By Michael Childs
mchilds@coe.uga.edu
American students’ progress toward proficiency in mathematics requires major changes in instruction, curricula and assessment in the nation’s schools, says the UGA professor who headed a study on math learning for the National Research Council of the National Academies. To help schoolchildren successfully develop all aspects of mathematics learning, a coordinated and systematic approach to mathematics education from pre-kindergarten through eighth grade is critical.
“Too few students leave elementary or middle school with adequate mathematical knowledge, skill and confidence for the nation to be satisfied with the condition of school mathematics,” says Jeremy Kilpatrick, chair of the committee that wrote the report and Regents Professor of Mathematics Education at UGA.
“Simply developing speed in pencil-and-paper arithmetic may have been sufficient when their parents and grandparents were in school, but today’s students need a deeper understanding of mathematics to thrive in an increasingly technical economy,” Kilpatrick says. “Improvement requires a comprehensive and sustained effort among policy makers, administrators, teachers, university faculty, parents and others to enhance both instruction and achievement.”
Knowledge of mathematics is important for making sense of a high-tech world, yet the nation’s approach to school mathematics in pre-kindergarten through eighth grade has been inconsistent and marked by an emphasis on routine arithmetic—with a heavy dose of memorization and repetition, the committee reported. Furthermore, recent studies have shown that many elementary and middle school teachers have only a shaky grasp of mathematics themselves, and often are unable to clarify key concepts for students or solve problems that involve more than basic calculations.
This failure to explore mathematics fully limits an individual’s potential and hampers national progress by insufficiently preparing future workers and citizens, the report points out. Results from state, national and international assessments conducted over the past 30 years indicate that U.S. students can adequately perform straightforward computational procedures, but they have a limited understanding of fundamental ideas. They also have trouble applying mathematical skills to solve even simple problems. And these trends may further impede the academic advancement of at-risk students.
Following its exhaustive review and synthesis of scientific literature on mathematics education in pre-kindergarten through eighth grade, the committee’s paramount recommendation is that the nation can and should groom all students to be “mathematically proficient,” mastering much more than disconnected facts and procedures. Moreover, this target should drive school-improvement efforts, the committee emphasized.
Five intertwined and equally important strands comprise the committee’s definition of mathematical proficiency. First, capable students should be able to understand and apply important concepts. They also should be able to compute with ease, formulate and solve problems, and explain their reasoning. Finally, they should have confidence in their abilities and view mathematics as a sensible and worthwhile subject. Each strand requires constant attention, the report says.
The committee concentrated on how students learn about numbers and operations. Relevant research was abundant, and debates over mathematics curricula and instruction in elementary and middle schools often center on arithmetic. Nonetheless, the goal of proficiency also applies to other important areas of mathematics, including algebra, geometry and statistics, the report says.
Mathematical proficiency develops over time, building on a knowledge base that begins to take shape in infancy. The committee did not endorse any single approach to effective instruction, but recommended that teachers use students’ informal understanding of mathematics as a stepping stone toward mastery of more challenging skills and concepts.
Beginning in preschool, educators should offer students opportunities to extend their rudimentary comprehension of numbers. In subsequent years, the curriculum should link calculation to everyday situations to help students make such connections. And it should illustrate numbers and operations in various ways, the report adds. For example, one-half can be shown as a fraction, a decimal or a percentage, as a point between zero and one on a number line, or as a shaded portion of a figure.
In addition, educators should teach important concepts in depth, instead of covering a multitude of topics superficially, the committee said. Significant time also should be devoted to daily mathematics instruction in every grade of elementary and middle school.
Exams should test students’ progress in all five strands of mathematical proficiency.
To prepare teachers better for elementary or middle school math instruction, the committee recommended that colleges and universities should create programs that emphasize thorough knowledge of mathematics and of processes through which schoolchildren come to understand the subject. On the job, schools should give teachers more time and other resources—such as continuous and high-quality training, as well as useful instructional materials—to acquire a solid understanding of mathematics and improve their techniques. Teachers who have special training in the subject should be available in elementary schools to assist their colleagues.
Proficiency is an ambitious goal, and the United States will never reach it by continuing to tinker with the controls of education policy, the report says. In recent years, many states and school districts have raised academic standards in mathematics, introduced new assessments, and offered teachers new professional-development opportunities. But these efforts have been fragmented.
While a solid base of scientific evidence supports the committee’s call for immediate action to help all students become mathematically proficient, additional research is needed to shed more light on the elements of successful mathematics teaching and learning, as well as obstacles that block progress. Such investigations, coupled with data from systematic evaluation of programs and initiatives, should routinely inform improvement efforts, the report points out. |
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