Efforts to improve math instruction and achievement must move beyond the single- minded debates over how the subject should be taught to a more comprehensive view of what students need to become proficient, a long-awaited report from the National Research Council recommends.
“Adding It Up: Helping Children Learn Mathematics” calls for an overhaul of instruction, curricula, and testing for elementary and middle school students. The report, released last week, also urges investment in more rigorous and ongoing professional development for teachers and further research on successful mathematics programs.
While both computational skills and a deep understanding of math concepts are essential parts of a complete math education, it concludes, other elements—including problem-solving and reasoning abilities, as well as an awareness of the relevance of math in everyday life— are also necessary for mathematical proficiency.
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| Read the report, “Adding It Up: Helping Children Learn Mathematics,” from the National Academy Press. |
“We wanted to get away from the debates about teaching skills or teaching understanding,” said Jeremy Kilpatrick, a mathematics professor at the University of Georgia and the chairman of the Mathematics Learning Study Committee, which produced the report. “It’s not a question of teaching one or the other. It’s about teaching skills and understanding, and much more.”
Essential for All Students
The 16-member committee, composed of mathematicians, math educators, cognitive psychologists, teachers, and a business representative, maintains that all students can and should acquire a deep knowledge and understanding of math in order to succeed in an increasingly technological world. But U.S. students’ performance on state and national tests, as well as in international comparisons—viewed as disappointing by many educators and policymakers—has forced a re-examination of how the subject is taught.
While test scores of 4th and 8th graders on the National Assessment of Educational Progress in math have been rising, just two-thirds of those students demonstrated basic skills on the test given in 1996. Results from the latest test, administered in 2000, are due out this spring.
The Third International Mathematics and Science Study, first conducted in 1995 and repeated for 8th graders only in 1999, found that American students were about average in math achievement compared with their counterparts in more than three dozen other nations. Moreover, the U.S. performance tended to drop off by 8th grade. The TIMSS report points to a shallow curriculum, inadequate instructional materials, and a lack of math expertise among most elementary and middle school teachers as barriers to improving math education.
Those findings have fueled recent debates over whether instruction should emphasize skill-building or deeper understanding of math concepts—arguments that draw parallels with the long-standing “reading wars.”
The National Research Council, a division of the congressionally chartered National Academy of Sciences, modeled “Adding It Up” after the NRC’s influential report on reading written by a panel of experts in 1998. (“NRC Panel Urges End to Reading Wars,” March 25, 1998.)
Similar to the reading panel, the math-committee members represented varying perspectives on how math should be taught and how students learn the subject. Beginning in 1999, the committee reviewed research on teaching and learning in the subject before making its recommendations.
Successful Strategies
The 444-page report presents a portrait of mathematics learning, using examples of how students acquire proficiency in whole numbers, rational numbers, and integers, as well as beginning algebra, geometry, measurement, and probability and statistics. It also describes how the relationship between teachers and students, as well as their attitudes toward the subject, affect how the material is taught and how well students learn it.
Vignettes included in the report show how different instructional strategies can lead to students’ proficiency, according to Deborah Loewenberg Ball, a professor of math education at the University of Michigan and a member of the panel.
“Our review of the research makes plain that the effectiveness of mathematics teaching and learning does not rest in simple labels,” the report says. “Rather, the quality of instruction is a function of teachers’ knowledge and use of mathematical content, teachers’ attention to and handling of students, and students’ engagement in and use of mathematical tasks.”
In addition to its primary recommendations, the committee came to a number of other conclusions for improving teaching and learning in the subject:
•While algebra for all middle school students is a worthwhile and attainable goal, the report says, simply moving Algebra 1 from 9th grade to 8th is a formula for failure. Instead, the panel suggests, algebraic principles should be built into the curriculum beginning in the early grades.
- A sufficient amount of time— at least an hour a day—should be allotted for teaching math, beginning in prekindergarten.
- The use of calculators and computers can benefit students, though further investigation is needed into how they can be used to improve learning.
- Textbooks and assessments should better reflect the strands of mathematical proficiency students need and should gauge how well students are learning them.
- Teacher education and professional development should not simply require teachers to take more math courses, but should stress courses that reflect the complex interplay between mathematical knowledge and effective teaching.
Shelf Life
The initial reaction to “Adding It Up” was positive among math educators, who see it as a unifying document amid the often-fierce “math wars.”
“There were a lot of people on the committee who brought very different perspectives, and they were able to come to consensus,” said John Thorpe, the executive director of the National Council of Teachers of Mathematics.
How much immediate influence the report might have in shaping education policy or improving classroom practice is hard to gauge, some observers said. Most states have already set—and some are already in the process of revising—the standards that are meant to drive instruction. The textbooks intended to help teachers meet those standards are either ready for sale or in the latter stages of development.
California, the most profitable state for publishers, adopted its K-8 mathematics textbooks earlier this month, and its next adoption is not scheduled for six years.
Committee members hope the report influences national initiatives that may come out of President Bush’s education agenda.
The report, sponsored by the Department of Education and the National Science Foundation, will also have a long “shelf life,” according to Michael Feuer, the director of the NRC’s Center for Education. As states and districts continue their work to improve math instruction, he said, it can provide guidance.
In the meantime, a sustained and comprehensive effort is needed, said Mr. Kilpatrick, the committee’s chairman. “We have never done well in this country in teaching mathematics to elementary and middle school children,” he said. “But that is not an excuse for complacency. It is time to take action.”
