Traditional mathematics
Encyclopedia
Traditional mathematics (sometimes classical math education) 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. 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 mathematics
(i.e. Standards-based mathematics) based on NCTM standards, which is federally supported and has been widely adopted, but subject to ongoing criticism.
In general, traditional methods are based on direct instruction
where students are shown one standard method of performing a task such as decimal addition, in a standard sequence. A task is taught in isolation rather than as only a part of a more complex project. By contrast, reform books may omit or even discourage standard methods of division or fractions. The formula for the area of a circle, for example, may be left as a discovery exercise rather than printing the formula anywhere in the student text where it could be quickly referenced. A page on adding fractions would ask "devise a method of adding that applies to these examples" rather than actually giving instructions to convert to a common denominator and then add the numerators. A traditional sequence early in the 20th century would leave topics such as algebra or geometry for high school, and statistics until college, but newer standards require coverage of such concepts in the elementary grades. In the 21st century basic geometric concepts and "algebraic thinking" (number patterns) are taught every year in the United States beginning in kindergarten; children are taught statistical concepts of organizing data as early as first grade. More sophisticated concepts such as algebraic expressions with numbers and letters, geometric surface area and statistical means and medians occur in sixth grade in the newest standards.
. These critics cite studies, such as The Harmful Effects of Algorithms in Grades 1-4
, which found specific instances where traditional math instruction was less effective than alternative methods. Advocates of alternative methods argue that traditional methods of instruction over-emphasize memorization and repetition, and fail to promote conceptual understanding or to present math as creative or exploratory. Critics also cite the fact that history of mathematics often focuses on European advancements and methods developed by men, thus ignoring equity issues and potentially alienating minorities and women.
Beyond just misplaced emphasis, critics contend that traditional mathematics instruction is ineffective, implying that a reformed math curriculum might be more effective. Critics note that only a small percentage of students achieve the highest levels of mathematics achievement such as calculus
. Some argue that too few students master even algebra.
The general consensus of large-scale studies that compare traditional mathematics with reform mathematics is that students in both curricula learn basic skills to about the same level as measured by traditional standardized tests, but the reform mathematics students do better on tasks requiring conceptual understanding and problem solving.
The use of calculator
s became common in United States math instruction in the 1980s and 1990s. Critics have argued that calculator work, when not accompanied by a strong emphasis on the importance of showing work, allows students to get the answers to many problems without understanding the math involved.
Mathematics educators, such as Alan Schoenfeld, question whether traditional mathematics actually teach mathematics as understood by professional mathematicians and other experts. Instead, Schoenfeld implies, students come to perceive mathematics as a list of disconnected rules that must be memorized and parroted. Indeed, research suggests that certain approaches to traditional mathematics instruction impresses upon students an image of mathematics as closed to imagination and discovery, an image in clear opposition to how experts view the field.
" during the first decade of the 21st century as reform organizations such as the National Council of Teachers of Mathematics
and national committees, such as the National Mathematics Advisory Panel convened by George W. Bush
, have concluded that elements of both traditional mathematics (such as mastery of basic skills and some direct instruction) and reform mathematics (such as some student-centered instruction and an emphasis on conceptual understanding and problem-solving skills) need to be combined for best instruction.
and have given poor reviews to textbooks such as TERC
, Mathland
and Core-Plus Mathematics Project
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...
in the early-to-mid 20th century. The term is often used to contrast historically predominant methods 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
New 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...
, a now largely abandoned and discredited set of alternative methods, and most recently 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...
(i.e. Standards-based mathematics) based on NCTM standards, which is federally supported and has been widely adopted, but subject to ongoing criticism.
Traditional methods
The topics and methods of traditional mathematics are well documented in books and open source articles of many nations and languages. Major topics covered include:In general, traditional methods are based on direct instruction
Direct instruction
Direct Instruction is an instructional method that is focused on systematic curriculum design and skillful implementation of a prescribed behavioral script....
where students are shown one standard method of performing a task such as decimal addition, in a standard sequence. A task is taught in isolation rather than as only a part of a more complex project. By contrast, reform books may omit or even discourage standard methods of division or fractions. The formula for the area of a circle, for example, may be left as a discovery exercise rather than printing the formula anywhere in the student text where it could be quickly referenced. A page on adding fractions would ask "devise a method of adding that applies to these examples" rather than actually giving instructions to convert to a common denominator and then add the numerators. A traditional sequence early in the 20th century would leave topics such as algebra or geometry for high school, and statistics until college, but newer standards require coverage of such concepts in the elementary grades. In the 21st century basic geometric concepts and "algebraic thinking" (number patterns) are taught every year in the United States beginning in kindergarten; children are taught statistical concepts of organizing data as early as first grade. More sophisticated concepts such as algebraic expressions with numbers and letters, geometric surface area and statistical means and medians occur in sixth grade in the newest standards.
