Learning, teaching, and knowing

Photo: Marcus Hansson via Flickr

When you learn things, you know them. Then, if you try to teach someone else, you realize you don’t know them, and you learn them at a deeper level.

I recently tried to teach my teenager to parallel park. I’ve been successfully parallel parking for many decades, of course, but we needed to practice together to get ready for the driving test. So we parallel parked — a lot.

Eventually, I provided not just useful advice on what was going wrong and right in each attempt, but a sort-of algorithm for doing it well, developed on the fly.

The kiddo took the driving test and failed parallel parking. Apparently, I taught it the wrong way. The driving instructors taught it a better way.

Do I know how to parallel park? Or do I just think I know?

The five stages of knowing

Whenever you learn a skill, you go through five stages.

  1. Ignorance. For example, you don’t know how to parallel park.
  2. Learning. Trial and error. You park, sometimes you get it right, sometimes you don’t. You form a mental model of what you are doing and refine it.
  3. Mastery. You can perform the skill successfully and regularly. Parking is no longer a problem.
  4. Internalization. If you do something enough, you no longer need to think about it. For most of us drivers, there is no longer a mental checklist associated with parking, we just do it. Sometimes called “muscle memory.”
  5. True understanding. You understand what you’re doing well enough to teach it. I didn’t get here with parallel parking, but the instructors at the driving school have.

Understanding writing through editing

I have always liked to teach. As a result, when I reach stage 4, I often don’t stop. Curiosity drives me to introspection, which helps me to get to stage 5.

Let’s take writing as an example. I got lots of advice and feedback from writing teachers. In my head, I was always asking why. Why is passive voice a problem? Why are transitions important? Why must lists be parallel?

Eventually, I mastered writing (stage 3) and then became an unconscious writer (stage 4). But I didn’t stop there.

Good writers typically edit as well. When editing, you are learning as well as teaching. As I edited people, I began to see what sort of problems they had with writing, and how I could help them. This developed my ideas about writing well beyond mastery or internalization. I could teach writing, both to adults and to homeschooled teenagers.

I could write a book about it.

Algebra, bicycle riding, coaching, and understanding

I’m good at math — I was in a math Ph.D. program for a while. I internalized algebra long ago.

As I taught both of my kids to do algebra, I could see where they were succeeding and where they had problems. This enabled me to teach them well, because I had reached stage 5.

I also taught both of my kids to ride a bike. The younger one had a lot of trouble. Because I was a stage 4 bicycle rider (aren’t we all?), I understood too well how to ride and not well enough how others learn to ride. But I realized that the kid was having trouble doing steering and balance at the same time. Riding on a bike path requires going straight, which isn’t easy if you’re still working on balance.

I conceived the idea of going to a flat, relatively soft place to learn — a baseball field. We started in the center of the diamond. Freed of the need to go straight, the kid concentrated on balance — and in short order, mastered the skill. Even as the learner reached stage 4, I was moving on to stage 5.

I am now teaching my older kid how to ride on the road. He learned balance a long time ago, but now he will be riding on the streets to go back and forth to college. So I am teaching road safety, shifting, cycling form, maintenance, and what to do when there’s a pothole in front of you on a busy street. Stage 5 stuff.

How to learn anything better

It’s fine to master things and stop there. Not everyone needs to become a parallel parking or algebra coach.

But if you’re learning a new skill, pay close attention in stage 2. Notice not only what you’re learning, but how you’re learning.

Coach others when you are in stage 3. Learn more about how things work by seeing how others learn.

Don’t rest at stage 4. Internalized skills crystallize at this stage. Whatever you know how to do, you will have to learn how to do differently, because the world is changing.

I’m privileged to have learned writing and algebra at stage 5. I’ll never get there for parallel parking, but I hope to for other skills, like public speaking. Stage 5 is a great place to be — and worth striving for.


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  1. An interesting application/variation on your “5 Stages” — Our Computer Science professor assigned each of us students a topic from a reference manual for us to teach to our classmates. As I recall, it was a Computer Architecture class and I would have spent less than an hour on my assigned material if I was on my own. Mastering it enough to teach it took 10 hours.
    I can’t recall any other involvement in this student-as-teacher model (although doing a major presentation to customers and colleagues is similar.) But now retired from computer engineering, I am a volunteer math teacher to small classes of adults. I’m waiting for an adequate alignment of students and subject matter in which I can try this role reversal technique.

  2. lots of worthwhile thoughts, here … my prob is often getting stuck at the mastery stage and not having enough natural self confidence to move on to the insight stage … keep rechecking and rechecking till eventually sink into a bog of frustration.

    prac prob arises with fluidity.