The expert may not be the best teacher

As we mentioned last week, our navigator was out of the office teaching a professor how to use his sextant.  Having decades of experience in both the observations and the calculations involved, he certainly has a firm grasp of the subject.  But that’s not always the quality you need in a teacher.

A sextant is used by sailors at sea for celestial navigation, that is, for figuring out where the ship is by measuring the angles of stars (and other bodies) above the horizon. The concept was familiar to our professor, especially in the particularly simple case of Local Apparent Noon, but he’d never actually gone through the process.

Now, most mariners are not astronomers or mathematicians or professors of Physics.  So over the years the process of taking a sight and reducing it to a useful number has been simplified to an easily-remembered sequence of steps, which you can do without having to think of the theory behind them.  This is good when you haven’t had enough sleep or are under stress, things that happen at sea.  Our navigator has done them so many times that they happen almost automatically.  But that could easily have been an opaque mastery: an exercise of rote memory, taught to someone else without any real understanding of what’s going on.

In this case it wasn’t.  Our navigator does know the theory, and more importantly how and when to simplify an explanation.  But the lesson still took much longer that he’d anticipated, a useful reminder.  And it highlighted a larger lesson: mastering the material is not the same as being able to teach it.

In fact our consultants have all been on the other end of this process, for instance in learning mathematics.  They’ve concluded that the subject should not be taught by mathematicians.  The reason a mathematician studies the subject, his or her motivation and the things he or she finds interesting, are not the same as for a scientist.  It was far from unknown for our astronomer to ask a question and a mathematician to answer a different one.  (“Why?” is a pretty ambiguous word.)

Of course, understanding the subject is necessary.  Indeed, a teacher must have a much better grasp than anything to be demanded of the students.  This is not only to retain credibility by being able to answer questions; it’s necessary to be able to make the deep connections that allow useful explanations.  But it’s also necessary to make the connection all the way to the students.