National Council of Teachers of Mathematics

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National Council of Teachers of Mathematics
National Council of Teacheres of Mathematics logo.svg
Formation1920
Headquarters Reston, VA
President
Robert Q. Berry III
Website http://www.nctm.org
Education in the United States
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Founded in 1920, The National Council of Teachers of Mathematics (NCTM) is the world's largest mathematics education organization. [1]

Contents

NCTM holds annual national and regional conferences for teachers and publishes five journals.

Journals

NCTM publishes five journals. All are available in print and online versions.

Teaching Children Mathematics , an official journal of the National Council of Teachers of Mathematics (NCTM), supports improvement of pre-K–6 mathematics education by serving as a resource for teachers so as to provide more and better mathematics for all students. It is a forum for the exchange of mathematics idea, activities, and pedagogical strategies, and or sharing and interpreting research.

Mathematics Teaching in the Middle School , an official journal of the National Council of Teachers of Mathematics, supports the improvement of 5–9 mathematics education by serving as a resource for practicing and prospective teachers, as well as supervisors and teacher educators. It is a forum for the exchange of mathematics idea, activities, and pedagogical strategies, and or sharing and interpreting research.

Mathematics Teacher , an official NCTM journal, is devoted to improving mathematics instruction for grades 8–14 and supporting teacher education programs. It provides a forum for sharing activities and pedagogical strategies, deepening understanding of mathematical ideas, and linking mathematical education research to practice.

Mathematics Teacher Educator , published jointly with the Association of Mathematics Teacher Educators, contributes to building a professional knowledge base for mathematics teacher educators that stems from, develops, and strengthens practitioner knowledge. The journal provides a means for practitioner knowledge related to the preparation and support of teachers of mathematics to be not only public, shared, and stored, but also verified and improved over time (Hiebert, Gallimore, and Stigler 2002).

NCTM does not conduct research in mathematics education, but it does publish the Journal for Research in Mathematics Education (JRME). Summaries of the most important findings in mathematics educational research in regard to current practices can be found on their website. JRME is devoted to the interests of teachers of mathematics and mathematics education at all levels—preschool through adult. JRME is a forum for disciplined inquiry into the teaching and learning of mathematics. The editors encourage the submission of a variety of manuscripts: reports of research, including experiments, case studies, surveys, philosophical studies, and historical studies; articles about research, including literature reviews and theoretical analyses; brief reports of research; critiques of articles and books; and brief commentaries on issues pertaining to research.

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). Education officials lauded these math standards, and the National Science Foundation funded several projects to develop curricula consistent with recommendations of the standards. The Department of Education cited several of these programs as "exemplary". However, implementation of the reform has run into strong criticism and opposition, including parental revolts and the creation of antireform 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 . Principles and Standards is widely considered to be a more balanced and less controversial vision of reform than its predecessor.

Post–World War II plan

In 1944, NCTM created a postwar plan to help World War II have a lasting effect on math education. Grades 1-6 were considered crucial years to build the foundations of math concepts with the main focus on algebra. In the war years, algebra had one understood purpose: to help the military and industries with the war effort. Math educators hoped to help their students see the need for algebra in the life of an everyday citizen. [2] The report outlined three strategies that helped math educators emphasize the everyday usage of algebra. First, teachers focused on the meanings behind concepts. Before, teachers were expected to use either the Drill or the Meaning Theory. Now, teachers gave students purpose behind every concept while providing an ample number of problems. Second, teachers abandoned the informal technique of teaching. This technique was popular during the 1930s and continued during the war, and in essence depended on what the students wanted to learn, based on their interests and needs. Instead, math teachers approached the material in an organized manner. The thinking was that Math itself had a very distinct organization that could not be compromised simply because the student was uninterested in the matter. Third, teachers learned to adapt to the students by offering the proper practice students needed in order to be successful. [2] After the sixth year, seventh and eighth grades were considered key in ensuring students learned concepts, and were increasingly standardized for all pupils. During these years, teachers verified all key concepts learned in the previous years were mastered, while preparing students for the sequential math courses offered in high school. The army credited poor performance of males during the war to the men forgetting math concepts; it was recommended that reinforcing past concepts learned would solve this problem. The report lists the organization of the topics that should be taught in these years. "(1) number and computation; (2) the geometry of everyday life; (3) graphic representation; (4) an introduction to the essentials of elementary algebra (formula and equation)." [2] At the same time, these years were meant to help students gain critical thinking skills applicable to every aspect of life. In middle school, students should gain maturity in math, and confidence in past material. [2] In ninth grade, NCTM expressed the need for a two track curriculum for students in large schools. Those who have a greater desire to study math would go on one track, studying algebra. Those who did not have a large interest in math would go another route, studying general mathematics, which eliminated the problem of students being held back. [2] Finally, grades 10-12 built math maturity. In the tenth year, courses focused on geometry through algebraic uses. The eleventh year focused on a continuation of more advanced algebra topics. These topics were more advanced than those discussed in the ninth grade. However, if the student took an advanced algebra class during the ninth year, then he took two of the semester classes offered the twelfth year.

