**ERIC Number:**EJ1016749

**Record Type:**Journal

**Publication Date:**2013-May

**Pages:**7

**Abstractor:**ERIC

**ISBN:**N/A

**ISSN:**ISSN-1072-0839

**EISSN:**N/A

Strip Diagrams: Illuminating Proportions

Cohen, Jessica S.

Mathematics Teaching in the Middle School, v18 n9 p536-542 May 2013

Proportional reasoning is both complex and layered, making it challenging to define. Lamon (1999) identified characteristics of proportional thinkers, such as being able to understand covariance of quantities; distinguish between proportional and nonproportional relationships; use a variety of strategies flexibly, most of which are nonalgorithmic, to solve proportion problems and compare ratios; and understand ratios as being separate from the quantities they compare. It is well documented that proportionality is a complex and time-consuming concept to master (Hoffer and Hoffer 1988; Lesh, Post, and Behr 1988). This is compounded by the tendency to teach proportional reasoning through the cross-multiplication algorithm (Lesh, Post, and Behr 1988). Although this algorithm is a useful tool for solving proportion problems, students can successfully implement the algorithm without using or demonstrating proportional thinking. Using Singapore strip diagrams (Beckmann 2004) can be a particularly effective strategy for solving proportion problems, building proportional reasoning skills, and connecting proportionality to other mathematical topics. These simple, visual models use strips to represent known and unknown quantities in problems in a meaningful way by displaying relationships between those quantities. In this article, the author describes preservice elementary and middle-grades teachers' use of strip diagrams and highlights their evolving perception of the usefulness of the strategy and the use of the strip diagrams to build insight about the cross-multiplication algorithm. Although the problems described were used with preservice teachers, many tasks in the unit were adapted from materials intended for middle school students. A bibliography is included.

Descriptors: Middle Schools, Mathematics Instruction, Mathematical Concepts, Teaching Methods, Secondary School Mathematics, Problem Solving, Mathematical Logic, Thinking Skills, Visual Aids, Preservice Teachers, Elementary School Mathematics, Elementary School Teachers, Middle School Teachers

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: orders@nctm.org; Web site: http://www.nctm.org/publications/

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Elementary Education; Middle Schools

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Grant or Contract Numbers:**N/A