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Mapping variation in children’s mathematical reasoning: the case of ‘what else belongs?’

Vale, Colleen, Widjaja, Wanty, Herbert, Elizabeth, Bragg, Leicha and Loong, Yook-Kin 2016, Mapping variation in children’s mathematical reasoning: the case of ‘what else belongs?’, International journal of science and mathematics education, vol. 15, pp. 1-22, doi: 10.1007/s10763-016-9725-y.

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Title Mapping variation in children’s mathematical reasoning: the case of ‘what else belongs?’
Author(s) Vale, ColleenORCID iD for Vale, Colleen
Widjaja, WantyORCID iD for Widjaja, Wanty
Herbert, ElizabethORCID iD for Herbert, Elizabeth
Bragg, LeichaORCID iD for Bragg, Leicha
Loong, Yook-Kin
Journal name International journal of science and mathematics education
Volume number 15
Start page 1
End page 22
Total pages 22
Publisher Springer
Place of publication Amsterdam, The Netherlands
Publication date 2016-03
ISSN 1571-0068
Keyword(s) Social Sciences
Education & Educational Research
Comparing and contrasting
Variation theory
Summary Explaining appears to dominate primary teachers’ understanding of mathematical reasoning when it is not confused with problem solving. Drawing on previous literature of mathematical reasoning, we generate a view of the critical aspects of reasoning that may assist primary teachers when designing and enacting tasks to elicit and develop mathematical reasoning. The task used in this study of children’s reasoning is a number commonality problem. We analysed written and verbal samples of reasoning gathered from children in grades 3 and 4 from three primary schools in Australia and one elementary school in Canada to map the variation in their reasoning. We found that comparing and contrasting was a critical aspect of forming conjectures when generalising in this context, an action not specified in frameworks for generalising in early algebra. The variance in children’s reasoning elicited through this task also illuminated the difference between explaining and justifying.
Language eng
DOI 10.1007/s10763-016-9725-y
Field of Research 130208 Mathematics and Numeracy Curriculum and Pedagogy
1302 Curriculum And Pedagogy
Socio Economic Objective 970113 Expanding Knowledge in Education
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2016, Ministry of Science and Technology, Taiwan
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Document type: Journal Article
Collection: School of Education
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