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The radical changes in mathematics instruction advocated by the NCTM standardshave led to a polarized debate over textbooks and curricula which became known as the Math Wars.

"Reform" textbooks teach concepts which were once reserved for advanced students in higher grades. Procedural and traditional arithmetic skills such as long division are de-emphasized, or some say nearly totally deleted in favor context and content which has little or nothing to do withe mathetmatics. Some textbooks have a separate index solely for non-mathematics content called "contexts". Reform texts favor problem-solving in new contexts over template word problems with corresponding examples. Reform texts also emphasize verbal communication, writing about mathematics and their relationships with disenfranchised groups such as ethnicity, race, and gender identity, social justice, connections between concepts, and connections between representations.

By contrast, "traditional" textbooks emphasize procedural mathematics, such as arithmetic calculation, by providing step-by-step examples skill exercises. However, even many traditional textbooks such as Saxon math usually include some projects and exercises meant to address the NCTM Standards.

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?

Innovative curricula

• Mathland asks 2nd graders to cut out and paste a Fantasy Lunch.
• Investigations in Number, Data and Space does not contain instruction on any traditional computation methods, except to mention that they are to be discouraged. These include regrouping, the standard formulas for computing an average and volume, the standard notation for longhand division, and using "R" to indicate a remainder.

It has no student textbook. It uses 100 charts and skip counting, but not mulitiplication tables to teach multiplication. A study shows that a second grader who used his knowledge of the properties of negative numbers got more accurate results than another who used a traditional borrowing method. The second grade book includes sheet music to the song "happy birthday" which is meant to be sung in several languages although words to other languages are not provided. Decimal math is taught using colored pencils and 10,000 grid chart. Converting to a common denominator to add fractions is not taught.

• The introductory chapter for Matrices in the Core-Plus Mathematics Project spends a page explaining about Nike and the running shoe industry. It contains no information on how to solve any of the charting or data problems which follow. A matrix is used as a place to put a data table at the high school level. It has a separate "index of contexts" to non-mathematics topics such as "Monopoly", "Nike" or "global warming".

By contrast, math texts such as Singapore Math and Saxon math contain very little content or methods outside the field of traditional mathematics, and they make little use of sophisticated graphic calculators, or pictures of many diverse cultural or disabled groups.

NCTM 2006 Recommendations

In 2006, the NCTM released “Curriculum Focal Points,” a report on the topics considered central for school mathematics, consistent with the stand taken in the landmark 1989 standards document which launched the math wars of the 1990s and 2000s. Francis Fennell, president of the council made clear that there had been no change of direction or policy in the new report, and said that he resented talk of “math wars.” Interviews of many who were committed to the standards said that, like the 2000 standards, these merely refined and focused rather than renounced the original 1989 recommendations.

Nevertheless, newspapers like the Chicago Sun Times reported that the "NCTM council has admitted, more or less, that it goofed". The new report cited "inconsistency in the grade placement of mathematics topics as well as in how they are defined and what students are expected to learn." The new recommendations are that students are to be taught the basics, including the fundamentals of geometry and algebra, and memorizing multiplication tables.

Many school districts and states are committed to curricula and frameworks based on the mathematics standards which some parents and citizens claim robbed their children of an education in basic arithemetic skills.

Notes

Also see

• Principles and Standards for School Mathematics
• Education in the United States
• Mathematically Correct Leading source of propaganda about alleged defects in the standards.
• Traditional mathematics
• Outcome-based education

1. Reform Mathematics vs. The Basics: Understanding the Conflict and Dealing with It John A. Van de Walle Virginia Commonwealth University: "Debate has degenerated to 'math wars'"
2. Report Urges Changes in the Teaching of Math in U.S. Schools by TAMAR LEWIN New York Times September 13, 2006
3. Chicago Sun Times "Fuzzy teaching ideas never added up" September 13, 2006

• Education reform
• Mathematical publications
• Mathematics education
• Mathematics education reform
• Standards-based education