TITLE: Two Quick Hits with a Mathematical Flavor AUTHOR: Eugene Wallingford DATE: December 09, 2016 1:54 PM DESC: ----- BODY: I've been wanting to write a blog entry or two lately about my compiler course and about papers I've read recently, but I've not managed to free up much time as semester winds down. That's one of the problems with having Big Ideas to write about: they seem daunting and, at the very least, take time to work through. So instead here are two brief notes about articles that crossed my newsfeed recently and planted themselves in my mind. Perhaps you will enjoy them even without much commentary from me. • A Student's Unusual Proof Might Be A Better Proof
I asked a student to show that between any two rationals is a rational.
She did the following: if x < y are rational then take δ << y-x and rational and use x+δ.
I love the student's two proofs in article! Student programmers are similarly creative. Their unusual solutions often expose biases in my thinking and give me way to think about a problem. If nothing else, they help to understand better how students think about ideas that I take for granted. • Numberless Word Problems
Some girls entered a school art competition. Fewer boys than girls entered the competition.
She projected her screen and asked, "What math do you see in this problem?"
Pregnant pause.
"There isn't any math. There aren't any numbers."
I am fascinated by the possibility of adapting this idea to teaching students to think like a programmer. In an intro course, for example, students struggle with computational ideas such as loops and functions even though they have a lot of experience with these ideas embodied in their daily lives. Perhaps the language we use gets in the way of them developing their own algorithmic skills. Maybe I could use computationless word problems to get them started? I'm giving serious thought to ways I might use this approach to help students learn functional programming in my Programming Languages course this spring. The authors describes how to write numberless word problems, and I'm wondering how I might bring the philosophy to computer science. If you have any ideas, please share! -----