Explanation and Proof in Mathematics
pp 223236
Proof, Mathematical ProblemSolving, and Explanation in Mathematics Teaching
 Kazuhiko NunokawaAffiliated withDepartment of Learning Support, Joetsu University of Education Email author
Abstract
We expect mathematical proofs to explain why the propositions in question are true or why certain mathematical phenomena occur in certain situations. In this paper, I reexamine explanationbuilding processes by taking them as problemsolvers’ understanding processes and by referring to research that has analyzed the relationships between explorations, understandings, and explanations in mathematical problemsolving. I discuss some interactive features among these components during problemsolving processes by introducing some examples and referring to that research. I then use those features to offer an elaborated conception of explanationbuilding processes that takes into consideration local explanations, full explanations, and the direct and indirect relationships between local and full explanations.
 Title
 Proof, Mathematical ProblemSolving, and Explanation in Mathematics Teaching
 Book Title
 Explanation and Proof in Mathematics
 Book Subtitle
 Philosophical and Educational Perspectives
 Book Part
 3
 Pages
 pp 223236
 Copyright
 2010
 DOI
 10.1007/9781441905765_15
 Print ISBN
 9781441905758
 Online ISBN
 9781441905765
 Publisher
 Springer US
 Copyright Holder
 Springer Science+Business Media, LLC
 Additional Links
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 Editors

 Gila Hanna ^{(ID1)}
 Hans Niels Jahnke ^{(ID2)}
 Helmut Pulte ^{(ID3)}
 Editor Affiliations

 ID1. Ontario Institute for Studies in, University of Toronto
 ID2. FB Mathematik, Universität DuisburgEssen
 ID3. Inst. Philosophie, Universität Bochum
 Authors

 Kazuhiko Nunokawa ^{(1)}
 Author Affiliations

 1. Department of Learning Support, Joetsu University of Education, Joetsu, Japan
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