A lesson that worked

I originally wrote this blog in a word file and was writing it on my wish list, but then I ended up teaching a lesson on one of the things I said that I wished other teachers would teach... and it worked! So rather than recount my lengthening list of things I wish my students would walk in here knowing I here's a bit about a recent lesson that worked.

I meant my lesson to be a quick brush up on using sines and cosines to find x and y components of vectors, but what I found was that the students really didn't even know how to punch sine and cosine into their calculators, much less have any idea of what they meant. However, since I have been making a big stink in my class about how I really don't care if my kids can punch numbers into calculators or even plug them into equations, I forged ahead with my "review" of sine and cosine as the ratio of lengths of the sides of a right triangle. (maybe you remember Soh Cah Toa ?)

As it turned out nearly every one of the students ate up this more basic, version of sine and cosine than whatever they had been working with since first taking geometry or whatever. In physics, the point of doing such analysis is to find out what portion of a vector "goes in a certain direction". We talked about how pulling on something in the direction you actually want it to go is more efficient than pulling at some angle and that the bigger the angle, the less force actually ends up "going" the way you want it.

Nearly every student had one of those lightbulb moments right in front of me. Even though I thought the lesson was about as boring as could be, over half of the students said it was one of the best lessons they had this year and that they wish I had taught them sine/cosine in the first place! To be honest I think that the result was more due to the fact that the students had covered the material many times before, but it was satisfying nonetheless to see them actually get excited about learning some math.

What I'd like to think made the lesson work was the fact that it was applied math. It makes me want to work more to find lessons that integrate into them the learning of things they should already know. Too often I find myself trying to teach lessons that merely depend on them knowing things they should have already learned. It makes me want to find a way to help the students learn applied math in the first place, as opposed to learning math and then trying to apply their skills in physics. I think that the fact that the stated goal of the lesson was not to learn some math was important. The students seemed to treat the whole thing as if they were learning something other than math, and, since they claimed never to have seen it done the way I was showing them, they acted as if the whole thing were new and interesting!