Traditional mathematics
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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 or in the context of, say, recycling or controlling global warming. 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 concepts such as "median" and "mode" as early as elementary grades.[citation needed]
[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 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 students achieve the highest levels of mathematics achievement such as calculus. Some argue that too few students master even algebra.
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. 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.
[edit] Traditional mathematics texts
In general, any math textbook which contains instruction in standard arithmetic methods can be categorized as a traditional math textbook. Any math textbook which de-emphasizes or omits significant standard methods can be considered to be standards-based. The following current texts are often cited as good for those wishing for a traditional approach, often also favored by homeschoolers.
[edit] Organizations promoting traditional mathematics
Most of these organizations are critical of standards-based 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] Which to choose
Mathematics texts are generally chosen by local school districts, or promoted by state education agencies, often with the support of business organizations such as the Business Roundtable by a consensus process. A blue ribbon panel is created to determine that current math standards are inadequate and unacceptable, and draw up a plan to implement texts which are compliant with standards-based education reform, of which mathematics is only one field of curricula. At no time is there a place for public debate of whether such new standards should be adopted. Instead, the public is invited to be informed of the new standards, and are invited to provide input, and break up into small groups on how they can help adopt and embrace the new standards.
Similar standards-based curricula also exist for science, social studies, and language arts, also with their own controversies. Many districts apply for the federal grants which are generally given only to districts which adopt standards-based curricula. In general, only a small number of parents or mathematics experts are even aware of such an adoption process, and a few parents and citizens will be recruited to support such an adoption. Once these curricula are adopted, citizens often find it difficult or impossible to persuade education officials to discard them, despite a wide body of information about the ineffectiveness of them, but citizens in some states and districts have succeeded in some cases such as California, and Tacoma, 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
[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.
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