Methodology of teaching children geometric representations

Type or paste methodology of teaching children geometric representations DOI name into the text box. This article is about traditional mathematics teaching in the United States.

For other uses, see Mathematics education. United States in the early-to-mid 20th century. This contrasts with non-traditional approaches to math education. The topics and methods of traditional mathematics are well documented in books and open source articles of many nations and languages. 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. 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. Criticism of traditional mathematics instruction originates with advocates of alternative methods of instruction, such as Reform mathematics.

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. Mathematics educators, such as Alan Schoenfeld, question whether traditional mathematics actually teach mathematics as understood by professional mathematicians and other experts.