the Math Wars:
Reflections From the Front Lines
by W. Gary Martin
My first sense that the
reform of mathematics education could be controversial came in 1995. I was deeply
engrossed in a curriculum development project based on the Curriculum and
Evaluation Standards of the National Council of Teachers of Mathematics
[NCTM]. It was an exciting time. My project was producing some excellent outcomes
with students, and seemingly hundreds of people across the nation were engaged
in exciting projects that were making tremendous progress. But then began a
string of increasingly negative reactions from critics of the NCTM Standards
on e-mail list serves and elsewhere. At first I naively thought that these critics
just did not understand and that if I only explained things well enough, they
would see the light. However, it soon became clear to me that some of these
critics were not the least bit interested in understanding the issues. As the
level of rhetoric escalated, I was astounded at their anger, and at the total
lack of scruples displayed by some (although certainly not all). But most of
all, I was totally bewildered.
I am still somewhat bewildered.
Who would have ever thought that mathematics education would be the subject
of heated editorials in the newspaper, of morning talk show head-to-heads, and
of political intrigue at all levels? Yet that is where we find ourselves today
and that is why we must get smarter very quickly in order for us to continue
to promote improvement in mathematics education for all students. In this short
paper, I will outline a few of my personal perspectives on how we can productively
deal with the so-called "Math Wars," the backlash to mathematics education
I will begin by outlining
a few lessons I have learned over the past years, all too often the hard way.
1. We must engage.
I think many people have naively thought that if we just ignore the critics,
they will go away. That clearly has not and will not happen, as colleagues from
California to Massachusetts have found. This so-called "high road"
approach was nearly the undoing of NCTM at the end of the 1990's. If we believe
in the tenets of reform and seek mathematics programs that work for all students,
we need to respond, forcefully and proactively, to the questions that are raised,
the attacks that are launched and the challenges that are presented.
2. We must all take responsibility.
There is no point in waiting for someone else to do the job. Even NCTM may or
may not be able, or even willing, to respond. When an article hits the newspaper
in your community, YOU must immediately call the reporter to correct errors,
YOU must submit a letter to the editor or an op-ed piece in response. When trouble
stirs up around a textbook adoption in your district, YOU must be at the meeting
and rally your friends to do the same. If there is a hearing on mathematics
education at any level, YOU should try to be there, and YOU should request an
opportunity to testify. The critics like to fashion themselves a grass-roots
effort, whether or not that is really true. In actuality, we ARE the grassroots.
3. We must focus on non-educators.
One of the strengths of the opponents to reform has been their ability to capture
the imagination of the general public. Phrases such as "New New Math"
and "Fuzzy Math" caught on quickly and became easy put-downs. Meanwhile,
many of us have been put on the defensive, forced to address attacks based far
more on emotion than on logic or evidence. In working with public relations
experts in the release of Principles and Standards for School Mathematics, NCTM's
updated Standards released in 2001, I was constantly amazed at how pedantic
we sound, how uncomfortable we are to resort to sound bites, and how little
the general public understands our messages. We need to get the best advice
possible from PR people, and we need to try out our arguments on friends before
going public. If a message cannot be easily communicated to a non-educator in
a sentence or two, it is too complex and needs to be simplified.
4. We must make partnerships.
The critics have gotten a lot of attention by featuring mathematicians, who
tend to have public credibility, no matter whether or not they are knowledgeable
about educational issues. The critics also love to put angry parents in front
of the camera, who paint pictures of change run amok. When WE then speak for
ourselves, we run the risk of looking self-important and sounding self-serving.
We need to identify and cultivate parents whose children are thriving in reform
classrooms. And we need to attract mathematicians and scientists who understand
that memorizing is not learning to do real mathematics, and business people
who want students who can think and solve problems. In many cases, these people
can communicate our messages far better than we can ourselves.
5. We must base our arguments
on evidence. The critics of reform frequently employ sheer emotion to make
their case, relying on anecdotal scare stories. We need to be able to counter
their claims in a calm, reasonable, and knowledgeable manner. The evidence is
on our side, and we must be prepared to respond. We need our own anecdotes illustrating
the positive results that reform can bring. But we also need a command of more
formal evidence that bears on the issues, including research studies as well
as evaluations of improvement projects. The Mathematically Sane Web site makes
a start of compiling both kinds of evidence at www.MathematicallySane.com/evidence/.
