Thursday, January 13, 2011

Math Myths

Bruce Landsberg wrote about Math Myths in this month's AOPA Pilot. Here is the letter to the editor I sent about the column.



Since I am both a CFI and a mathematics professor, I was intrigued by Bruce Landsberg’s “Math Myths” column in January’s AOPA Pilot.

The FAA’s Aviation Instructor’s Handbook (FAA-H-8083-9A) details four levels of learning: rote, understanding, application, and correlation. Landsberg emphasizes the rote part of learning, which is unusual in a safety-oriented column. Safety comes from application, which comes from understanding.

To see the value in understanding, consider the role of formulas, which express a lot of information in compact form. In Landsberg’s example of the increase in landing distance from increased speed, he presents a rote rule, but that application comes from under- standing the equation for lift. Correlation occurs when one uses the same equation to understand minimum control speed (Vmc) in a multiengine aircraft.

Many former myths about aviation were dispelled by mathematics. For example, pilots who did not understand the difference between true air speed and indicated air speed thought that they flew faster at lower altitudes. It took the mathematical model of the International Standard Atmosphere, as outlined in the beginning of Aerodynamics for Naval Aviators, to set us straight.

The real danger lies in not understanding that mathematical problems like computing takeoff distance, endurance, and landing distance must be solved before flying. No amount of mathematical skill can compensate for inadequate preflight planning. Flying well demands that we use our whole intellect, not just part.

The mathematics of flying is still not fully understood, especially in the area of atmospheric phenomena like icing and microclimates. We have to rely on “conceptual understanding” to handle these phenomena safely. But the line between conceptual understanding and superstition is very thin. Tackling these problems does not mean that every pilot needs to study more mathematics, but understanding and applying their solutions means that many pilots should.

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Thursday, August 28, 2008

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.




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.




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.




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.




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.

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