The Area of A Basketball Court

One of my classes this semester is Exercise Science. It's a grade 12 University level course that has 14 of our top students. Many have their acceptances in-hand and some will be pursuing health related post-secondary studies in Canada or the US.

I've really enjoyed this class because it has taken me back, in a new-fashioned way, to my teaching-roots. Yes, it's true, some time ago I wanted to be a Physical Education teacher and I graduated with a degree in that very same field. (Many of you just said, "WHAT?")...Pause...Teaching computer science was my (very successful) back up plan.

It's been a long semester and this is a very heavy course with so much content that is new for my students. We've worked hard to learn about anatomy, physiology, and biomechanics. As you can imagine at this time of year, the students are tired and keeping them engaged in new material is tough! 

Our current topic is "Human Growth and Development". Wednesday we were looking at Piaget's Theory of Cognitive Development.  I'd like to say they were absorbing this riveting material but by the fourth stage you might be yawning too: "Formal Operational Stage ... children demonstrate intelligence through their ability to solve increasingly complicated abstract problems using logic, and by understanding how to use symbols related to abstract concepts."

I had lost at least one to slumber and two more were looking ready to nod off.  It was time to make this a little more real.

I didn't have to look to hard to find a real story that had "abstract problems", "logic" and "symbols" -- I teach math, after all.

I started to talk about the difference between real-life problems and math textbook problems. They gave the usual puzzled, "who is this guy?" look.  Then I gave a problem from our grade 10 text -- "If the area of a tennis court is represented by the equation A = x² + 9x + 8, what are the lengths of the two sides?"

Instantly, one my grade 12's blurted, "That's real basic, sir". Everyone in the room knew how to solve this problem -- but they missed the point (ah, the curse of knowledge...). Becoming slightly animated and narrowly focusing on "real-life problems" vs "abstract problems" I said, "Ok, three things: First, in real-life, you are never going to need to find the area of a tennis court. Second, in real-life, a quadratic equation will never be used to represent area and third, in real-life, you will never measure a rectangle's length with a binomial."  This is why grade 10 students fit nicely into Piaget's stage 4 and why grade 12 students do not.