Revisit of “rote understanding”

I originally wrote about this in an October 2014 article published in Heartlander.  I re-read it recently and decided it’s still true.  I have reprinted it here with minor updates.

During a course in math teaching methods I took in ed school, I watched a video of a teacher leading his students to do a variety of tasks, ostensibly to teach them about factoring trinomials, such as x² + 5x + 6. But rather than teaching factoring techniques, as is done in traditionally taught classes, the session was a mélange of algebra tiles (plastic squares and rectangles used to represent algebraic expressions) and a graph of the equation being factored (a parabola).

The teacher “facilitated” the class into making connections between the factored equation and where the graphed parabola crossed the x-axis. The class had not done factoring, quadratic equations, nor a host of other things that would have…