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…
Overthinking my teaching 
What I find frustrating is the reaction of some people to Kamii’s work, who have only done a superficial reading of it, and reject it because it doesn’t match with their intuitive notion of how learning math works. Our intuition is wrong so often – this is one of the primary reasons we do research rather than relying on an Aristotelian perspective of the world.
My son once added 78+78 and got 1416. Interested in reading more about this author? professor? you speak of. Does she have a blog or articles? By the way I just ordered some abacases (abaci?) not sure what the plural is here – for my two girls. I haven’t really used them before; I’m interested in reading up on how these deal with place value.
Chris
My 9 year old son will be encountering some of this soon as our school uses Everyday Mathematics through 6th grade. I have mixed emotions about it. I generally like how verbal their approach is and I think he is learning some good math ideas. However, I teach in our upper school and have a number of pretty good students who claim that they never moved beyond lattice models for multiplying and that they never understood what they were doing with division. They probably would not have made Griffin’s mistake but they might not arrive at any correct solution comfortably. sigh…
A bit off topic here, but I am reaching out for the collective wisdom of the readers of this blog. Our school is undertaking the beginnings of a STEM initiative in the fall. Our director has an idea to explore the election process across the curriculum through different lenses and she has asked me to bring the math department on board with some activity ideas that are appropriate for different math levels. I know that NCTM has a few activities posted in the Illuminations section and I am hoping to gather some wisdom from the math blogosphere. My email is jdoherty@wyomingseminary.org and I thank you in advance for any ideas to share.
Thanks also for letting me invade your space and for opening my eyes on a regular basis to important teaching and learning questions.