The Second Great Math Rebellion By
Tom Loveless
Few truisms exist in the politics of education, but
you can usually count on two things. When reformers seize control of
the policy agenda, whether at the local, state, or national level,
they almost always go too far in jettisoning what they don't like and
too far in embracing the new, unproven practices they favor. Not only
is the baby thrown out with the bathwater, but the baby and the
bathwater are frequently replaced by something bizarre.
In 1989, a group of experts in the field of math
education, under the auspices of the National Council of Teachers of
Mathematics, launched a campaign to change the content and teaching
of mathematics. In the intervening eight years, the reforms have been
slowly seeping into the schools, ostensibly in an effort to raise
standards. Now the earmarks of a grassroots rebellion are appearing.
From coast to coast, articles in newspapers and magazines report
parents organizing against their districts' math programs. Op-ed
pieces are regularly popping up with horror stories about a warm,
fuzzy mathematics that values student happiness over student
competency. Web sites are buzzing with protest. California is
scrambling to write new state standards so it can undo the damage of
dancing on "the cutting edge" of math reform. Many of the critics are
political conservatives, but not all. This past summer, Sen. Robert
Byrd, D-W.Va., took to the floor of the U.S. Senate to warn the
nation about the spread of "whacko algebra," declaring that "it is
not just nonsense, it is unfocused nonsense."
We've been through this before. In the 1960s, the
curriculum known as the New Math was routed from classrooms by angry
parents and teachers. Parents didn't recognize the mathematics that
children were bringing home from school, and teachers found it almost
impossible to instruct students on the strange new topics recommended
by reformers. Despite the support of the most prominent reformers of
its day, including the NCTM, the New Math fizzled when it hit real
classrooms with real kids and teachers.
The second great math rebellion centers on three
grievances:
First, teaching. The NCTM math embraces the
longstanding doctrine of progressive education. Student-initiated
learning is favored over teacher-led instruction. Students spend a
lot of time playing math games in small groups. The process of
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problem-solving is valued over right answers because right answers
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don't have an objective existence; they are "constructed" by
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learners. But what happened to reformers' insistence on real-world
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math? From engineers to airline pilots, people use mathematics to
model the world in which they actually work, not to construct their
own, more accommodating versions of reality.
The state and district policies that have followed
the NCTM standards tend to present reform as religion. And
conventional practices appear as sins: teachers delivering direct
instruction; students individually working on pencil-and-paper
problems at their desks; corrected work (wrong answers clearly marked
wrong) cycling back and forth between teacher and student.
No wonder teachers and parents
have trouble with these reforms. To promote student-centered
learning, teachers are to keep an elaborate diary on each child's
"mathematical disposition." The teaching that parents most likely
hear about is conducted by their children's peers.
The second complaint centers on the downgrading of
basic skills. Until recently, the math curriculum from kindergarten
through 8th grade focused on basic skills: in particular, learning
how to use four forms of number (integers, fractions, decimals, and
percents) in performing four operations (addition, subtraction,
multiplication, and division). Students who mastered the 16
manipulations embedded in this knowledge, including when and how to
employ them in solving problems, were in good shape to move on to
higher math.
Not anymore. Basic skills are now de-emphasized.
They represent the facts-based learning that math reformers abhor.
How will students get the basics? Memorization isn't an option
because it's boring. The hope is that basic facts will seep into
students--by playing games, working with manipulatives (blocks,
beans, and counting sticks), and by using calculators.
It's even inferred that computational skills are
becoming unnecessary with calculators in wide use. Besides, math
reformers argue, the insistence that students learn these skills
before progressing in the curriculum condemns countless youngsters to
a low-level, repetitious math program.
