National Council of Teachers of Mathematics

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National Council of Teachers of Mathematics
Formation	1920
Headquarters	Reston, VA
Membership	nearly 100,000
President	Francis "Skip" Fennell
Website	http://www.nctm.org

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.

1 NCTM Standards
2 1989 Curriculum and Evaluation Standards for School Mathematics
3 2006 Curriculum Focal Points
4 See also
5 External links
- 5.1 Proponents
- 5.2 Critics

[edit] 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 many other mathematicians have expressed at least some serious criticism of the reformers in the past. Given the strong support for the reform among math educators, the conflict over the reform has created tensions between them and mathematicians.

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. Most current reform curricula and policies, however, were shaped primarily by the original Standards from 1989.

[edit] 1989 Curriculum and Evaluation Standards for School Mathematics

The controversial 1989 NCTM standards recommended teaching elements of algebra as early as grade 5, and elements of calculus as early as grade 9, though this was rarely adopted even as late as the 2000s. In standards based education reform, all students, not only the college bound must take advanced mathematics. In some large school districts, this means requiring algebra of all students by the end of junior high school, compared to the tradition of tracking only college bound and the most advanced junior high school students to take algebra.

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.

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 calculator and manipulatives are encouraged, but algebra skills and rote memorization are deemphasized, and there is writing about mathematics as well as computation. Some controversial math curricula such as Investigations in Numbers, Data, and Space were based on research papers such as those by Constance Kamii which assert that teaching of traditional arithmetic methods such as borrowing "not only are not helpful in learning arithmetic, but also hinder children’s development of numerical reasoning".^[1] All students are expected to master enough mathematics to succeed in college, and rather than defining success by rank order, uniform, high standards are set for all students. Explicit goals of standards based education reform are 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, which are congruent with the democratic vision of outcome-based education and standards based education reform that all students will meet standards, refute past research which shows an achievement gap in scores between groups of different education development on every test and assessment, even those aligned with reformed mathematics standards and instruction. The U.S. Department of Education would name several standards based curricula as "exemplary", though academics would respond in protest with an ad taken out the in the Washington Post, and they would note selection was made largely on which curricula implemented the standards most extensively rather than on demonstrated improvements in test scores. The reform standards, while widely accepted as a consensus by education agencies from local to federal levels, were met with intense criticism from groups such as Mathematically Correct; the controversy was widely characterized by newspapers such as the Wall Street Journal as "math wars".

In the era of standards based education reform, a curriculum framework is often set at a state level. For example, 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.^[2] In a standards based system, the curriculum is aligned with the standards. The final step in the system is that by 2006, nearly two-thirds of students in the USA would have to pass high school graduation examination set to World class standards of what every student must know and be able to do to succeed in the 21st century. However in states such as Washington, the success of mathematics reform was in question as half of sophomores and four-fifths of minorities were still struggling to pass the math standard needed to make the promise made in the 1993 education reform bill a reality that most or all would graduate two years later with a diploma. While some officials blamed this on incomplete adoption of the 1989 standards, other districts which had already embraced the 1989 standards were deciding instead to replace or supplement standards-based curricula with more traditional instruction such as Saxon math or Singapore Math in face of poor standardized test results.

The style of instruction can also vary from traditional direct instruction of multi-digit multiplication in books such as Singapore Math to standards-based instruction such as Investigations in Numbers, Time, and Space which may omit instruction or even discourage use of any standard calculation algorithm or method in favor of guiding students to invent their own mathematical power by using 100 charts, colored pencils, glue, writing, and singing songs in different languages. Some education officials have stated that achieving a numerically correct result is secondary to the higher order thinking process.^[3]

In standards-based curriculum frameworks, math topics and goals may include the history and legacy of diverse multicultural groups in mathematics, mathematical communication, number sense, mathematical power, and equity. Real life examples integrate contemporary issues such as the rain forests, environment, careers, and other topics which integrate other fields of knowledge. Critics including US senators would dub one such text as "rainforest algebra" with 812 pages of seemingly anything but algebra content.^[4]

Related to issues of equity in mathematics, where some groups are under-represented in math and science fields, and others tend to dominate mathematics research, the field of Mathematical Relationships concerns how persons form relationships with mathematics, how they identify with the subject and how they dissidentify with it, around social class, gender, race/ethnicity, dis/ability, nationality, and sexuality.^[5] Some critics such as David Klein of California State University Northridge believe such issues belong in social studies, not mathematics, and that mathematics should be taught in a classical method to all students without regard to a student's group affinities.

In a February 9, 1994 article in Education Week on the Web, Steven Leinwand wrote: "It's time to recognize that, for many students, real mathematical power, on the one hand, and facility with multidigit, pencil-and-paper computational algorithms, on the other, are mutually exclusive. In fact, it's time to acknowledge that continuing to teach these skills to our students is not only unnecessary, but counterproductive and downright dangerous." Leinwand was part of the expert panel that in early October of 1999 directed the United States Department of Education to endorse ten K-12 mathematics as"exemplary" or "promising." The "exemplary" programs announced by the Department of Education were:

Cognitive Tutor Algebra
College Preparatory Mathematics (CPM)
Connected Mathematics Program (CMP)
Core-Plus Mathematics Project
Interactive Mathematics Program (IMP)

The "promising" programs were:

Everyday Mathematics
MathLand
Middle-school Mathematics through Applications Project (MMAP)
Number Power
The University of Chicago School Mathematics Project (UCSMP)

The American Institutes for Research lauded the new U.S. standards for giving greater than nations like Singapore to developing important 21st century mathematical skills that go beyond the skill sets used to develop 20th century technologies such as computers and space flight:^[6]

Representation
Reasoning
Making connections
Communication
Statistics, powerpoint-style charts and probability

Some mathematicians such as David Klein of California State University Northridge challenged the emphasis given to gender and race "equity" in the mathematics reform movement.^[7] One of the themes of the mathematics reform movement is that traditional mathematics fails because women and members of ethnic minority groups are treated differently than white males. Objections to mathematics curricula which introduced multicultural writing while often omitting traditional arithmetic methods recognizable to parents came largely from mathematicians rather than educators whose "real life" applications might be to use linear algebra to compute bake sale proceeds.^[8]

A few states such as California which were early adopters of the 1989 standards would later revise their math standards and assesements, leading a new movement to reject the assumptions of the original 1989 standards as fatally flawed in favor of traditional skills and memorization of math facts.^[9] Some public schools in the mid 2000s started to supplement or replace their standards-based mathematics curricula with texts which emphasized direct instruction of traditional mathematics such as Saxon math, popularized by homeschoolers who often rejected standards-based curricula, and Singapore Math because of poor performance on standardized tests compared to other nations and frustration over standards-based approaches which de-emphasized rather than taught arithmetic as it had been known for generations.^[10].

[edit] 2006 Curriculum Focal Points

In September 2006, NCTM released Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence. These focal points present the most important mathematical topics for each grade level and comprise related ideas, concepts, skills, and procedures that form the foundation for understanding and lasting learning.

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 from anywhere between 26 and 89 topics. At just three per grade, 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. 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.

Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics thus represents an important, initial step in advancing collaborative discussions about what mathematics students should know and be able to do.