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The Common Core Math Standards: When Understanding is Overrated

Barry Garelick, via email:

Earlier this month, the Common Core State Standards Initiative (CCSSI)–a state-led effort coordinated by the National Governors Association Center for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO)–issued the final version of its math standards for K-12.
The draft standards were released in March and CCSSI allowed the public to submit comments on the draft via their website. Over 10,000 comments were received. The U.S. Coalition for World Class Math was one of the commenter’s and I had a hand in drafting comments. We were concerned with the draft standards’ use of the word “understand” and pointed out that the use of this verb results in an interpretation by different people for different purposes. I am pleased to see that the final version of the standards has greatly reduced the use of the word “understand”, but I remain concerned that 1) it still is used for some standards, resulting in the same problems we raised in our comments, and 2) the word “understand” in some instances has been replaced with “explain”.
I am not against teaching students the conceptual underpinnings of procedures. I do not believe, however, that it is necessary to require students to then be able to recite the reasons why a particular procedure or algorithm works; i.e., to provide justification. At lower grade levels, some students will understand such explanations, but many will not. And even those who do may have trouble articulating the reasons. The key is whether they understand how such procedure is to be applied, and what the particular procedure represents. For example, does a student know how to figure out how many 2/3 ounce servings of yogurt are in a ¾ ounce container? If the student knows that the solution is to divide ¾ by 2/3, that should provide evidence that the student understands what fractional division means, without having to ask them to explain what the relationship is between multiplication and division and to show why the “invert and multiply” rule works each and every time.