Wednesday, August 9, 2017

Do Students Really Need To Know Full Proofs?

Child, Study, Boy, Proof, Learning  I read a wonderful article in Medium by Junaid Mubeen where he questions the need for students to remember entire proofs in Math.

He speaks of a friend who can reconstruct proofs from a math class he took 7 years previously yet had not been practicing mathematics in at least 5 years.

So how did he remember the proofs.  It turns out, he remembered a couple of key idea, not everything.  He was able to fill in the rest of the proof because he understood the ideas and their relationships.   It is compared to remembering information about a novel.  People remember the important parts, not every single detail.  Its like weaving the important ideas together into a story so as to remember more.

The author observes that he memorized every single step of a proof without understanding the main ideas and how they related to each other. So he struggles to remember the steps of the proof.  It has been suggested people take the material and create story lines out of the material because our memories remember key elements of stories better and longer.

Stories also show the interplay between memory and thinking.  So people's ability to recall information is predicated upon their ability to think.  Unfortunately in math, facts are often presented in a disjointed way, making it harder for people to understand the material. 

According to the author,"mathematics is an act of storytelling that supports the dual goals of memory and understanding".  He believes a good proof will tell a story filled with turns and twists, and integrates the key elements into the story. 

After reading this, I fear I am guilty of teaching proofs for students to learn as written, just the way I learned.  This article provided a new perspective on teaching proofs.  Perhaps, I should have students identify the key ideas in a proof so they understand and remember the material.

I'd love to hear your opinion on this idea.  Please feel free to comment.  I love the idea.  Have a good day.