Maybe Repetition Had A Place, After All

I'm finding that many of the common Math terms or techniques that used to be second nature to my generation when we were in high school have much less of a foothold (not to mention name recognition) now than they used to. For example, I referred to "the origin" in the context of graphing a function recently, and the high school student I was working with responded, "Where's that?" [It's the point (0,0) on the Cartesian plane, for those who don't remember.]

One of my two high school students has never heard of cross-multiplication, and therefore never uses it to simplify his work when solving equations where the variable is in a denominator.

Even something as fundamental as the concept of factoring an expression (or, conversely, expanding a factored expression) gives pause to some students today. One of my pupils knew factoring had something to do with dividing everything by a common value, but thought that he could do that to a standalone expression. He attempted to turn 6x + 8 into 3x + 4 by arguing that he could simply divide everything by 2.

The only conclusion I can come to is that teachers perhaps are more leery of repetition these days than they ever were with past generations. I know that some of the updates to the curriculum over the past 10+ years has specifically been aimed at making the material more interesting and relevant, which is a laudable goal. But does that mean that gone are the days when a high school Math teacher would stand at the front of a classroom and step his or her class through an elaborate solution, slowly and carefully explaining each step while using the correct terminology? I didn't know that (0,0) was called "the origin" because I read it in a textbook; I knew it because Mr Pease, in Grade 9 Math, narrated the solutions that he blackboarded every day and referred to that particular point by that specific name every chance he could. In other words, he used repetition to drill the correct name into our heads. After a few weeks of that, even the slowest student in the class had picked up on the fact that (0,0) was simply "the origin."

Perhaps that style of edification has gone out of fashion now, since I often read that teachers standing at the front of the room "lecturing" isn't an effective way to educate. And I'd agree that a non-stop diet of that can be pretty boring. But has the pendulum swung too far the other way now, such that students are missing out on the chance to learn proper Math-speak? When I tutor, I try to bring some of that old-school approach back. I do my best to lead by example, in the hope that my students will pick up a trick or two from me... not because I tell them they have to, but because I use them myself, over and over. The jury's still out as to whether or not it's working at all (these things take time, after all). But I'm hopeful.