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) 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.
The NSF is not the only funding source for defective math programs.
Corporate foundations also contribute. In 2001, for example, the Bill
& Melinda Gates Foundation and the William and Flora Hewlett
Foundation teamed up to award the San Diego Unified School District
$22.5 million, but only under the condition that the school board
retain its superintendent and chancellor of instruction so that they
could institute educational “reforms.” The two administrators required
schools to use a controversial high school physics program, an
ineffective reading framework for elementary school, and Everyday Mathematics, an
NSF-funded, K-6 series not aligned to the state’s standards.[14]
By the next school board election, both administrators had left the
district, but San Diego school math scores had already declined
relative to the state as a whole. Because I have written and
spoken publicly about issues in math education, I regularly receive
emails and phone calls
from parents across the country asking for help and advice on how best
to avoid the negative effects of NSF-funded math programs in their
children’s schools. I receive more complaints about Everyday
Mathematics than all of the other NSF-funded programs combined. And the
complaints are legitimate. Like TERC, Everyday Mathematics eschews the
standard algorithms and does not develop fluency in basic arithmetic.
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.
[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.
[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.