Solid evidence of success is the best antidote to the overblown rhetoric of
6. We must take heart
and carry on. Consider how long it took for the critics to emerge after
the release of the 1989 Standards. Consider their timing. My best guess is that
their attacks began only after they saw that something was happening - that
reform was actually taking root and beginning to make a difference. So if they
are attacking what you are doing, they are admitting that what you are doing
is important and really might have a positive impact. That is why they feel
they need to respond to you. Our efforts are having an impact. We cannot give
up the fight just because a group of people (usually quite small, nearly always
quite loud) object to what we are doing.
Strategies for Winning
Given these lessons, let
us now take a closer look at some of the underlying issues that are driving
this debate, so that we can better formulate our tactics. While there are certainly
legitimate philosophical differences that underlie some of the debate, I believe
that there is often much more going on beneath the surface. How else can one
explain the raw emotion and venomous outrage of many of the critics? To better
examine this issue, I will break up my discussion, addressing the different
populations from which the critics have emerged.
Mathematicians are clearly
the most vociferous group. They are probably the group who has been able to
get the most attention, and very likely, the group that has done the most damage.
Certainly there are mathematicians who are dismayed about the state of mathematics
education, but this really is not a new phenomenon nor can it be particularly
pinned on the reform movement. In fact, the reformers share much of this dismay.
What puzzles me, however, is that most mathematicians with whom I have worked
over the years have almost naturally been supporters of major tenets of the
reform movement. I frequently find that we hold in common the concern that students
do more than just plug-and-chug, that they learn to actually do mathematics-to
solve problems, to think creatively, and to reason and communicate about mathematics.
Perhaps the critical mathematicians
think the old system should be preserved since it served them well on a very
personal level. Indeed, the mathematicians are the success stories of the old
regime. They cannot imagine that anyone could reach their heights under a different
system. Or perhaps they are fearful of the consequences of that old regime falling,
that their priesthood of mathematics will crumble unless replenished from those
who have gone through the same system. I do believe their concern for nurturing
high-achieving students is legitimate, although our concern extends far beyond
those relatively small numbers. We need to communicate that our concern "for
all students" does not preclude a concern for the mathematically gifted,
and we are committed to meeting the needs of those students.
Some have suggested (perhaps
with some merit) that the Math Wars may be in part a turf battle. Mathematicians
may feel that they are being ignored on issues in which they feel deeply vested.
Accordingly, we must do a better job of including reasonable mathematicians
in our conversations and making sure that their perspectives are heard in important
decisions. Certainly Principles and Standards was a start; we included
mathematicians on all the writing groups and sought substantial input from the
mathematical community throughout the writing of the document. By bringing mathematicians
into the conversation, we may help defuse feelings of disenfranchisement and
the consequent anger. We must respectfully listen to the mathematical issues
they raise based on their expertise, while asserting our own expertise in working
with real students in real classrooms.
Finally, some mathematicians
may be feeling pressure to change their own teaching. Programs like the Harvard
program in calculus have caught on in many prestigious universities. Indeed,
until we can see further penetration of reform efforts into post-secondary education,
or at least until we find better ways of articulating between the differing
demands of pre-college and post-secondary education (whether traditional or
reform), our students will continue to suffer. We need to help our colleagues
in college or university mathematics departments see the value of the reform,
not just for pre-K-12, but for post-secondary students as well. You might start
by finding at least one "friendly" in the mathematics department at
your local college or university. Perhaps you could work with that person to
set up a colloquium or seminar addressing issues of reform, with both pre-college
and post-secondary folks invited to participate.
