How about replacing trig? But with what?

“You can’t get rid of trig! It’s my favorite unit!”

Said no one ever.

Well, that’s not quite true. Some of us quite like trig, at least if it’s approached as a set of functions rather than ratios in right triangles. More to the point, it’s a necessary prereq if you’re going to take calculus — but that doesn’t make anyone love it.

So what’s going on here? For 11 consecutive summers we’e included Trigonometric Models as the fourth of our four units in the two-summer Quantitative Reasoning course at the Crimson Summer Academy. But why did we add it in the first place, 11 years ago? The answer has to do with the structure of our program. Although we teach our own courses to rising sophomores and juniors, our rising seniors take regular college courses at Harvard Summer School. A majority of those seniors in 2006–2008 were having difficulties with their math courses. A trig background would reduce those difficulties by preparing them well, especially those taking calc or pre-calc at Harvard, but also those taking Math Models.

So what went wrong? Was there both an upside and a downside?

The upside was that it seemed to accomplish what it was supposed to. But as for the downside… well, first you need to know that we kept the trig going even in years when our rising seniors were no longer required to take a math course. Yes, this was mostly inertia. So the unit was achieving its goal for a smaller and smaller group. Now I’m sure that it was also helpful for those who ended up taking calculus in high school, but that isn’t really what we’re about. The summer of 2020, of course, motivated us to make some changes, as you can’t just move a curriculum online and teach the same material via Zoom that you used to teach in person. We have devised a two-part solution:

  • This summer, as our first experience with remote teaching to this group, we are replacing trig with a shorter unit on the mathematics of epidemics. No need to explain why. I’ll let you know the details after we figure them all out, which will probably take two more weeks.
  • In 2021, when we might or might not be back to in-person teaching, we’ll replace the trig unit with one on statistical models. For most students this will be more useful, and it will be much more convincing when we bring in real-life applications, as our Quantitative Reasoning course is supposed to be an interdisciplinary applied math class, not a pure math class. We can still fold in materials from the mathematics of epidemics, of course, and we can have tie-ins with the sophomore unit on the mathematics of voting and demographics, neither of which connect with trig. I am hoping this will be a win all around.

Categories: Math, Teaching & Learning