Structuring the mathematical practices

In the progressions project we’ve been discussing how best to represent the standards for mathematical practice. The practices are signposted throughout the documents, but we’ve also been thinking about how to provide some structure for the practice standards that will help people avoid fruitless tagging exercises in their efforts to integrate the practice standards into the content standards. If you think about it long enough you can associate just about any practice standard with any content standard, but this sort of matrix thinking can lead to a dilution of the force of the practice standards—if you try to do everything all the time, you end up doing nothing. This diagram is an attempt to provide some higher order structure to the practice standards, just as the clusters and domains provide higher order structure to the content standards.

About Bill McCallum

I was born in Australia and came to the United States to pursue a Ph. D. in mathematics at Harvard University, met my wife, and never went back. I am a professor at the University of Arizona, working in number theory and mathematics education.
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One Response to Structuring the mathematical practices

  1. Tracey Dunn says:

    Hi Bill!
    I have a quetion about how to present a double number line diagram for the following problem:
    “the ratio of trucks to cars in the parking lot is 2:5. If there are 40 cars in the parking lot, how many trucks are there?”
    I need to explain to administrators how to draw a double number line for this problem. I am pretty sure I know how to model and discuss it. But, I would like your feedback on how you would do it, and relate it to the Mathematical Practices.

    Thank you,

    Tracey