Yesterday I gave my students the Cognitive Reflection Test:
Seriously, answer the questions. It’ll only take a minute. I’ll wait.
Great. The answers are all the way at the bottom of the post where you won’t have the fun spoiled for you. You can go check. See how you did. The questions come from some psychological research — there’s a full paper here, and I stumbled across it in the book Thinking Fast and Slow, by Daniel Kahneman.
Short version is — MIT students average a little over 2 questions right, and the full sample in the study, consisting mostly of college students, averaged a little over 1 question right. These are questions that are written to fool the reader into picking an easy, intuitive answer, rather than slowing down to think through whether that answer makes sense.
We talked through the answers, and then went on to discuss what Kahneman writes about as he summarizes the study. It highlights the differences between the two “systems”, as he calls them, in our brain. The first is the intuitive, quick-thinking system that does well-learned, instinctual tasks quickly and easily — recognizing that a face is happy or sad, writing your name, finding 2+2, climbing stairs, and other simple tasks. The second is the reasoning and processing system that works much more slowly, but is capable of reasoning and applying prior knowledge to a problem — finding 17 x 24, or designing a bridge made of toothpicks and marshmellows, or finding evidence that Elizabeth is a better match for John Proctor than Abigail.
The point was pretty simple. One thing I hope my students take from my class is to look at a problem and, instead of rushing to the first, easiest solution that their mind jumps to, slowing down. Our brains want to live in the first system, doing things as quickly and mindlessly as possible. But I’m looking for students to think carefully about what a question is asking, constructing an answer, and checking to see if it makes sense. That’s the type of reasoning that will make them successful in every area of their life. And problem solving in math is a great opportunity to practice this — looking at a new problem and considering it carefully rather than rushing to a conclusion, the same way I would love my students to reason about events in the news or their relationships with their peers.
So the Cognitive Reflection Test is one measure of a type of intelligence, associated with applying reasoning to simple problems rather than rushing to easy answers. I didn’t want to send the message that that is the only way that humans can be smart. Next we did a quick test that I first saw in a psychology class —
Take two minutes to think of as many uses for a paperclip as you can. Go.
Some students wrote one or two and gave up. But some wrote that they could use it as a clothes hanger for doll-sized clothes, or an earring, or an axle for a toy car. It’s not perfect, obviously — neither is the CRT or the SAT or anything else — but it’s one way to measure creativity. And creativity — seeing as many solutions for a problem as possible, and looking for more after finding one — is one of the values I want to bring into my class more often, and this was my way of impressing that on my students.
We discussed for a few minutes whether students thought the CRT or the paperclip test measured a more important aspect of intelligence. Kids had some great ideas to share, pretty evenly split between the two, and I especially enjoyed hearing kids say that they were equally important, just different.
Anyway, after our little sojourn in psychology I gave them a problem set for partner work. Some fun questions — like this one:
Didn’t see any huge, amazing strides in reasoning, but kids were engaged and there was some really productive talk about the mathematics. Definitely wasn’t a life-changing class for any of my students, but I have some ideas to come back to as I try to push my students’ reasoning and problem solving skills.
1. 5 cents (5 cents + 105 cents = 110 cents)
2. 5 minutes (1 machine takes 5 minutes to make 1 widget)
3. 47 days (it doubles every day, so one day later, it’s totally covered)