Beyond the question and the answer: the process

Where do you even start?

I’ve noticed a pattern in the way people learn to teach math.

At first, someone is thrilled just to know how to solve a particular kind of problem and show someone else how to do it. They can teach a student how to carry out a procedure that they have learned.

The next step in the development of the aspiring teacher or tutor is to lead a student toward an understanding of a concept strong enough that the procedure becomes self-evident.

In this way, usually through strategic questions, a student can be guided toward answering his or her own question, both in the moment and thereafter.

Math is a thinking exercise. So ideally, we leave room for the person we are teaching to do their own thinking.

Teachers, and even coaches, sometimes get this backward. We are so in love with the material we are teaching that we try to transfer it from ourselves to our students instead of allowing them to take an active role in the process.

For example, guitar teachers often provide their students with chord charts for songs they would like to learn. Common song requests are prepared in advance, and custom charts can be made on the fly, during the lesson. The teacher listens to the song piece by piece, quickly figures out the chords, and ten minutes later, the student takes home a completed chord chart in order to learn the song herself.

However, learning to figure out songs by ear is, itself, an important part of learning to play guitar. Week by week, instead of simply modeling that skill, a teacher should teach his own students how to do it. That way, it’s not only the teacher who is getting the benefit of the lesson. The student should get a chance to sharpen her ear, too.

This is not to say that teachers and coaches should take a passive role, like Betty Draper’s dour and taciturn psychoanalyst on Mad Men. It’s not very good coaching to simply turn every earnest question around (“What time is it?” “Well, what time do you think it is?”). Ideally, there is a feeling of collaboration between the teacher and the student, the coach and the coached, that forms a scaffold that knowledge and skills can be built upon.

If I’m teaching you, I’m not just walking you through the steps to get the answer; if I’m coaching you, I’m not just asking you questions so you can figure it out yourself. There is a balance in which I’m sharing not only the procedure, but the process — the questions I would be asking of myself along the way, the bigger picture and how the work fits into that. I’m helping you to build the framework that will allow you to make your own decisions and guide yourself.

It’s nice to know the answer or how to get it, but that’s not the important part of teaching. The task is to help someone else to get there, which requires a much deeper understanding of the material. The teacher can’t simply explain it. They can’t just show someone. It’s a start, but it’s not enough.

If I want to teach you to swim, mere instructions won’t get the job done. Demonstrating my own swimming ability doesn’t do it, either. And I certainly can’t just throw you in and force you to thrash your way to figuring it out on your own. Instead, I might start as my own excellent swim instructor Ann Grinnell did, by helping you to get accustomed to the water. Let’s put our mouths in and blow bubbles. Let’s put our faces in! Let’s hold onto the side of the pool and kick. Now let’s use a kickboard and practice kicking across the pool. Each of these experiences helps the student to become familiar with the water and gradually experience the feeling of buoyancy and mobility that will allow her to be a successful swimmer.

The best teachers and coaches don’t have all the answers — they have a deep understanding of the journey to find those answers. They are there to guide your way. You’ll always have a companion to help you make sense of what you’re seeing and learning and challenge you to discover more along the path. You’ll walk it (or swim it) yourself, but you won’t be alone.