Before we get into the next unit on ratios and proportions, I was thinking about how students complain about homework, and find repetitive drills boring. I will speak about interleaving and blocking in one of the early chapters of the book, but do want to go on record amidst “learning scientists” and researchers that as beneficial and necessary as interleaving is, it is also necessary to learn the procedures that will eventually be interleaved—that is, some blocking in the beginning is essential.
Within the blocked exercises, there should be some variation in difficulty and complexity, starting with easier problems that provide the scaffolding and experience to tackle the more complex ones. Despite variation in difficulty and challenge, students still will complain that the exercises are boring. Some of these students are the same ones who can practice the same basketball shots in solo practice for hours.
Of course there’s a difference between practicing basketball shots and doing math problems. That difference is the narrative going through the head of the one shooting hoops. That narrative goes something like this: “It looks like he may have to give up making a shot; too many people on him—but wait! He’s going up for it and—he shoots, he scores!” Something like that.
I had a similar narrative going when I did my algebra homework: “And he’s going at breakneck speed; so far no one can touch him in the trinomial factoring competition. But now they’re getting a bit harder—the leading coefficient is negative two, how will he handle it? I DON’T BELIEVE IT—he factored out negative one and then he factored the whole thing into two binomials. The crowd is on its feet. He’s going to the semi-finals for sure!”
I relayed this technique to my daughter who waited a few seconds after I finished before giving me her pronouncement: “You really were quite the nerd, weren’t you, Dad?”
I hadn’t looked at it quite like that, but yes, I suppose I was. And I’m not ashamed of it either!