Pythagoras Lost

A few years ago I volunteered to help coach a team for a mathematics competition called MathCounts at my child's middle school. During a practice session the following question was asked:

Does the Pythagorean Theorem apply to all triangles or just right triangles?

The young man on the hot seat confidently answered, "Only to right triangles."

The math teacher said, "No, it applies to all triangles."

It was all I could do to stay in my seat. I have a degree in mathematics, but any schoolboy knows that the Pythagorean Theorem applies only to right triangles. The math teacher had just eliminated the student from our mock competition.

Showing all the restraint I could muster, I raised my hand and pointed out that the Pythagorean Theorem did in fact apply only to right triangles and the student had answered correctly. The teacher informed me that she had not been sure of the answer and the previous day she had asked several others in the teachers lounge and they had convinced her that the theorem applied to all triangles.

This teacher was a middle school mathematics teacher with a degree in mathematics. I do not know whether I was more concerned that she did not know the answer with certainty or that the other teachers were able to talk her out of the correct answer.

I have always believed that a great teacher is one who can lift the corner of the tent and let students peer inside to see the magic. Unfortunately teachers like Ms. Bourbaki (not her real name) are unable to see the magic themselves much less impart a sense of wonder to their students. What a shame.