Why Do We Learn About Cosine Functions? asks Forrest Hinton on The Quick and the Ed. I’ve waited more than 40 years for the answer — which he has not got.
Hinton flashes back to his Algebra III classroom in a Raleigh suburb. A girl asks why she has to learn about cosines. What’s the point?
He asks her what she wants to be when she grow up. She answers: a beautician.
I went on to describe how the business cycle oscillated between recession and expansion, much like a cosine function, and how she would have to follow this trend as a small business owner. The young woman was unimpressed.
He continues with “a vague, cop-out” answer:
On the whole, mathematics is a useful subject because it teaches you how to think logically, problem solve, and justify the things you do. It also stretches your mind as you deal with abstract complexities and forces you to be concerned with small, but important, details. Now, let’s take a look at example three…
There’s a lot that high school juniors might learn, Hinton writes. Teachers should understand why they’re teaching certain pieces of knowledge and skills, so they can motivate students to learn.
Are they learning it merely because it’s tradition? Will 10% of the Algebra III class eventually use this in their professional lives? Are students, in reality, learning to generally solve problems and confront complexities?
I took Algebra II/Trig because I needed it to apply to selective colleges. (In those days, only math-science types took AP Calculus.) Algebra was fine, but I hated trig. I was running out of enthusiasm for jumping through hoops and trig seemed more like a strategy for torturing 16-year-olds than an essential subject. I repeatedly asked my teacher why those of us with no aspirations for math, science or engineering majors had to learn sines, cosines, logarithms and so on. What was the point? He couldn’t answer the question. At the end of the year, he gave me a higher grade than I deserved. I was so surprised that I asked him if he’d made a mistake. He said he’d factored in my classroom participation. I guess he liked being asked, even though he had no answer suitable for a future English major.