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ERIC Number: EJ937229
Record Type: Journal
Publication Date: 2011-Aug
Pages: 8
Abstractor: ERIC
Reference Count: 4
ISSN: ISSN-1072-0839
Representations and Rafts
Hartweg, Kimberly Sipes
Mathematics Teaching in the Middle School, v17 n1 p40-47 Aug 2011
To build on prior knowledge and mathematical understanding, middle school students need to be given the opportunity to make connections among a variety of representations. Graphs, tables, algebraic formulas, and models are just a few examples of representations that can help students explore quantitative relationships. As a mathematics educator, the author conducts workshops and teaches courses for middle school teachers. By experiencing the problem-solving process themselves, these teachers can help their own students make the aforementioned connections. Students often have preconceived ideas or even misconceptions and may know a list of steps or algorithms. Although they can perform these calculations, they may not always understand the concept or mathematical connections. This article shows how a problem-solving task can be used to help students make sense of mathematics, construct meaning, and make algebraic connections between existing and new mathematical ideas. The author uses one open-response problem, called the Raft Maker Task, with middle school students and both preservice and in-service teachers. This task was adapted from Building Rafts with Rods (Annenberg Media 1997). Building a rod raft allows students to make mathematical connections among a model, a table, a formula, and a graph. (Contains 6 figures.)
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