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We can do better at teaching kids math

FOR DECADES the United States has not been producing a population that is fully competent and confident in mathematics. Recent test data from the Program for International Student Assessment indicate that 15-year-old students in the United States perform below average in mathematics literacy and problem solving compared with teenagers in other developed nations. Why are students not learning to solve math problems like those they might encounter in the workplace or other real-world situations?

One view is that we should build on the traditional mathematics curriculum we grew up with, in which we learned a procedure and then practiced it on pages of problems. Yet too often this approach goes no further, giving students skills without the knowledge needed to apply them. When James Stigler of UCLA and and James Hiebert of the University of Delaware studied eighth-grade classrooms in countries such as Hong Kong, Japan, and the Netherlands, where students outperform US students, they concluded that US students rarely spend time on "serious study of mathematical concepts."

Another view says that before students practice procedures, they should focus on the ideas behind those procedures: ideas about how numbers are related, how our base 10 number system works, what the arithmetic operations do and how they are related to each other. The National Science Foundation has funded the development of elementary, middle, and high school curriculums grounded in this approach.

TERC, a nonprofit research and development organization based in Cambridge, designed one of the elementary curriculums, "Investigations in Number, Data, and Space." Investigations has been extensively tested, with thousands of hours spent in urban and suburban classrooms documenting student learning to inform the development of the materials.

Given the current state of mathematics education, it is worth trying different approaches. But we must monitor them. Student performance on state-mandated tests shows that school systems incorporating curriculums funded by the National Science Foundation into a long-term plan for mathematics -- including Boston -- can make marked improvement.

In Boston, the percentage of failing students on the MCAS in grade 4 decreased from 46 percent to 30 percent between 2000 and 2004. During the same period, students scoring in the Proficient and Advanced categories increased from 14 percent to 22 percent.

A study by Comap Inc. included more than 100,000 students in Massachusetts, Illinois, and Washington. About half had studied at one of the three Science Foundation-funded elementary curriculums for at least two years; the other half, from comparison schools, were rigorously matched by reading level, socioeconomic status, and other variables.

The average scores in the first group, including scores on all computation subtests, were significantly higher than in the comparison schools. These results hold across different ethnic and income groups, and across the different state-mandated tests, including the MCAS.

Should students learn basic facts? Yes. Should they learn to add, subtract, multiply, and divide fluently? Certainly. But too often we lose sight of the fact that we must achieve both good computation skills and a good understanding of the mathematics. Curriculums, new or old, are only tools to improve mathematics in the classroom. Those who advocate a more traditional approach have a responsibility to show how they plan to go beyond the failed implementations of the past.

Schools must commit to coherent plans that include establishing learning goals, providing professional development to support teachers in learning more about mathematics and how children learn it, and implementing good assessment tools to evaluate progress. There is no such thing as a low-maintenance mathematics curriculum.

We must not succumb to the fantasy that there is an easy way out. Educators must provide --and parents should demand -- a balanced, rigorous curriculum in which all children, not just those in privileged communities, learn serious mathematics in a serious way -- with understanding.

William McCallum is a professor of mathematics at the University of Arizona. Susan Jo Russell, a mathematics educator at the Education Research Collaborative at TERC, directed the development of the Investigations curriculum. 

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