Does Two Plus Two Still Equal Four?

Good afternoon. I am pleased to be here, and I appreciate the opportunity to address this distinguished audience. I’m here today as president of the National Council of Teachers of Mathematics, which is the world’s largest organization dedicated to improving mathematics education in grades prekindergarten through grade 12.

We all agree that we want and need to improve the mathematics education of American students. I want to emphasize that NCTM is dedicated to a high-quality mathematics education for all the students we serve. And although there may be some questions about how best to go about achieving that goal, there are certainly some things we can all agree on.

Education in the United States is a multifaceted, complex endeavor. Parents, teachers, policymakers, and business leaders all have their own views about what’s most important, but we all agree that there is a critical need for improvement. In a world that increasingly demands specialized skills in the workplace, a sound mathematics education is the crucial gateway to professional and economical success. In a world that demands a greater understanding of people and ideas, mathematics education with problem solving as a foundation is needed more than ever.

In 1983, the report A Nation at Risk raised awareness of the state of K–12 education in the United States. That report led to the historic 1989 education summit in Williamsburg, Virginia, where the nation’s governors mapped out a list of goals that our schools would strive to meet by the year 2000. One clear goal was that "by the year 2000, United States students will be the first in the world in mathematics and science achievement."

We have fallen short of this goal. The 1995 Third International Math and Science Study (TIMSS) showed that whereas U.S. fourth-grade students scored above the international average in science and mathematics, eighth-grade students scored below their international counterparts, and the TIMSS results from U.S. twelfth-grade students were disappointing. However, in 1999, the results of TIMMS-Repeat found that "students in classes emphasizing reasoning and problem-solving had higher achievement than those in classes with a low emphasis on these activities."

There is other encouraging news about the performance of U.S. students. In August 2001, the National Assessment of Educational Progress (NAEP) released its Mathematics 2000 assessment. The results show that since 1990, the number of American fourth-graders at proficiency level in mathematics doubled from 13 percent to 26 percent, and 69 percent of fourth-graders in 2000 were above the basic level. In the eighth grade, those at proficiency level increased from 15 percent to 27 percent. The scores of fourth- and eighth-graders at all levels improved since 1996, and twelfth-graders at the highest level of proficiency also showed improvement.

So we are encouraged by the steady progress in mathematics learning by most of our students over the past decade. But we can and must do better. In today’s rapidly changing world, it is more important than ever that we provide a high-quality mathematics education for all students.

NCTM’s Principles and Standards for School Mathematics

The National Council of Teachers of Mathematics produced its Principles and Standards for School Mathematics in April 2000. Our updated Standards sets forth a vision of high-quality mathematics education for all students, a vision of mathematics education for the future. We say, "higher standards for students; higher standards for ourselves," the teachers of mathematics. It is my hope that Principles and Standards for School Mathematics will guide the development of future mathematics curricula and help K–12 teachers become even better teachers of mathematics. It is essential that our Principles not be ignored or dismissed, and that some not be treated as less important than others. Among these Principles are the Equity Principle and the Teaching Principle. The Equity Principle states, "Excellence in mathematics education requires equity—high expectations and strong support for all students." The Teaching Principle says, "Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well."

As our Standards become more widely integrated into teaching and implemented in more curricula, we should see evidence of even better student learning and higher scores on future NAEP and TIMMS assessments.

I think it is worth noting that the NAEP Mathematics 2000 assessment shows gradual improvement in the mathematics competence of American students over the past decade. These gains coincide with the 1989 release of NCTM’s Curriculum and Evaluation Standards for School Mathematics, which Principles and Standards for School Mathematics has served to update.

If we need to do more, what must we do? It is worth noting that far too many teachers of mathematics in the United States are teaching out of their fields or have little training in mathematics or mathematics education. Of the 300,000 middle- and high-school science and mathematics teachers in the United States, nearly 30 percent—46,000 mathematics teachers and 40,000 science teachers—neither majored nor minored in the subjects they teach. In high-poverty schools the situation is even worse: Students there have less than a 50 percent chance of having a science or mathematics teacher who holds both a license and a degree in these subjects.

How to Improve Mathematics Education

Improving student achievement requires a coherent plan that includes high expectations for students and teachers, rigorous curricula and assessment, and a local, state, and national commitment to improving science and mathematics achievement for all students. It must begin with prekindergarten day care. We should require that all day-care facilities become learning centers for our nation’s children, staffed with qualified teachers and support staff. As the Glenn Commission report, "Before It’s Too Late," states, "The most direct route to improving mathematics and science education for all students is better mathematics and science teaching."

We need to make a much greater commitment to training our teachers at all levels, including the universities. Many teachers, especially in elementary and middle grades, have neither the content knowledge nor the pedagogical preparation to teach mathematics. We need to provide better preparation for these teachers. Starting immediately, we should require that all middle-grades teachers of mathematics be certified to teach mathematics.