Criticism of Traditional Math
Criticism of traditional mathematics instruction originates with advocates of alternative methods of instruction, such as Reform mathematicsReform 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...
. These critics cite studies, such as The Harmful Effects of Algorithms in Grades 1-4
The Harmful Effects of Algorithms in Grades 1-4
The Harmful Effects of Algorithms in Grades 1-4 is a research paper published in the NCTM 1998 Yearbook and written by Constance Kamii and Ann Dominick...
, which found specific instances where traditional math instruction was less effective than alternative methods. Advocates of alternative methods argue that traditional methods of instruction over-emphasize memorization and repetition, and fail to promote conceptual understanding or to present math as creative or exploratory. Critics also cite the fact that history of mathematics often focuses on European advancements and methods developed by men, thus ignoring equity issues and potentially alienating minorities and women.
Beyond just misplaced emphasis, critics contend that traditional mathematics instruction is ineffective, implying that a reformed math curriculum might be more effective. Critics note that only a small percentage of students achieve the highest levels of mathematics achievement such as calculus
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
. Some argue that too few students master even algebra.
The general consensus of large-scale studies that compare traditional mathematics with reform mathematics is that students in both curricula learn basic skills to about the same level as measured by traditional standardized tests, but the reform mathematics students do better on tasks requiring conceptual understanding and problem solving.
The use of calculator
Calculator
An electronic calculator is a small, portable, usually inexpensive electronic device used to perform the basic operations of arithmetic. Modern calculators are more portable than most computers, though most PDAs are comparable in size to handheld calculators.The first solid-state electronic...
s became common in United States math instruction in the 1980s and 1990s. Critics have argued that calculator work, when not accompanied by a strong emphasis on the importance of showing work, allows students to get the answers to many problems without understanding the math involved.
Mathematics educators, such as Alan Schoenfeld, question whether traditional mathematics actually teach mathematics as understood by professional mathematicians and other experts. Instead, Schoenfeld implies, students come to perceive mathematics as a list of disconnected rules that must be memorized and parroted. Indeed, research suggests that certain approaches to traditional mathematics instruction impresses upon students an image of mathematics as closed to imagination and discovery, an image in clear opposition to how experts view the field.
Traditional mathematics texts
In general, math textbooks which focus on instruction in standard arithmetic methods can be categorized as a traditional math textbook. Reform math textbooks will often focus on conceptual understanding, usually avoiding immediate instruction of the standard algorithms and frequently promoting student exploration and discovery of the relevant mathematics. The following current texts are often cited as good for those wishing for a traditional approach, often also favored by homeschoolers.- Saxon math
- Singapore math
- Modern Curriculum PressModern Curriculum PressModern Curriculum Press is one of the Pearson Learning Group publishers, specializing in direct skill instruction style curriculum materials.-Modern Curriculum Press Mathematics:...
Recent trends
In the United States there has been general cooling of the "Math warsMath 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...
" during the first decade of the 21st century as reform organizations such as 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....
and national committees, such as the National Mathematics Advisory Panel convened by George W. Bush
George W. Bush
George Walker Bush is an American politician who served as the 43rd President of the United States, from 2001 to 2009. Before that, he was the 46th Governor of Texas, having served from 1995 to 2000....
, have concluded that elements of both traditional mathematics (such as mastery of basic skills and some direct instruction) and reform mathematics (such as some student-centered instruction and an emphasis on conceptual understanding and problem-solving skills) need to be combined for best instruction.
Organizations promoting traditional mathematics
Most of these organizations are critical of reform mathematicsReform 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...
and have given poor reviews to textbooks such as TERC
TERC
TERC may refer to:*Telomerase RNA component, a human gene.*The developers of the Investigations in Numbers, Data, and Space mathematics curriculum.*Technical Education Research Centers*CSIRO Tropical Ecosystems Research Centre...
, 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...
and 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...
- 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...
a website which supports traditional mathematics - NYC HOLDNYC HOLDNew York City HOLD is an American national education advocacy organization, founded in January 2000 by a group of Manhattan parents and NYU mathematicians...
a New York-based organization of teachers, professional mathematicians, parents and others which has been extremely active in recent years in working for adoption of mastery-based, traditional math programs - Illinois LoopIllinois LoopThe Illinois Loop is an organization of parents, teachers, school board members, and others working to restore academic substance and effective teaching methods into schools....
- extensive web coverage of math issues and specific math programs - Where's The Math - a website which supports traditional mathematics and more focused standards for the state of Washington
External links
- Mathematically Correct, a website which supports traditional mathematics
- NYC HOLD, a New York-based organization of teachers, professional mathematicians, parents and others which has been active in recent years in working for adoption of mastery-based, traditional math programs
- Illinois Loop - extensive web coverage of math issues and specific math programs
- Where's The Math, a website which supports traditional mathematics and more focused standards for the state of Washington
- Mathematically Sanehttp://mathematicallysane.com/home.asp, a site critical of traditional mathematics