Book | Chapter
(2010) Explanation and proof in mathematics, Dordrecht, Springer.
Proof, mathematical problem-solving, and explanation in mathematics teaching
Kazuhiko Nunokawa
pp. 223-236
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 explanation-building processes by taking them as problem-solvers' understanding processes and by referring to research that has analyzed the relationships between explorations, understandings, and explanations in mathematical problem-solving. I discuss some interactive features among these components during problem-solving processes by introducing some examples and referring to that research. I then use those features to offer an elaborated conception of explanation-building processes that takes into consideration local explanations, full explanations, and the direct and indirect relationships between local and full explanations.
Publication details
DOI: 10.1007/978-1-4419-0576-5_15
Full citation:
Nunokawa, K. (2010)., Proof, mathematical problem-solving, and explanation in mathematics teaching, in G. Hanna, H. N. Jahnke & H. Pulte (eds.), Explanation and proof in mathematics, Dordrecht, Springer, pp. 223-236.
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