Today, there is a follow-up on yesterday’s Non Sequitur comic – in which Danae’s new math system is revealed: henceforth, she will start with the answer and work back to get an equation that fits the problem. This way, she will always be right.

Once again, the comic serves to reveal shared cultural attitudes about mathematics and mathematics education. We can call this one The Tyranny of the Right Answer. Here is how it goes: every math problem has an answer. There is a single right answer. Nothing is more important than the right answer. The teacher is the final source and authority on the right answer. Your job, in math class, is to chant the proper magical invocation and conjure up the Right Answer.

Now wait a minute, some people might respond. Are you suggesting that when a student answers 2 + 2 = 5 you don’t mark it wrong? What kind of a message would that send to our students?

Fair enough. What we do in math class does send a message to the students, a message that in some few cases stays with the students for their whole life. Yet I think we’ve been, as a rule, more attentive to the message we mean to send than to the message we’ve actually been sending. How do you find out what message you’ve actually been sending? Well, by watching carefully at what message the students pick up. And I’m suggesting that one such message – one you can check by listening carefully to the students and ex-students in your area – is this one: Math is about getting the *right answer*. There* is* a right answer, and there is *one* right answer. The *teacher* has the right answer, and *I* don’t. And the teacher won’t give it to me. And I am powerless in this arena. And math isn’t really for *me*.

One way a kid can reclaim their power is to do like Danae and remake some of the rules of the game. Yet the rule she hasn’t remade is the one about the importance of the right answer.

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One minor error in your premise “there is a single right answer”, is that many math problems have multiple “right answers”, (or at least a right answer consisting of multiple pairs/sets, etc), however, that doesn’t affect the validity of your premise. Math is typically taught and perceived as stated, that there is a correct answer, the teacher has it, and the students’s job is to find that the answer that matches the correct answer the teacher has.

Even most teachers relate to it that way. An example from high school. I was in a trigonometry/analytic geometry class and we were reviewing the homework (which I rately did) from the previous night. On one problem, when the teacher announced the answer, the group of 5 or 6 students I was near looked at one another and told the teacher she had the wrong answer. The teacher argued with us for about 10 minutes in class before pointing out that her answer was the one in the back of her teacher’s edition textbook. We said the book was wrong. She said she would research it and let us know, and returned the next day to say the book was wrong. While she did eventually agree with us, the assumption was that she and the book were correct and she was determined to argue for that position.

Most people do learn from the specific to the general (e.g. from specific examples, they can accept and learn the concept). I’m one of the small percentage that learns most quickly from concepts and can apply those concepts so solve problems. However, when I was tutoring and later teaching, I had to teach for the 90+% who learn specific examples, and can then see how a generalized formula/theorem can be used to solve a problem. At the same time, I always watched for students who learn better by learning concepts first and I would then address those separately for the students who were interested.

I was fortunate to have had teachers who would work with me on concepts and allow me to learn in my fashion. I was willing to compromise with my teachers (e.g. I wouldn’t “show my work” or I would show minimal steps so they could see the line of reasoning I was using, but I didn’t expect or get any “partial credit” for minor errors, my answer was either correct or incorrect). Likewise, I would only do any math homework if I thought I needed practice (and that was very rare), so I was graded on my tests alone.

BTW, nice series of articles. Math needn’t be magical, mystical, or authoritarian, when the teachers listen for what the students are missing or questioning.

Geoff,

I appreciate your comments!

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