Proof, mathematical problem-solving, and explanation in mathematics teaching
pp. 223-236
in: Gila Hanna, Hans N. Jahnke, Helmut Pulte (eds), Explanation and proof in mathematics, Berlin, Springer, 2010Abstract
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.