4 ms·

Maybe I just got lucky, but that's pretty much exactly how I remember being taught in high school calculus class. No ODEs or anything of course, but the teacher

Maybe I just got lucky, but that's pretty much exactly how I remember being taught in high school calculus class. No ODEs or anything of course, but the teacher started from the geometry, then moved to the trig functions and identities, and finally to derivatives and Taylor / Maclaurin series. It's a good post, and I agree--there is just no hope in getting students to develop any kind of intuition in math without starting from something really simple like the geometry of the problem. Plus, it's way more fun!

darkwater 3y ago
I think fun in learning comes mostly from the "intuition reward". If you understand and _feel_ some abstract concept in an intuitive manner, you will feel happy and you will probably want more of that. So, for teachers finding ways to teach concepts that can trigger students intuition, in my experience as a student, will get more engaged students.
Ensorceled 3y ago
I have my old high school calculus text book and that is definitely how trig was introduced. The proof of Pythagorean Theorem using sin and cos was literally part of my undergrad CALC101 (I remember because my high school teacher demonstrated it for fun so it was a rehash)
- lupire 3y ago
  When were you in Calc 101? Before or after 2009? https://forumgeom.fau.edu/FG2009volume9/FG200925.pdf https://forumgeom.fau.edu/FG2009volume9/FG200925.pdf
  - Ensorceled 3y ago
    Before. It was clearly circular since the identity was assumed, the calc prof might have acknowledged this at the time.
gedy 3y ago
My math teacher was teaching us Trigonometry without ever showing the unit circle, and the class was completely befuddling to me and other students. This was pre-internet, and I stumbled across the unit circle in a book and the meaning of sine, cosine, etc. on it - and was like a huge revelation to me and others. I've enjoyed trig since, and one of the few math topics I continue to use to this day.
- bbitmaster 3y ago
  I remember just learning to code at a young age, but not knowing trig or seeing how it applied because I only knew it as being about triangles. I had learned to use some game graphics library (specifically DJGPP with Allegro, coding in C) and I was trying to make a 2d spaceship game, think like asteroids, where you can turn the ship and apply thrust. I couldn't figure out how to take the angle the ship was facing and get a direction to move. Basically I needed to understand the unit circle. I eventually found what I needed probably on some old internet forums. From that point on, trigonometry really started making sense to me.

darkwater 3y ago

I think fun in learning comes mostly from the "intuition reward". If you understand and _feel_ some abstract concept in an intuitive manner, you will feel happy and you will probably want more of that. So, for teachers finding ways to teach concepts that can trigger students intuition, in my experience as a student, will get more engaged students.

Ensorceled 3y ago

I have my old high school calculus text book and that is definitely how trig was introduced. The proof of Pythagorean Theorem using sin and cos was literally part of my undergrad CALC101 (I remember because my high school teacher demonstrated it for fun so it was a rehash)

lupire 3y ago
When were you in Calc 101? Before or after 2009? https://forumgeom.fau.edu/FG2009volume9/FG200925.pdf https://forumgeom.fau.edu/FG2009volume9/FG200925.pdf
- Ensorceled 3y ago
  Before. It was clearly circular since the identity was assumed, the calc prof might have acknowledged this at the time.

gedy 3y ago

My math teacher was teaching us Trigonometry without ever showing the unit circle, and the class was completely befuddling to me and other students. This was pre-internet, and I stumbled across the unit circle in a book and the meaning of sine, cosine, etc. on it - and was like a huge revelation to me and others. I've enjoyed trig since, and one of the few math topics I continue to use to this day.

bbitmaster 3y ago
I remember just learning to code at a young age, but not knowing trig or seeing how it applied because I only knew it as being about triangles. I had learned to use some game graphics library (specifically DJGPP with Allegro, coding in C) and I was trying to make a 2d spaceship game, think like asteroids, where you can turn the ship and apply thrust. I couldn't figure out how to take the angle the ship was facing and get a direction to move. Basically I needed to understand the unit circle. I eventually found what I needed probably on some old internet forums. From that point on, trigonometry really started making sense to me.