Many years later, I realized the algebra teacher was both bored with the topic and unable to realize at least half the class couldn't follow him. For all I know, he was a fine, perhaps even a brilliant algebraist; I can assure you, however, he was an utterly incompetent teacher.
More in spite of than with my father's well intended, but equally rigid, bungled "help," I muddled through the year with barely passing grades, and looked forward to geometry in dread verging upon horror. To my astonishment, geometry was veritable child's play for me: I could see what was going on. The idea of having to prove things gave me pause at first, but once I was over that internal barrier, I was off and running. I brought home an A at the end of every grading period, and was one of the stars of my class. Being able to see what I was doing was half the difference; the other half was the teacher, who accepted at face value geometry isn't easy for everyone, and did his best to teach it this way, that way, and as many other ways as we students needed.
My junior year's advanced algebra class was misery all over again. To the extent I could graph things, I made clear sense of them: about what you'd expect of an artistic, verbal kid; to the extent I had to work in formulæ, I was in over my head: about what you'd expect of a kid who'd made sense of geometry rather than algebra. I memorized, memorized, memorized, and muddled through with Bs and occasional Cs. Again, the teacher knew the material inside-out, frontward, backward, upside-down, and every other whichway, but clearly didn't understand all students don't learn algebra the same way.
Senior year trigonometry wasn't a breeze, though nothing like the misery of algebra and advanced algebra. Again, I could see much of what was going on in graphs, and that year's teacher was versatile rather than set in his ways.
I went on to teach assorted subjects from college freshman English to graphics software to safe shooting and concealed carry. At the start of every course, I've made a point of telling my students: "What matters isn't what I teach, but what you learn. If you don't get something, let me know, please: I don't read minds."
Is any given class about teaching or learning? I say that's all the difference in the world.
Well said and an excellent post on the subject. Your experiences mirror mine in many ways. Ninth-grade algebra was a struggle and convinced me, incorrectly, that math wasn’t my thing so I stopped there as nothing further was required, at that time, for HS graduation.
My college major only required a minimal 4-hour math course. When I was commissioned from Army ROTC into the Field Artillery, I found out the folly of my choices because trigonometry was going to be part of missile flight firing calculations. It’s amazing how motivation can remove misplaced “fear of math” and I found out I actually understood it, likely in the same way you did with geometry and trig.
My next epiphany was when I went into construction and got another exposure to practical geometry/trig when figuring stairs and curved balcony openings for railings. Then I went to grad school where statistics were my next hurdle that I actually understood because the applications seemed very graphic.