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ERIC Number: EJ915181
Record Type: Journal
Publication Date: 2011-Feb
Pages: 8
Abstractor: ERIC
Reference Count: 0
ISSN: ISSN-1072-0839
The Leap from Patterns to Formulas
Beigie, Darin
Mathematics Teaching in the Middle School, v16 n6 p328-335 Feb 2011
Initial exposure to algebraic thinking involves the critical leap from working with numbers to thinking with variables. The transition to thinking mathematically using variables has many layers, and for all students an abstraction that is clear in one setting may be opaque in another. Geometric counting and the resulting algebraic patterns provide an ideal setting to help students make the abstract leap from numbers to variables. The visual context of a geometry problem plays an integral role in the discovery of number patterns and algebraic expressions. The geometric setting for many pattern problems is a sequence of two-dimensional shapes, which is ideally suited to support the recognition of algebraic patterns. The geometric relevance of these sequences, however, is generally defined by their role in facilitating pattern recognition. This article highlights some of the geometric counting problems the author uses in his prealgebra curriculum. Situations are emphasized in which the patterns lead to rich perspectives in both geometric and algebraic thinking. Within the concrete (three-dimensional) and pictorial (two-dimensional) geometric settings, students are able to instinctively handle algebraic manipulations that are usually reserved for more abstract courses. Geometric measurement that uses counting can help students discover basic geometric formulas as they recognize patterns. (Contains 7 figures, 1 table, 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: Middle Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A