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 20th century. The term is often used to contrast historically predominant methods with non-traditional approaches to math education. [http://findarticles.com/p/articles/mi_qa3673/is_200307/ai_n9265187] A comparison of traditional and reform mathematics curricula in an eighth-grade classroom Education, Summer 2003 by Alsup, John K., Sprigler, Mark J.] 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.

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:

* Elementary arithmetic
* addition
* carry
* subtraction
* multiplication
* Multiplication table
* division
* long division
* Arithmetic with fractions
* Lowest common denominator
* Arithmetic mean
* Volume

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 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.

Traditional Math and Homeschooling

Home school students and parents often favor traditional texts. Since the parents are teachers, they are more familiar with standard methods that they were taught. Traditional texts also tend to be much simpler since they take generally only a few minutes to explain a skill, and a few more minutes to practice rather than long group-oriented projects that require mathematical communication, music or art projects, and nightly homework which requires a half to an hour of work on the part of the student and the parent, or the rest of the family in the case of interviews. They are generally based on inexpensive, thin books which contain only mathematical information rather than contexts on rain forests or running shoes or a tour of the United States, and do not require expensive manipulatives such as number cubes or blocks. Standards-based methods usually require a significant investment and specialized teacher training, often with federal grant money to be adopted by a large school district, and are not suitable for use in home school environment.

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.

* Saxon math
* Singapore math
* Modern Curriculum Press

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

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.

External links

* [http://www.mathematicallycorrect.com/ Mathematically Correct,] a website which supports traditional mathematics
* [http://www.nychold.org/ 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
* [http://www.illinoisloop.org/math.html Illinois Loop] - extensive web coverage of math issues and specific math programs
* [http://www.wheresthemath.com/ Where's The Math,] a website which supports traditional mathematics and more focused standards for the state of Washington

Research

* [http://72.14.253.104/search?q=cache:_Zr0GZPeh6MJ:www.nait.org/jit/Articles/ligh0399.pdf+traditional+mathematics&hl=en&ct=clnk&cd=2&gl=us A Comparison of the Effectiveness of Applied and Traditional Mathematics Curriculum by Dr. Stanley L. Lightner, "Journal of Industrial Methodology" Vol 15, Number 2, Feb 1999 to April 1999]

Notes