Letter on teaching, to Bryn, when she taught Math at UP

BRYN MAI P. DAVID

Dear Bryn,

How do you find teaching? Are your students learning from you or with your kind of guidance? Do they do well enough in their tests and class exercises? No teacher ever knows for sure the degree by which her students learn from or with her. Test results are very indirect feedback, as you can figure out. They may be due to the students’ own work and study outside the classroom, more than to their instructors or professors. What a teacher can immediately hope for is whether she transmits her knowledge and understanding of her subject-matter as lucidly, briefly, and with as much life as possible. What she can aim at is whether what she transmits is received at least 75% or so. She has this item of knowledge. A set of ideas. She puts order into them, so that they assume a form, almost like an object. She transmits them in the most effective medium or vehicle she can master or muster. And she hopes that they’ll be received and understood in approximate form and order. That is, the recipient gains the knowledge or the set of ideas.

I imagine that mathematics is harder to teach or transmit. I base my imagining from the number of persons who readily admit, out of at times unmeant humility tinted with lowliness, unsolicited, that the persons are weak in mathematics. And that, despite their formal preparation in some prior and basic courses, they come forth as though they’re blank boards as regards mathematics. I imagine it is harder to excite an average person with mathematics, inasmuch as most if not all of mathematics, by definition and domain, lacks the body–flesh and blood, as it were–which the person can perceive with the colors of feelings, emotions, and motives. In this respect, it is amazing that some uncommon individuals see something in the abstractness of mathematics, which approaches the vividness and colorfulness of objects of life. That is, they not only perceive things which assume the dimensions of the physical, but derive thrill, meaning, and personal repletion or replenishment. It takes aptness to pure law and order to enjoy points, lines, geometries, number systems, theorems and proofs.

[At this point, Dr. David asks Bryn to derive an equation for two sets of numbers, with instructions like “Take the first value in each pair as X and the second as Y.”, and so on.]

I’m ok. Weatherwise, Winter has come. Snow fell to as much as four inches last night. It will again fall come Saturday and Sunday. And the temperature stays sub-freezing. It’s good to eat, just to keep up with the need for energy to deal with the cold. It’s nice to be indoors, where it’s warm, like Weiss Hall normally, to work on things that only require minimal physical exertion but a good deal of mentation. If food is aplenty, it’s impelling to indulge and overeat. I imagine that, today being cold and Thanksgiving when food is plenty at many tables and the mood is for celebrating, a lot of people will indulge. Perhaps tonight, I’ll cook more than I usually do for a single meal. And I myself will eat more.

Try to find time to write. I like to remember, as it were, my first days of teaching, in your shoes. Love, Dad

Temple University

Written 23 November 1989

Received 19 December 1989