Terror and Delight: Pre-Calculus, Year One

I’ll just be out with it:  I’m terrified of Pre-Calculus.  Actually, I’m terrified to teach Pre-Calculus.  In my experience Pre-Calculus is, at best, a year-long cram session of sorts – its all of the stuff you need just before you get to enroll in Calculus.  At its worst, Pre-Calculus is a mind-numbingly boring, hopelessly disconnected mess of skills, techniques and mathematical miscellany.  The problem is that students actually do need to learn most of this content and these skills are essential to their future success in mathematics; the are just too many topics to cover well.  My colleage David calls it, “Mathematical weight-lifting.”

There is no point in the spectrum drawn by these two extremes that is palatable for me.  I feel a bit like Jesus when he promises to “Spew the lukewarm from his mouth.”  I would much rather not teach this course, but I have been quick to comment on how it might be fixed.  I talk a good game about the ills and evils of Pre-Calculus but this year, I am getting to test out my theories.  I can see my dad smiling as he says to me, “Well son, you’ve got the talking part of that done now don’t you?”

So, here I am teaching Pre-Calculus and I am now responsible for making this year meaningful.  Turns out, that’s pretty hard.  But, I am excited to report that I now believe its actually possible.

I actually knew last spring that I would be teaching this course.  I did some planning with my colleague who also teaches this course but then went on to a blissfull summer filled exactly zero hours spent preparing for teaching this course.  As you can imagine I was sweating as summer came to a close.  I was, after all, about to take on this fire-breathing demon having spent too much time in the last few years bragging to the locals about all of my skills.

Task number one was to create meaningful learning targets.  I’ll skip the painful details but I can say with certainly that, THAT IS REALLY HARD.  So, I have a workable version of targets for our first unit of study.  Now, on to the real work: How to teach this in a way that forces student thinking.

I have waxed pedagogical about the value I place on student thinking and discourse in my classroom, so I set out to create meaningful discussions and problems worth solving within the Pre-Calculus content.  For the past two days my students have worked on understanding function composition and decomposition.  We made analogies to the telephone game, different ways to cook eggs, legos and Russian nested dolls.  They saw our work as solving puzzles and bless them, they rose to the challenge and thought deeply for two days.

I am elated.  Our work has meaning.  We built new skills in a context, not skills that exist for their own sake.  We worked in groups because the problems we were solving required collaboration.

The beast of Pre-Calculus is still very much alive, but I have new-found confidence that he can be defeated, that this year can be so much more and so much different than what Pre-Calculus has been for so many students.  It is possible.

I’m pretty excited about that.