WHAT IF THOSE MATH STANDARDS ARE WRONG?
What If Those Math Standards Are Wrong?
Chester E. Finn, Jr.,
Education Week Date: 01/20/1993
At the time of the writing of this article, it was stated that Chester Finn was
a former assistant U. S. Secretary of Education, a founding partner and senior
scholar with the Edison Project and a professor (on leave) at Vanderbilt
University.
Even in this faddy world of K-12 education, the “standards” issued by the
National Council of Teachers of Mathematics have met with rare acceptance.
Seldom has so profound a change to conventional wisdom and standard practice had
such homage paid to it, so little resistance shown to its onrush, so few doubts
raised about its underpinnings. Republican and Democrat, textbook publisher and
test maker, governor and businessman, federal official and local school board
member -- just about everyone is rushing to implement “the NCTM standards.”
What’s more, they’re commonly cited as the example par excellence of what
national education standards should look like. Governor Roy Romer of Colorado,
for example, has said so hundreds of times as has outgoing U.S. Secretary of
Education Lamar Alexander. We’ve seen national, state, and local groups,
struggling with standards in their own domains, cite the NCTM, embrace the NCTM
standards and yearn to emulate the NCTM.
We’d better hope the NCTM has got it right. If not, American education’s
lemming-like rush to follow its lead could find us hurtling off a precipice.
Worries about the NCTM approach to math began to stir in me several years back.
They took two forms then: I’ve lately added a third.
The first had to do with what I’ve come to realize is vast misunderstanding of
what the NCTM has actually wrought. It is centered in confusion between
“content standards” and “student performance standards” --to borrow the
terminology of the National Counsel of Education Standards and Testing,
co-chaired by Mr. Romer.
Oversimplifying only a bit, content standards describe what schools should teach
and --presumably--their pupils should learn. Retro examples might be “state
capitals” in grade 4 and diagramming complex sentences by grade 7. Content
standards are about curriculum: its goals, frameworks, scope and sequences,
etc. They are intended mostly for educators.
Student-performance standards are something else. They involve how well
youngsters must do in order to be said to have met the expectations of the
content standards. How many state capitals must that 4th grader actually know?
Must she have them memorized or is it okay to match up states and capitals from
two lists? If she only gets 42 of them right has she fulfilled the standard?
Must all these names be spelled properly? As for diagramming, just how
intricate a complex sentence do we have in mind? How many must the student
diagram? How many errors are acceptable? Such are the issues we must resolve
when we set student-performance standards. Note, though, that only when these
standards are in place can students and parents see how well they -- and their
schools--are doing vis a vis what’s expected of them. Student-performance
standards are truly about results and outcomes. They’re meant mostly for
laymen.
To date, what the National Council of Teachers of Mathematics has provided are
content standards only. Educators are properly grateful, as are many
policymakers. But what most nonprofessionals have in mind when they talk about
education standards are student-performance standards and those
-regrettably--the NCTM has not yet given us.
So how satisfactory are the content standards? We now come to my second worry.
It flickered to life when I began to hear of elementary school classrooms where
teachers were passionate about “problem solving” but where students were
counting on their fingers as late as 3rd or 4th grade because they hadn’t
learned rudimentary “math facts” to the point where these came automatically. I
contrasted this with what I know of Japan’s “Kumon” math program and with the
teaching strategies developed by John Saxon, an eccentric textbook author who is
shunned by the math establishment but whose pupils seem adept both in basic
arithmetic and in solving complex math problems. (The math establishment
despises Kumon, too, of course.)
Was it possible, I asked, that children taught according to NCTM standards might
have all sorts of imaginative ideas about tackling a problem yet seldom get the
right answer to it because five times 11 was beyond their ken?
Math sophisticates pooh-pooh my concern, arguing that of course the NCTM intends
both results, that arithmetic and accuracy are not being sacrificed on the
problem solving altar, indeed that these will develop hand-in-hand.
That, of course, is what everyone yearns for: deft skills and reliable “math
facts” combined with imagination and deep understanding. And in the hands of
terrific math teachers, that’s pretty much what happened long before the NCTM
was heard from. But U. S. schools don’t boast a surfeit of such teachers,
especially in the early grades, and in trying to compensate for this kind of
shortage (not just in math) we’ve tended to lurch from one extreme to another,
grabbing for the latest miracle cure, forcing tradeoffs, opposing “a” to “b”
rather than molding them. For a vivid example drawn from another field, look at
the endless war between the “whole language” crowd and the partisans of
“phonics,” notwithstanding ample research showing that both are needed for young
students to read effectively and enjoyably.
Great teachers do use both language-arts lessons, just as they attend both
problem-solving strategies and rapid calculation of the right answer in math
class. They know these fierce arguments involve spurious choices and phony
tradeoffs. But what happens when their professional association slips--or is
perceived as slipping--over to one side? In particular, what happens to
millions of children whose less-than-gifted instructors rely on prepackaged
programs, the latest nostrums, and what others tell them is the approved way to
proceed?
So long as many teachers are dependent in this way, it’s vital to ask of any new
approach being thrust upon the education world whether it has been fully tested
with students to insure that it yields the desired results--and is not just
being promoted because it appeals to grown ups caught up in ideological battles.
Which leads to my third and newest anxiety about NCTM math, seeded by a flawed
but compelling (and widely ignored) book by Siegfried Engelmann called
War
Against the Schools’ Academic Child Abuse (Halcyon House, 1992).
