Shaping the future of math instruction

Last May, Education Secretary Margaret Spellings announced the 17 expert panelists, and six “ex-officio” members, chosen to advise educators and policy makers on the best use of scientifically based research to advance the teaching and learning of mathematics. “To keep America competitive in the 21st century, we must improve the way we teach math, and we must give more students the chance to take advanced math and science courses in high school,” Spellings said.

The National Math Advisory Panel, chaired by Larry Faulkner, president of the Houston Endowment and President Emeritus of the University of Texas at Austin, released its first progress reports on Jan. 11. However, because the panel’s research is not complete and its final report is not scheduled for release until next February, these preliminary reports did not include any recommendations.

The panel consists of four working groups: Conceptual Knowledge and Skills, Learning Processes, Instructional Practices, and Teachers. Each group presented its own report.

Conceptual Knowledge and Skills Task Group

This group aims to define the key math concepts and skills that should be taught at various grade levels. Its progress report included a topical list of the concepts and skills needed for pre-kindergarten through eighth grade math, derived from an analysis of state curriculum standards and the math curricula for Japan, Korea, Flemish-Belgium, Singapore, and Chinese Tapei, among other sources.

The group has pinpointed the key concepts and skills that students should learn regarding numbers and operations, algebra, geometry and measurement, and data analysis and probability. In putting together its list, the group appears to have sought a proper balance between computational fluency and conceptual understanding.

For example, under numbers and operations are 11 distinct skills, including “develop automaticity of multiplication facts and related division facts and fluency with the multiplication and division of whole numbers,” as well as “define ratio and rate in terms of multiplication and division” and “develop an understanding of and apply proportionality, including similarity.”

The group also is looking at having some algebra learned before high school: “Write, interpret, and use mathematical expressions and equations” and “analyze and represent linear functions and solve linear equations and systems of linear equations” appear in the list.

“With the following topical list for levels preK-8, it is important to provide the instructional time and emphasis needed for students to develop concepts, solve problems, and compute,” the group notes.

It also says the panel’s final recommendations might articulate grade-by-grade expectations–and, if so, the National Council of Teachers of Mathematics’ Curriculum Focal Points “will be seriously considered.”

In addition, the Conceptual Knowledge and Skills Task Group’s report outlined the key algebra skills and concepts that students should learn, ranging from symbols and expressions to quadratic relations and functions–but it noted that, while there is general agreement about the scope and sequence of skills in pre-kindergarten through eighth grade, no such agreement exists yet regarding algebra skills.

Learning Processes Task Group

This group aims to identify the key principles of learning and cognition and apply them to the study of mathematics, to help shape and inform the work of the other groups.

In its work so far, the group has explored how children learn, why they “choke” during testing, individual and group differences in how kids learn, and how brain science and learning math work together.

In examining the available research on how kids learn, the group has identified what skills children already bring to school–there is an inborn sense of quantity that each child possesses, but it’s not sufficient by itself to begin school-based learning–and has looked at whole-number learning. Its next steps are to examine how students learn fractions, estimation, algebra, and geometry, and to draw explicit links with the work of the other task groups.

The Learning Processes group’s work so far demonstrates why a healthy balance between computational fluency and conceptual understanding is so necessary.

Studies show that practice leads to automatic retrieval of declarative information or execution of procedures, the group’s report says–but conceptual knowledge is what promotes the transfer of skills to new situations.

Still, this automatic retrieval of math facts is necessary to help students overcome the anxiety often associated with testing. “Choking” on tests occurs when competency-related thoughts–that is, the high stakes involved in the exam–intrude on students’ working memory, according to the group’s preliminary report. Its solution: “automaticity” of test-related content.

Instructional Practices Task Group

This group is looking at what research says about the effectiveness of various instructional approaches to mathematics. It has focused in particular on teacher-centered (direct) versus student-centered (“inquiry-based”) instruction, as well as the importance of “real-world” problems and approaches.

According to the group, the benefits of real-world instruction–which uses problems and examples grounded in practical applications of math–include greater student motivation before lessons and engagement during lessons. Supporters of real-world approaches also say they have the potential to raise achievement and lead to greater long-term retention. But there are dangers in this approach as well, the group’s report suggests.

