Reform mathematics
Encyclopedia
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 (ages 5-18) 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.
Mathematics instruction in this style has been called standards-based mathematics or reform mathematics.
" of the 1960s and 1970s. The work of Piaget and other developmental psychologists was shifting the focus of mathematics educators from mathematics content to how children best learn mathematics. The National Council of Teachers of Mathematics
summarized the state of current research with the publication of Curriculum and Evaluation Standards in 1989 and Principles and Standards for School Mathematics
in 2000, bringing definition to the reform movement in North America.
Reform mathematics curricula challenge students to make sense of new mathematical ideas through explorations and projects, often in real contexts. Reform texts emphasize written and verbal communication, working in cooperative groups, making connections between concepts, and connections between representations. By contrast, "traditional" textbooks emphasize procedural mathematics and provide step-by-step examples with skill exercises.
Traditional mathematics
focuses on teaching algorithms that will lead to the correct answer. Because of this focus on application of algorithms, the traditional math student must always use the specific method that is being taught. This kind of algorithmic dependence is de-emphasized in reform mathematics. Reformers do not oppose correct answers, but prefer to focus students' attention on the process leading to the answer, rather than the answer itself. The presence of occasional errors is deemed less important than the overall thought process. Research has shown that children make fewer mistakes with calculations and remember algorithms longer when they understand the concepts underlying the methods they use. In general, children in reform classes perform at least as well as children in traditional classes on tests of calculation skill, and considerably better on tests of problem solving.
The development and large-scale adoption of curricula such as Mathland
have been criticized for partially or entirely abandoning teaching of standard arithmetic methods such as regrouping or common denominators. Protests from groups such as Mathematically Correct
have led to many districts and states abandoning such textbooks. Some states such as California have revised their mathematics standards to partially or largely repudiate the basic beliefs of reform mathematics, and re-emphasize mastery of standard mathematics facts and methods.
The American Institutes for Research (AIR) reported in 2005 that the NCTM proposals "risk exposing students to unrealistically advanced mathematics content in the early grades." This is in reference to NCTM's recommendation that algebraic concepts, such as understanding patterns and properties like commutativity, should be taught as early as first grade.
Some, such as the 2008 National Mathematics Advisory Panel, have called for a balance between reform and traditional mathematics teaching styles rather than a "war" between the two styles. In 2006 NCTM published its Curriculum Focal Points, which made clear that standard algorithms were to be included in all elementary school curricula, as well as activities aiming at conceptual understanding.
A common misconception is that reform educators do not want children to learn the standard methods of arithmetic. As the NCTM Focal Points make clear, such methods are still the ultimate goal, but reformers believe that conceptual understanding should come first. Reform educators believe that such understanding is best pursued by allowing children at first to solve problems using their own understanding and methods. Under guidance from the teacher, students eventually arrive at an understanding of standard methods. Even the controversial NCTM Standards of 1989 did not call for abandoning standard algorithms, but instead recommended a decreased emphasis on complex paper-and-pencil computation drills and greater attention to mental computation, estimation skills, thinking strategies for mastering basic facts and conceptual understanding of arithmetic operations.
During the peak of the controversy, unfavorable terminology for reform mathematics appeared in press and web articles, including Where's the math?, anti-math, math for dummies, no-math mathematics, rainforest algebra, math for women and minorities, and new new math. Most of these critical terms refer to the 1989 standards rather than the PSSM.
Mathematics education
In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research....
, particularly in North America. It is based on principles explained in 1989 by the National Council of Teachers of Mathematics
National Council of Teachers of Mathematics
The National Council of Teachers of Mathematics 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). The NCTM document, Curriculum and Evaluation Standards for School Mathematics, attempted to set forth a vision for K-12 (ages 5-18) mathematics education
Mathematics education
In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research....
in the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
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...
. 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
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). 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.
Mathematics instruction in this style has been called standards-based mathematics or reform mathematics.
Principles and standards
The momentum for reform in mathematics education began in the early 1980s, as educators reacted to the "new mathNew math
New Mathematics or New Math was a brief, dramatic change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries, during the 1960s. The name is commonly given to a set of teaching practices introduced in the U.S...
" of the 1960s and 1970s. The work of Piaget and other developmental psychologists was shifting the focus of mathematics educators from mathematics content to how children best learn mathematics. The National Council of Teachers of Mathematics
National Council of Teachers of Mathematics
The National Council of Teachers of Mathematics 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....
summarized the state of current research with the publication of Curriculum and Evaluation Standards in 1989 and 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...
in 2000, bringing definition to the reform movement in North America.
