National Council of Teachers of Mathematics
Encyclopedia
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.
The National Council of Teachers of Mathematics is a public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.
NCTM holds annual national and regional conferences for American teachers and publishes four print journals. Its published standards have been highly influential in the direction of mathematics education in the United States and Canada.
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.
The 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.
The NCTM does not conduct research in mathematics education, but it does publish the Journal for Research in Mathematics Education (JRME), which is the most influential periodical in mathematics education research worldwide and the fourth most referenced educational research journal of any kind. Summaries of the most important findings in mathematics educational research as regards current practices can be found on their website. The 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.
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.
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).” 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
In ninth grade, the 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
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.
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 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.
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 framework
s. 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 http://www.cde.ca.gov/be/st/ss/mthmain.asp was one of the first to embrace the 1989 standards, and also among the first to move back towards traditional standards
.
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 new Common Core State Standards, which have been adopted by most states as the basis for new math curricula.
Mathematics education
In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research....
, having close to 100,000 members across the USA and Canada
Canada
Canada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...
, and internationally.
The National Council of Teachers of Mathematics is a public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.
NCTM holds annual national and regional conferences for American teachers and publishes four print journals. Its published standards have been highly influential in the direction of mathematics education in the United States and Canada.
Journals
The NCTM publishes four print journals for elementary school, middle school, and high school teachers of mathematics, as well as a research journal for mathematics education.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.
The 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.
The NCTM does not conduct research in mathematics education, but it does publish the Journal for Research in Mathematics Education (JRME), which is the most influential periodical in mathematics education research worldwide and the fourth most referenced educational research journal of any kind. Summaries of the most important findings in mathematics educational research as regards current practices can be found on their website. The 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). These math standards were widely lauded by education officials, and the National Science FoundationNational Science Foundation
The National Science Foundation is a United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health...
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
United States Department of Education
The United States Department of Education, also referred to as ED or the ED for Education Department, is a Cabinet-level department of the United States government...
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
Mathematically Correct
Mathematically Correct is a website created by educators, parents, mathematicians, and scientists who were concerned about the direction of reform mathematics curricula based on NCTM standards...
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 for School Mathematics
Principles and Standards for School Mathematics are guidelines produced by the National Council of Teachers of Mathematics 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...
.
PSSM is widely considered to be a more balanced and less controversial vision of reform than its predecessor.
Post World War II Plan
In 1944 the NCTM created a post war 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 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 amount 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 successfulAfter 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).” 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
In ninth grade, the 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
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.
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.In reform mathematics
Reform mathematics
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 . The NCTM document, Curriculum and Evaluation Standards for School Mathematics, attempted to set forth a vision...
, 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
Achievement gap
Achievement gap refers to the observed disparity on a number of educational measures between the performance of groups of students, especially groups defined by gender, race/ethnicity, and socioeconomic status. The achievement gap can be observed on a variety of measures, including standardized...
and produce a productive labor force. Such beliefs were considered congruent with the democratic vision of outcome-based education
Outcome-based education
Outcome-based education is a recurring education reform model. It is a student-centered learning philosophy that focuses on empirically measuring student performance, which are called outcomes. OBE contrasts with traditional education, which primarily focuses on the resources that are available...
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.
The standards soon became the basis for many new federally funded curricula such as the Core-Plus Mathematics Project
Core-Plus Mathematics Project
The Core-Plus Mathematics Project is one of the five NCTM-standards-based high school mathematics curriculum development projects funded by the National Science Foundation. The project has developed, tested, and published a four-year comprehensive high school mathematics textbook series...
and became the foundation of many local and state curriculum framework
Curriculum framework
A curriculum framework is an organized plan or set of standards or learning outcomes that defines the content to be learned in terms of clear, definable standards of what the student should know and be able to do....
s. 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
Math wars
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 and subsequent development and...
" erupted in some communities that were opposed to some of the more radical changes to mathematics instruction such as Mathland
Mathland
MathLand was one of many controversial 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...
'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 http://www.cde.ca.gov/be/st/ss/mthmain.asp was one of the first to embrace the 1989 standards, and also among the first to move back towards traditional standards
Traditional mathematics
Traditional mathematics is a term used to describe the predominant methods of Mathematics education in the United States in the early-to-mid 20th century. The term is often used to contrast historically predominant methods with non-traditional approaches to math education...
.
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.
The Focal Points were one of the documents used in creating the new Common Core State Standards, which have been adopted by most states as the basis for new math curricula.
See also
- American Mathematical Association of Two-Year CollegesAmerican Mathematical Association of Two-Year CollegesThe American Mathematical Association of Two-Year Colleges is an organization dedicated to the improvement of education in the first two years of college mathematics in the United States and Canada. AMATYC hosts an annual conference, summer institutes, workshops and mentoring for teachers in and...
- Mathematical Association of AmericaMathematical Association of AmericaThe Mathematical Association of America is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists;...
External links
- NCTM's Official Website
- Principles and Standards for School Mathematics
- NCTM's 2006 Curriculum Focal Points
Critics
- Mathematically CorrectMathematically CorrectMathematically Correct is a website created by educators, parents, mathematicians, and scientists who were concerned about the direction of reform mathematics curricula based on NCTM standards...
- Washington math advocacy group campaigning against NCTM math