Moments from #nctm12

Freshly back from Philadelphia, prepping for the last week of classes. Moments, quotes and ideas from sessions that left a lasting impression on me…


Constance Kamii is amazing. I love a person who takes a strong stand and lives true to it. Kamii is that person. Among my favorite Kamii quotes from her session on Friday:

“You can tell kids all kinds of things…and they will obey you, and that’s sometimes called learning.”

“If I have not published on the uselessness of base-10 blocks, it’s because Teaching Children Mathematics has rejected my manuscripts. They are ignorant and in power, so…”

“Algorithms unteach place value”

“I think math educators are too hung up on writing. The important things in math is thinking. If they can think, they can write and it doesn’t really matter what they write.”

“Numbers are not seeable. Three is three and ten is ten, no matter how you arrange them.”

“These errors are usually considered careless errors. They are not careless errors; they come from an inability to think.”

Like I said…a woman with principles.


Karen Fuson’s session, on the other hand, left me puzzled. I could not tell whether she was doing her duty in reporting out details of the Common Core Progressions for 5—8 rational number and proportion, or whether she actually believed that nonsense. Two examples…

Regarding the proportion \frac{6}{10} = \frac{x}{5}, she asked Is that a fraction? The answer, surprisingly was No.

Consider the ratio A:B. She claimed that the C in y=Cx was \frac{B}{A} and emphatically not \frac{A}{B} because of the proportion \frac{y}{x}=\frac{B}{A}. But this presumes that we always write ratios so that the independent variable is first. But this is nonsense. In most mathematical relationships, which variable is dependent and which independent is arbitrary, and it is certainly arbitrary which we write first in a ratio.

I left feeling like no progress had been made in the last eight months since I hashed out some of these issues with Bill McCallum.


Jack Smith and Funda Gonulates spoke about their research work on the measurement strand in the Common Core. Their talk was everything the Progressions are not. Thoughtful, research based and useful. If you are at all interested in the development of measurement in elementary and middle school curriculum, you should read their paper.

My favorite quotes from the session were both Jack’s:

“The cognitive action is at the corners.”

“Length is the workhorse of learning measurement.”


Breedeen Murray put together the kind of teacher session I love. Active and practical with a huge helping of ideas. Lots to think about.

“In the puzzle world, the rules are like your axioms. And if you change the rules, you get a different system.”

“It is productive to build the formal structure of proof outside of working on the formal content…is students are juggling both proof and content, the cognitive load may be too high.”


Once I finished chuckling immaturely over how much Ed Berger was talking about my “doodle”, (and his own, to be fair), I captured the following:

“Where do questions come from? Out of thin air.”

This was in the context of a mnemonic (which I have mostly forgotten-I found it to be rather forgettable) for his 5 keys to creative thinking (or something like that). And as such it’s not really clear whether he meant that.

I’ll be coming back to this topic later in the week, when I’ll report on moments outside of sessions.

9 responses to “Moments from #nctm12

  1. I really want to read more about Constance Kamii’s work, simply because she is the target of so much consternation by the WISE Math and similar movements. She must be on to something if these people disagree with her so much.

    • Kamii starter kit sent by email. Enjoy.

      • akismet-457375c2686d2ce6aa9740f00ee2f8f4

        I hadn’t heard of the WISE Math people so I looked them up. They’re simply another arm of Mathematically Correct, HOLD, and the like. Utter baloney, closed-minded traditionalists who couldn’t care less if YOUR kid isn’t learning mathematics as long as THEIR kid gets the same approach to math that worked for them (and thus, their kid gets “ahead” in the race to the “top”). It’s twisted, it’s generally racist, classist, sexist, and pretty much every form of anti-progressive, anti-child thinking imaginable, EVEN when those subscribing to it are self-professed liberals or socialists. I would say to ignore them, but to do so would be foolish. Their American cousins have done immeasurable damage over the last two decades.

      • Yeah, I received it, read it, and printed it out for some other key people at my school. Great read, thank you!

  2. I tracked down the full quote from Kamii that I’ve always loved, “There is just no end in capitulating. If your score gets higher, the principal is going to want higher and higher scores. All that for whom? Not the kids. My recommendation is: Do what’s best for the kids.” Amen.

  3. Plz send a Kamii starter kit to me too! :^)

    Those two quotes from Jack Smith don’t sound like much on their own. I’ll go read the paper, but I’d love to know what they mean to you.

  4. I’d like the “starter kit” too, if you could.

  5. Me three! (in regards to the much-in-demand starter kit).

    And thank you for your kind words about my session. It’s good to know that I wasn’t the only one who had a good time and learned something. 🙂

  6. Pingback: This is entirely predictable (Algorithms edition) | Overthinking my teaching

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