A great article titled Waiting for Supermath came through my inbox today. It includes commentary on a video (below) of a third grader showing how she solves a four-digit addition problem using what she learns at school, or the Investigations curriculum, versus what her mother (a math intervention specialist) teaches at home, the traditional “stacking” algorithm.
What strikes me most about the video is that the first method, using the graphic model, shows what seems to me an overuse of the conceptual level of addition.
One strength of Singapore Math is that it starts with the conceptual level, which is essential, but then it moves to the abstract. In this process, the student starts with concrete representations of a problem, like manipulatives, then to pictorial or graphic representations, and finally to the algorithm, once they have mastered the concept.
But in the video, the girl starts out solving the problem with what could be drawings of base 10 blocks – and way too many of them. This is keeping her stuck at the concrete stage and leads to inefficiency and inaccuracy in her calculations.
It also strikes me, as the video points out in the end, that this method of teaching creates the myth that larger numbers are harder to calculate. Is this what we want to perpetuate in our students? I know if I had, I wouldn’t have had a group of second and third graders who decided, on their own, to learn 50 or more digits of pi.
One other note: I did use Investigations for one year in a middle school classroom. That was the year that some parents and I convinced the administration to finally adopt a curriculum that made sense. And what did they choose? Singapore Math!
Watch the video: