Common Core State Standards: Our Mathematics Problem

William H. Young

As they did for “our literacy problem,” progressivism since the 1930s and postmodern multiculturalism since the 1960s have produced “our mathematics problem” in public education—and a concomitant decline in individual prosperity and national economic competitiveness—which the Common Core State Standards (CCSS) aim to correct.

The 2012 ACT study that analyzed the requirements of “occupations paying a wage sufficient to support a family” found that necessary basic mathematics skills were lacking in more than 40 percent of even community college graduates, let alone mere high school graduates.[1]

The Global Competitiveness Report 2012‒2013 of the World Economic Forum ranks the U. S. a stunning 48th in quality of science and mathematics education when compared with 65 other industrialized nations. American students ranked 31st in mathematical competency.[2] How and why did we fall so far?

Over the mid-twentieth century, progressive education gradually reduced the academic content of mathematics instruction in many public schools. CSU Northridge mathematician David Klein summarizes the consequences of that history:

In the 1940s, it became something of a public scandal that army recruits knew so little math that the army itself had to provide training in the arithmetic needed for bookkeeping and gunnery….By the end of the decade, the appearance of radar, cryptography, navigation, atomic energy, and other technological wonderments changed the economy and underscored the importance of mathematics in the modern world….

[That problem]…received little attention until the U.S.S.R. launched Sputnik. The American press treated Sputnik as a major humiliation, and called attention to the low quality of math and science instruction in the public schools….[3]

Admiral Hyman Rickover, father of the nuclear Navy, argued in his 1959 book Education and Freedom that “the nation was hobbled in its competition with the Russians for technological supremacy by a school system that failed to prepare young people with a rigorous education.”[4] I was fortunate to have received a rigorous education and to be working in Rickover’s Washington headquarters at that time.

The misguided New Math movement prevailed during the 1960s, introducing calculus at the high school level but failing to properly teach basic skills and their applications.[5] New Math was abandoned by the early 1970s, and the education monopoly turned to postmodern multiculturalism.

Education professor emerita Sandra Stotsky describes that turn:

Educators…argued that the traditional curriculum needed to be more “engaging” and “relevant” to an increasingly alienated and unmotivated—or so it was claimed—student body. Some influential educators sought to dismiss the traditional curriculum altogether, viewing it as a white, Christian, heterosexual-male product that unjustly valorized rational, abstract, and categorical thinking over the associative, experience-based, and emotion-laden thinking supposedly more congenial to females and certain minorities.[6]

Around 1972, the average SAT mathematics score began a significant decline.[7] A Nation at Risk, released in 1983, commented about growing shortcomings in mathematics education.

Between 1975 and 1980, remedial mathematics courses in public 4-year colleges increased by 72 percent.…Business and military leaders complain that they are required to spend millions of dollars on costly remedial education and training programs in such basic skills as reading, writing, spelling, and computation.…[8]

But in 1980, the National Council of Teachers of Mathematics (NCTM)—part of the education Blob—released a new agenda for American public education which proclaimed that “requiring complete mastery of skills before allowing participation in challenging problem solving is counterproductive.” The NCTE codified its agenda in Curriculum and Evaluation Standards for School Mathematics, published in 1989 for grades K‒12.[9] Public education historian Diane Ravitch points out in Left Back that

The NCTM standards were at heart a pedagogy, a way of teaching, rather than what most people would recognize as standards. Standards customarily involve a progression of accomplishments or competencies that are to be demonstrated at defined times in children’s schooling. The NCTM standards gave no concrete description of what should be taught or the sequence of topics. Instead, they consisted of nebulous goals that were admirable but difficult to implement, such as valuing mathematics, becoming confident problem solvers, reasoning and communicating mathematically, and developing appreciation for the power of mathematics.[10]

Moreover, the NCTM standards reinforced the general themes of progressive education, advocating student-centered, discovery learning, the same pedagogy of “constructivism” adopted for reading and writing.[11] As Ravitch describes them, the standards

put a premium on student-led activities, mathematical games, working with manipulatives (e.g., blocks and sticks)… and group learning, and discounted the importance of correct answers.[12]

Stotsky notes that “the underlying goals of the standards—never made clear to the general public—were social, not academic.”

