What Teachers Know

Here are two parallel tales about teaching. Mathematics and flying share the tradition of using teachers who have a "knack" for the subject, which is great for students who have the knack.

It as around 1990. I was teaching at a small college in New York State. The Space Shuttle was flying a high-inclination orbit, so I did some calculations and determined that it would be visible overhead. Cool, I thought, and made a flier that explained the trigonometry. I invited people to join me to watch. The problem was that it was mid-Winter with temperatures around 10F/-10C, and the pass would be at 2am. Only one student joined me. It turned overcast and we saw nothing, but it was worth the try. He went on to get a PhD in Mathematics.

I offer to take all of my instrument students on a long cross-country, the kind involving an overnight and some real weather and real terrain. Most decline; in fact, only one has really gone through with it. He did a great job. The best part was after he botched the ILS approach into Pendleton, Oregon. We landed for a snack and a discussion, and he shook it right off and flew a great ILS into Portland. He went on to become a captain at a regional airline.

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What do teachers know? More and more I think that teachers know nothing, not in the sense that we don't know our subject, but in the sense that we don't know our students' minds. The point of the two stories is that I really managed to get into the heads of two students, but they were like me as far as goals and dedication. Not everyone is like me, or even like you, which is how it should be. But how can we teach people who see things so differently? A private pilot student can become a good pilot even though he may never get an instrument rating, probably won't become a commercial pilot, and will almost definitely never get an ATP. A calculus student can become a good scientist or engineer or economist, even though he may never take any more mathematics, probably won't become a math major, and will almost definitely never get a PhD. Everyone has unique tastes and talents and desires and backgrounds. So by definition the teacher's goals and motivations are, or were, different from the students. What worked for you may not work for them.

Some of you may disagree, but there is an art to algebra. Algebra is actually the simplest thing in the world, much simpler than baking a cake (which I am doing as I write). There are four operations, a fixed rule for deciding in which order to do them, and an associative law that guarantees that everything is unambiguous. Algebra is simpler than music, which has twelve tones, not just four, and all of the complications of rhythm and dynamics and feel. But both simple systems produce an endless range of expression, which is part of what makes them art. There is also art in knowing when to factor, when to simplify, and when to just leave it alone. There is art is in seeing that "3+0" carries more information that just "3", even though they are equal: the former fits into a pattern, while the latter is just a number.

But algebra is different than flying, right? Algebra is abstract, and flying is visceral. That is of no consequence: what matters is that in each case the operation is easy, so learning means learning to perceive, learning where to look and when to look and how far out to focus and to what to expect when you get there.

The teacher's disadvantage is in never seeing what the student sees. There are exceptions, like the two students above, but they began with goals like mine. They're easy to teach. The work and the art are in teaching the student who is completely unlike you by learning and speaking the student's language.

Here's an example. In a Cessna 172, the nose pitches up when flaps are added. "Don't let the nose come up," I say as the student reaches for the flap lever, "Hold this attitude." I watch the windshield view change from grass to clouds, but the student cannot perceive it until the airspeed decreases, which is already too late. How could I have said it differently? Should I insist on rote ("When you lower the flaps trim nose down one turn of the wheel.") That may be enough! It might not have been enough for you, but it may be enough for this student, for now. The commercial student needs to understand the pitch change and explain its aerodynamics; the instrument student needs to apply this knowledge to keep the proper pitch attitude during configuration changes; the ATP candidate needs to correlate this knowledge with other effects of control manipulation.

You need to need to know more than the student; that's why you became an instructor.

I'm afraid that we end up teaching people to do all kinds of things the same way that we teach children to talk: we allow them to hang around and listen, and as they try we offer critiques. It works pretty well for talking, but while a Chomskyite might claim that we are pre-wired to learn talking, and some people appear to be pre-wired for mathematics, nobody claims that we are pre-wired to learn flying. While my twins might have learned to talk listening to me and their mother converse over dinner, my twin-engine students are less likely to learn from watching me and my wife try to synchronize our engines. (If you know what I mean...)

Knowing that just watching isn't enough, we throw stuff at our students. "Here's the theory," we say, giving one each more or less according to individual taste. "Here's a drawing of what it looks like," although we only produce a cartoon. "Here's a silly mnemonic," we say, reciting "True Virgins Make Dull Company." We make up colorful reminders: "Tail in the weeds!" I say before a short field takeoff, meaning to use the full length of the runway.

(In calculus class all these efforts go for naught when the student can only think about how attractive the girl next to him is.)

