How to motivate students to do proofs?

[matqkks]

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.

 

[symbolipoint]

May depend on the type of students and what or why they are studying.
What level of students? What level of courses?

Very very broadly, at some point in the future, a student (now) may ultimately need to ask himself, which side of this does he want to be on:
"Come, Mr. Tally Man, tally my bananas."

 

[jedishrfu]

You can find some examples of where commonsense indicates one answer but the proof shows otherwise. The one problem with students is the drive to get good marks trumps thinking more deeply about problems. Proofs like great literary works requires a depth of understanding that students may not want to exert.

The Abel theorem is a good example wher a proof proves once and for all there is no formula like the quadratic formula for quintic polynomials. In essence saying you can stop looking for one.

 

[matqkks]

May depend on the type of students and what or why they are studying.
What level of students? What level of courses?

Very very broadly, at some point in the future, a student (now) may ultimately need to ask himself, which side of this does he want to be on:
"Come, Mr. Tally Man, tally my bananas."

They are undergraduates doing a discrete mathematics module.

 

[vela]

Are they any good at writing proofs? Most students are horribly bad at it initially, and that may be part of the reason they're reluctant to do it.

One thing you might try is giving them incorrect proofs and asking them to figure out where the errors are.

 

[jedishrfu]

I think geometric or set based proofs are a good starting point.

 

[jedishrfu]

With respect to bad proofs, the angle trisection proofs are good where you can’t decide whether two arcs and a line intersect at the same point.

Another idea is to show the economy of expressions in proofs. As an example, there are many ways to prove the Pythagorean theorem some of which are more elegant and profound than others.