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.

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I already used this with classes today as an illustration of thinking about the plan/structure/model before “throwing darts” at a solution. Great post!

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“…there is enormous value in having students show their work, and go from the concrete to the abstract!” from http://www.bootstrapworld.org/blog/curriculum/Testing.shtml

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Here’s another puzzle from Mr. Kahneman:

“Adam switches from a gas-guzzler of 12 mpg to a slightly less voracious guzzler that runs at 14 mpg. The environmentally virtuous Beth switches from a 30 mpg car to one that runs at 40 mpg. Suppose both drivers travel equal distances over a year. Who will save more gas by switching?”The intuitive answer of identifying -10mpg as a bigger savings than -2mpg is incorrect.

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