My teaching career began with sporadic part-time assignments in the seventies and finally became my full-time profession in the eighties. Of course, with decades of teaching experience under my belt, nothing can surprise me anymore.
During a prealgebra final exam, a student came up to me with a question. My students know that they can ask me questions at any time, even during tests. It's possible, of course, that I might respond by saying, “I can't tell you that,” but it doesn't hurt to ask. Sometimes all a student needs is the tiniest nudge, after which the light comes on in their eyes and they demonstrate their knowledge instead of their confusion.
That's the theory, anyway.
In this instance, my prealgebra student comes up to me with a question about finding the area of a rectangle. She points to a figure on her exam, and says, “Dr. Z, is this a square?”
I'm sure you know what happened next. I calmly prompted her to give me the definition of a square, after which she quickly perceived her mistake and returned to her desk prepared to solve the problem.
The first thing I really said, as best as I can reconstruct it, was “Gak!” After recovering my equilibrium and taking a deep, calming breath, I added, “Why do you think it's a square?”
She wasn't sure. She just wanted to know which area formula to use. Which was better, A = LW or A = s2?
Maybe it was my fault. I had focused on the notion of length times width for the area of rectangles, letting the area of a square fall out as a special case of no special interest. Besides, we were already used to the word “square” to indicate the product of a number with itself. Did we have to belabor it?
Evidently we did.
One of my students has made it to adulthood without ever learning the definition of a square. I remain capable of surprise.
I was pleased when—without undue prompting on my part—my student decided that she wanted to use A = LW to find the area of the rectangle. As I discovered later while grading the exam, she had proceeded to add L and W to get her answer. She gave me half the perimeter instead of the area.
Oy. I am a really bad teacher.