Thread: How to motivate students to do proofs?

1. How to motivate students to do proofs?

I am finding it difficult to motivate students on why they should how to prove mathematical results. They learn them just to pass examinations but show no real interest or enthusiasm for this.
How can I inspire them to love essential kind of mathematics? They love doing mathematical techniques. Any resources or any answers would really help me.

2. Re: How to motivate students to do proofs?

Originally Posted by Euclid
I am finding it difficult to motivate students on why they should how to prove mathematical results. They learn them just to pass examinations but show no real interest or enthusiasm for this.
How can I inspire them to love essential kind of mathematics? They love doing mathematical techniques. Any resources or any answers would really help me.
I would change your thinking just a little.

Not Helpful: "essential kind of mathematics"
More helpful: essential way to think

Causes have effects. Effects come from causes. You can't pick both. "When you choose the very first step on the road, you also choose the last."
Logical progression helps simplify decision making.
Facts matter, not just impressions. In the accounting world, there is, "Is it a fact, or did you pull it out of a hat?"
Linear and logical thought will save you from the vain imaginations of those who would have you believe anything they can imagine.
What you want to be the case may be so. Can you prove it?
Why should we loan you money to start your business? Do you have a plan we can follow?

3. Re: How to motivate students to do proofs?

It's my impression that when you say "they learn them", that you mean they learn a certain set of "proofs" and not actually learning how to prove results. Honors math courses require knowing how to prove results - homework and exams will contain questions not covered in class, but instead test the student's domain knowledge and proving techniques.

Speaking from personal experience, though learning how to prove results was a difficult path, the deeper understanding of the domains I was learning made understanding proofs instrumental in my undergrad studies. Understanding how the proofs worked in a lecture often provided hints on how to proceed with homework problems, and during exams, it was much easier to remember a result because I knew and understood the proof. I wish I was exposed to proof theory in high school for this reason, so that I didn't have to rely on retaining an algorithm in memory without understanding it. Understanding a concept in proving it allows extension.

If your class is familiar with geometric proofs, I'd recommend Euclidea for students who are interested. https://www.euclidea.xyz/
Otherwise, you can give examples of proofs in class, but give them problems to prove for themselves.

Thanks