In this week’s Problems of the Week, we revisit some claims found on the website of the Montgomery Counter, MD public schools (MCPS):
Computation and procedures were sufficient to reach success in previous curriculum [sic] and assessments. The CCSS requires students to show greater depth by demonstrating their Understanding, Computing, Applying, Reasoning and Engagement (UCARE) in mathematics. As a result, the math content at each grade level is more difficult than previous curriculum [sic].To illustrate this, the MCPS makes the following comparison:
The MCPS website asks us to note that the PARCC question “assesses similar content a year earlier”; that it’s “a multi-step question that requires application of content learned in earlier grades”; and that “it cannot be successful ly completed by memorizing a procedure, it requires reasoning.”
Note, however, that while the most obvious strategy for the MSA problem involves dividing a three-digit number, the most obvious strategy for the PARCC problem involves repeatedly multiplying and adding one and two digit numbers. It’s less the case that the PARCC problem is similar in its content to the MSA problem, or that it requires more reasoning, than that that it requires a heck of a lot more busy work.
The vice of simply memorizing a procedure is inadequate for either problem: in both cases, you have to figure out which procedure(s) to apply. What about the virtues: reasoning and “number sense”? Assuming that speed affects test performance, these are at least as important in the MSA problem as in the PARCC problem. In the latter, where only one choice is possible, reasoning tells you to use number sense to eliminate choices, and number sense immediately rules out A and B as too small, and D as ending in the wrong digit.
Side note: many people assume that speed tests (especially multiple choice speed tests) measure only rote knowledge. But they’re also a great way to measure conceptual understanding. Performance speed reflects, not just rote recall, but also efficiency, and efficiency, in turn, is a function of reasoning, strategizing, and number sense.
Not that the MSA 5th grade problem is something to be proud of. For a math curriculum that is actually more challenging than the old MCPS curriculum, one need only look backwards a decade at a something that several MCPS schools tried out for four years and then, despite positive results, abandoned (for more on that, see this very illuminating article by Barry Garelick).
That spurned something was Singapore Math.