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ERIC Number: EJ1044583
Record Type: Journal
Publication Date: 2014-May
Pages: 6
Abstractor: ERIC
ISSN: ISSN-0025-5769
Multiple Representations and Connections with the Sierpinski Triangle
Kirwan, J. Vince; Tobias, Jennifer M.
Mathematics Teacher, v107 n9 p666-671 May 2014
To understand multiple representations in algebra, students must be able to describe relationships through a variety of formats, such as graphs, tables, pictures, and equations. NCTM indicates that varied representations are "essential elements in supporting students' understanding of mathematical concepts and relationships" (NCTM 2000, p. 67). By using assorted representations, students have the opportunity to make sense of each display and see how each relates to the others (Yerushalmy and Schwartz 1993) Difficulties that students have with learning algebra are often rooted in a lack of understanding associated with various representations (Kieran 2007), especially symbolic notations (Poon and Leung 2010). Having students work with symbolic representations--that is, algebraic expressions or equations--is a common classroom approach to teaching algebra. Further, teachers often incorporate varied representations when teaching a topic, such as graphing an equation in two variables. However, if students are not making sense of, understanding, or connecting these representations, they will often struggle with representing the situation symbolically. NCTM's Algebra Standard expects students in grades 9-12 to "... select, convert flexibly among, and use various representations" (2000, p. 296). Thus, the activity described herein was designed to engage students with using varied representations as they worked within a unit on exponential relationships. The goal was to have students develop connections among representations and then generalize the relationship symbolically through this connecting process. Students in this class were given the first four iterations of the Sierpinski triangle fractal and asked to investigate the relationship between the step and the number of black triangles displayed in each step. This article describes the activity and class discussions that followed and provides teaching strategies to help students make connections among multiple representations.
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: Secondary Education; High Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A