to call on this knowledge when dissuaded by a task's extrinsic features. Conversely, they were more likely to call on it when considering a task similar to one previously used.
Implications
This work contains messages for those choosing mathematics materials. The principal one is that teachers are more likely to evaluate the mathematical potential of a task rather than its formal appearance, if they are examining content they are familiar with teaching. One possible strategy when evaluating new materials might therefore be for teachers to look initially at those sections dealing with work of which they have recent
practical experience.
A further message is cautionary. It relates to the effect the advent of setting may be having on task selection. Our
findings suggest that teachers of different sets are likely to make different choices of materials and adapt them in different ways. In particular, bottom set teachers tended to
remove from work many of those aspects currently associated with using and applying mathematics. Investigative activities were seen as particularly suitable for top sets, potentially depriving lower sets of important developmental opportunities. M
References
Bird, M. 1986 Mathematics with Nine and Ten Year Olds, Mathematical Association, Leicester.
Blinko, J. in collaboration with Buckinghamshire County Council 1996 Teaching and Learning Number, Buckinghamshire County Council, Buckinghamshire.
Edwards, R., Edwards, M. and Ward, A. 1989 Cambridge Primary Mathematics, Module 5, Book 1, Cambridge University Press, Cambridge.
Gold, K. 2000 '3 Rs on Target?', TES Primary, 28 January 2000. Houssart, J. 1999 'Seeing the Pattern and Seeing the Point', British Society
for Research into Learning Mathematics, Proceedings of the Day Conferences held at University of Warwick, Friday 12 and Saturday 13 November 1999.
Houssart, J. 2000 "I Haven't Used Them Yet': Primary Teachers Talk about Calculators', Micro-math, 16, 2.
Kirkby, D. 1989 Go Further with Investigations, Unwin Hyman, London. Llinares, S. 2000 'Secondary School Mathematics Teacher's Professional
Knowledge: a Case from the Teaching of the Concept of Function', Teachers and Teaching: Theory and Practice, 6, 1.
Shulman, L. S. 1986 'Those who Understand: Knowledge Growth in Teaching', Educational Researcher, 15, 2.
Woodman, A. 1999 'All Part of the Greater Scheme', The Times Educational Supplement, 1 October 1999.
Keywords: Primary Teachers; Resources.
Author Jenny Houssart, Centre for Mathematics Education, The Open University, Walton Hall, Milton Keynes MK7 6AA. e-mail: j.houssart (yopen.ac.uk
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