Preservice mathematics teachers are entrusted with developing their future students' interest in and ability to do mathematics effectively. Various policy documents place an importance on being able to reason about and prove mathematical claims. However, it is not enough for these preservice teachers, and their future students, to have a narrow focus on only one type of proof (demonstration proof), as opposed to other forms of proof, such as generic example proofs or pictorial proofs. This article examines the effectiveness of a course on reasoning and proving on preservice teachers' awareness of and abilities to recognize and construct generic example proofs. The findings support assertions that such a course can and does change preservice teachers' capability with generic example proofs.
Shiv Karunakaran, Ben Freeburn, Nursen Konuk and Fran Arbaugh
Harold B. Reiter, John Thornton and G. Patrick Vennebush
Through KenKen puzzles, students can explore parity, counting, subsets, and various problem-solving strategies.
Applying known facts to derive unknown facts results in efficiency, flexibility, and an understanding of number combinations for young students.
Carol J. Bell
Reasoning and Proof is one of the process standards set forth in NCTM's principles and standards for school mathematics (2000).