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ERIC Number: EJ879355
Record Type: Journal
Publication Date: 2010-Apr
Pages: 7
Abstractor: ERIC
Reference Count: 0
ISSN: ISSN-0025-5769
Connected Representations: From Proportion to Linear Functions
Baltus, Christopher
Mathematics Teacher, v103 n8 p590-596 Apr 2010
Mathematics may be inconceivable without its diagrams and symbols--its representations. Mathematical representations help individuals organize their thinking; they bring a visual component to abstract ideas and serve as templates for computation with understanding. But the inevitability of representations is no guarantee that they are used effectively. This article presents a sequence of problems that suggests how a cohort of related representations can trace a path from proportion to linear functions. The related representations include two-sided number lines, t-tables, graphs, and function rules. The linked representations can begin with the study of proportion in middle school mathematics; the study of proportion and its representations at the beginning of the first high school algebra course leads directly into linear functions, the heart of the course. In setting out a path of representations from proportion to linear functions, the author suggests a central role for t-tables, tied closely to graphs and function rules. (Contains 4 tables, 9 figures, and a bibliography.)
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: High Schools; Middle Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A