This is a preprint of the published version that appeared in the American Journal of Physics, Vol. 75, No. 2, pp. 101–102, February 2007

School math books, nonsense, and the National Science Foundation

David Klein
Department of Mathematics
California State University, Northridge

Problem: Find the slope and y-intercept of the equation 10 = x – 2.5.

Solution: The equation 10 = x – 2.5 is a specific case of the equation y = x – 2.5, which has a slope of 1 and a y-intercept of –2.5.

This problem comes from a 7th grade math quiz that accompanies a widely used textbook series for grades 6 to 8 called Connected Mathematics Program or CMP.[1] The solution appears in the CMP Teacher’s Guide and is supported by a discussion of sample student work.

Richard Askey, a mathematician at the University of Wisconsin at Madison, reported, “I was told about this problem by a parent whose child took this quiz. The marking was exactly as in the text.”[2]  Students instructed and graded in this way learn incorrect mathematics, and teachers who know better may be undermined by their less informed peers, armed with the “solution.” This example is far from the only failing of CMP. Among other shortcomings, there is no instruction on division of fractions in the entire three year CMP series, and the other parts of fraction arithmetic are treated poorly.[3]

Is CMP just an anomaly? Unfortunately not. CMP is only one of more than a dozen defective K-12 math programs funded by the National Science Foundation. More specifically, the NSF programs were created and distributed through grants from the Education and Human Resources (EHR) Division within the NSF. In contrast to the NSF’s admirable and important role in supporting fundamental scientific research, the EHR has caused, and continues to cause, damage to K-12 mathematics education.

At the elementary school level, one of the worst NSF funded programs is the widely used K-5 series TERC: Investigations in Number, Data, and Space.[4]  The program relies heavily on calculators and does not include textbooks in the usual sense. Harvard mathematician Wilfried Schmid evaluated it and concluded that by the end of 5th grade, TERC students were roughly two years behind where they should be according to the California, Indiana, and Massachusetts state mathematics standards, the best state math standards in the U.S.[5]  Schmid added, “The TERC authors are also opposed to the teaching of the traditional algorithms of arithmetic, such as long addition, subtraction with borrowing, and the usual pencil-and-paper methods of multiplication and division. Not only do they refuse to teach the algorithms, they make clear their preference not to have the students learn them outside of the classroom, either.”[6]

Schmid’s observations are confirmed by a resource book for K-6 teachers entitled, Beyond Arithmetic, which “provides support for teachers, administrators, and curriculum specialists who are transforming mathematics learning and teaching and are implementing curricula such as Investigations in Number, Data, and Space,” according to promotional materials from the publisher (which also publishes TERC).  Beyond Arithmetic explains, “In the Investigations curriculum, standard algorithms are not taught because they interfere with a child’s growing sense and fluency with the number system.”[7]

Contemporary Mathematics in Context (Core-Plus) and Interactive Mathematics Program (IMP) and are two NSF-funded secondary math programs that are supposedly college preparatory.[8]  But Core-Plus students do not learn how to expand (a + b)2 until their third year of high school,[9] and IMP delays the quadratic formula until 12th grade, at which time a derivation is not even provided.

Despite sharp criticisms by mathematicians and strenuous opposition from parents of school children,[10] IMP, Core-Plus, and CMP, were designated “exemplary” by the U.S. Department of Education in 1999.  Several other controversial math programs were also labeled “exemplary” or “promising” at the same time.[11]

The imprimatur of the National Science Foundation and the U.S. Department of Education certification of some of the worst math textbooks in the industrialized world makes it particularly difficult to dissuade school districts from using them. Even so, more than 200 mathematicians and scientists attempted to warn the public about these books in an open letter to the U.S. Secretary of Education.[12]  Among the signatories were department chairs of many of the nation’s leading math departments and several Nobel laureates and Fields Medalists.  Parents cite that letter in their efforts to save their children from mathematical nonsense in the schools, but the NSF, oblivious to the criticisms, continues to fund newer editions of these “fuzzy math” programs, and awards multimillion dollar grants to distribute them to schools.

One of many examples is the \$35 million NSF grant to “System-wide Change for All Learners and Educators” (SCALE).[13]  In addition to other activities, SCALE promotes IMP, CMP, and TERC even in California where those books are not state approved. These textbooks lack the mathematical content necessary to meet the state’s K-12 math standards.

During the previous decade, the goal for students to achieve fluency in algebra and arithmetic was often derided by educators as “mindless symbol manipulation” or “drill and kill.” This point of view guided the creation of math textbooks. The resulting radical deemphasis of algebra and arithmetic — the prerequisite to algebra — in NSF-funded and NSF-distributed math programs has stark consequences for science education, especially physics. When the isolation of a variable in a simple equation is laborious for students rather than automatic, the depth of instruction in high school physics courses is severely limited. At the university level, students struggling with elementary algebra find themselves adrift in their calculus classes, and success thereafter in physics courses is elusive.

The root cause is money badly spent. The NSF and corporate foundations maintain a gravy train of education grants and awards that stifle competent mathematics education. Although it is conceivable that ongoing NSF grants for new editions of defective math programs, such as those I have described, will improve matters, that is a poor strategy. It amounts to throwing good money after bad. The most that one can realistically hope for is that the original NSF-funded math programs will eventually rise to the level of mediocrity.

The organization’s strategy is analogous to placing in charge of the hospital the surgeon who consistently amputates the wrong leg. School district grant recipients involved in implementing low quality K-12 math education programs gain prestige from their association with the NSF and often gain authority over school district math programs. But the reputation of the NSF is suffering from this association. The National Science Foundation logo, prominently displayed on promotional materials for its math programs, has become a warning symbol for parents of school children. It identifies programs that are best avoided, much like the skull-and-cross-bones symbol on poisons. The NSF should drastically change course, or get out of the business of funding K-12 mathematics education altogether.

References

[1] Lappan G. et al, Connected Mathematics Project, series of 24 books for middle school mathematics, Dale Seymour, Menlo Park, CA, 1998.

[3] A recent new edition of CMP marginally covers fraction division; students are essentially expected to “discover” it.

[4] Investigations in Number, Data, and Space is a K-5 curriculum developed by TERC Inc., Cambridge, MA, and marketed through Pearson Scott Foresman and previously by Scott Foresman - Addison Wesley and by Dale Seymour.

[5] This ranking is according to the Fordham Foundation report, The State of State Math Standards 2005 of which Schmid and I along with four other mathematicians were co-authors: It is posted at www.edexcellence.net/foundation/publication/publication.cfm?id=338.

[6] Quoted from www.nychold.com/forum01-schmid.html.

[7] Jan Mokros, Susan Jo Russell and Karen Economopoulos, Beyond Arithmetic (Dale Seymour Publications, White Plains, NY, 1995), p. 74. I thank Richard Askey for identifying this passage.

[8] For bibliographic information and reviews see: www.nychold.com/#prog-nctm

[9] www.nctm.org/dialogues/2001-01/20010113.htm.

[10] Parents’ organizations such as, “Mathematically Correct,” “New York City Honest and Open Logical Debate,” and “Where’s the Math?” among dozens of others continue to resist the imposition of “fuzzy math” in their schools.

[11] David Klein, Math problems: Why the U.S. Department of Education’s recommended math programs don’t add up, Am. School Board J. 187 (4) (2000) www.mathematicallycorrect.com/usnoadd.htm.

[12] The Open Letter of which I was a co-author is posted along with the signatories at mathematicallycorrect.com/nation.htm.

[13] See: scalemsp.wceruw.org/IHEConference2005/main.htm

[14] For bibliographic information and reviews see: www.nychold.com/#prog-nctm