1961 The Revolution in School Mathematics

NCTM participated in promoting the adoption of the New Mathematics also known at that time as Modern Mathematics. In 1960, NCTM with the financial support of the National Science Foundation, conducted eight Regional Orientation Conferences in Mathematics in various parts of the United States, pushing to "make a concerted effort toward rapid improvement of school mathematics". [3] In 1961 it issued a report The Revolution in School Mathematics subtitled A Challenge for Administrators and Teachers.

Morris Kline, a Professor of Mathematics, asserted in his book Why Johnny Can't Add: The Failure of the New Math that The Revolution in School Mathematics described the New Math curricula as a necessary milestone for establishing new and improved mathematics programs, and "implied that administrators who failed to adopt the reforms were guilty of indifference or inactivity". [4] Most school administrators "did not have the broad scientific background to evaluate the proposed innovations", [4] so they faced the choice of either adopting one of the modern programs, or admit that they are not competent to judge the merits of any one. Ultimately, "many principals and superintendents urged the modern curricula on their teachers just to show parents and school boards that they were alert and active". [4]

Kline criticised the Modern Mathematics approach to mathematics education and labelled the term "Modern Mathematics" as "pure propaganda". He noted that "traditional connotes antiquity, inadequacy, sterility, and is a term of censure. Modern connotes the up-to-date, relevant, and vital". [4]

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 NCTM has refuted this interpretation. [5]

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 de-emphasized. 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 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 are set at the state or local level. The California State Board of Education was one of the first to embrace the 1989 standards, and also among the first to move back towards traditional standards. [6]

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, 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). Principles and Standards 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.

The Focal Points were one of the documents used in creating the 2010 Common Core State Standards, which have been adopted by most states as the basis for new math curricula.

See also

Related Research Articles

Mathematics education Mathematics teaching, learning and scholarly research

In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research.

New Math Style of teaching mathematics in the 1960s

New Mathematics or New Math was a dramatic change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries and elsewhere, during the 1950s–1970s. Curriculum topics and teaching practices were changed in the U.S. shortly after the Sputnik crisis. The goal was to boost students' science education and mathematical skill to meet the technological threat of Soviet engineers, reputedly highly skilled mathematicians.

Principles and Standards for School Mathematics (PSSM) are guidelines produced by the National Council of Teachers of Mathematics (NCTM) in 2000, setting forth recommendations for mathematics educators. They form a national vision for preschool through twelfth grade mathematics education in the US and Canada. It is the primary model for standards-based mathematics.

Physics First is an educational program in the USA, that teaches a basic physics course in the ninth grade, rather than the biology course which is more standard in public schools. This course relies on the limited math skills that the students have from pre-algebra and algebra I. With these skills students study a broad subset of the introductory physics canon with an emphasis on topics which can be experienced kinesthetically or without deep mathematical reasoning. Furthermore, teaching physics first is better suited for English Language Learners, who would be overwhelmed by the substantial vocabulary requirements of Biology.

Saxon math, developed by John Saxon, is a teaching method for incremental learning of mathematics. It involves teaching a new mathematical concept every day and constantly reviewing old concepts. Early editions were deprecated for providing very few opportunities to practice the new material before plunging into a review of all previous material. Newer editions typically split the day's work evenly between practicing the new material and reviewing old material. Its primary strength is in a steady review of all previous material, which is especially important to students who struggle with retaining the math they previously learned. However, it has sometimes been criticized for its heavy emphasis on rote rather than conceptual learning.

Core-Plus Mathematics Project

Core-Plus Mathematics is a high school mathematics program consisting of a four-year series of print and digital student textbooks and supporting materials for teachers, developed by the Core-Plus Mathematics Project (CPMP) at Western Michigan University, with funding from the National Science Foundation. Development of the program started in 1992. The first edition, entitled Contemporary Mathematics in Context: A Unified Approach, was completed in 1995. The third edition, entitled Core-Plus Mathematics: Contemporary Mathematics in Context, was published by McGraw-Hill Education in 2015.

Mathematically Correct was a U.S.-based website created by educators, parents, mathematicians, and scientists who were concerned about the direction of reform mathematics curricula based on NCTM standards. Created in 1997, it was a frequently cited website in the so-called Math wars, and was actively updated until 2003. The website went offline sometime in late 2012 or early 2013 but has been preserved on the Internet Archive.

Traditional mathematics was the predominant method of mathematics education in the United States in the early-to-mid 20th century. This contrasts with non-traditional approaches to math education. Traditional mathematics education has been challenged by several reform movements over the last several decades, notably new math, a now largely abandoned and discredited set of alternative methods, and most recently reform or standards-based mathematics based on NCTM standards, which is federally supported and has been widely adopted, but subject to ongoing criticism.

