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The purpose, design and use of examples in the teaching of elementary mathematics

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Abstract

This empirical paper considers the different purposes for which teachers use examples in elementary mathematics teaching, and how well the actual examples used fit these intended purposes. For this study, 24 mathematics lessons taught by prospective elementary school teachers were videotaped. In the spirit of grounded theory, the purpose of the analysis of these lessons was to discover, and to construct theories around, the ways that these novice teachers could be seen to draw upon their mathematics teaching knowledge-base in their lesson preparation and in their observed classroom instruction. A highly-pervasive dimension of the findings was these teachers’ choice and use of examples. Four categories of uses of examples are identified and exemplified: these are related to different kinds of teacher awareness.

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Notes

  1. Suggestions by scholars such as Wittmann that this step-by-step management might in fact be overdone are summarily dismissed by Bierhoff (1996, p. 30)

  2. The research reported in this paper was undertaken in collaboration with Cambridge colleagues Peter Huckstep, Anne Thwaites, Fay Turner and Jane Warwick. I use the pronoun ‘we’ in this text as a natural way of acknowledging their contribution.

  3. Compulsory education in England is organised in chronological ‘Years', normally beginning at age four or five with between one and three terms in Year R (for ‘reception’). The youngest children in Year 1 will be just five at the beginning of the academic year, the oldest nearly seven at the end. The Primary (elementary) phase of schooling covers Years R to 6, with Year 6 pupils aged 10–11.

  4. The National Numeracy Strategy Framework (DfEE 1999) guidance effectively segments each mathematics lesson into three distinctive and readily-identifiable phases: the mental and oral starter, the main activity (an introduction followed by groupwork) and the concluding plenary.

  5. This data comes from an extension of the original project, in which we interviewed the trainee-teacher at the end of the school day. One team member met with him or her to view the videotape and to discuss some of the episodes.

  6. 2 × 9 = 18 and then 18+6 = 24, so the hundreds digit is one more than that first indicated by the partial product 20 × 9. Of course, ‘carrying’ from the units to the tens is involved in all the tu x u exercises, with the exception of 42 × 4.

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  1. University of Cambridge, Cambridge, UK

    Tim Rowland

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  1. Tim Rowland
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Rowland, T. The purpose, design and use of examples in the teaching of elementary mathematics. Educ Stud Math 69, 149–163 (2008). https://doi.org/10.1007/s10649-008-9148-y

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