# It's Not Just About the Numbers

Recent results of international math assessments make one thing clear: American students are consistently outperformed in mathematics by their international counterparts.

That said, there's widespread disagreement over why. Some undoubtedly see the scores as an indictment of reform mathematics-too much emphasis on process and not enough on product. For this camp, the federal No Child Left Behind Act's emphasis on testing is just the right thing. Others argue precisely the opposite: that the No Child Left Behind law's focus on test outcomes is hurting teacher innovation and limiting inquiring minds through "drill and kill"-style education.

As teacher-educators and lifelong mathematics enthusiasts, we think that America's problems with math are not new news; they predate both the No Child Left Behind Act and the reform-math movement. To us, the story here is less about test scores and more about the nation's attitudes toward math. Simply put, America is math-phobic-to an extent that profoundly influences our country's policies, teaching practices, and, ultimately, the performance of our students.

At bottom, most people in this country-including educators and policymakers at the highest levels-believe that math is a subject in which only a small subset of naturally gifted people can do well. (That will only be reinforced by the recent findings of the Program for International Student Assessment, or pisa, which reveal what could be called-with apologies to W.E.B. Du Bois-a "talented tenth" in mathematics in the United States.) Thus, children get the message from adults that math is something to be feared-to rush through and to memorize rather than to savor, appreciate, and enjoy. They overhear conversations among parents, teachers, school administrators, and other adults about "mathematics genes" and "natural ability."

One result of this is that we don't expect very much of our students. We allow them to say, "I can't do math," when we would be chagrined if they said, "I can't read." Where we might expect A's from our children in other subjects, we are often content when they achieve merely passing grades in math. When students do receive A's for their math work, often it is for doing simple and basic-skills math, not the rigorous mathematics they could and should be doing. Perhaps worst of all, we don't demand that math be interesting and challenging to students at all levels, instead of mind-numbingly boring, as it so often is.

In fact, the finding in several curricular studies (including the Trends in International Mathematics and Science Study, or TIMSS) show repeatedly that the U.S. mathematics curriculum is very broad and not at all deep. This means that students and teachers spend a lot of time doing largely "introductory" problems without ever really getting to the essence of mathematics-as a mechanism to solve problems in several domains. Because of the necessity of teaching many concepts simultaneously, teachers have little opportunity to get students involved in thinking about unknown situations, developing new, nonroutine approaches and procedures, and selecting-on their own-applicable techniques to solve problems.

The fact is that everyone can learn mathematics, and even enjoy doing so. But our current efforts at improvement, while well-intentioned, are mired in a simplistic, one-shot approach. We focus on one thing at a time-adopting radical curricular changes without restructuring teacher professional development; revising assessments without considering student opportunities to learn in school-while disregarding the potential magic, the challenges, and the hard realities of mathematics classrooms in this country.

Learning about best practices and mathematics curricula from other countries may be part of a solution. But what's often missing from attempts to implement these is recognition that teachers in the United States go through a professional process very different from that of teachers in other countries. For the most part, teachers here are themselves products of an education system that teaches students merely to match the right procedure to the right problem, rather than actually problem-solve.

So instead of focusing on how we stack up compared to other countries, let's talk about real solutions: revisiting teacher education and professional development; using assessment in timely ways to address student misconceptions and errors and to inform teacher practice and curriculum organization; equalizing mathematics resources in poor, urban, and rural schools; and building in a problem-centered approach to mathematics, in which students and teachers have time to engage in exploring interesting mathematics problems, reasoning, testing new ideas, and applying new mathematics knowledge. It's an ambitious agenda, but all of these would be significant new steps.

In short, it's easy to state the solution to America's math problem and much more complicated to enact it: We've got to address our own national phobia about math. Because it's not just students and teachers who need help with mathematics. It's all of us.

*Published Wednesday, Feb. 9, 2005*

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# It's Not Just About the Numbers

Recent results of international math assessments make one thing clear: American students are consistently outperformed in mathematics by their international counterparts.

That said, there's widespread disagreement over why. Some undoubtedly see the scores as an indictment of reform mathematics-too much emphasis on process and not enough on product. For this camp, the federal No Child Left Behind Act's emphasis on testing is just the right thing. Others argue precisely the opposite: that the No Child Left Behind law's focus on test outcomes is hurting teacher innovation and limiting inquiring minds through "drill and kill"-style education.

As teacher-educators and lifelong mathematics enthusiasts, we think that America's problems with math are not new news; they predate both the No Child Left Behind Act and the reform-math movement. To us, the story here is less about test scores and more about the nation's attitudes toward math. Simply put, America is math-phobic-to an extent that profoundly influences our country's policies, teaching practices, and, ultimately, the performance of our students.

At bottom, most people in this country-including educators and policymakers at the highest levels-believe that math is a subject in which only a small subset of naturally gifted people can do well. (That will only be reinforced by the recent findings of the Program for International Student Assessment, or pisa, which reveal what could be called-with apologies to W.E.B. Du Bois-a "talented tenth" in mathematics in the United States.) Thus, children get the message from adults that math is something to be feared-to rush through and to memorize rather than to savor, appreciate, and enjoy. They overhear conversations among parents, teachers, school administrators, and other adults about "mathematics genes" and "natural ability."

One result of this is that we don't expect very much of our students. We allow them to say, "I can't do math," when we would be chagrined if they said, "I can't read." Where we might expect A's from our children in other subjects, we are often content when they achieve merely passing grades in math. When students do receive A's for their math work, often it is for doing simple and basic-skills math, not the rigorous mathematics they could and should be doing. Perhaps worst of all, we don't demand that math be interesting and challenging to students at all levels, instead of mind-numbingly boring, as it so often is.

In fact, the finding in several curricular studies (including the Trends in International Mathematics and Science Study, or TIMSS) show repeatedly that the U.S. mathematics curriculum is very broad and not at all deep. This means that students and teachers spend a lot of time doing largely "introductory" problems without ever really getting to the essence of mathematics-as a mechanism to solve problems in several domains. Because of the necessity of teaching many concepts simultaneously, teachers have little opportunity to get students involved in thinking about unknown situations, developing new, nonroutine approaches and procedures, and selecting-on their own-applicable techniques to solve problems.

The fact is that everyone can learn mathematics, and even enjoy doing so. But our current efforts at improvement, while well-intentioned, are mired in a simplistic, one-shot approach. We focus on one thing at a time-adopting radical curricular changes without restructuring teacher professional development; revising assessments without considering student opportunities to learn in school-while disregarding the potential magic, the challenges, and the hard realities of mathematics classrooms in this country.

Learning about best practices and mathematics curricula from other countries may be part of a solution. But what's often missing from attempts to implement these is recognition that teachers in the United States go through a professional process very different from that of teachers in other countries. For the most part, teachers here are themselves products of an education system that teaches students merely to match the right procedure to the right problem, rather than actually problem-solve.

So instead of focusing on how we stack up compared to other countries, let's talk about real solutions: revisiting teacher education and professional development; using assessment in timely ways to address student misconceptions and errors and to inform teacher practice and curriculum organization; equalizing mathematics resources in poor, urban, and rural schools; and building in a problem-centered approach to mathematics, in which students and teachers have time to engage in exploring interesting mathematics problems, reasoning, testing new ideas, and applying new mathematics knowledge. It's an ambitious agenda, but all of these would be significant new steps.

In short, it's easy to state the solution to America's math problem and much more complicated to enact it: We've got to address our own national phobia about math. Because it's not just students and teachers who need help with mathematics. It's all of us.