Investigations in Numbers, Data, and Space is a K–5 mathematics curriculum, developed at TERC in Cambridge, Massachusetts, United States. The curriculum is often referred to as Investigations or simply TERC. Patterned after the NCTM standards for mathematics, it is among the most widely used of the new reform mathematics curricula. As opposed to referring to textbooks and having teachers impose methods for solving arithmetic problems, the TERC program uses a constructivist approach that encourages students to develop their own understanding of mathematics. The curriculum underwent a major revision in 2005–2007.

Basic skills can be compared to higher order thinking skills. Facts and methods are highly valued under the back-to-basics approach to education.

MathLand was one of several elementary mathematics curricula that were designed around the 1989 NCTM standards. It was developed and published by Creative Publications and was initially adopted by the U.S. state of California and schools run by the US Department of Defense by the mid 1990s. Unlike curricula such as Investigations in Numbers, Data, and Space, by 2007 Mathland was no longer offered by the publisher, and has since been dropped by many early adopters. Its demise may have been, at least in part, a result of intense scrutiny by critics.

The Interactive Mathematics Program (IMP) is a four-year, problem-based mathematics curriculum for high schools. It was one of several curricula funded by the National Science Foundation and designed around the 1989 National Council of Teachers of Mathematics (NCTM) standards. The IMP books were authored by Dan Fendel and Diane Resek, professors of mathematics at San Francisco State University, and by Lynne Alper and Sherry Fraser. IMP was published by Key Curriculum Press in 1997 and sold in 2012 to It's About Time.

Integrated mathematics is the term used in the United States to describe the style of mathematics education which integrates many topics or strands of mathematics throughout each year of secondary school. Each math course in secondary school covers topics in algebra, geometry, trigonometry and analysis. Nearly all countries throughout the world, except the United States, follow this type of curriculum.

Math wars is the debate over modern mathematics education, textbooks and curricula in the United States that was triggered by the publication in 1989 of the Curriculum and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM) and subsequent development and widespread adoption of a new generation of mathematics curricula inspired by these standards.

Connected Mathematics is a comprehensive mathematics program intended for U.S. students in grades 6-8. The curriculum design, text materials for students, and supporting resources for teachers were created and have been progressively refined by the Connected Mathematics Project (CMP) at Michigan State University with advice and contributions from many mathematics teachers, curriculum developers, mathematicians, and mathematics education researchers.

Recall of facts is a value of education which is to be de-emphasized in reform of science according to new American national curriculum standards. Recall facts is often associated with rote learning.

Reform mathematics is an approach to mathematics education, particularly in North America. It is based on principles explained in 1989 by the National Council of Teachers of Mathematics (NCTM). The NCTM document, Curriculum and Evaluation Standards for School Mathematics, attempted to set forth a vision for K-12 mathematics education in the United States and Canada. Their recommendations were adopted by many education agencies, from local to federal levels through the 1990s. In 2000, NCTM revised its standards with the publication of Principles and Standards for School Mathematics (PSSM). Like the first publication, these updated standards have continued to serve as the basis for many states' mathematics standards, and for many federally funded textbook projects. The first standards gave a strong call for a de-emphasis on manual arithmetic in favor of students' discovering their own knowledge and conceptual thinking. The PSSM has taken a more balanced view, but still emphasizes conceptual thinking and problem solving.

From kindergarten through high school, the mathematics education in public schools in the United States has historically varied widely from state to state, and often even varies considerably within individual states. With the recent adoption of the Common Core Standards by 45 states, mathematics content across the country is moving into closer agreement for each grade level.

The Secondary School Mathematics Curriculum Improvement Study (SSMCIS) was the name of an American mathematics education program that stood for both the name of a curriculum and the name of the project that was responsible for developing curriculum materials. It is considered part of the second round of initiatives in the "New Math" movement of the 1960s. The program was led by Howard F. Fehr, a professor at Columbia University Teachers College.

Sybilla Beckmann is a 2011 Josiah Meigs Distinguished Teaching Professor of Mathematics at the University of Georgia and is a previous recipient of the Association for Women in Mathematics Louise Hay Award.

References

  1. "Overview - National Council of Teachers of Mathematics".
  2. 1 2 3 4 5 National Council of Teachers of Mathematics (1941) [1941], Arithmetic in general education : The final report of the national council committee on arithmetic, Bureau of Publications, Teachers College, Columbia University.
  3. "The Revolution in School Mathematics: A Challenge for Administrators and Teachers" (PDF). 1961.
  4. 1 2 3 4 Kline, Morris (1973). Why Johnny Can't Add: The Failure of the New Math . New York: St. Martin's Press. ISBN   0-394-71981-6.
  5. http://www.nctm.org/standards/focalpoints.aspx?id=284
  6. http://www.air.org/news/documents/Singapore%20Report%20(Bookmark%20Version).pdf Archived 2013-05-31 at the Wayback Machine AIR report in pdf "The California mathematics framework is modeled on Singaporean and Japanese frameworks"

Proponents

Critics