The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal calculus, although the eighteenth century shyness toward it had long lost all point.
Yes, I took a remedial algebra course in college. I struggled in math in high school and didn’t have confidence to plunge in with a for-credit algebra course. The remedial course gave me a lot of confidence so that when I took the for-credit algebra course it was fairly easy and I got a ‘B,’ of which I remain proud today!
Through algebra you easily arrive at equations, but always to pass therefrom to the elegant constructions and demonstrations which usually result by means of the method of porisms is not so easy, nor is one's ingenuity and power of invention so greatly exercised and refined in this analysis.
My algebra was relatively poor. I found it very difficult to use equations that substituted numbers - to which I had a synesthetic and emotional response - for letters, to which I had none. It was because of this that I decided not to continue math at Advanced level, but chose to study history, French and German instead.
At the heart of good education are those gifted, hardworking, and memorable teachers whose inspiration kindles fires that never quite go out, whose remembered encouragement is sometimes the only hard ground we stand upon, and whose very selves are the stuff of the best lessons they ever teach us. Most of us, no matter how long ago it's been, can name our kindergarten teacher. Our first music teacher. Our junior high algebra teacher. Good teachers never die.