I have been following the #stopcommoncore hashtag on Twitter to keep abreast of the debate that is growing across the country about whether states should continue to implement the Common Core State Standards (CCSS). One argument against the implementation of the CCSS that has been advanced on a number of occasions is the idea that a particular lesson aligned to the CCSS is evidence that the CCSS are bad. This argument is an example “affirming the consequent”, which is a logical fallacy.

The argument, which I will call the “Bad Assignment” argument, made the rounds perhaps most recently in response to a story reported, among other places, in the Daily Caller and EAG News. In this story, a sixth-grade, Washington DC history teacher assigned students a project where they were asked to revise the Bill of Rights. Many people found this assignment, which you can find here, objectionable. Assuming their premise is true–that the assignment is bad–the “Bad Assignment” reasoning goes as follows. The assignment was in a Washington DC classroom. Washington DC has adopted the CCSS. If a state (or, in this case, a district) adopts the CCSS, then the assignments and curriculum are mandated to be aligned to the CCSS. This assignment is bad. Therefore, the CCSS is bad. Put more succinctly in modus ponens form:

If the CCSS are bad, then the curriculum aligned to the CCSS is bad.
The curriculum aligned to the CCSS is bad.
Therefore, the CCSS are bad.

In an “affirming the consequent” fallacy, we assume that some consequence of some idea is proof that the idea is true. It is represented formally here:

If P, then Q.
Q.
Therefore, P.

A clearer example of how this reasoning is flawed is stated below:

If it rains, the sidewalk will be wet.
The sidewalk is wet.
Therefore, it rained.

The argument is flawed because there are other ways that the sidewalk could have gotten wet. There could have been a water balloon fight in which water balloons exploded on the sidewalk. Or I could have sprayed the sidewalk down with a hose in order to illustrate a logical fallacy. Either way, even if the first two premises are true, the reasoning does not follow.

The reason that the “Bad Assignment” argument does not work is that there other ways in which the assignment could have become bad. For example, it could have been poorly aligned, and therefore not REALLY representative of a CCSS-aligned curriculum. If it IS aligned (and I think it probably fulfills these history literacy standards), then it is possible that the assignment is bad in other ways–by asking students to use important skills in inappropriate ways. For example, most people would agree it is important for students to be able to compose logical arguments, as the CCSS contend. However, it may be inappropriate to have students learn that skill by constructing logical arguments about whether it is better to use heroin or cocaine. This assignment regarding the Bill of Rights may be just an inappropriate way to fulfill the standards–the standards themselves needn’t be the reason why the assignment is bad.

Some may contend that the argument in modus ponens form should be written like this:

If the curriculum aligned to the CCSS is bad, then the CCSS are bad.
The curriculum aligned to the CCSS is bad.
Therefore, the CCSS are bad.

This is not a valid argument either because its initial implication is vulnerable. It does not necessarily follow that a single instance (a curriculum aligned to the CCSS) can imply something about a more general class (the CCSS). The only way this could be true is if every assignment in every curriculum aligned to the CCSS was bad. If the “Bad Assignment” argument took this form, it would be basing its conclusion on a few examples, which is a hasty generalization.

The “Bad Assignment” argument is a bad argument. There are many valid criticisms of the CCSS, but the “Bad Assignment” is not one of them. I hope the debate, which is sure to continue, can do so as a civil discourse involving valid logical reasoning. If that happens, the debate can be a productive exercise in democratic education policy development.

ACKNOWLEDGEMENT: Thanks to Thomas J. Dall Jr. Esq. for his consultation on the formal logic in this post.