In its 2005 “State of State Math Standards” report, a review of the math standards of all 50 states, the Fordham Foundation described “excessive emphases” on “real-world problems,” the group says. The foundation reportedly warned, “Excessive emphasis on the ‘real world’ leads to tedious exercises in measuring playgrounds and taking census data, under headings like ‘geometry’ and ‘statistics,’ in place of teaching mathematics.”

Some of the topics the Instructional Practices group will be examining more closely are the ideal sequencing of tasks–that is, are real-world tasks more appropriate at the beginning of a lesson, where they can boost students’ motivation, or at the end of the lesson, where students can apply what they’ve learned?–and the appropriate amount of time that math teachers should spend on real-world tasks.

Teachers Task Group

This group has four areas of focus: teachers’ knowledge of mathematics, teacher education and professional development programs, elementary math specialists, and recruitment and retention of math teachers.

In this first area of focus, the group aims to develop “a firmer understanding of the mathematical knowledge needed for teaching.” The answer to this question, the group says, is “crucial” to its understanding of the other focus areas.

In these other three areas, the group seeks to determine which approaches might be most effective. For example, what kinds of teacher education programs have been shown to be effective? Do particular designs or curricula make a difference in teachers’ instructional skills, or their students’ achievement?

Implications of the panel’s work

“The buzz in the air is that the recommendations of the math panel will emphasize more basic skills,” says Steve Ritter, chief product architect and founder of Carnegie Learning. He adds, “My expectation is that the report will have a reasonable balance between understanding the need for students to become fluent in their basic mathematics skills and the need for application of mathematics and problem solving.”

One of the concrete things Ritter imagines will happen as a result of the panel’s work is that the ratio of basic, “naked” math to application problems offered in textbooks and practice sets will start to change–with more application problems, and fewer basic problems, being included.

On the other hand, Mary Ann Stine, director of curriculum and instruction for the Everett School District in Washington, is not certain how much influence the math panel’s recommendations really will have, particularly when it comes to curriculum.

“Some schools don’t get any federal money, so I suppose if you don’t get federal dollars, you wouldn’t have to pay any attention to the math panel at all,” she said. “If [federal officials] want people to pay attention to the math panel, they’ll have to tie dollar amounts” to implementing the group’s recommendations.

Who’s who on the National Math Panel

In addition to Faulkner, panelists include:

“Deborah Ball, Dean, University of Michigan School of Education;

“Camilla Benbow, Dean of Education and Human Development, Vanderbilt University’s Peabody College;

“A. Wade Boykin, Professor and Director of the Developmental Psychology Graduate Program, Howard University Department of Psychology;

“Francis Fennell, Professor of Education, McDaniel College, and National Council of Teachers of Mathematics President;

” David Geary, Curators’ Professor, University of Missouri at Columbia’s Department of Psychology;

” Russell Gersten, Executive Director, Instructional Research Group; Professor Emeritus, University of Oregon College for Education;

“Nancy Ichinaga, former Principal, Bennett-Kew Elementary School, Inglewood, Calif.;

“Tom Loveless, Director, Brown Center on Education Policy and Senior Fellow in Governance Studies, The Brookings Institution;

“Liping Ma, Senior Scholar for the Advancement of Teaching, Carnegie Foundation;

“Valerie Reyna, Professor of Human Development and Psychology, Cornell University; “Wilfried Schmid, Professor of Mathematics, Harvard University;

“Robert Siegler, Teresa Heinz Professor of Cognitive Psychology, Carnegie Mellon University;

“Jim Simons, President, Renaissance Technologies Corp.; former Chairman of the Mathematics Department, State University of New York at Stony Brook;

“Sandra Stotsky, independent researcher and consultant in education; former Senior Associate Commissioner, Massachusetts Department of Education;

“Vern Williams, Math Teacher, Longfellow Middle School, Fairfax, Va.; and

“Hung-His Wu, Professor of Mathematics, University of California at Berkeley.

–Jennifer Nastu

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