Math standards and Common core
Equity versus excellence, conceptual understanding versus procedural expertise, and classroom experience versus ivory-tower pedigree. When it comes to math instruction, opposing camps of experts dispute the correct set of priorities to emphasize among the above when directing how math is taught in K-12 classrooms.
Recently, the debate over math instruction has been mistakenly rolled into the debate over the Common Core and other state math standards. These standards are a set of academic targets. Their stated purpose is to create a roadmap for what students need to know in which grades to become college and career ready. Backers of the standards say they were intentionally written to be flexible—so states, districts, and educators wedded to different teaching styles could continue to teach math in the manner their leaders thought best.
Opponents of the standards have argued that, in actuality, the way the standards were implemented constituted a top-down imposition of how reading and math were to be taught in classrooms. Nonetheless, many of the social media posts objecting to “Common Core math” are actually objections to practices used to teach the math, rather than the underlying content of what is being taught.
Herein lies another frequent point of confusion. In recent years, political backlash to the Common Core led many states to “repeal” the standards. While these repeal efforts have satisfied the grassroots who objected to Washington interference in state curriculum policy, in most states, Common Core repeal meant changing the name used to refer to the academic targets, while keeping the substance of the standards in place. While many states no longer use the “Common Core” in a strict sense, in actuality, the majority of states’ standards are still aligned to the principles undergirding the Common Core targets.
Despite the conflation between the packaging of state standards, the actual substance of the academic targets, and teaching procedure, the real debate over the practice of how to best teach math is a longstanding one with serious implications that predates the development of the Common Core.
Alan Schoenfeld is a professor at the Berkeley School of Education with a high-level background in mathematics. In a 2004 paper entitled “Math Wars,” he traced back the politics of the teaching practices debate to the early 1900’s.
In essence, the paper argued that, historically, the political left has backed the teaching of a more accessible mathematics that prioritizes understanding concepts over rote repetition. The political right, meanwhile, has backed a focus on traditional mathematics that stresses rigor, memorization, and procedural skill.
In an email exchange with InsideSources, Schoenfeld said that the Common Core had become a “Rorschach test” that people use to project their feelings about education. So while the debate over math practices is real, and the Common Core aligned math standards actually are more amenable to progressive teaching styles, the math standards themselves do not mandate how the subject should be taught.
“I’m willing to bet that the majority of the people who blog about the Common Core and blame it for this or that pedagogy haven’t read the Common Core and don’t know that whatever pedagogy they’re reacting to was the product of a local decision,” wrote Schoenfeld.
So while it is true that some left-wing progressive groups have allied with the broader coalition of right-wing opposition to the Common Core aligned standards movement, the teaching practices commonly associated with the math standards are actually rooted in the political left’s historical preference for how math should be taught.
A physics professor fired the latest salvo in the ongoing debate last month by penning for Forbes: “Why Writing About Math Is the Best Part of Common Core.” The author’s work was a response to an article in the Atlantic from 2015 “Explaining Your Math: Unnecessary at Best, Encumbering at Worst.”
The left-leaning “reformers,” cited by Schoenfeld, argue that learning math should be made easier through visual models and encouraging students to write to prove understanding. The right-leaning “traditionalists” argue that the models quickly become crutches, and writing about math is a distraction from hours spent working with the numbers.
The Case for ‘Reformed’ Math Instruction
Steve Leinwand is a lead research analyst at the nonpolitical, nonprofit American Institutes for Research (AIR). His strong views in favor of more accessible math instruction are rooted in his previous work on the board of the National Council of Teachers of Mathematics. His arguments do not reflect the stance taken by AIR, which stays out of these debates as an institution.
“One of the positive and powerful qualities of the Common Core is that it supports learning mathematics in ways that gives kids opportunities to communicate” along with the expectation that those communications reflect “a manifestation of their reasoning,” said Leinwand.
Leinwand was speaking in support of the item that appeared in Forbes, in which a physics professor with school-aged children wrote: “explanation is an essential part of math and science. In fact, open communication of results among scientists is the crucial step that separates modern science from alchemy, and necessarily entails explaining how you got your answer” (emphasis in the original).
Leinwand’s argument is that educators should do everything they can to make mathematics accessible to all students by using all available teaching aids, including graphs, charts, pictures, words, and equations rather than solely teaching how to crunch numbers.
“The idea of practicing and practicing and regurgitating a procedure flies in the face of everything we know about how to take this body of knowledge called mathematics and have it work for everyone,” rather than just those at the top of the class, said Leinwand.
He argues that despite the noise, the Common Core, and the similar math standards states have held onto, are working for parents, students, and teachers. He rejects the arguments made by the traditionalists, whom he said are only animated about protecting their supply of high achieving math majors, rather than ensuring that each student has a solid foundation in the subject.
“Why the hell, after 100 years of that kind of math teaching” said Leinwand of the traditionalists, “was the U.S. doing so poorly, until recently?”
The Case for ‘Traditional’ Math Instruction
Jim Milgram is one of the traditionalists. A former mathematics professor at Stanford, Milgram was a lead author of a set of rewritten standards in California in the 1990’s that marked a backlash against the teaching practices promoted by Leinwand and the National Council of Teachers of Mathematics.
More recently, Milgram was a top math representative for California during the Common Core standards writing process. When the process was over, Milgram was the highest profile participant to refuse to endorse the math standards. He was featured prominently in a documentary “Building the Machine.” That movie was produced by the homeschooling lobby, which has been outspoken in its opposition to the Common Core.
While “Building the Machine” focused primarily on the hardball methods used to pound out the standards, which Milgram agreed were objectionable, his real opposition isn’t to the idea of having national standards, but instead to the quality of the Common Core. He argues that the final product is not rigorous enough.
“From the beginning I thought national standards were a very good idea,” but in the final calculus, he said, “the standards are nowhere near what they