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by Joshua A. Taton, Ph.D. | September 11, 2023 | 2 min read

This post was featured by EdLight here.

One of the most important findings in education research is known as "opportunity to learn" (OTL). OTL can be summarized, neatly, by this line of reasoning: it is difficult—though not impossible—for students to learn something they haven't been taught; further, to ensure equity of instruction and alignment within schools and districts, opportunities to learn that are provided to students should be analogous to one another.

One way that alignment is hampered, of course, is when teachers receive mixed messages about what they are to teach. And without alignment, opportunities to learn differ by classrooms and schools, which—in turn—can impact the outcome of assessments. (It makes assessments less useful.)

Here's a concrete example. It's been known, for some time, that Pennsylvania's academic standards (or PA Core Standards) in mathematics need a complete overhaul. Desperately. (I'd encourage you to read the linked report and to write @governorshapiro to demand immediate action.)

One of the Eligible Content (EC) descriptors in Pennsylvania's Assessment Anchors (AA) for Algebra I—and don't even get me started on the unnecessarily complex relationship between the PA Core Standards, themselves, and the ECs and AAs—is:

A1.1.1.3.1. Simplify/evaluate expressions involving properties/laws of exponents, roots, and/or absolute values to solve problems. Note: Exponents should be integers from –10 to 10. 

What's important to know is that the ECs are supposed to represent the "conceptual and practical limits" of the items on which students can be assessed on the "PA Keystone Exam." (Also, don't get me started on the convoluted and unnecessary numbering system.)

Now, it's nice that the writers of this EC descriptor limited the exponents to integers from –10 to 10. But does that include –10 and 10?

And what about the roots? And why does this standard also include absolute value—unless they are alluding to the connection between the square root of x-squared and the absolute value of x?

Consequently, I've heard from educators around Pennsylvania that they teach:

• Only simplifying and evaluating square roots

• Simplifying and evaluating square roots and cube roots (but nothing else)

• Simplifying and evaluating rational roots (e.g., the square root of 2-cubed).

And, furthermore, the phrase "to solve problems" in the PA Core Standards often means "to solve applied problems" (or word problems). Since the EC descriptor, here, doesn't really explain or define what is meant by "solving problems," we are left to guess.

This certainly doesn't help with aligning instruction and assessments. Nor with providing equitable opportunities to learn to students across the Commonwealth.

I know that the committee that developed the PA Core Standards—and, later, the Assessment Anchors and Eligible Content descriptors—worked very hard. And I know enough about the political context, at the time, to realize that they had many cards stacked against them.

That said, I'm shocked that some of these under-specified issues—of which their are many—weren't caught and addressed as part of the process. One element, that I'd recommend Pennsylvania consider well before rolling out new standards, involves having them reviewed by outside experts who are known specialists in the field AND by teachers themselves.

I welcome your thoughts.