Traditional mathematics

Traditional mathematics (sometimes classical math education) was the predominant method

of mathematics education in the United States in the early-to-mid 20th century. This contrasts 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

Traditional method

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 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[edit]

See also: Math Wars and Reform mathematics

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.

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. However,

others such as Conrad Wolfram argue for a more radical use of computer-based math in a complete

departure from traditional math.

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.