Common Core State Standards: Mathematics Proficiency

Like the Common Core State Standards (CCSS) for English language arts and literacy, the CCSS for mathematics have been structured to correct the failed pedagogies imposed by the education monopoly that have made most public high school graduates unqualified to perform jobs leading to a middle-class way of life and uncompetitive with workers in other nations, dragging down our economy as well as limiting their opportunities.

I examined the causes and outcomes of this national catastrophe previously in "Our Mathematics Problem." Progressivism and postmodern multiculturalism harnessed mathematics education to the advocacy of “social justice.” Standard algorithms and knowledge developed over centuries in the West were cast aside in favor of student “construction” of their own ways to solve mathematical problems.

The CCSS establish grade-specific standards defining what students should understand and be able to do in mathematics by the end of each K‒12 year. The CCSS also return to more traditional, coherent, focused, and rigorous instruction.[1]

In response to calls to abandon the CCSS, two UC-Berkeley mathematics professors, Edward Frenkel and Hung-Hsi Wu, argue in an op-ed in The Wall Street Journal:

Mathematical education in the U. S. is in deep crisis… caused by the way math is currently taught in schools. Today, most students are forced to learn mathematics through textbooks that are often incomprehensible and irrelevant. These textbooks, which are widely adopted across the states, create mediocre de facto national standards—and, worst of all, alienate students from the material. The Core Standards address those issues head-on and finally offer hope for a better math education….

The only way to combat the current lock-step march to the bottom of international student performance in math and science is to implement rigorous national standards. That is why parents, teachers, and policy makers should oppose efforts to scale back the hard-won and necessary Common Core State Standards.[2]

The Heritage Foundation leads the charge against the CCSS, quoting mathematician Ze’ve Wurman, who argues that the standards do not expect students to learn Algebra I by eighth grade, which both “reverses the most significant change in mathematics education in America in the last decade” and is “contrary to the practice of the highest-achieving nations.”[3] Another CCSS opponent, the Pioneer Institute, cites mathematician James Milgrim, who argues that not taking Algebra I in eighth grade, “means that the large majority of students will not reach calculus in high school as expected by elite colleges.”[4]

To that charge, the drafters of the CCSS reply:

The Standards do accommodate and prepare students for Algebra in 8^th grade, by including the prerequisites for this course in grades K‒7. Students who master the K‒7 material will be able to take Algebra in 8^th grade. At the same time, grade 8 standards are also included; these include rigorous algebra and will transition students effectively into a full Algebra I course.[5]

The 2013 Brown Center Report on American Education of the Brookings Institution presents some history and findings about the concept of accelerating mathematics instruction.

In 1982, Robert Moses…called algebra “the new civil right”…The Clinton administration tied the equity theme to international competitiveness and pushed for more students to take algebra before high school…. Algebra soon became known as a “gatekeeper” course standing like a sentry at the gateway to college.[6]

Taking calculus in the senior year of high school also became a goal, which added to the need to take Algebra I by eighth grade. By 2011, the percentage of students taking advanced math courses in eighth grade nearly tripled.[7]

But the Brookings report finds that the decades-long effort to accelerate Algebra I instruction to eighth grade has not led to higher achievement in National Assessment of Educational Progress (NAEP) assessments.

Stronger math students take algebra in eighth grade, and although they indeed may benefit academically from the course, that does not mean that weaker students will also benefit from taking algebra earlier…. Accelerating the conventional first course of algebra into earlier grades, in the absence of other changes in the math curriculum, is for most students decidedly harmful…

States with more eighth graders taking advanced math classes are no more likely to register a higher NAEP score in math than states with lower enrollments in those classes.

Indeed, states that are “not aggressively accelerating eighth graders into advanced courses are more likely to show achievement gains….”[8]

The report also investigated whether boosting the percentage of students in higher level courses is associated with decreases in the mean scores of those courses—suggesting a watering-down effect.

The evidence is consistent with watering down…Negative correlations were found for Algebra I and Pre-Algebra. In those courses, mean achievement gains declined as enrollments increased.[9]

The lead writer of the CCSS for mathematics, Jason Zimba, comments that:

I actually think the questions about algebra are better formulated as questions about acceleration. How will kids who are ready for advanced work accelerate to reach courses like calculus during high school? But those are questions for policy, not for standards…. Decisions about acceleration and ability grouping are still the purview of local districts, just as they’ve always been. For example, I’ve seen where the state of Massachusetts has provided some interesting guidance for districts showing several different models for acceleration, all of them ending at calculus in the senior year of high school.[10]

Ironically, the CCSS properly leave such decisions to parents and local school systems, contrary to Heritage’s mistaken “national curriculum” narrative. The CCSS also contain more advanced, or “plus,” standards for students who plan to pursue a STEM major in college.[11]

Perhaps the most important independent assessment of the CCSS comes from William Schmidt, a Michigan State University distinguished professor of education and statistics and co-director of its Education Policy Center, in a commentary for Education Week:

For years now it has been clear that the U. S. mathematics curriculum is a mile wide and an inch deep, and that the fragmented quality of mathematics instruction is related to our low ranking on international assessments. Nearly a generation after the first Trends in International Mathematics and Science Study [which Schmidt oversaw]…the Common Core State Standards for mathematics…may finally give American students the high-quality standards they deserve.

