### Proof and Discourse in Mathematics: Teaching for Competency

#### Abstract

Recent changes to the standards for mathematics education have shifted focus towards the importance of proof, reasoning, explanation, all of which are essential components of understanding, recording, communicating, and doing mathematics. Yet research continues to show that American students (high school and beyond) struggle to understand the idea of proof in mathematics. The research demonstrates the importance of teaching mathematics through the lens of proof, and how meaningful mathematics discourse can be the catalyst for learning mathematical proof. Evidence shows that students become more capable learners and doers of mathematics when they understand and can construct mathematical proofs. Additionally, research shows that through engaging in mathematical discourse, students can learn the process of developing mathematical arguments more effectively.

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