What to think of your first guess

“Go with your gut. Your first guess is usually right.” Everybody’s heard or said some version of this popular meme. In fact, this morning, I heard it from a fifth grader who heard it from his teacher. It’s an interesting idea, harmless enough. There’s even some good sense in it. Today, however, it was clear to me that some harm had been done by this little idea.

I can’t be sure of the phrase’s origin. Perhaps hundreds of people have invented it independently, in a variety of circumstances, but here the root was clear. “On a multiple choice test, usually your first guess is right. Your second guess is wrong,” is what he actually said. He called it a strategy, surely one of his many – a trick of the trade, designed to help succeed in school. For that I give it credit. He is a very good student who works and answers questions quickly and gets A’s in our summer session, in part because of strategies like this one that allow him to learn material and test well. Today, however, it got in the way of his thinking.

We were working on some probability questions, so I brought up the Monty Hall problem. Ready? There are three doors, behind which are a car and 2 goats. After you pick a door, the host opens a different door to reveal one of the goats. He asks if you want to switch or stay. This is a famously tricky and deceptive problem, so I was not surprised when they were convinced of the wrong answer. Then, this fifth grader brought up the “first guess” strategy, which I found fascinating. Maybe making-the-right-choice brought up test-taking, but my gut tells me he was using it to justify his answer, applying the rule to this circumstance as though it were a way to handle tough problems — avoid them.

Here’s the problem with that. First and foremost, that this seemingly innocent strategy promotes not thinking! In some sense, the phrase teaches students to trust their instincts, which is actually great! But with the other hand it tells them to ignore their second guess and forgo the thinking process that would allow them to actually solve the problem! Thinking through problems and figuring answers out is mathematics, and when you cut that out, you’re no longer studying it. This is just a probabilistic attempt at affecting scores. Go with your first guess and move on.

Secondly, this idea was taught and learned in response to artificial problems, answering a lot of questions in a little time and dealing with self-doubt on multiple choice tests. It has nothing to do with him as a student, and it has nothing to do with mathematics or any other school subject. Students are paying a price for the mechanisms of a standardized school system, and it often includes critical thinking and creativity, mathematical lifeblood. What they need instead, is a school system that allows interpersonal assessment and individual interest to guide everything that happens. The top priority must always be the brain activity of the people in the classrooms and elsewhere.

If you’re still wondering whether to stay or switch doors, then you and I are on the same page. Good thing we have some time to think about it, huh? I’d love to hear your thoughts…

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8 responses to “What to think of your first guess

  1. Good point – we shouldn’t be promoting environments that reward or encourage mindless guessing.

    I have a more productive bit of advice that I remind my son of when he is struggling with a problem:

    When something doesn’t make sense, check your assumptions. There are always plenty of assumptions.

    • Yeah, that feels spot on, Bill, and it has everything to do with mathematics. Is your thinking sound?

    • Though mindless guessing should be discouraged, having kids guess what they think the answer is is a good idea. It makes the problem more interesting for them because they want to know whether they are right or not. This problem is great for that since it defies intuition. This is what I call a neat phenomenon. Kids like that. On the other hand I haven’t used it much with younger students because it’s hard for them to understand why that it works. I still have to review the logic of the solution every time I think about because it doesn’t stick in my head. Here’s an explanation I do like by Keith Devlin: http://www.stanford.edu/~kdevlin/Movies/MontyHall.mov

      -ihor

      • Completely agreed. That’s what makes this problem (and many other math problems so good!) it surprising how wrong we humans can be. Glory be to math for showing helping us disillusion ourselves. Guessing and intuition is so crucial in my class room. Indispensable. Thanks for the comment.

      • Oh yes, guessing is part of the process, and the scientists call that hypothesizing. When I advise to check assumptions, I might phrase that as testing hypotheses. We can define it formally use many different nomenclatures – all depending on the field of endeavor – but it boils down to: Think Again.

        Paul’s comment about the glory of math in disillusioning strikes home to me because my work frequently involves a process of disillusionment that constantly hammers home the notion that I am fallible. So let’s play What’s My Line… What do I do and what process am I describing?

      • Great stuff, Bill! “Think again,” I love that.

  2. Interesting post. Thinking about, not guessing the right answer of, the Monty Hall problem is the FUN part! The problem-solving process is what’s worth learning, whether you get the right answer is secondary to having the ability to think through the problem. Providing different explanations or ways of thinking about the same thing was what inspired me to create the site. It should be a stimulating experience!

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