This is certainly a bizarre piece of scribbles to include on my blog. I might as well post a picture of chicken scratches, or sastrugas in the snow. But it is an authentic piece of scratch paper from this past weekend when I was recording my son Bruce(6.5)’s thinking out loud while he solved a long division problem. His current strategy is to think about long division in terms of multiplication, and to keep multiplying until he gets the right answer.
One of the biggest questions people have when they first hear about Constructivism is “How in the heck would you do long division?” The answer to that question is that there are lots of ways to solve long division problems, and that each child will explore and then settle on a strategy that best makes sense to that particular child’s brain. Maybe that will be choosing to use the traditional algorithm, maybe not.
In a true Constructivist program, the traditional algorithm would not be introduced until the child had already mastered several other methods. If a teacher introduces the traditional algorithm too early, thinking and exploration could suddenly halt, which would really crimp the development of true number sense.
This is why it is important for me as a parent to give Bruce lots of opportunity to learn how to do long division at home many months before he learns at school through Houghton Mifflin Math Expressions, which is not “Constructivist enough” in my opinion. Stay tuned for more examples of creative ways to do long division!