A Problem with Problem Solving

When trying to teach problem solving as a process, students are very resistant to approaching it systematically. They love guess and check. As an example, try to solve this quick simple word problem:

A bat and ball cost $1.10
The bat costs one dollar more than the ball.
How much does the ball cost?

“A number came to your mind. The number, of course is 10: 10¢… it is intuitive, appealing, and wrong.” states Kahneman in Thinking, Fast and Slow. If you attempted to work the problem, you probably used guess-and-check, even though it was introduced within the context of using systematic problem solving!

Getting students to overcome quick answers and instead intentionally design solutions rather than random trials is a challenge.

“Many thousands of university students have answered the bat-and-ball puzzle… More than 50% of students at Harvard, MIT, and Princeton gave the intuitive — incorrect — answer… These students can solve much more difficult problems when they are not tempted to accept a superficially plausible answer that comes readily to mind. The ease with which they are satisfied enough to stop thinking is rather troubling.”

Unfortunately, most of the book is analyzing the ‘intuitive’ reasoning that gets erroneously applied. What would interest me more is ways to disrupt the ‘appeal’ of a fast/easy solution. Would more respondents slow down if simply instructed to “Show your work”?

bat = $1 + ball
$1.10 = bat + ball
$1.10 = ($1 + ball) + ball
$1.10 = $1 + 2*ball
$0.10 = 2 * ball
$0.05 = ball

For most projects in my classes, I require design work/drafts/plans/etc as part of the submissions. This has been my way of the glimpsing into the thought process of my students. Now, I wonder if there may be another benefit to this.

Next school year, I think I’m going to include this bat-and-ball question in an opening-week assignment. I won’t penalize students for incorrect answers, but I’m very curious what answers I’ll get.