1 Why teach mathematical proof in schools?

There are many discussions around the world about whether mathematical proof should be part of the school curriculum. Teachers often struggle with teaching proof and students often struggle with learning it. It is also not always clear what mathematical learning is addressed by working on proof. Some countries have abandoned teaching mathematical proof altogether, although others approach it more as reasoning in mathematics. In India, mathematical proof is still prevalent in the school curriculum and a number of chapters in textbooks for Class IX and X include mathematical proofs.

There are many positives for learning mathematical thinking to be gained from working on mathematical proof in schools. Researchers suggest working on mathematical proof offers a variety of mathematical learning opportunities. Hanna (2000) summarised these as:

• verification of the truth of a statement
• explanation by providing insight into why it is true
• systematisation by organising various results into a deductive system of axioms, major concepts and theorems
• discovery or invention of new results
• communication in order to transmit mathematical knowledge
• construction of an empirical theory
• exploration of the meaning of a definition or the consequences of an assumption
• incorporation of a well-known fact into a new framework and thus viewing it from a fresh perspective.

This unit will explore and give suggestions on how the process of mathematical proving can be used as a tool for developing students’ understanding of mathematics by working on learning opportunities like those above.

Pause for thought What are your thoughts and opinions about mathematical proof in the school curriculum? Should it be there? Do you agree with the list of learning opportunities suggested by these researchers? Which ones do you consider to be most important? Does this kind of mathematical learning currently happen in your classroom? If so, how do you make it happen? If not, do you have any ideas about what you would like to change in your current practice?