We also need to take a more realistic approach to professional development for teachers. Too often it’s the case that if a teacher receives any kind of professional development it’s in the form of attending one meeting or one session a year. Meaningful professional development should be ongoing, and it should include the mentoring by experienced peers and the contributions of mathematicians and mathematics educators from institutions of higher learning. The math-science partnerships described in the education bill recently signed into law would draw from businesses and higher education to form partnerships that would offer the best of what each partner has to offer. And schools should put in place systems to allow teachers on the job more time to discuss and develop their skills among their peers. Finally, we must pay our teachers what they are worth. The average tenure of today’s teacher entering the workforce is short for a variety of reasons, but one of these is pay. Businesses often hire away the best educators, and in many cases they’re luring them out of the classroom with wages that our education system has not chosen to match.

What Does This Mean?

Our children are simply not receiving the world-class education in mathematics that they deserve and we expect. While this fact alone is serious, perhaps more troubling are the long-term implications for our nation’s economic growth, national security, workforce development, and the science, mathematics, and technology literacy of our citizens.

It is estimated that nearly half of all economic growth in the United States results directly from research and development in science and technology. Our pre-K–12 education is not producing the intellectual capital necessary to ensure that future generations of scientists and engineers can maintain the research and development vital to our continued economic growth. As the economy becomes increasingly global and technologically complex, it is essential that pre-K–12 education be strengthened to prepare today’s students to be tomorrow’s productive workers and citizens.

The less-than-adequate preparation of potential scientists, mathematicians, and engineers in the formative pre-K–12 years can also pose a serious threat to national security. Mathematics, science, and engineering supply the basis for the development of satellite communications technologies, information technologies, and other high-tech methodologies now employed by our nation’s armed forces. In fact, the Defense Department relies on university researchers and their students to perform over half of its basic research.

Our changing workforce demands new workers who will be equipped with ever sharper skills in mathematics. In today’s market, businesses are begging for skilled technical workers to fill open positions. For several years now, Congress has raised the ceiling on the number of H-1B visas, allowing more skilled foreign workers into the United States. Congress has raised that ceiling to just under 200,000 workers per year until 2003. What’s more, U.S. businesses spent $62.5 billion in 2000 to upgrade basic employee skills. There is an urgent need to develop a technologically capable workforce that can compete in the global economy. Employers are increasingly concerned about the lack of technically skilled workers. Much more emphasis must be placed on the education we provide to pre-K–12 students to overcome these skill deficits.

Mathematical, scientific, and technological literacy is critical for an informed democracy and the continuation of a vibrant high-tech society. Research has shown that pre-K–12 education is not producing citizens who are able to understand even basic science and technology concepts, let alone the knowledge needed to understand emerging issues such as cloning, DNA, and global warming.

The Federal Government’s Role in Improving Science and Mathematics Education

Although states play the lead role in funding education and shepherding education reform, the federal government must strengthen its longstanding effort to improve the quality of science and mathematics education. Bold, systemic changes are necessary now in pre-K–12 math and science education before we’re faced with the problems inherent in a workforce and citizenry woefully ignorant of basic science, mathematical, and technology principles.

There should be federal investments in professional development programs and activities challenging state and national standards in mathematics and science education that are long-term, content based, and aligned with Principles and Standards for School Mathematics. We should also provide increased resources and incentives for the recruitment, preparation, and retention of mathematics and science teachers in grades pre-K through 12. More testing of students is not going to solve the problem if we are not prepared to use the results to help all students benefit from the information. The point of testing at the national level must not only be about how well did students do, but rather, what does the nation need to provide to students and school systems to improve on their performance?

If the reason a child is scoring low is because his teacher is not well prepared, how does holding the student back help matters? If the reason a child is performing poorly is because her curriculum is not providing high-quality mathematics and opportunities to learn that mathematics, how does holding her back help the situation? If turnover among teachers at a school is high, how does withholding dollars to that school help?

The recently signed education bill creates partnerships among the private sector, universities and colleges, industry, professional societies, and schools and teachers to develop quality education programs for students and professional development opportunities for teachers. These partnerships should benefit from the best contributions that each partner has to offer and should draw on the best resources of each, especially business and industry. All these interested parties should be encouraged to contribute what they can to promote higher achievement among teachers and students.

The public support to strengthen our pre-K–12 educational system means that federal investments must be expanded to include bold, large-scale national and state initiatives that are required to change the ways in which mathematics and science are taught throughout these United States. Federal programs must work closely with the states to provide needs-based professional development that meets state goals and is aligned with national and state standards.

Conclusion

Collectively, the most recent NAEP results bring good news. Nevertheless, more needs to be done to better prepare all students in school mathematics. We need to attract bright and dedicated individuals to the teaching profession and encourage those already teaching to stay. We need to invest in teachers’ preservice education, support professional development throughout their careers, and provide higher pay for all teachers. Elevating teaching to a valued profession will help attract and retain more qualified teachers in every field, and especially in mathematics and science.

We should build on the promise of recent improvements and rededicate ourselves to more significant progress in the future. We owe it to our children, we owe it to our nation, and we owe it to ourselves to do the best we can for all of our children.

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