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Mathematical Explanatory Strategies Employed by Prospective Secondary Teachers

Authors
  • Cofer, Tanya1
  • 1 Northeastern Illinois University, Chicago, IL, USA , Chicago (United States)
Type
Published Article
Journal
International Journal of Research in Undergraduate Mathematics Education
Publisher
Springer International Publishing
Publication Date
Apr 01, 2015
Volume
1
Issue
1
Pages
63–90
Identifiers
DOI: 10.1007/s40753-015-0007-9
Source
Springer Nature
Keywords
License
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Abstract

This study proposes a framework for examining ways in which prospective teachers integrate mathematical knowledge acquired in advanced topics courses into explanatory knowledge for school teaching. Participants, all of whom had recently completed coursework in abstract algebra, were asked to explain concepts connected to the school mathematics curriculum, such as division by zero and even numbers. The analysis shows that students used three distinct explanatory strategies: Abstract Mathematical Argument, Analogy, and Rules. Students experienced competition among and within strategies. Moreover, students often derived different conclusions using different strategies. When faced with this conflict, they felt compelled to choose a strategy and to draw a conclusion derived from applying that strategy, regardless of sense-making. Students’ ability to integrate explanatory strategies appeared to depend on their possession of coherent mathematical meanings, suggesting that strategy integration is indicative of students’ having a key developmental understanding of the underlying mathematical ideas.

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