# TI-AIE: Developing mathematical reasoning: mathematical proof

## What this unit is about

Mathematical proof is often considered to be one of the cornerstones of mathematics. Professional mathematicians spend a lot of time developing conjectures and then working on whether they hold true for all cases, for some or for none. Proofs and justifications have to be rigorous and based on known mathematical facts and properties. Understanding and knowledge of mathematics is examined and extended in this process of proving, and connections across mathematical ideas and concepts are made.

Proving can also be an excellent activity to undertake in the classroom to develop an understanding of mathematics, engaging students in activities undertaken by real mathematicians. But often in school mathematics, proof is perceived by the students as something to be memorised and learned by rote. This method only serves to re-emphasise that mathematics is about learning facts and procedures by heart, while the purpose of the concept of proof is often not made clear.

In this unit you will think about mathematical proof and how it can be used to develop deeper mathematical understanding with your students. You will learn how to help your students become more verbally fluent in their reasoning and how they can learn effectively from discussions.

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