I didn't
really see how beautiful math was until I took Differential Equations, honestly. Which I took in order to meet my major's math requirements
without taking that very last quarter of calculus. {ahem}
My advisor thought that I was crazy, incidentally, and I never worked so hard for a B in my life, never having
seen any linear algebra (which I had to teach myself along the way)...
but that's when it hit me that this stuff was AMAZING, and that I
enjoyed working that hard on interesting problems. OMG, the take-home exams in that class. They were comprised of a part A (vicious in-class midterm on Fri) and part B (take-home extended problems, often 3 of them, due first thing Monday morning).
Think of it as a 4-day, non-stop math marathon, with completely untested problems made up by the prof. Surreal-- sometimes they were problems that didn't HAVE solutions.
Still. After that, I voluntarily took math every quarter until I graduated, and I was then the go-to girl in my grad school lab for advanced stats and for non-linear modeling. I
am the mathy person in about 95% of the professional settings I've been in since I got my B.S. Which is surreal for a kid that flunked algebra II and calculus I and II the first time through (really, not kidding). I never saw the point in Algebra II concepts until dealing with some advanced applications work later, honestly. To be fair, though, I also had a horrible high school teacher for that class.
That mathy way of
looking at problems was completely transformative for me in
every way. It flipped the switch for me into "growth mindset" and ultimately broke my perfectionistic inner voice.
If I could bottle that, I'd give it to every HG+ kid in America.
When I say past tense here, I mean most recently in trigonometry where my DD was attempting to learn in a vacuum due to an AWOL teacher, and no contact with classmates in a virtual setting. Not working. She's a high school senior this year, and that's where I have regrets-- one of her dearest friends would have been an AMAZING study partner, if only they'd lived closer to one another over the years. Sadly, they also plan to attend colleges 2h apart, too. But we've routinely used the other strategies outlined by JS, and I can attest to their efficacy.
It's the same pedagogical framework that I tried to set up for my own students in upper division analytical chemistry-- give them HARD problems to work, and let them work together on them over an extended (and self-determined) period of time each week.
