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.

## 2 comments:

The two are also fundamentally not equivalent in different way. You could have a kid do about 5 different problems, showing different skills and knowledge in the time it would take them to do the PARCC problem.

A better assessment of the strengths of the two tests would be to show the number of problems a child can reasonably do in a set amount of time from each, and see how many skills the child has to master to do well on those problems.

The PARCC problem has an even greater difficulty: A a student who is truly thinking critically might waste time puzzling over the following issues:

1) The problem specifies the number of seats in each vehicle type, not the number of passengers it can carry. Does the correct answer presume that you have added a driver for each vehicle when calculating the total number of people transported?

2) If you need to make room for drivers, are the teachers driving a vehicle? So is the number of people in the vehicles equal to 69 students plus 3 teachers plus a driver for each vehicle, or three less than that total since the teachers could double as drivers.

Admittedly, the three "correct" answers all exceed any the total number of students, teachers, and drivers, but how much valuable time might be wasted by a student who thinks about this issue?

In addition, there is a third issue:

Who is driving the vehicles? The problem only mentions three adults (i.e., the three teachers), but no combination of vehicles can accommodate all the teachers and students with only three vehicles. So a student who is thinking critically might well conclude that it is impossible for all the students to be taken on the field trip.

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