To perform a reasonable analysis of the quality of mathematics teaching requires an understanding not only of the essence of mathematics but also of current research about how students learn mathematical ideas, Mr. Battista points out. Without extensive knowledge of both, judgments made about what mathematics should be taught to schoolchildren and how it should be taught are necessarily naive and almost always wrong.
RECENT NEWSPAPER and newsmagazine articles, public debates at local school board meetings, and even the California State Board of Education1 have aimed a great deal of criticism at the current "reform movement" in mathematics education. Exploiting the growing "talk show/tabloid" mentality of Americans, opponents of reform support their arguments with hearsay, misinformation, sensationalism, polarization, and conflict as they attempt to seize control of school mathematics programs and return them to traditional teaching - that is, to the "basics." As they cite isolated examples of alleged failures of mathematics reform, they ignore the countless failures of traditional curricula. Their arguments lack understanding both of the essence of mathematics and of scientific research on how students learn mathematics.
Unfortunately, flawed as these arguments are, they nonetheless persuade citizens, legislators, and educational decision makers to adopt policies that are inconsistent with relevant professional, scholarly, and scientific recommendations about mathematics teaching. Consequently, they threaten the quality of the mathematics education received not only by the general citizenry but also by future mathematicians, scientists, and engineers. Thus they endanger the entire scientific/technical infrastructure of our country. In this article, I analyze the issues that are relevant to the reform of mathematics education from the perspective of the scholarly analysis that undergirds the reform movement and the current scientific research on mathematics learning.
How would you react if your doctor treated you or your children with methods that were 10 to 15 years out-of-date, ignored current scientific findings about diseases and medical treatments, and contradicted all professional recommendations for practice? It is highly unlikely that you would passively ignore such practice.
Yet that is exactly what happens with traditional mathematics teaching, which is still the norm in our nation's schools. For most students, school mathematics is an endless sequence of memorizing and forgetting facts and procedures that make little sense to them. Though the same topics are taught and retaught year after year, the students do not learn them. Numerous scientific studies have shown that traditional methods of teaching mathematics not only are ineffective but also seriously stunt the growth of students' mathematical reasoning and problem-solving skills.2 Traditional methods ignore recommendations by professional organizations in mathematics education, and they ignore modern scientific research on how children learn mathematics. Yet traditional teaching continues, taking its toll on the nation and on individuals.
For the nation, the economic costs of the traditional system of mathematical miseducation are staggering. According to the National Research Council, 60% of college mathematics enrollments are in courses ordinarily taught in high school,3 and the business sector spends as much on remedial mathematics education for employees as is spent on mathematics education in schools, colleges, and universities combined. The mathematical ignorance of our citizenry seriously handicaps our nation in a competitive and increasingly technological global marketplace.
For individuals, the effects of mathematical miseducation are like a long-term hidden illness that gradually incapacitates its victims. The results of testing by the National Assessment of Educational Progress indicate that only about 13% to 16% of 12th-graders are proficient in mathematics. …