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## Improving Preservice Secondary Mathematics Teachers' Capability With Generic Example Proofs

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.

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## Using KenKen to Build Reasoning Skills

Through KenKen puzzles, students can explore parity, counting, subsets, and various problem-solving strategies.

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## For ELLs: Vocabulary beyond the Definitions

A classroom teacher discusses ambiguities in mathematics vocabulary and strategies for ELL students in building understanding.

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## Graphing Polar Curves

Graphing the polar function on a rectangular plane simplifies graphing, increases student understanding, and reinforces connections.

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## Delving Deeper: Approximating π Using Similar Triangles

This article presents a method for approximating π using similar triangles that was inspired by the author's work with middle school teachers. The method relies on a repeated application of a geometric construction that allows us to inscribe regular polygons inside a unit circle with arbitrarily large number of sides.

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## Proofs without Words: A Visual Application of Reasoning and Proof

Reasoning and Proof is one of the process standards set forth in NCTM's principles and standards for school mathematics (2000).