Reform mathematics curricula challenge students to make sense of new mathematical ideas through explorations and projects, often in real contexts. Reform texts emphasize written and verbal communication, working in cooperative groups, making connections between concepts, and connections between representations. By contrast, "traditional" textbooks emphasize procedural mathematics and provide step-by-step examples with skill exercises.
Traditional mathematics
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...
focuses on teaching algorithms that will lead to the correct answer. Because of this focus on application of algorithms, the traditional math student must always use the specific method that is being taught. This kind of algorithmic dependence is de-emphasized in reform mathematics. Reformers do not oppose correct answers, but prefer to focus students' attention on the process leading to the answer, rather than the answer itself. The presence of occasional errors is deemed less important than the overall thought process. Research has shown that children make fewer mistakes with calculations and remember algorithms longer when they understand the concepts underlying the methods they use. In general, children in reform classes perform at least as well as children in traditional classes on tests of calculation skill, and considerably better on tests of problem solving.
Controversy
While "Principles and Standards for School Mathematics" has been championed by educators, administrators and some mathematicians as raising standards for all students, it has been criticized for valuing understanding processes more than learning standard procedures. Parents opposing reform mathematics have complained about decreased focus on basic computation skills and confusion caused by the increased emphasis on exploration and explanation.http://www.nytimes.com/2007/06/14/nyregion/14math.html Proponents of reform mathematics have countered that research has shown that, when done correctly, students in reform math curricula learn basic math skills at least as well as those in traditional programs, and additionally understand the underlying concepts much better. Communities that have adopted reform curricula have generally seen increased math scores by their students.The development and large-scale adoption of curricula 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...
have been criticized for partially or entirely abandoning teaching of standard arithmetic methods such as regrouping or common denominators. Protests from groups 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...
have led to many districts and states abandoning such textbooks. Some states such as California have revised their mathematics standards to partially or largely repudiate the basic beliefs of reform mathematics, and re-emphasize mastery of standard mathematics facts and methods.
The American Institutes for Research (AIR) reported in 2005 that the NCTM proposals "risk exposing students to unrealistically advanced mathematics content in the early grades." This is in reference to NCTM's recommendation that algebraic concepts, such as understanding patterns and properties like commutativity, should be taught as early as first grade.
Some, such as the 2008 National Mathematics Advisory Panel, have called for a balance between reform and traditional mathematics teaching styles rather than a "war" between the two styles. In 2006 NCTM published its Curriculum Focal Points, which made clear that standard algorithms were to be included in all elementary school curricula, as well as activities aiming at conceptual understanding.
A common misconception is that reform educators do not want children to learn the standard methods of arithmetic. As the NCTM Focal Points make clear, such methods are still the ultimate goal, but reformers believe that conceptual understanding should come first. Reform educators believe that such understanding is best pursued by allowing children at first to solve problems using their own understanding and methods. Under guidance from the teacher, students eventually arrive at an understanding of standard methods. Even the controversial NCTM Standards of 1989 did not call for abandoning standard algorithms, but instead recommended a decreased emphasis on complex paper-and-pencil computation drills and greater attention to mental computation, estimation skills, thinking strategies for mastering basic facts and conceptual understanding of arithmetic operations.
During the peak of the controversy, unfavorable terminology for reform mathematics appeared in press and web articles, including Where's the math?, anti-math, math for dummies, no-math mathematics, rainforest algebra, math for women and minorities, and new new math. Most of these critical terms refer to the 1989 standards rather than the PSSM.
See also
- National Council of Teachers of MathematicsNational Council of Teachers of MathematicsThe National Council of Teachers of Mathematics 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....
- Mathematics education in the United StatesMathematics education in the United StatesFrom kindergarten through high-school, the mathematics education in public schools in the United States varies widely from state to state, and often even varies considerably within individual states...
- Education in the United StatesEducation in the United StatesEducation in the United States is mainly provided by the public sector, with control and funding coming from three levels: federal, state, and local. Child education is compulsory.Public education is universally available...
- 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...
, which opposes the NCTM standards - Prof David Klein (California State University Northridge)David Klein (California State University Northridge)David Klein is a professor of Mathematics at California State University in Northridge. He is an advocate of increasingly rigorous treatment of mathematics in school curricula and a frequently cited opponent of reforms based on the NCTM standards...
, who opposes the NCTM standards - Mathematically Sanehttp://mathematicallysane.com/home.asp, which supports the NCTM standards
External links
- NCTM standards online 120-day free access, otherwise the public is required to pay to purchase or view the standards.
- Original 1989 Curriculum and Evaluation Standards
- 1991 Professional Standards
- 1995 Assessment Standards