SMP elaborations — two questions

[ekmath]

I have been using the elaborations of the SMP with elementary teachers and have found them enormously useful. Two questions have come up in this work that may be useful as the document gets further refined and expanded.
In MP6, the following sentence, “They calculate accurately and efficiently and use clear and concise notation to record their work” led some readers I was working with to connect precision with efficiency. I think the relevant part of this sentence for elaborating MP6 is the use of “clear and concise notation” rather than efficient calculation. It may be worth noting that.

A second issue I would like to raise is further elaboration about the meaning of the phrase “critique the reasoning of others” in MP3. Readers may associate critiquing the reasoning of others with “criticizing” the reasoning of others. The examples in the elaborations convey the way elementary students construct mathematical arguments. The elaborations could help us communicate that critique and criticize are not synonymous. Students are engaged in critiquing each other’s reasoning when they are coming to understand and evaluate a peer’s sound reasoning in a valid solution, not as the word may connote, finding the shortcomings in a faulty solution (although students may also engage in troubleshooting problematic arguments and revising them to make them better).

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