The problem with this argument is that it's based on
conjecture. We don't know if learning by osmosis really works, nor
the long-term consequences of students' failing to master basic
skills. We don't know whether students who can't grasp, say, the
equivalence of ? and 0.25 and 25 percent actually go on to
successfully learn calculus. Research has yet to document large
numbers of students who fly through algebra but are clueless when it
comes to fractions. Moreover, parents worry when their 5th graders
can't multiply single-digit numbers without pocketfuls of beans and
sticks. Teachers are concerned that the mastery of basic skills
signifies something more than computational proficiency, that
students who learn these facts to an automatic level also gain a
deeper knowledge of mathematics, a sense of number unfathomable to
those who don't know them.
The third complaint has to do with the dramatic
transformation of math textbooks. Progressive educators have never
really liked textbooks, feeling that teachers rely on them too much
and that texts narrow learning to a series of dull, repetitive tasks.
But the textbook has its virtues. Texts publicly declare the
curriculum. They link home and school, and by providing a calendar
for learning, allow parent, teacher, and child to see what has been
covered and what lies ahead. The textbook is the closest thing we
have to an enforceable learning contract in the American school, and
for the last century, no serious academic subject has been taught
without one.
Some of the new math programs either use kits rather
than texts or provide texts that are flashy in appearance but short
on substance. Sen. Byrd couldn't find an algebra expression until
Page 107 in the book that appalled him. What fills the book's pages?
Discussions of endangered species, air pollution, the Dogon people of
West Africa, the role of zoos in society--anything but math. Marianne
Jennings, the Arizona State University professor who brought the book
to Mr. Byrd's attention, refers to it as "Rain Forest Algebra."
As suggested by this example, the math that is
presented in texts may be inexplicably dressed in PC garb. It's no
surprise that this irritates conservatives, but readers of all
political persuasions should be annoyed because public policy is
partly to blame. The California math framework, for example, urges
teachers to "illuminate the mathematical side of social issues,"
offering on Page 26 the following problem as a model: "The 20 percent
of California families with the lowest annual earnings pay an average
of 14.1 percent in state and local taxes, and the middle 20 percent
pay only 8.8 percent. What does that difference mean? Do you think it
is fair? What additional questions do you have?" The framework then
boasts, "Such problems take percents, one of the most prosaic
workhorses in mathematics, and open them up, breathing new life into
them by introducing questions about reporting, statistics, and social
justice."
Is this problem (which is computation-free, of
course) a clear case of injecting ideology into the curriculum, or
are 6th graders really perched on the edge of their seats, just
waiting to be mesmerized by the distributional effects of the tax
code?
The objections I have discussed constitute a
rejection of the philosophy, content, and materials of contemporary
mathematics programs. They are not trivial. But across the country,
disillusioned parents and teachers report a response to their
objections that reveals a breathtaking arrogance on the part of
administrators implementing these reforms, a belief that teachers
with traditional teaching styles need to have their preferences
"professionally trained" out of them and that wary parents simply
don't have the professional standing to understand why a different
mathematics is needed. And things might get worse. If reformers get
their way, the new,instruction, new curriculum, and new materials in
vogue will be,evaluated by new assessments. The old tests, you see,
can't adequately,measure the learning now taking place. This raises a
terrible prospect, a Dorian Gray education where everything looks
great on the outside--happy children playing games, receiving A's,
testing wonderfully--while below the surface there is nothing but
ignorance: irreparable and undetected.
Two simple rules should govern all standards-setting
projects. First, their purpose is to define the skills and knowledge
that students must learn, not to declare some forms of teaching good
and others bad. If a particular teacher's students learn what they
should learn, who cares about that teacher's pedagogical philosophy
or methods? Second, the skills and knowledge stipulated in the
standards should be recognized as valuable to the average person on
the street. Put simply, parents shouldn't be mystified about what
their kids are learning in school.
Today's math reforms violate both of these rules,
and in doing so, debase the expertise of teachers and jeopardize the
trust ofparents--pillars on which the public school stands.
Tom Loveless is an associate professor of public
policy at Harvard University'sJohn F. Kennedy School of Government in
Cambridge, Mass.