Parents can be either our
most powerful allies or our most effective detractors. When they tell their
horror stories of how "little Jimmy doesn't know how to do basic arithmetic...
and he's a senior in high school!" it makes a compelling story, and it
has an emotional impact on the audience. Likewise, their calls and letters to
school board members, legislators, and other elected officials can have a big
Many people have made this
point, but I think the biggest lesson we learned over the past decade is the
importance of informing and sharing with parents. If parents see their children
doing things that they themselves didn't do and frankly still don't understand,
those parents may naturally think something is suspect. And if their child gets
a low grade, parents may well jump to the conclusion that the reform effort
is the problem, no matter what else may be going on. In fact, it is increasingly
clear that when parents are given a chance to see what the reform is all about,
many (though not all) will support the effort. If parents can see the value
for their children, they can often be won over. If they are given a chance to
personally taste just a bit of reform mathematics, they can generally understand
how it better prepares students for the future. However, efforts to reach parents
are often made far too late in the game. Parents need to be brought on board
from the very beginning of the change process. When a decision is a done deal,
it's hard to forge the necessary support.
It is also important to
recognize that there can be other factors motivating parental resistance that
get mixed in with attempts to reform the curriculum. For example, perhaps the
gifted-and-talented program will be restructured as a part of an improvement
project. That may be the real target for some parents, but the change in curriculum
is an easier target to hit. In fact, it is not uncommon for issues of access
and equity to drive parental resistance. More affluent parents are good at working
the system to get what their students need. An improvement effort that attempts
to open the doors to more students can be viewed as taking something away from
their own children; wouldn't that money be better spent beefing up the GT program
that serves their children? As I once heard argued, "If the less-able students
receive a greater benefit from this program, that really means that my child
is being disadvantaged." Clearly, it is in the best interests of society
for everyone to succeed. But even the most socially aware and well meaning parents
can easily fall back to an elitist perspective when it is their own children
Perhaps the best way out
of this quandary is to emphasize the win-win nature of educational improvement.
For example, studies show that students using reform programs perform as well
as, or better than, students in traditional programs on college entrance and
college placement tests. And there is a value-added bonus: The reform students
are better able to apply their knowledge, and they have better attitudes about
mathematics to boot. (See, for example, evidence about the Core-Plus Mathematics
Project at www.wmich.edu/cpmp/info/faq-pieces/evidence.html.)
There are more than a few
teachers who oppose the reform efforts. However, these teachers tend not to
be in the forefront of the opposition. Without a doubt, we need to do a better
job of communicating to our teacher colleagues, because they will ultimately
be the heart and soul of any long-term change. From what I have seen, presenting
reform as a religion, in which one must be saved from the evil of one's past
sins, does little to help make the case. We must also acknowledge that some
teachers have implemented some of the reform recommendations as a religion,
focusing on cooperative groups, writing in journals, and other "creative"
activities at the expense of solid content. This tends to reinforce the viewpoint
that the reform is just another bandwagon that will come and go.
In order to help our teacher
colleagues understand the need for change, we must demonstrate
its practical value. The vast majority of teachers care deeply about their students,
and they are willing to pursue things that they perceive to be of real benefit
for their students. We need to do a better job of demonstrating that reform
is not a short-term fad. It is the result of years of effort, extensive research,
and intensive curriculum development. We also need to present a balanced view
of reform, emphasizing that re-examining our instructional practices and priorities
does not mean an abandonment of challenging mathematics.
A two-pronged approach might
be useful with skeptical colleagues. First, show them the hard research data
supporting reform. (See, for example, the resources at www.MathematicallySane.com/evidence/.)
Second, invite your colleagues to visit a class (preferably your own) to see
what reform looks like up close and personal. Be sure to ask them for their
impressions, rather than merely giving your interpretations (or excuses) for
what they see. Respond honestly and directly to their questions and concerns,
rather than trying to win an argument. We have the evidence on our side, but
we must be honest that real change is not easy. It is not an overnight miracle;
it is a long but ultimately rewarding journey.
Business people can be won
over if approached in the right way. Their future success depends on having
mathematically literate workers. We need to take the time to find out what their
needs are, and to show how what we are doing helps support those needs. Business
and industry spends billions of dollars in retraining, money that could possibly
be saved if the educational system were more effective. And they clearly need
workers who can do more than crunch numbers; they need mathematically literate
problem solvers, as shown in the 1991 SCANS report (U. S. Department of Labor).
Most businesses have a community outreach program or foundation. Contact businesses
in your area to see if they have such a program and, if they do, the persons
running the program might be a good starting point for making contacts.
