“Wax on! Wax off!”
Most people can identify these words as being from the classic 80s movie “Karate Kid”. In the film, Daniel, a karate student, is told his lessons will involve waxing a car. This makes no sense to him, but he follows instructions. Following this “lesson” are others involving painting the fence, sanding the floor, and painting the house. None of these things make sense to Daniel and his frustration grows until he is ready to quit. Mr. Miyagi, the wise old teacher, then shows Daniel the reason for all of the chores. It is revealed the moves are actually made to defend oneself using karate (e.g. “wax off” becomes a way to block a punch).
While this movie was a favorite of mine for a long time, I propose that this is not a great way to teach, especially in mathematics. Unfortunately, it is a very familiar model used in many math classrooms including, at times, my own. The teacher shows the class some skills which seem tedious and uninspiring, followed by another lesson unrelated to the previous one. Students must feel like each day brings another task disconnected from what they want to understand, another set of mysterious rules the teacher inexplicably finds exciting.
At least Daniel had a moment where Mr. Miyagi ties it all together and shows how all of these skills can be used. Often in math classes, this moment never happens. Or if it does, it is meaningless or unimportant to the students and the connection to their world is lost.
Recently I was challenged by an article by Catherine Ulrich, in which she states, “If instruction does not help the student adapt her ways of experiencing the world…while at the same time demands are made on the student to change her external behaviors to match those of the teacher, then the external behaviors she is asked to enact by her teacher become increasingly divorced from her reality. School math becomes an increasingly irrational and illogical endeavor, and the student will lose the ability to engage in problem solving” (Ulrich, 2014). (emphasis added)
In short, if the tasks presented by the teacher do not help a student make sense of their world, the behavior becomes a chore instead of a tool for understanding. Even worse, it becomes irrational. As weeks, months, and grade-levels go by, the wider this gap can become between the math behaviors expected by the teacher and the sense-making of the students. No wonder students begin disliking math. No wonder teachers repeatedly say, “the kids just don’t get it.” Daniel didn’t enjoy engaging in irrational behavior, and nobody else does either.
Mr. Miyagi’s model of teaching might be great in 80s feel-good films, but we should avoid this model in our classrooms.
Ulrich, C., Tillema, E. S., Hackenberg, A. J., & Norton, A. (2014). Constructivist model building: Empirical examples from mathematics education. _Constructivist Foundations_, _9_(3), 328–339\.