3 ms·

I can’t remember the details now, but my recollection was that the unit circle enlightened me that they were ratios. It was even possible to reason about “round

I can’t remember the details now, but my recollection was that the unit circle enlightened me that they were ratios. It was even possible to reason about “round” angles (like 90° and 45°), in your head without the need of a calculator. I never tried a random angle like 13° in my head, but I figured it was kind of on a scale between the “round” numbers which I knew, which would give a good sense of the actual number, even if not accurate enough. The point is, the unit circle explained the figures to me instead of them being just some magic numbers. Likewise, there was an actual explanation of concepts like cos and sin in that they are the names for relationships between angles/sides (again, I can’t remember now, but it made sense), rather than them just being tools you’re told to use when.

dhosek 4y ago
Wasn’t there at least right triangle math for sin = adjacent/hypotenuse and cos = opposite/hypotenuse? This sounds like serious educational malpractice.¹ ⸻ 1. Although when I think about educational malpractice, I remember a program I was teaching in where the director asked me about why the numerator and denominator were called what they were and I explained the denominator identified what kind of fraction (and made the analogy to denominations of currency) and the numerator was how many (the “number”) of that kind of fraction. She then, that same day, gave a talk to the assembled teachers saying that she’d asked me and I’d said that’s just what they were called. I nearly stood up and screamed in anger. If I hadn’t desperately needed the money, I would have quit on the spot.
- jonathanlydall 4y ago
  My recollection is that we were taught the hypotenuse rule earlier in the year, might have even been just before trigonometry, but I have no recollection of being informed of any "connection" between them during school. We were simply taught which equation to use for particular scenarios and how to use calculators with particular equations. When you bought it up, I do recall the connection being used by Open University to explain things, which I also found a bit thrilling to learn. Although only anecdotal evidence, I have asked a few South African colleagues over the years about the unit circle and it seems like none of them were taught it during school, so it seems like it's just not in the curriculums over here, which I feel is a tragedy.

dhosek 4y ago

Wasn’t there at least right triangle math for sin = adjacent/hypotenuse and cos = opposite/hypotenuse? This sounds like serious educational malpractice.¹ ⸻ 1. Although when I think about educational malpractice, I remember a program I was teaching in where the director asked me about why the numerator and denominator were called what they were and I explained the denominator identified what kind of fraction (and made the analogy to denominations of currency) and the numerator was how many (the “number”) of that kind of fraction. She then, that same day, gave a talk to the assembled teachers saying that she’d asked me and I’d said that’s just what they were called. I nearly stood up and screamed in anger. If I hadn’t desperately needed the money, I would have quit on the spot.

jonathanlydall 4y ago
My recollection is that we were taught the hypotenuse rule earlier in the year, might have even been just before trigonometry, but I have no recollection of being informed of any "connection" between them during school. We were simply taught which equation to use for particular scenarios and how to use calculators with particular equations. When you bought it up, I do recall the connection being used by Open University to explain things, which I also found a bit thrilling to learn. Although only anecdotal evidence, I have asked a few South African colleagues over the years about the unit circle and it seems like none of them were taught it during school, so it seems like it's just not in the curriculums over here, which I feel is a tragedy.