Professor Engelmann, of course, is the father of dozens of instructional
programs, especially for the primary grades, the best known of which are DISTAR
reading and math. He is also one of the world authorities on “direct
instruction,” a highly structured approach that relies on clear expectations for
teachers and students, tight performance requirements, “behavioral” (rather than
“developmental” instructional practices, and strong emphasis on accountability
for results.
Here’s what Mr. Engelmann has to say about math a la NCTM:
The Standards de-emphasize anything teachers have failed to
teach…The most serious problem with the Standards, however, is its
arrogance. In the tradition of the sorting machine, it assumes
that it can derive a curricular reform through metaphysical
masturbation of words, not through experimental evidence about what
works and what doesn’t. The writers of the Standards did not first verify
these activities, suggestions, and standards by first demonstrating that
they worked and that they created kids who performed well in math.
Instead, they made it up and then presented it as an authoritative
document.
If Professor Engelmann is right, we may be buying a pig in a poke, a radical yet
unproven overhaul of math curriculum, instruction, and assessment that massages
the nerve centers of the “math community” but won’t necessarily produce more
numerate young Americans.
Mr. Engelmann asserts that the NCTM approach has a lot in common with the
debacle known as “new” math. “The manipulatives, the exposures, the acting-out,
and the moral insistence on problem-solving,” he writes, “has been a theme of
math educators since the mid-60’s. The approach is actually one of the reasons
kids currently don’t know long division and are not proficient at
paper-and-pencil work in math.”
The kind of instruction that Mr. Engelmann favors--direct instruction--isn’t
popular with today’s educators. It smacks of rote learning, drill and practice,
even memorization, thus a “canon” of skills and knowledge that every teacher
should impart and every pupil acquire. This is unfashionable. It’s not what we
find in the NCTM standards. But it’s performance-oriented, hence amenable to
assessment--including the kinds that emphasize right answers and thereby lend
themselves to accountability, high stakes, and other such scorned practices.
Unfashionable to be sure. But we err when we slight the acquisition of facts,
specific knowledge, and simple skills, both as building blocks of more complex
intellectual structures and as potent motivators. Many teachers and parents can
attest to the satisfaction that kids get from knowing things: precise, definite
things that they know they know, can tell they’re good at, and from the
accumulation of which they can gain a sense of steady progress--in contrast to
the subtleties and ambiguities that experts favor. As an example, I recently
observed the ardor, pride, and feeling of accomplishment palpable in an
elementary school in the much-afflicted South Bronx, a school that is using E.
D. Hirsch’s “core knowledge” program.
E. D. Hirsch isn’t the main point, though, nor is Siegfried Engelmann, nor even
the NCTM. What’s important is whether U.S. youngsters actually reach higher
levels of skill and knowledge. As yet--a full decade after the National
Commission on Excellence in Education labeled us a “nation at risk”--there’s
scant evidence that our reform strategies are working. The cures we’ve tried
have done little to boost outcomes. To that glum news some people respond by
seeking (as often before) to ease the press for results and go back to indices
of input, effort, and intention. Others want to replace the measuring sticks,
hopeful that different assessments will reveal--and perhaps stimulate--better
results from today’s voguish curricular and pedagogical strategies. A few,
however, are turning away from those strategies themselves, returning to what
Marilee C. Rist, in a useful article in The Executive Educator, terms “learning
by heart.” Memorization. Direct instruction. Recitation. Plenty of practice.
And gobs of core knowledge.
We oughtn’t dump all our eggs into that basket, either. Or any other. No single
container is capacious enough. Diverse classroom strategies should be
welcome--so long as solid learning occurs. The reason for standards isn’t to
impose a regimen of what Diane Ravitch terms “pedagogical imperialism.” Rather
it’s to be clear and prescriptive about the ends--and then laid-back and
versatile about means.
I doubt this was intended but the NCTM may have given a boost to such
imperialist tendencies of math. By focusing on content rather than performance
standards, this organization has probably led its members and followers to dwell
overmuch on what happens in their classroom instead of the results obtained
there. “Problem solving works in some situations, to be sure, but “learning by
heart” may accomplish more in others. Usually both are vital. Teachers may
feel free to adapt their strategies in specific situations, not harnessed to a
single pedagogical approach.
Says Thaddeus Lott, the maverick principal of the Wesley Elementary School in Houston, an
institution attended by hundreds of “at risk” youngsters, a place where DISTAR
is used in both math and reading--and where test scores are soaring: “You don’t
send a guy to dig gold without the proper tools; and you don’t build a house
without a saw and a hammer.” By giving his children the tools they need, he is
empowering them to build all sorts of structures. But it takes courage to stand
up to conventional wisdom. And today that wisdom insists that the NCTM and its
ilk have things figured out just right and that everyone had better do things
their way. What if they turn out to be wrong?
Professor Finn was prophetic twenty-one years ago when he wrote this article. The
NCTM Standards, even in their revised condition are a joke, and time has shown
that their creators were indeed “wrong.” And in the meantime, an entire
generation or two or three of students has been cheated out of a basic math
education. The
arrogance of this national math teachers’ organization to presume that an
untried methodology would work just because they said it would, is contemptible.
The presupposition that public schools would have teachers with IQ’s over 140
so they could stimulate intuitive thinking in their classrooms is just
incredible. And if those teachers with such IQ’s aren’t there, these standards
most assuredly don’t work. As Professor Finn anticipated, we have “hurtled off a
precipice.”
In case you’re wondering, the Katy ISD math administrators and teachers long ago embraced these standards as
their own.
Mary McGarr