Some of the report’s authors, for example, sought to make mathematics “accessible” to low-achieving students, yet meant by this….the employment of trendy, though empirically unsupported, pedagogical and organizational methods that essentially dumb down math content. Math educators proclaimed a brand-new objective—conveniently undefinable and immeasurable—called “deep conceptual understanding.”[13]

A report for the William Pope Center for Higher Education Policy further explains teaching mathematics for “social justice”:

A major purpose of the NCTM standards was the redefinition of mathematics as a way to correct social inequities. The authors of these standards asserted that traditional mathematics instruction was a vehicle for the perpetuation of socio-economic privilege. They pointed out that math performance often functions as a gatekeeper, preventing students with poor math ability from advancing academically. Acceptance into college programs and jobs often depends on a student’s success in acquiring high-level functioning in math.

The authors of the NCTM standards wanted a math instruction curriculum that would allow all students to do high-level math without mastering the “low-level” problem-solving skills. To achieve this goal, the 1989 NCTM math standards decoupled math performance from the mastery of math fundamentals. They did this by eliminating traditional algorithms, or sequences of rules, for performing such mathematical operations as long division, multiplication, and dividing fractions. Instead of requiring students to learn these algorithms, students were given the opportunity to “discover” creative ways of finding the answers. Supposedly, they would acquire fundamental math skills along the way to discovering how to solve higher-level problems.[14]

Egalitarian postmodern academic social construction of knowledge and reality replaced Western concepts and tenets of mathematics.

By 1997, Klein notes, most state governments had adopted instructional materials in close alignment with the NCTM standards, which began to draw criticism from parents.

The mathematics books and curricula…typically failed to develop… arithmetic and algebra skills. Elementary school programs encouraged students to invent their own arithmetic algorithms, while discouraging the use of the superior standard algorithms…Calculator use was encouraged to excess…Arithmetic and algebra were de-emphasized. Mathematical definitions and proofs for the higher grades were generally deficient, missing entirely, or even incorrect. Some of the elementary school programs did not even provide books for students, as they might interfere with student discovery….

Perhaps the general attitude of parents was best captured by Jaime Escalante, the nationally famous mathematics teacher immortalized in the film Stand and Deliver, when he said, “whoever wrote… [the NCTM standards] must be a physical education teacher.”[15]

One parent, Marianne M. Jennings, a professor at Arizona State University, wrote a vivid critique of her teenage daughter’s algebra textbook:

An 812-page full-color tome replete with Dogon art from Africa, poetry, maps of South America, and warnings about pollution and endangered species.

Jennings called this approach “rain-forest algebra.”[16]

Ironically, in the face of rising public criticism, the Clinton administration endorsed instructional materials based on the NCTM standards:

In October 1999, the U. S. Department of Education recommended to the nation’s 15,000 school districts a list of math books, including several that had been sharply criticized by mathematicians and parents of school children across the country for much of the preceding decade. Within a month of that release, 200 university mathematicians added their names to an open letter to Secretary Riley calling upon his department to withdraw those recommendations….The [letter] was published on November 18, 1999 as a full page ad in The Washington Post…. The NCTM responded to the open letter by explicitly endorsing all ten of the “exemplary” and “promising” programs….

The culminating event for mathematics education of the 1990s occurred in April 2000 when the NCTM released a new document entitled, Principles and Standards for School Mathematics (PSSM)…. a revision of the 1989 NCTM Standards…PSSM continues to abhor direct instruction in, among other things, standard algorithms, Euclidean geometry, and the uses of memory….[17]

 From the early-1990s, “the percentage of high school graduates who signed up for rigorous-sounding classes nearly tripled.”[18] But American Enterprise Institute scholar Mark Schneider concludes that “decades of efforts to boost the number of students taking rigorous math classes has caused a substantial dilution of those courses.”

