Papers and Presentations, Mathematics and Science Initiative
Today the President addresses a serious issue in American education—How well we as a nation do in educating our children in mathematics. Dr. Loveless has addressed this issue using data from our nation's report card—NAEP. I will address the same issue but from an international point of view.
The data are clear. Recent results from the Third International Mathematics and Science Study (TIMSS) show that US eighth and twelfth graders do not do well by international standards—ranking below average in both grades and, in fact, near the bottom of the international rankings on a mathematics literacy test at the end of high school. Even our best students in mathematics taking an advanced mathematics test do not fare well against their counterparts in the other countries. Those results were obtained in 1995 but even a retesting four years later in 1999 produced the same disappointing results. Put simply—there is no evidence to suggest that we as a nation are doing better, at least relative to other countries. New international results will soon become available as a third retesting will occur this spring, but I fear there is little reason to expect major improvement.
Why do I feel this way? When you add the fourth grade results where our students were above average to the picture, a pattern emerges of a steady decline in our international ranking from fourth to twelfth grade. This suggests that our students do not start out behind but increasingly fall behind during the middle and high school years. This suggests that the problem lies not with our children, but that it is the education system that is failing them. This, I believe, strongly supports the need for a major national initiative in mathematics education.
Make no mistake—the problems in mathematics education have implications that are real and not just academic. The implications are for individual children as they seek employment in an increasingly technological economy where, given the lowering of trade barriers, they are competing not only with each other, but with children from around the world. The TIMSS data suggest they will not fare well in such a competition. This has implications for our nation as a whole, as well. It is not clear how long we can make up for deficiencies in our own educational system by importing the needed talent from other countries. Such a brain chase has become more competitive as other nations also compete for the same individuals. As the New York Times recently reported, the nation may soon regret not being concerned with the proper education of its own native born.
To stop here only restates what many already know—we, as adults, are failing our own children. What else have we learned from the international studies that might help us to respond to this serious situation. Other nations' representatives often ask me why does our student achievement not improve especially given that we are constantly reforming mathematics education in the US. The short answer is that we often engage in reform that is not based on scientific evidence but rather on opinion and someone's ideology. TIMSS offers us a good opportunity to use scientifically collected data on some 50 countries to find a more promising answer to the question of what we should do to improve the mathematics education of all children so that we truly do not leave any of them behind.
TIMSS results suggest that the top achieving countries have coherent, focused and demanding mathematics curricula. What would a coherent curriculum look like? A coherent curriculum leads students through a sequence of topics and performances over the grades that reflects the logical and sequential nature of knowledge in mathematics. Such a curriculum helps students to move from particular knowledge and skills toward an understanding of deeper structures, more complex ideas and mathematical reasoning including problem solving. For example, students should be expected to master the basic concept of number and basic computational skills in the early grades before they tackle more difficult mathematics.
What does the US curriculum look like? The US curriculum as reflected in many of the states' standards and in our nation's textbooks tends to reflect an arbitrariness where topics appear somewhat haphazardly throughout the grades. For example, teachers are expected to introduce relatively advanced mathematics in the earliest grades before students have had an opportunity to master basic concepts and computational skills. Secondly, the curriculum continues to focus on basic computational skills through grade eight and perhaps beyond. I would argue that if the logic of mathematics is not transparent to students, then it becomes difficult for them to develop a deep understanding that would lead to higher achievement.
What does a focused and rigorous curriculum look like in the top achieving countries? The number of topics that children are expected to learn at a given grade level is relatively small, permitting a thorough and deep coverage of each topic. For example, nine topics are the average number intended in the second grade. The US by contrast expects second grade teachers to cover twice as many mathematics topics. The result is a characterization of the US curriculum as a mile wide and an inch deep.
Coherent standards move from the simple to the complex. By the middle grades the top achieving countries do not intend that children should continue to study basic computation skills but rather that they begin the transition to the study of algebra, including linear equations and functions, geometry and even in some cases, basic trigonometry. By the end of eighth grade in these countries children have mostly completed US high school courses in algebra I and geometry. By contrast, most US students are destined to mostly continue the study of arithmetic. In fact, we estimate that at the end of eighth grade US students are some two or more years behind their counterparts around the world.
All of this is related to what students learn. That is why schools matter. The major policy implication of all of this is if we are serious about providing all students with a challenging mathematics curriculum it must be coherent, focused and demanding not by our own sense of what this might mean, but by international standards. We expect this of our companies, why would we expect less for our children's education. This implies we must secure the advice of the research mathematics community in this process together with those who understand children and how they learn mathematics.
But, this will not be enough. It is necessary to change our curricular expectations, but it is not sufficient to increase the achievement of all of our students. Recent research involving the top achieving countries suggests that the preparation of middle school teachers in mathematics includes a demanding level of preparation in theoretical mathematics as well as preparation in topic specific pedagogy, i.e., how to teach particular mathematics topics to children of a certain age. The level of formal mathematics training is very demanding in these countries. This required level of knowledge for eighth grade teachers gives some insight as to how such a demanding curriculum can be required in other countries and not just for their elite, but for all children—a goal we only seek, but one that is realized in many European and Asian countries.
Secretary Paige and his department have identified the national problem that many mathematics teachers do not have a major or even a minor in mathematics. The problem, however, is even more severe. Data collected from a group of districts that are in many ways similar to the US indicate the severity of the problem. Over half of the sixth through eighth grade mathematics teachers have neither a major or a minor in mathematics. For those teachers only onefourth feel, by their own assessment, well prepared academically to teach a basic set of topics—most dealing with arithmetic only. We must address this issue of teacher quality and one important way is to begin by including mathematical knowledge as a key component in the definition of teacher quality.
We, in this nation, have set a goal to provide all children with a demanding mathematics curriculum that leads to greater learning. The goal is right, but the road there is demanding. Curriculum must be rigorous and coherent by international standards. It must be focused. It must require our middle schools to expect more of our students. It must be taught by teachers well prepared in mathematics and in instructional approaches that themselves are steeped in mathematics as well as cognitive theories of how children learn. And, it must be for all children.
Excellence in mathematics must be our highest national priority if we are to fulfill the true promise of America for all of our children. To do otherwise is unconscionable.


