Precalculus, and Making Sense

I’m getting sick of teaching precalculus. Don’t get me wrong, there are some gems in there. I love teaching probability and bringing in Ben Orlin’s excellent The Bear in the Moonlight series of fables. Teaching sequences and series is a ton of fun; I get introduce students to some fascinating and thought-provoking perspectives on infinity.

But too much of the curriculum is there for the same reason: “you’ll need this in calculus.” Nothing deadens my soul like hearing that students needs to learn something for the sake of learning something else in the future, on and on forever.

Juxtapose with the big event in the mathematical news this week:

My favorite response:

The first has become a bit of a trope. Problems like it come along every few months, with the apparent goal of making people feel dumb and reinforcing the idea that math is this inscrutable language with arbitrary rules that don’t make sense. The second isn’t a thing; while language can be ambiguous, we understand that meaning comes from context and don’t feel stupid if we aren’t sure what the writer is saying.

Back to precalculus. One negative experience I have had more times than I can count teaching this course for the last four years goes something like this. Let’s say I’m teaching logarithms. Most students have seen them before, and most students have forgotten what they are and why they might be important. We take our time making sense of the idea of a logarithm, first informally (credit to Kate Nowak) and then with more precision. It seems a bit arbitrary that students have to learn this, but it makes sense. Then we move into the other log rules and it all goes to shit.

Sure, if I was a great teacher we could take our time and do this all right — there’s plenty to make sense of here. But precalculus is a race. There’s so much to cram in that spending the time to do log rules right gives short shrift to something else. More likely I skim a few key ideas and move onto the next thing.

The problem is the curriculum. It’s not designed for students to understand a coherent body of mathematics. The goal is to be able to push symbols around and remember some disembodied rules that might be useful in the future. And students often come out the other end with their worst ideas about math confirmed. Math is about manipulating letters and numbers in weird ways, doing what you’re told, and getting on with your life.

Much of high school math works like this. It’s a race to calculus, with everyone’s pet topic shoved in just in case. And it leaves teachers with a choice. Take the time to do things right and skip out on some topics, or sprint through everything and pray.

Right now, the central goal of high school math is to prepare students for calculus. What if, instead, our goal was for students to believe that math makes sense? What wouldn’t we teach? What would we add? What would math class look and feel like?

2 thoughts on “Precalculus, and Making Sense

  1. mathacognitive

    “But precalculus is a race. There’s so much to cram in that spending the time to do log rules right gives short shrift to something else. More likely I skim a few key ideas and move onto the next thing. ” ….. My summer’s frustration. Not pre-calc for me, but the ever accelerating race to cram too much in.

    Reply
    1. dkane47 Post author

      Yea. It sucks.

      On one hand, I want better high school standards. On the other, I don’t want anything to do with the next battle over standards in the United States.

      Reply

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