TITLE: Two Quick Hits with a Mathematical Flavor
AUTHOR: Eugene Wallingford
DATE: December 09, 2016 1:54 PM
DESC:
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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!
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