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 or standards-based mathematics based on NCTM standards, which is federally supported and has been widely adopted, but subject to ongoing criticism.

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 often postpone standard methods until students have the necessary background to understand the procedures. Students in modern curricula often explore their own methods for multiplying multi-digit numbers, deepening their understanding of multiplication principles before being guided to the standard algorithm. Parents sometimes misunderstand this approach to mean that the children will not be taught formulas and standard algorithms and therefore there are occasional calls for a return to traditional methods. Such calls became especially intense during the 1990s. (See Math wars.)

A traditional sequence early in the 20th century would leave topics such as algebra or geometry entirely for high school, and statistics until college, but newer standards introduce the basic principles needed for understanding these topics very early. For example, most American standards now require children to learn to recognize and extend patterns in kindergarten. This very basic form of algebraic reasoning is extended in elementary school to recognize patterns in functions and arithmetic operations, such as the distributive law, a key principle for doing high school algebra. Most curricula today encourage children to reason about geometric shapes and their properties in primary school as preparation for more advanced reasoning in a high school geometry course. Current standards require children to learn basic statistical ideas such as organizing data with bar charts. 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.

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