The average number of math credits completed by a high-school graduate rose from 3.2 to 3.8 between 1990 and 2005, and… average math GPAs rose over that time from 2.2 to 2.6. While only a third of students completed algebra II in 1978, more than half did in 2008. And yet NAEP scores for students in algebra I, geometry, and algebra II were higher in 1978 than in 2008. In other words, more students were taking more advanced math and getting better grades—and yet our students knew less in 2008 than they did 30 years earlier. Schneider terms this phenomenon the “delusion of rigor.”[19]

Finally, UC Berkeley mathematician Hung-Hsi Wu expressed the view of many of his peers when he warned in 1997:

The brand of mathematics purveyed by the NCTM’s 1989 report “has the potential to change completely the undergraduate mathematics curriculum and to throttle the normal process of producing a competent corps of scientists, engineers, and mathematicians.”…The math wars, which started in debates about pedagogy, may end up in questions about the long-term prospects for American prosperity.[20]

Wu’s concerns about the adverse effects of the mathematics taught in public education were justified.

American students are now a dismal 31st in mathematical competency when compared with 65 other industrialized nations. The share of American workers in the scientific and engineering professions fell to 4.9 percent of the labor force in 2010, down from a peak of 5.3 percent in 2000—the first such decline since 1950.[21] Corrective action is urgently needed.

The CCSS address “our mathematics problem” by setting grade-specific standards defining what students should understand and be able to do by the end of each K‒12 year. The CCSS also return to more coherent, focused, and rigorous instruction.[22] Those CCSS for mathematics, and issues raised by critics, will be examined in a later article.

Michigan State professor William Schmidt, an international math expert, conducted an independent assessment of the CCSS in 2012. He concluded:

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….

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….[23]

This is probably the best chance we’ve had to improve America’s mathematics education in 50 years if not more.[24]

The next article will explain a key objective of the CCSS—inducing knowledge-based curricula for our local public schools.

______________________________________________________________________________

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).

 



[2] Klaus Schwab, The Global Competitiveness Report 2012‒2013, World Economic Forum, January 2013. Miles Gilburne, “Global Connections, Common Core Standards Can Boost U. S. Student Competitiveness, Education Ranking,The Huffington Post, 30 January 2013.

[3] David Klein, “A Brief History of American K‒12 Mathematics Education in the 20th Century,” in James Royer, Mathematical Cognition (Charlotte: Information Age Publishing, 2003).

[4] Hyman G. Rickover, Education and Freedom (New York: E. P. Dutton, 1959).

[5] Klein, “A Brief History of American K‒12 Mathematics Education in the 20th Century.”

[6] Sandra Stotsky, “Who Needs Mathematicians for Math, Anyway?” City Journal, Manhattan Institute, 13 November 2009.

[7] "SAT Performance and Participation,” College Board.

[8] National Commission on Excellence in Education, A Nation at Risk: The Imperative for Education Reform, U. S. Department of Education, 26 April 1983.

[9] Klein, “A Brief History of American K‒12 Mathematics Education in the 20th Century.” Diane Ravitch, Left Back: A Century of Failed School Reforms (New York: Simon & Schuster, 2000), 438‒441. Stotsky, “Who Needs Mathematicians for Math, Anyway?”

[10] Ravitch, Left Back, 441.

[11] Klein, “A Brief History of American K‒12 Mathematics Education in the 20th Century.” Stotsky, “Who Needs Mathematicians for Math, Anyway?” Ravitch, Left Back, 439‒41.

[12] Ravitch, Left Back, 439.

[13] Stotsky, “Who Needs Mathematicians for Math, Anyway?”

[14] George K. Cunningham, University of North Carolina Education Schools: Helping or Hindering Potential Teachers? Pope Center for Higher Education Policy, January 2008.

[15] Klein, “A Brief History of American K‒12 Mathematics Education in the 20th Century.”

[16] Ravitch, Left Back, 440.

[17] Klein, “A Brief History of American K‒12 Mathematics Education in the 20th Century.”

[18] Sam Dillon, “High School Classes May Be Advanced in Name Only,” The New York Times, 25 April 2011.

[19] Frederick Hess, “Our Achievement-Gap Mania,” National Affairs ( Fall 2011)

[20] Klein, “A Brief History of American K‒12 Mathematics Education in the 20th Century.”

[21] Conor Dougherty and Rob Barry, “Share of Workers in Scientific Fields Shrinks,” The Wall Street Journal, 17 February 2012.

[23] William Schmidt, “Seizing the Moment for Mathematics,” Education Week, 17 July 2012.

[24] Andy Henson, “Study Supports Move Toward Common Math Standards,” MSU Today, 5 November 2012.

 

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