The British mathematician J. E. Littlewood once began a math class for freshmen with the following statement: “I’ve been giving this lecture to first-year classes for over twenty-five years. You’d think they would begin to understand it by now.”
People involved in the debate about how math is best taught in grades K-12, must feel a bit like Littlewood in front of yet another first year class. Every year as objectionable math programs are introduced into schools, parents are alarmed at what isn’t being taught. The new “first-year class” of parents is then indoctrinated into what has come to be known as the math wars as the veterans - mathematicians, frustrated teachers, experienced parents, and pundits - start the laborious process of explanation once more.
It was therefore a watershed event when the President’s National Mathematics Advisory Panel (NMP) held its final meeting on March 13, 2008 and voted unanimously to approve its report: Foundations for Success: The Final Report of the National Mathematics Advisory Panel.
Unlike Littlewood addressing his perpetual first-year students, the report assumes that the class has actually begun to understand it by now and moves on. It does so quickly and efficiently: “[T]he system that translates mathematical knowledge into value and ability for the next generation - is broken and must be fixed. This is not a conclusion about teachers or school administrators, or textbooks or universities or any other single element of the system. It is about how the many parts do not now work together to achieve a result worthy of this country’s values and ambitions.”
The report provides benchmarks for the critical foundations of algebra, setting out grade level expectations of mastery for fluency with whole numbers, fluency with fractions, and geometry and measurement. It also provides recommendations for the major topics of an algebra class.
It assumes that most readers have taken that first year class in “math wars”, and can pick up on the nuances. For example, parents whose children have suffered through programs like Everyday Mathematics or Investigations in Number, Data and Space or other programs that grew out of grants from the Education and Human Resources Division of the National Science Foundation (NSF-EHR), know perfectly well what the following statement is about: “A focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula. Any approach that continually revisits topics year after year without closure is to be avoided.” Parents and others have heard the philosophy about “if they don’t learn it now, they’ll learn it later” - otherwise known as “spiraling”. They’ve seen the results and they don’t fall for the line. In a similar vein, parents (and teachers) who don’t fall for alternative and “student-invented” algorithms will be glad that the report prescribed the “standard” arithmetic algorithms, a topic on which the National Council of Teachers of Mathematics (NCTM) has looked the other way, even in the Focal Points, and something the NSF-EHR-engineered programs don’t even mention, let alone require.
When the report talks about the paucity of valid research on instructional practices, those who have taken the first-year class nod knowingly, recalling the countless times they have heard that “research shows” what they know not to be true. The report offers this statement: “Instructional practice should be informed by high-quality research, when available, and by the best professional judgment and experience of accomplished classroom teachers. High-quality research does not support the contention that instruction should be either entirely ’student-centered’ or ‘teacher-directed.’ Research indicates that some forms of particular instructional practices can have a positive impact under specified conditions.” This statement will no doubt be read many ways.
Teachers who have bought into many of the NSF-EHR-flavored math programs will say that they use a “balanced approach” to teaching, even though they may use programs that favor a “student-centered” approach. There are also teachers who maintain a truly balanced approach and who, while rejecting the discovery-oriented and textbook-less programs being foisted on schools across the country, are admonished by their administrators to do as they are told.
I attended the final meeting of the NMP. It was held at the Longfellow Middle School, where one of the panelists, Vern Williams, teaches math. Some statements of individual panelists stand out. Deborah Ball, Dean of the School of Education at University of Michigan stated she would be disappointed if the report were reduced to yet another math wars story, and people look for areas of disagreement, and reduce it to simplistic slogans. (I wonder then if she is disappointed in a statement by Steven Rasmussen, publisher of Key Curriculum Press, which publishes math textbooks in which he said “This report is biased in favor of teaching arithmetic and not [modern] mathematics…and it’s biased in favor of procedures and not applied skill.” The statement, while of the type Ms. Ball was deploring, was on the side of the quarrel she probably didn’t have in mind.)
David Geary, a cognitive developmental psychologist at University of Missouri, said that the reason a panel such as NMP was formed was because of the failure of schools of education to do what the country wants: Train teachers using research-based techniques, rather than running a playground for untested methods. Schools of education should be held accountable for their work, he said.
Vern Williams noted the current state of affairs in math education in which correct answers have been deemed over-rated and algebra has been redefined to include statistics and pattern recognition. He expressed his hopes that as a result of the NMP report teachers will feel it is once again crucial to consider content - and correct answers.
During a break in the meeting, however, an event occurred which to my mind simultaneously underscored and transcended the importance of NMP’s report. Williams’ 8th grade algebra class which had assembled at the back of the gym gathered, in rock fan fashion, around Hung-Hsi Wu - a panelist and math professor from Berkeley - to get his autograph and take pictures.
“I guess this shows that kids can get excited about math without sitting in groups doing projects and using math textbooks that look like video games,” Williams said.
I hope for the best in this post-NMP world.
Barry Garelick is an analyst for the U.S. Environmental Protection Agency in Washington, D.C. He is a national advisor to NYC HOLD, an education advocacy organization that addresses mathematics education in schools throughout the United States.