Traditional mathematics
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.[1] 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.
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[edit] 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 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[citation needed] 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"[citation needed] 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[2]. 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.[2]
[edit] Criticism of Traditional Math
Criticism of traditional mathematics instruction originates with advocates of alternative methods of instruction, such as Reform mathematics. 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.[3]
The use of calculators 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.[citation needed] 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.[citation needed]
[edit] 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.
[edit] Recent trends
In the United States there has been general cooling of the "Math wars" 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.
[edit] Organizations promoting traditional mathematics
Most of these organizations are critical of reform mathematics and have given poor reviews to textbooks such as TERC, Mathland and Core-Plus Mathematics Project
- 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 extremely 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
[edit] 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 Sane[2], a site critical of traditional mathematics
[edit] Research
[edit] Notes
- ^ [1] A comparison of traditional and reform mathematics curricula in an eighth-grade classroom Education, Summer 2003 by Alsup, John K., Sprigler, Mark J.
- ^ a b Common Core State Standards Initiative. "Common Core Standards for Mathematics". http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf. Retrieved 27 February 2011.
- ^ NCTM research brief: Selecting the Right Curriculum
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