Critics’ math doesn’t add up
Until now, I have generally kept out of the politics of the Common Core State Standards, in favor of helping teachers, districts, and states understand and implement them. But the recent editorial by James Milgram and Emmett McGroarty was so misleading that it demands a response.
Just how rigorous are the Common Core State Standards?
- The standards received a perfect score for content and rigor in the Fordham Institute’s 2010 review.
- Research by William Schmidt, a leading expert on international mathematics performance and a previous director of the U.S. TIMSS study, has compared the Common Core to high performing countries in grades K–8. The agreement was found to be high. Moreover, no state's previous math standards were as close a match to the high-performing countries as the Common Core.
- Milgram and his circle are a decided minority on the question of Common Core. The presidents of every major mathematical society in America support the Common Core, including the American Mathematical Association, the Mathematical Association of America, and the National Association of Mathematicians. These presidents lead organizations representing literally hundreds of research mathematicians.
Milgram and McGroarty have misrepresented the standards in an attempt to frighten policymakers and the public. To read their editorial, you would never know that the Common Core State Standards require students to demonstrate fluency with the standard algorithm for each of the four basic operations with whole numbers and decimals. (See pages 29, 35, and 42.)
Even the previous California standards never expected California students to demonstrate fluency in the standard algorithm for each of the four operations. (That oversight has now been corrected, thanks to California’s adoption of the Common Core.)
The standards also require students to know addition facts and multiplication facts from memory. (See pages 19 and 23.)
Milgram and McGroarty describe a “two-step process” in the Common Core for bringing students to fluency with the standard algorithms. But I was one of the lead writers of the Common Core, and I do not recognize the two-step process they are talking about.
These authors’ mischaracterization of the standards is extreme. There are no expectations in the Common Core for students to invent, construct, or discover algorithms. One reason no such expectation can be found is that “constructivism,” whatever you think of it, is a teaching method—and the standards do not prescribe teaching methods.
It is true that fluency with the standard algorithm is explicitly required only after students have worked with place value and the properties of operations. But clearly, nobody would expect a child to demonstrate fluency with the standard algorithms of arithmetic without building up to them first. Milgram himself appeared to understand this point perfectly well just a week or two ago, when, I am told, he testified before the Arkansas legislature that the right way to prepare for the standard algorithms is by “first carefully studying and understanding the meaning of our place value notation, as they do in the high achieving countries.” Although Milgram’s Arkansas testimony appears to have been the model for his editorial with McGroarty, that particular sentence was left on the cutting-room floor.
Also left out was the sentence in which Milgram characterized the Common Core as being “better than 90% of the state standards…that they replace.” Milgram’s positive assessment of the Common Core in Arkansas gives the lie to the hysterical tone he takes in the editorial.
The Common Core State Standards aren’t “fuzzy math.” In fact, calling the Common Core “fuzzy” is not only misreading the standards—it is also, I fear, sanctioning others to misread them in the same way. When Milgram and McGroarty minimize the standards’ attention to algorithms in order to terrify the public and policymakers, they give comfort and cover to the true proponents of “fuzzy” math, who are only too eager to act as if the standards don’t really require the standard algorithms to be taught and learned to fluency.
Tough standards don’t implement themselves. State departments of education should ensure that their implementation efforts fully respect the balance of rigor in the standards—including the Common Core’s rigorous expectations for fluency with pencil-and-paper computation.
James Milgram, Ze’ev Wurman, and Sandra Stotsky have been barnstorming the country trying to convince state legislators that the sky is falling because of the Common Core State Standards. One point they commonly raise has to do with the definition of college readiness in the standards.
What are their stunning revelations? In mathematics, they are twofold: First, that the Common Core includes three years of mathematics at the level of Algebra II. And second, that this level of mathematics will not prepare you for a STEM major, like physics or engineering, or get you into more selective universities.
But both of these things are obvious. And it’s factually incorrect to say, as these critics frequently claim, that the definition of college readiness in the Common Core is pegged to a community college level. The definition of college and career readiness in the standards is readiness for entry-level, credit-bearing courses in mathematics at four-year colleges, as well as courses at two-year colleges that transfer for credit at four-year colleges.
Milgram, Wurman, and Stotsky want the term “college ready” to mean something beyond Algebra II. They want to call students college ready only if they go beyond Algebra II to take trigonometry, precalculus, or calculus. At the risk of giving more oxygen to what strikes me as being fundamentally a dispute about language, what Milgram, Wurman, and Stotsky think of as “college ready” is what I might call “STEM ready.” I think it makes sense to most people that college readiness and STEM readiness are two different things. The mathematical demands that students face in college will vary dramatically depending on whether they are pursuing a STEM major or not.
Students in high school should take as many rigorous mathematics courses as they can. Students who intend to pursue STEM majors in college should know what is required. All of that was true before the Common Core, and it remains true today.
The Common Core has every promise of increasing the number of students in our country who actually attain advanced levels of performance. Nothing is being “dumbed down” here. Just because the Common Core State Standards end with Algebra II doesn’t mean the high school curriculum is supposed to end there. California had calculus standards before adopting the Common Core, and the state still has them now, as it should. The difference in California today is that better standards can help more of California’s students gain the strong foundations they need to succeed in calculus.
States still can and still should provide a pathway to calculus for all students who are prepared to succeed on that pathway—not only because it is at the heart of many STEM fields but also because calculus is one of the greatest intellectual developments in human history.
But the real problem, not only in California but everywhere, is that so many students who take calculus today aren’t ready for it. The most common score on the AP Calculus exam is 1 out of 5. This striking level of failure is just one of the reasons we need the stronger foundation of the Common Core State Standards to propel students into advanced mathematics.
Research shows the standards to be world class. The presidents of every major mathematical society in America support the standards and attest to their rigor. James Milgram, Ze’ev Wurman, and Sandra Stotsky are entitled to their opinions, but misrepresenting the Common Core does a disservice to policymakers and the public.
Jason Zimba was a lead author of the Common Core State Standards for Mathematics and is a founding partner of Student Achievement Partners, a nonprofit organization. He holds a BA from Williams College with a double major in mathematics and astrophysics; an MS by research in mathematics from the University of Oxford; and a PhD in mathematical physics from the University of California at Berkeley.
This article was updated on August 8, 2013, for the Education Gadfly Weekly.