National Council of Teachers of Mathematics

The National Council of Teachers of Mathematics (NCTM) was founded in 1920. It has grown to be the world's largest organization concerned with mathematics education, having close to 100,000 members across the USA and Canada, and internationally.

NCTM holds annual national and regional conferences for American teachers and publishes four print journals and one on-line journal. Its published standards have been highly influential in the direction of mathematics education in the United States and Canada.

Journals

The NCTM does not conduct research in mathematics education, but it does publish the Journal for Research in Mathematics Education, which is the most influential periodical in mathematics education research worldwide and the fourth most referenced educational research journal of any kind.^[1] Summaries of the most important findings in mathematics educational research as regards current practices can be found on their website.

The NCTM also publishes three other print journals for elementary, middle school and high school teachers of mathematics.

NCTM Standards

NCTM has published a series of math Standards outlining a vision for school mathematics in the USA and Canada. In 1989 NCTM developed the Curriculum and Evaluation Standards for School Mathematics followed by the Professional Standards for Teaching Mathematics (1991), and the Assessment Standards for School Mathematics (1995). These math standards were widely lauded by education officials, and the National Science Foundation funded a number of projects to develop curricula consistent with recommendations of the standards. Several of these programs were cited by the Department of Education as "exemplary". On the other hand, implementation of the reform has run into strong criticism and opposition, including parental revolts and the creation of anti-reform organizations such as Mathematically Correct and HOLD. These organizations object especially to reform curricula that greatly decrease attention to the practice and memorization of basic skills and facts. Critics of the reform include a contingent of vocal mathematicians and some other mathematicians have expressed at least some serious criticism of the reformers in the past.

In 2000 NCTM released the updated Principles and Standards for School Mathematics. PSSM is widely considered to be a more balanced and less controversial vision of reform than its predecessor.

1989 Curriculum and Evaluation Standards for School Mathematics

The controversial 1989 NCTM Standards called for more emphasis on conceptual understanding and problem solving informed by a constructivist understanding of how children learn. The increased emphasis on concepts required decreased emphasis on direct instruction of facts and algorithms. This decrease of traditional rote learning was sometimes understood by both critics and proponents of the standards to mean elimination of basic skills and precise answers, but the NCTM has refuted this interpretation.^[2]

In reform mathematics, students are exposed to algebraic concepts such as patterns and the commutative property as early as first grade. Standard arithmetic methods are not taught until children have had an opportunity to explore and understand how mathematical principles work, usually by first inventing their own methods for solving problems and sometimes ending with children's guided discovery of traditional methods. The Standards called for a de-emphasis of complex calculation drills.

The standards set forth a democratic vision that for the first time set out to promote equity and mathematical power as a goal for all students, including women and underrepresented minorities. The use of calculators and manipulatives was encouraged and rote memorization were deemphasized. The 1989 standards encouraged writing in order to learn expression of mathematical ideas. All students were expected to master enough mathematics to succeed in college, and rather than defining success by rank order, uniform, high standards were set for all students. Explicit goals of standards based education reform were to require all students to pass high standards of performance, to improve international competitiveness, eliminate the achievement gap and produce a productive labor force. Such beliefs were considered congruent with the democratic vision of outcome-based education and standards based education reform that all students will meet standards. The U.S. Department of Education named several standards-based curricula as "exemplary", though a group of academics responded in protest with an ad taken out the in the Washington Post, noting selection was made largely on which curricula implemented the standards most extensively rather than on demonstrated improvements in test scores.^{[citation needed]}

The standards soon became the basis for many new federally funded curricula such as the Core-Plus Mathematics Project and became the foundation of many local and state curriculum frameworks. Although the standards were the consensus of those teaching mathematics in the context of real life, they also became a lightning rod of criticism as "math wars" erupted in some communities that were opposed to some of the more radical changes to mathematics instruction such as Mathland's Fantasy Lunch and what some dubbed "rainforest algebra". Some students complained that their new math courses placed them into remedial math in college, though later research found students from traditional curricula were going into remedial math in even greater numbers. (See Andover debate.)

In the United States, curricula is set at the state or local level. The California State Board of Education [1] was one of the first to embrace the 1989 standards, and also among the first to move back towards traditional standards.^[3]

2000 Principles and Standards for School Mathematics

The controversy surrounding the 1989 standards paved the way for revised standards which sought more clarity and balance. In 2000, NCTM used a consensus process involving mathematicians, teachers, and educational researchers to revise its standards with the release of the Principles and Standards for School Mathematics (PSSM), which replaced all preceding publications. The new standards were organized around six principles (Equity, Curriculum, Teaching, Learning, Assessment, and Technology) and ten strands which included five content areas (Number and Operations, Algebra, Geometry, Measurement, and Data Analysis and Probability) and five processes (Problem Solving, Reasoning and Proof, Communication, Connections, and Representation). PSSM was not perceived to be as radical as the 1989 standards and did not engender significant criticism. The new standards have been widely used to inform textbook creation, state and local curricula, and current trends in teaching.

2006 Curriculum Focal Points

In September 2006, NCTM released Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence. In the Focal Points, NCTM identifies what it believes to be the most important mathematical topics for each grade level, including the related ideas, concepts, skills, and procedures that form the foundation for understanding and lasting learning. In the Focal Points, NCTM made it clear that the standard algorithms were to be included in arithmetic instruction.

Mathematics curricula in the United States are often described as “a mile wide and an inch deep” when compared with curricula from other countries. State content expectations per grade level range anywhere between 26 and 89 topics. At just three per grade (plus a few additional "connection" topics), the focal points offer more than headings for long lists, providing instead descriptions of the most significant mathematical concepts and skills at each grade level and identifying important connections to other topics. NCTM believes that organizing a curriculum around these described focal points, with a clear emphasis on the processes that Principles and Standards addresses in the Process Standards—communication, reasoning, representation, connections, and, particularly, problem solving—can provide students with a connected, coherent, ever expanding body of mathematical knowledge and ways of thinking.

See also

• American Mathematical Association of Two-Year Colleges
• Mathematical Association of America

References

External links

• NCTM's Official Website
• Principles and Standards for School Mathematics
• NCTM's 2006 Curriculum Focal Points

Proponents

• Mathematically Sane

Critics

• Mathematically Correct
• Washington math advocacy group campaigning against NCTM math