Reporters care about one
thing: A good story. That's their job, plain and simple. If there isn't a hook
that will catch public interest, reporters are rarely interested. This is why
some of the critics have been able to do so well with the media: They have been
able to manufacture crises, casting the reform movement as the villain. But
reporters also have an obligation to be even-handed and give all involved a
chance to make their sides of the story known. This is why it is so critical
to respond quickly and forcefully to negative stories. A well-crafted response
submitted four weeks after the original story appeared has very little value.
Attention has moved on to other topics. It is no longer news. However, a timely
response has an excellent chance of appearing.
Getting to know reporters
is also important, so that when an issue arises they have someone at hand who
can give them the other side of the story. A former reporter for one of the
major networks once told a session I was attending, "Reporters have their
Rolodex file of persons to contact about different topics. Your goal should
be to get into that Rolodex file." Make a point to know the reporters who
cover education stories in your area, both print and television. And keep an
eye out for stories that you think might have some appeal to them.
Legislators and policy-makers
The story with elected officials
is quite simple: It's about votes. When an issue involving reform mathematics
comes before an elected official, they need to hear an overwhelming reaction
from people who vote in their district. Appointed officials may be somewhat
susceptible to the same pressures, especially if they hope to move to an elected
position in the future. Every hearing and public meeting needs to have a large,
organized contingent of people present to make the case for reform. As with
reporters, it is worth the effort to get to know legislators, school board members,
and others who may affect educational policy in your area.
The importance of organizing
and mobilizing people who are committed to change in your area cannot be overstated.
And the optimal time to organize is BEFORE a crisis comes up. After the fact
may be too late. Many sites (such as www.yahoogroups.com)
provide free e-mail lists that can be used to keep in touch, exchange information,
provide updates, and make plans. As stated in the first section of this article,
do not wait for someone else to make the first move. Start talking to others
in your area NOW, get your e-mail list set up, and start discussing what you
can be doing.
At a national level, I continue
to hope that NCTM itself, along with its state and local affiliates, will take
a more forceful leadership role in creating support networks at all levels.
We should not look to NCTM as the savior. There are things that NCTM cannot
rightfully do without compromising its reputation as a respected professional
organization. That is the reason, for example, that an independent group of
concerned persons (some of whom not at all surprisingly have been long involved
with NCTM) put together the Mathematically Sane web site (see www.MathematicallySane.com).
On the other hand, NCTM needs to take its rightful leadership role in reaching
out to its nearly 100,000 individual members and in helping its affiliates mobilize
to meet the demands before us.
A Perspective on Moving
In this short article I
have tried to emphasize the importance of actively and personally engaging in
the Math Wars. I have tried to portray some of the reasoning and motivation
driving the critics of reform, suggesting tactics for addressing those critics.
However, I would like to close on a somewhat different tone. On the final examination
for a graduate course I was teaching last semester, I asked students to "briefly
discuss ideas for how the 'Math Wars' could be brought to a peaceful end."
One student wrote, "The Wars shouldn't end. The two sides need each other."
I think there is at least some truth in that response, although one might wish
for some changes in the rules of engagement.
We need to learn from the
critics, rather than treating them only as adversaries to be defeated. We must
honestly admit that some travesties have been visited on students by well-meaning
teachers involved in reform. I well remember a mantra I seemed to hear everywhere
I went a few years back, "It doesn't matter if the students get the right
answer or not. It's the thinking that counts." Now on the surface, that
sounds very reform-like. However, being able to find correct answers is also
pretty important when building bridges that don't collapse. Our critics can
help us see where we have gone too far, to help keep us in check. Some of their
concerns are valid. When they are, we should acknowledge them, learn from them,
and use them to move forward.
Whenever possible, we should
seek to engage our critics in productive discussion. There are critics who have
shown that they are not willing to talk in a civil manner, and we should not
waste our time on them. However, those who have legitimate concerns and convictions,
even though somewhat different from ours, should be treated as potential allies
-- people from whom we can learn and who can learn from us -- until we have
been shown otherwise. Perhaps we can find more common ground if we keep our
eyes focused on what should be our mutual goal, to improve mathematics education
for all students. But when it proves necessary, we need to fight back decisively
and with conviction.
article is a version of a paper that has been submitted elsewhere for publication.
W. Gary Martin is an associate professor at Auburn University. He served as
the project director for NCTM's Standards 2000 Project.
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