Part of CCSS-math 3.OA.5 may be ‘untestable’

As I looked over some of the items released by the New York State Department of Education, it occurred to me that the standards themselves, the new Common Core, have not been subject to review, testing, or close scrutiny. We can learn a great deal from New York’s blunder.

I am still a big fan of the standards themselves. If taken as they are, the standards promote critical thinking, perhaps at too young an age but critical thinking nonetheless. However, we are soon going to have to realize that some of the standards might just be beyond our ability as developers of standardized tests.

Case in point: The third-grade math standard OA(operations and algebraic thinking).5(distributive property). The standard says, “Apply properties of operations as strategies to multiply and divide. Examples: … Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property).”

The problem here, as New York test developers discovered, is that kids don’t learn how to perform the order of operations using parentheses, brackets, or any grouping symbols until fifth grade. This means they cannot be expected to know to use the parentheses in the above standard to perform the 8 × 5 and 8 × 2 before adding the two products together.

There is a third-grade standard that addresses order of operations, but it’s for word problems involving a maximum of two operations. Here, in “(8 × 5) + (8 × 2),” there are three operations: multiply 8 × 5, multiply 8 × 2, and then add 40 + 16.

What this means is the distributive property can’t be tested based on the strict grade-level notions of the Common Core itself. The standards are self-contradictory in that in order to solve a problem—or choose between answer options—for the distributive property in third grade, students need to have mastered a skill that is in the Common Core first at the fifth-grade level.

Another way to say this is, if you put an item on the test that tests the distributive property, you’re going to have to use parentheses. Parentheses are beyond the understanding of third graders, according to the Common Core itself. This means teachers and schools can’t be held accountable for this understanding in students, and items that test the distributive property in third grade are unfair.

It’s only through more precise testing and a thorough analysis of the results from each test question for each standard that we will uncover those parts of the Common Core that work within the assessment boundaries the Common Core document sets for itself and repeal all the parts that don’t work.

The bottom line is, we have to test kids somehow. Federal law requires it. You may agree or disagree with the implementation of Common Core, but it would be more practical to find a way to make it work in your classrooms. This can only be done by trial and error, along with a complete disclosure of the results of field testing. I’m sure there are other places within the set of standards that could be improved or need to be marked as “untestable” at a certain grade level, and the people who create the tests have got to listen to this type of analysis.

About the Author

Paul Katula
Paul Katula is the executive editor of the Voxitatis Research Foundation, which publishes this blog. For more biographical information, see the About page.