Math Wars and the Principles and Standards for School Mathematics

The NCTM Standards have led to changes in mathematics textbooks. Perhaps because of the abruptness of these changes, debate over textbooks has sometimes been polarized. This debate is known as the "Math Wars."

"Reform" textbooks teach concepts which used to be reserved for advanced students in higher grades, while de-emphasizing procedural skills such as long division. They often require the purchase of, and are dependent on graphic calculators which cost over US $100 since students are no longer expected to be proficient in manual arithmetic. Reform texts favor problem-solving in new contexts over template word problems with corresponding examples. Reform texts emphasize written and verbal communication, working in a group, connections between concepts, connections between representations, activities such as cutting, pasting, and in the case of "Investigations" singing that were once reserved for kindergarten. Some devote so much space in print on "contexts" that the Core-Plus Mathematics Project includes a separate index of contexts with topics ranging from the board-game Monopoly to Nike and rain forests.

The emphasis introducing so many topics so early has been criticized, even by the NCTM, as a curriculum that is a Mile wide and an inch deep. Some experts believe that many topics are introduced too early, though the 1989 standards call for bringing the introduction to algebra as early as elementary school, and calculus in early high school. Core-Plus introduces linear algebra and matrices, once taught in freshman college calculus, as early as junior high school in some districts. Teaching advanced mathematics to all students rather than only the students on the most advanced track may appear to promote equity, but may not be appropriate for students who have not even mastered basic arithmetic. Some integrated math texts have been criticized as covering too many topics in a haphazard sequence, while spending only brief time on topics such as solving linear equations which a traditional algebra class might devote months to deep understanding of a few important single topics.

By contrast, "traditional" textbooks emphasize procedural mathematics, such as arithmetic calculation. They provide step-by-step examples with skill exercises. Unlike texts which have been called Rainforest algebra, they have far fewer pages, and they devote little or no space to real-life contexts such as running shoe companies or geography. The entirety of the first page on matrices in Core-Plus is devoted to information on running shoe companies and their stores, and contains no content about what matrices are. Unlike the standards, texts adapted from Japan or Singapore include students and examples from only a single culture. They do not include historical figures to enhance cultural or gender identity diversity, make no reference to "mathematical power" and contain little or no content with regard to social justice or the equity sought by the standards. However, current traditional textbooks usually include some projects and exercises meant to address the NCTM Standards. Most of the parent and mathematics professional objections in the math wars have been in regard to the dearth or poor quality of mathematical content. In contrast, the lack of diversity, context, or equity laid out by the 1989 standards has mainly objected to by the administrators and officials who have promoted standards based mathematics, and have opposed adoption of more traditional texts such as Saxon math and Singapore math.

One of the subtexts to the debate over the Standards is the rapid development of technology. Has the invention of the calculator made some of the traditional mathematics curriculum obsolete? In the Information Age, are problem solving and communication more valuable than symbolic algebra?