These new math standards have attracted some criticism, however. Aside from more abstract arguments, a number of specific claims have been leveled against them, including that they are untested; that they are not world-class; and that some existing state standards are superior.

As part of our ongoing research, Richard Houang and I recently concluded a study of the math standards and their relation to existing state standards and the standards of other nations….What did our research uncover?... The common-core standards closely mirror those of the world’s highest-achieving nations…. We find three key characteristics in the curricula of the highest-performing countries: coherence (the logical structure that guides students from basic to more advanced materials in a systematic way); focus (the push for mastery of a few key concepts at each grade rather than shallow repetition of the same material); and rigor (the level of difficulty at each grade level). The common core adheres to each of these three principles.

Unfortunately, when one hears that a state’s existing standards are better than the common core, it usually means that those standards include more—and more advanced—topics at earlier grades. But this is exactly the problem the common core standards are designed to correct. It is a waste of time to expose children to content they are not prepared for, and it is counterproductive to skim over dozens of disconnected topics every year with no regard for student mastery. As it stands today, we simply hope that students will somehow “get it” at a later grade, and yet we know far too many students never do….

The common core offers the opportunity to revolutionize math instruction in this country, to improve student performance, to close the gap between the United States and its competitors, and to ensure that every American student has an equal opportunity to learn important mathematics content. But it is only a chance, and it is imperative that we seize it.[12]

Professor Schmidt’s work is also discussed in a subsequent article:

Schmidt found that states whose previous standards were most similar to the Common Core performed better on a national math test [NAEP] in 2009…. “This is another strong piece of evidence that we are moving in the right direction.”…

“This is probably the best chance we’ve had to improve America’s mathematics education in 50 years if not more,” Schmidt concluded.[13]

Confirming Schmidt’s points about coherence, focus, and rigor are reactions from the Albuquerque school system’s pilot program for implementing the CCSS, reported by Education Week. Gina Middleton, who is managing the district’s program, reports feedback from teachers:

What they love, love, love is…giving the depth to content and not teaching so much of the breadth…There are less standards, but they are dense, very compact.

Holly D. Zaluga-Alderate, a mathematics teacher in the city’s Polk Middle School, echoes that point:

I don’t have a mile long list of standards to cover…. For example, with the Pythagorean theorem, in the past we would say, “This is the Pythagorean theorem and how we use it” and move on. This year, we could get in depth, how it worked, the ins and outs…and knowing the whys…. It’s a lot more rewarding and letting me be a teacher.[14]

Educators are also properly nervous about CCSS tests to come in 2014. Both Georgia and Kentucky have experienced big proficiency drops in early CCSS testing:

As the Atlanta Journal-Constitution reported…58.6 percent of students failed to meet the proficiency standard on the new algebra test aligned to the common core…The obvious comparison is Kentucky, which last November publicized the first results from explicitly common-core-aligned tests and showed big proficiency drops, such as a 33-percentage-point drop in elementary school math proficiency…. Not surprisingly, they also highlight Florida as a state that has gone through similar score drops on new, tougher tests.[15]

Parents will have to prepare themselves for such outcomes and insist on the improvements needed by local school authorities to meet the CCSS requirements.

They will also have to resist efforts by local school authorities to pass off existing instructional approaches as aligned with the CCSS. A recent Brookings commentary illustrates that point.

A blog post by James V. Shuls in January 2013 tells the story of parents trying to understand the objectives of their son’s first grade math program…. The Shulses were alarmed that the standard algorithm for addition was being discouraged, let alone not being taught as the simplest, most efficient method for solving addition problems…. The parents met with the teacher and school principal…[who] explained that the district had adopted a math program from the 1990s, Cognitively Guided Instruction (CGI), to implement the Common Core State Standards for mathematics in first grade.[16]

Such programs of the Blob precipitated the disaster that is now mathematics education, and should be discarded outright. In April 2013, revised Publishers’ Criteria for instructional materials in mathematics were issued by Student Achievement Partners, reflecting feedback from the field.[17] States and localities should be demanding compliance with such criteria rather than falling prey to the Blob’s fallacious claims.

The CCSS are an important step advance towards recovering America’s prowess in mathematics, though it will take years to achieve student proficiency. And the CCSS include the flexibility to grow the future engineers and scientists needed to compete economically with other nations.

The next article will discuss the efficacy of the CCSS for college and career readiness.

Image: Public Domain

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This is one of a series of occasional articles applying the lessons of Western civilization to contemporary issues relevant to the academy.

The Honorable William H. Young was appointed by President George H. W. Bush to be Assistant Secretary for Nuclear Energy and served in that position from November 1989 to January 1993. He is the author of Ordering America: Fulfilling the Ideals of Western Civilization (2010) and Centering America: Resurrecting the Local Progressive Ideal (2002).