The Common Core Math Standards

Are they a step forward or backward?

By and

Education Next talks with Ze’ev Wurman and W. Stephen Wilson

0032_common_core_mathMore than 40 states have now signed onto the Common Core standards in English language arts and math, which have been both celebrated as a tremendous advance and criticized as misguided and for bearing the heavy thumbprint of the federal government. Assessing the merits of the Common Core math standards are Ze’ev Wurman and W. Stephen Wilson. Wurman, who was a U.S. Department of Education official under George W. Bush, is coauthor with Sandra Stotsky of “Common Core’s Standards Still Don’t Make the Grade” (Pioneer Institute, 2010). Wilson is a professor of mathematics at Johns Hopkins University, served on the National Governors Association-Council of Chief State School Officers “feedback group” for the Common Core standards, and was mathematics author of Stars by which to Navigate? Scanning National and International Education Standards in 2009: An Interim Report on Common Core, NAEP, TIMSS, and PISA.

Education Next: Are the Common Core math standards “fewer, higher, and clearer” than most state standards today? Can you provide some specific examples where you think the Common Core marks a step forward or backward?

Ze’ev Wurman: Common Core standards may in fact be clearer and more demanding than many, though not all, of the state standards they replaced. The Fordham Institute reviewed them last year and found them so. While I have no reason to doubt the technical quality of that review, there is good cause to note what it does not say.

It does not say that Common Core standards are fewer. Indeed, if one compares them to the better state mathematics standards like those of Minnesota or California, they are more numerous. Minnesota’s standards fill 42 pages and California’s 59 pages, while the Common Core takes 73 pages even without the advanced statistics or calculus sections that are included in California’s standards. Counting the standards rather than pages, in grades 1 to 4 California has, on average, a few more standards than Common Core, but in grades 5‒8 the Common Core standards are more numerous than California’s.

Fordham’s review does not unequivocally say the standards are higher, either. They may be higher than some state standards but they are certainly lower than the best of them. For example, the 2008 report of the National Mathematics Advisory Panel, Foundations for Success, called for fluency in addition and subtraction of whole numbers by the end of grade 3, and fluency in multiplication and division by the end of grade 5. This is also what California calls for, along with high achievers like Singapore and Korea. (Japan and Hong Kong finish with multiplication and division of whole numbers even earlier, by grade 4.) Yet the Common Core defers fluency in division to grade 6. Fractions are touted as the Common Core’s greatest strength, yet the Common Core pushes teaching division of fractions to grade 6 without ever expecting students to master working with a mix of fractions and decimals. Students in Singapore, Japan, Korea, and Hong Kong achieve fluency in fractions and decimals in grade 5.

Nor are the Common Core standards necessarily clearer. They may be clearer than many state mathematics standards, but they still tend to be wordy and hard to read. Table 1 compares a few grade 4 California standards with their Common Core counterparts.

Andrew Porter, dean of the University of Pennsylvania’s Graduate School of Education, recently evaluated the Common Core standards with his colleagues, and their conclusion was stark:

Those who hope that the Common Core standards represent greater focus for U.S. education will be disappointed by our answers. Only one of our criteria for measuring focus found that the Common Core standards are more focused than current state standards…Some state standards are much more focused and some much less focused than is the Common Core, and this is true for both subjects.

We also used international benchmarking to judge the quality of the Common Core standards, and the results are surprising both for mathematics and for [ELA].… High-performing countries’ emphasis on “perform procedures” runs counter to the widespread call in the United States for a greater emphasis on higher-order cognitive demand.

Another recent analysis, by University of Southern California professor Morgan Polikoff, found the Common Core mathematics standards similarly repetitive, and hence as unfocused across elementary grades as the state content standards they attempt to replace, with only somewhat less redundancy in the middle grades.

In summary, analyses of the Common Core standards find them to be mediocre and not obviously better than many sets of state standards.


W. Stephen Wilson: It turns out that nearly everyone was in favor of Common Core standards in mathematics if, and this is a big if, they got to write them. As it turns out, no one got to write the standards. A committee wrote them. Worse, the committee was hired by the very states whose standards would be replaced, so states got first crack at suggesting “corrections” to the standards. The pressures on the writing committee must have been enormous. The only reasonable expectation was that the result would resemble some sort of middle way between the states’ various standards. What is surprising is that the standards don’t rank in terms of quality in the middle 20 percent of state standards, but, instead, fall in the top 20 percent.

There is much to criticize about them, and there are several sets of standards, including those in California, the District of Columbia, Florida, Indiana, and Washington, that are clearly better. Yet Common Core is vastly superior—not just a little bit better, but vastly superior—to the standards in more than 30 states.

Where this gap is most obvious, and most important, is in laying the foundation for college readiness in mathematics early, by grade 6 or 7. Judging by state standards, few people see a connection between elementary school mathematics and college math, let alone really understand how the foundation is built.

Arithmetic is the foundation. Arithmetic has to be a priority, and it has to be done right. A number of things can and do go wrong with state standards for arithmetic in elementary school.

With the introduction of calculators, many states have downplayed the importance of arithmetic, apparently not realizing its true educational value. Instead, they spend time on statistics and probability, both of which Common Core has tossed out of early elementary school. Another thing that states love is geometric slides, turns, and flips, sometimes presented every year in grades K‒11, perhaps under the mistaken belief that they are really doing mathematics.

Fewer than 15 states are explicit about the need for students to know the single-digit number facts (think multiplication tables) to the point of instant recall. States love to have kids figure out many ways to add, subtract, multiply, and divide, but often leave off the capstone standard of fluency with the standard algorithms (traditional step-by-step procedures for the addition, subtraction, multiplication, and division of whole numbers). For example, only seven states expect students to know explicitly the standard algorithm for whole number multiplication. Fractions are even harder to find done well. Standards for fractions are generally so vague that nearly everything is left to the reader. Often states expect students to develop their own strategies or a variety of strategies for dealing with fractions. For example, only 15 states mention common denominators. Common Core does a pretty good job with arithmetic, even a very good job with fractions.