The National Mathematics Advisory Panel (NMAP), created by the U.S. Department of Education in 2006 at President Bush’s urging, released its final report last month, which raises more questions than provides answers on the best practices of math instruction.
“One of the most surprising findings was how little available high-quality research there is especially in the field of instructional practices,” said panel member Vern Williams, a middle school teacher who has won many awards for his math instruction.
NMAP’s task was to rely on the “highest quality research” to recommend best practices for American math education, particularly focusing on the basic skills needed to succeed in algebra by the eighth or ninth grade.
One goal was to compare U.S. teaching practices with those of the highest scoring regions and nations: Czech Republic, Flemish Belgium, Hong Kong, Japan and Singapore. Many of the most important questions concerned math instruction. What makes some math teachers more effective than others? What types of education and training best prepares teachers to improve students’ math achievement?
For example, the panel came to a clear agreement on “The Major Topics of School Algebra,” which should be taught to every student. However, no one knows the best way to teach them.
“Unfortunately, little is known from existing high-quality research about what effective teachers do to generate gains in student learning,” the report stated. It also confirmed the fact that research shows a clear relationship between a teacher’s overall mathematical knowledge and how well his or her students perform. But, few studies have ever measured teachers’ knowledge directly. Instead, most rely on proxy measures such as being certified in math, or having taken a certain number of math classes in college. Therefore, the NMAP stated, “Existing knowledge does not reveal the specific mathematical knowledge and instructional skills needed for effective teaching, especially at the elementary and middle school level.”
Because it strongly believes that teachers who know more math are better able to teach it, the panel recommended that the best way to improve elementary school instruction is by having a few experts in each school teach all the math classes. This is considered a much more practical solution than trying to improve the math skills of all elementary school teachers who typically teach a variety of subjects.
The report repeatedly expressed disappointment in not being able to provide more specific recommendations about teaching techniques. Nevertheless, the panel clearly identified several problem areas in math education, rejected one major educational theory, and drew some conclusions about helping Black and Hispanic students and those with learning disabilities.
Among the major problem areas in math education:
· Fractions: American students have serious problems understanding fractions. Twenty-seven percent of eighth-graders could not shade in one-third of a rectangle. After learning the basic arithmetic operations of addition, subtraction, multiplication and division, many students in the fourth to eighth grades are still unable to multiply or divide fractions or understand the relationships between fractions, decimals and percentages.
· Focusing on talent: Another major barrier is the widespread belief that success in math is due to innate talent rather than effort, practice and perseverance. This is a particular problem for Black and Hispanic students.
· Textbooks: One of the panel’s conclusions was that American math textbooks are much too long (700-1000 pages), expensive and contain too much material that does not relate directly to mathematics. This is partly because book publishers are trying to meet the curriculum requirements of many different states. Books published for a single state, usually California or Texas, are often 200 pages shorter.
· Teaching too many topics and repeating them each year: Many U.S. school systems teach many more topics per grade (as many as 16-17) than higher-performing nations, which may only focus on eight or nine in greater depth. Many Americans schools also spend several months at the beginning of the year reviewing past material. Higher performing nations try to have students achieve complete mastery of a topic before going on to more complicated materials.
One of the panel’s most intellectually controversial findings was to reject the conclusions of Jean Piaget, an influential developmental psychologist who believed that children must pass through specific stages of mental development, or be a certain age, before they can grasp more abstract concepts. The NMAP stated that there are no set ages to teach children specific topics and that “ … what is developmentally appropriate is largely contingent on prior opportunities to learn.”
Students who are struggling with math seem to benefit from “explicit instruction.” This involves having the teacher provide clear models and strategies for solving a problem, giving the students extensive practice in using those strategies and providing chances to think aloud and talk through the decisions they make and the steps they take.
Finally, the panel concluded that interventions that address social, affective and motivational factors, such as working together in groups or having appropriate role models, are important in improving the performance of certain minority groups.
It noted that, “Recent research documents that social and intellectual support from peers and teachers is associated with higher mathematical performance for all students, and that such support is especially important for many African-American and Hispanic students.”
Carmen Arroyo, director of research for the Education Trust, said, “The panel had two critical messages for these students and their teachers. One is the idea that it is more important to learn things better than faster. The second is the emphasis that math is a learned skill that improves if you keep working on it, rather than an innate talent that some people have and others just don’t.”
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