Why study math?

As usual, I was the house rabble-rouser at my institution today. Someone sent around a link to an article (subscription required, unfortunately) titled “Why study math?”

Reading the piece from the perspective of my inner middle-schooler, I was unimpressed. It felt to me like a rehashing of the usual vague unsubstantiated claims about transferring problem-solving skills and learning to reason. And also this:

Learning math develops stick-to-it-ness, defined as dogged perseverance or resolute tenacity, and develops perseverance, resilience, persistence, and patience. Students have opportunities to develop their work ethic in my math class by not making excuses, not blaming others, and not giving up easily.

Um, teacher? Do we have even one shred of evidence to support these claims?

So I wrote up my own reasons for studying math. Here they are:

I have two reasons people should study math.

First is that there is a set of very practical quantitative and spatial skills that are necessary for informed participation in society. Access to these skills ought to be both a civil right and an obligation.

The second is that there are many bodies of knowledge that we have agreed as a society are important; to be educated means knowing and having experienced certain things in the arts and sciences. In this way we pass on our culture.

I see these reasons as being quite different from more generalized claims about reasoning and problem-solving skills. An important part of the difference is that my reasons invite conversation and debate about exactly what mathematics we should teach.
If the practical skills are a major reason we impose math on students, we need to inspect the curriculum pretty closely to make sure we’re teaching the right ones. In a technologically advanced society, the long division algorithm for multi-digit decimals is pretty hard to defend from this perspective, for instance (to say nothing of polynomial long division!)

And if passing along mathematical knowledge and ways of thinking are culturally important, we ought to design curricula that give students experiences with mathematical ways of knowing. I would argue that our standard curriculum K-12 and through calculus does a pretty poor job of this.

But if we appeal vaguely to reasoning skills and stick-to-it-iveness, there is no further conversation. We tell students, “Take our word for it-studying this will make you better at that, and you’re gonna need that. So study this now and don’t ask any further questions.”

And while I don’t know everything about how to teach critical thinking, I know that when we talk to students this way-either explicitly or implicitly-we devalue it.
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4 responses to “Why study math?

  1. If we tell students that learning math develops perserverence, then we are implicitly admitting that math is hard and tedious.

    As far as teaching critical thinking, I don’t think critical thinking can be taught directly. Escpecially that higher thinking develops at different rates in different students. The best approach, in my opinion, is to expose children to different situations and let them work on the critical thinking on their own.

  2. I love your two reasons and have nothing to add. Thank you!
    I also wish we didn’t have to justify our reasons for studying math any more than why we need reasons to learn English or reading.

  3. I agree with Chris that we can’t teach critical thinking directly. But it does need to be fostered, encouraged, described and modeled. We can choose to set up classrooms in ways that encourage it. But we do need to choose it.

    When we tell students to do things in particular ways without offering, considering or listening to alternatives, we are choosing to operate a classroom that does not foster critical thinking. When we ask students to compare their ideas to new ones, or when we make clear in our words and actions that we value Why? questions, or when we tell a student, That’s a new idea for me; I had not thought of it that way before; when we do these things, we are choosing to help students develop critical thinking skills.

    And Fawn? Thanks for the kind words, but you definitely have something to add. Interestingly, one of my colleagues and friends here wrote in the email exchange today, “I am always uncomfortable with the thought that we have to justify teaching the skills that we do in math.” This echoes your concern, right? I can’t really say why,but this doesn’t bother me. I welcome exchanges with learners who are questioning the value of what they’re learning.

  4. Maybe because “math” is a general term, and yet you have stated the reasons beautifully and responsibly by saying “Access to these skills ought to be both a civil right and an obligation,” and “In this way we pass on our culture.”
    I can understand these questions arising, “Why study calculus?” or “Why study knot theory?” (You’re right of course about long division, it’s called a calculator.)
    And no doubt I’m biased because I love math so much that anyone asking the WHY question catches me off guard, kind of like someone questioning why I still wake up at 5:00 AM to make breakfast and lunch for my spoiled teenagers! :)
    Thanks, Christopher, I know you are a better person than I am because you said, “I welcome exchanges with learners who are questioning the value of what they’re learning.”

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