Remember that Kamii quote from a few weeks back?
These errors are usually considered careless errors. They are not careless errors; they come from an inability to think.
Oh, and that other one?
Algorithms unteach place value
Yeah. They’re strong claims. Overly strong. “An inability to think” isn’t really right. “Not thinking in this circumstance” is closer to the truth. Kamii is not a woman of nuance. That’s part of what I enjoy about her work. But it does require interpretation.
All of which builds up to an entirely predictable scenario yesterday morning. Griffin (who is seven years old, recall, and whose ability to think has been well documented here) has been well schooled in traditional addition and subtraction algorithms this year, and has learned the lattice algorithm. He loves the lattice, although he struggles to make a lattice neatly enough to do the algorithm (for reasons that will become apparent when you see his handwriting below).
All of these are digit-by-digit, ignore-place-value-as-you-work sorts of things.
Griffin asked at breakfast, Is 86 divided by 22, 43? and wrote the following:
Kamii saw it coming…