So, of course, Andrew Hacker’s article “Is Algebra Necessary?” had caused quite the stir, and the obvious answer to that question was “Yes, algebra is necessary.” But the article makes you think if all of what we learn of algebra is necessary. And I think it isn’t, but that comes from thinking about what high school is for.
Do we expect that, when a student gets to college, they can skip the lower levels of Biology because they took bio in high school? No, of course not. (Excepting AP courses, of course.) So what is our goal for learning biology in high school? It’s to provide a general foundation of the subject, that most people should know, and it prepares you for a college level course or major in Biology.
Really, all of what we learn in high school is designed to broaden our horizons, to provide experiences and content we wouldn’t see otherwise, and to provide a baseline of knowledge that we feel everyone should have.
I remember reading from someone, though I don’t recall who, that they had struggled through Algebra 2 and Pre-Calculus, slogging along, and then when they got to Calculus a light turned on. “This was why we’ve been learning everything we’ve done in the past two years! It was all for this!” Even the wikipedia page on Pre-Calc says “…precalculus does not involve calculus, but explores topics that will be applied in calculus.” It’s putting the work before the motivating problem, again.
But now thinking about the normal course sequence for a student that is not advanced: Algebra –> Geometry –> Algebra 2 –> Pre-Calculus –> Graduated from High School, so no Calc! So these students will have two whole years of math without the payoff that shows why we do it.
And as teachers we know that you need to start with the motivating factor, not have it at the end. So why don’t we have calculus first, before those two? If we consider our goal in high school is to spread ideas people might not see otherwise, I think Calculus has a lot of important ideas people should see that would improve their lives. Optimization? The very idea of it can improve how you look at all the problems in your life. Related rates, limits, the idea of changing rates and local rates, the relationships between functions, these are all good ideas to be familiar with.
Can the students learn these things without having done Algebra 2/Pre-Calc? I think so. As Bowman Dickson says, “The hardest part of calculus is algebra.” So what if we taught it in a way that didn’t rely on that? We can get the ideas across without jumping into the nitty-gritty of a lot of it. Save that for AP level classes, or for college calc. What you take in college is more in depth that high school, so it should be the same here.
Now, there would certainly be some stuff from Algebra 2/Pre-Calc that we really need first. But why not have those in Algebra 1? I accidentally taught several things from Alg 2 when I taught Alg 1 my first year, because they seemed like natural extensions of what we were doing, and I didn’t know they weren’t required until I started planning for the next year. But also, consider this. If we made Probability & Statistics one of the main courses of the math sequence, I don’t have to teach it in Algebra 1. I spent about 7 weeks on those topics last year. That’s 7 weeks of Alg 2 content I could fold in, without worrying about reviewing old stuff because we just did it.
So then the new math sequence could be Statistics –> Geometry –> Algebra –> Calculus. (And I think that might fit well with the science sequence of Biology –> Earth Science –> Chemistry –> Physics.)