Teaching Reasoning, or Teaching Math

Why teach math? One reason I hear often is to teach reasoning. I’d love to teach students how to reason, but I’m skeptical. I have enough trouble teaching them to complete the square or graph a rational function. Is it even possible to teach someone to reason?

I wonder if the idea that math teaches some broader skill like reasoning is a kind of reaction to the experience of many teachers that it’s really hard to teach content. Lots of students leave class without the mathematical knowledge we want them to have, and we might like to believe they have. But if content isn’t the point, then it’s just fine that students forget everything they learned about logarithms and polynomials within a month or two. It’s a nice idea!

So why teach math?

Mostly, for me, to learn math. I’m biased, I really like math. And primary math is really useful! I wouldn’t mind throwing out a few things, but facility with arithmetic, fractions, decimals, proportions, the basics of geometry, and few principles of statistics and probability help people to live in the world, to work, and to fulfill their civic responsibilities.

Most high school math, I could take it or leave it. If higher education wasn’t so obsessed with calculus, high school might look very different. Who’s to say that learning about polynomials is more useful than graph theory, or projective geometry, or number theory?

Here’s the fun part. I teach math because I think math can open doors, can empower students to see what they are capable of, can inspire wonder and beauty. Those are powerful experiences for students in school, when we get them right. And there’s lots of great thinking that goes into learning math. And I think that maybe, just maybe, as students learn more math, and they think in new ways in different contexts over time, it becomes a little more likely that they can apply that thinking somewhere new, in or out of math class. I’m a skeptic here; I’m not interested in teaching a “SWBAT reason” lesson, and I don’t think I get there with very many students. But I think math has that potential. Bit by bit, over time, it becomes more likely that those ways of thinking about proportions and linear models and function transformations and circle theorems become useful outside of mathematics.

I’m happy to be humble here. I teach math because I think math is worth knowing, and because the experiences one can have in math class are worth having. But I like to dream that what I teach could help someone to live a richer life outside of math class.

3 thoughts on “Teaching Reasoning, or Teaching Math

  1. mathacognitive

    “I teach math because I think math can open doors, can empower students to see what they are capable of,…” Yes!

    I teach math because I want my students to know they can learn math. I’m not sure how much content they’ll remember in the long run, but they’re adults who dropped out as teenagers, coming back for a second shot, and math is intimidating. Knowing that they can master this intimidating thing is powerful, whether they never solve another equation again, or go on to college and have to use what they learned for the next step on their path.

  2. Lorena

    Wow — I’ve just found your blog and it’s INCREDIBLE. I’m working on a teaching license now… didn’t go the traditional way about getting certified to teach. I think my calling in life is to be an inner city middle school math teacher.. and I’m getting there. Slowly.
    I appreciate everything you say in your posts. If you ever wonder whether your writing is reaching anyone — it is. Me.
    Thank you.


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