The airline-oriented flight schools and the military count on their students working hard to make up for any deficiencies in the teaching, but that model won't work in general aviation. Besides, it's inappropriate. So as teachers we must toe the line between discipline and laisser-faire. Most important of all, we have to offer the student what we have to offer and then listen.

Brain vs. Muscle

In flight instruction you just don't know what's going to work. The same thing is true in classroom instruction, but in flight instruction there is so much more intimacy. It's possible and even, I hope, likely, that in my classroom career I have said or done things that really helped students understand, but in a room with 32 faces it's easy to look at the wrong one, and miss the "Aha!" across the room.

One-on-one teaching is more satisfying. Take this evening: I was helping my 10-year-old son with his math homework, and for some reason there was something that just didn't make sense to him. I tried several explanations, really groping around trying to see what worked, and when I found something that worked his face lost that frustrated look and he actually said, "Oh! I get it!"

The difference between Math and Flying is that flying involves more muscle memory. Here are there examples from flight instruction in which I got a little lucky and said or did the right thing at the right time, and had the joy of watching someone jump the gap.

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A new glider student was having a lot of trouble flying formation with the tow plane. He was overcontrolling. We made wider and wider swings behind the poor bewildered tow pilot until I would have to take over. This is not unusual. My words and demonstrations just weren't getting through, even though I thought that they were brilliant. (It doesn't matter what the teacher says, it matters what the student hears.)

Almost in desperation, I suggested that he hold the stick closer to its base. I was trying to reduce his lever arm, which might or might not stop him from overcontrolling. It did! He got into position behind the tow plane and stayed there.

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A power student was struggling in the traffic pattern. He did OK when I made the radio calls, but he was getting ready to solo and I soon would not be there to help. Each time he thumbed the push-to-talk switch he would climb or descend or slow down or speed up or do something that he shouldn't have done.

This is not unusual, either. I had to find a solution. Sometimes I have done this on the ground, having the student mimic the actions in the pattern while telling a story. But that wasn't working.

He asked me to fly a pattern so he could watch. OK, I thought, but I try not to do a lot of flying while teaching. (More on this later.) So I flew a pattern.

"You key the mike with your forefinger," he said.

"I do?" I was unaware of this.

"I'm going to try that, too."

So on the next pattern he used his forefinger rather than his thumb to key the mike. Do not ask me to explain the neural pathways, or wrist physiology, or vagal response, but ... it worked! From then on his patterns were fine.

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A glider transition pilot was having a devil of a time with slips. As you probably know, a slip is when you use opposite bank and rudder to make the plane fly a little sideways. This increases the drag substantially, so you can lose a lot of altitude. This is so common in gliders, where we tend to approach the landing with extra energy, that it is required on the flight test.

This student already had a power license with a tailwheel endorsement, so I knew that he had done slips before. Maybe I didn't bear down enough, thinking that this was just a matter of checking off the box before sending him for a flight test, but he just couldn't do it. I explained, I waved my hands sideways through the air, I coaxed, cajoled, and encouraged, but it just wasn't taking.

Remember: I am a blogger. I like words.

On our second session of slips, I gave up on words and said, "Do you want to see me do one?" I don't like to fly while instructing; we are there for the student to fly. In this case the student was already a pilot, so I was even more reluctant to take his flying away from him.

So we told the tow pilot to take us to pattern altitude and I took the controls and did a slip. Not even a great one, really a barely adequate slip.

"I think I've got it!" he exclaimed. We did another pattern tow and now he did a slip and did a pretty good job if it, too.

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The unifying thread in these three stories is that words are not enough to teach an activity. We don't learn baseball, piano, driving with a clutch, how to draw blood, or a gazillion other physical skills by words alone. In medicine, the rule is "see one do one teach one:" the words come last, not first.

In other words, Do what I do, not what I say.

Student Joy

I flew with my student and friend Dennis the other day.  He has about six hours now and is having the usual trouble relaxing in the cockpit.  There were a few low level bumps, which bothered him, but even though the air smoothed out when we reached altitude I could see that he was still a little anxious.

We did steep turns (his first), and they were good, then we had the planned engine failure.  "What are you going to do?", I asked.  "I forget!", he said, but recovered and set up a good glide and picked a good field.

Then it was time for rectangular courses.   I was feeling a little discouraged since there was little or no wind.  I toyed with the idea of forgetting the whole thing and going home.  But I figured that there would be some training value in the maneuver, so I reluctantly pointed out a farm that took up a whole section, and Dennis started flying a rectangle around it.  I was busy pointing out landmarks and turnpoints and the like, and he was busy looking outside the airplane.  That's when it struck me: his hand was relaxed on the yoke, and we were flying straight and level effortlessly.  Eureka!  He can fly.