A Few Words About How I Coach

When I coach mathematics, I want the student or client, no matter their age, to set the agenda as much as possible. For the motivation and direction of what they are developing or learning to come from within them. Thus, one of my goals is for the client’s interests and their goals to govern our time together.

Another goal is for the client or student to develop a sense for what mathematics, at its best, can be. And that’s a lot of things: from a useful tool for problem solving in everyday life to a collection of art forms.

As a result, I have been drifting away from coaching students held within public or private schools and forced to take standard mathematics courses such as (at the primary level) algebra or precalculus. Focused largely on isolated abstractions and the (sometimes ad hoc) formal rules to manipulate these abstractions, devoid of meaningful connection not only to the students’ interests but to the ongoing history of the world at large, I have come to see the teaching and content of these courses as misleading: they usually lead students away from any sense of depth or playfulness in doing mathematical work. In my experience, only students who already have this sense of depth or playfulness – because their interests are already vested in mathematical work – will understand the point of the courses. Most students I have worked with leave school with little if any sense for what mathematics, at its best, is.

I no longer want to be complicit in teaching a widespread misunderstanding of what mathematics is.

Recently, a student of mine who is quite young, barely a so-called “teenager,” asked to learn probability theory. As I teach him and aid him in learning probability, he learns many other things. He develops his skill in working with fractions since calculating probabilities involves operations with fractions (all probabilities lie between zero and one, inclusive). He learns some set theory and basic operations with sets, since the foundations of probability involve working with finite sets. He learns combinatorics (permutations and combinations) since calculating probabilities often involves determining the sizes of large sets. We play with coins, dice, and especially cards: we discuss different kinds of poker: Five Card Draw, Seven-Card Stud, Razz, and so on. His motivation for learning probability and developing the above skills doesn’t come from external, ad-hoc authority, but from within. I hope in turn he is developing a sense for how mathematics proper relates to the wider world and to how playful it fundamentally is.