Monday, May 13, 2013

Teaching Fractions Beyond Pizza and Pie Charts

By Sharri Zachary, Mathematics Research Coordinator

Research shows that “algebra is the [career] gateway to success for many students” (Williams, 2011, pg. 1). For students to understand the concepts and symbolic representations for everyday situations in algebra, students must master certain foundational skills and concepts at the elementary and middle school levels. According to the U.S. Department of Education (2006), a solid foundation in math in early grades will assist in the development of critical thinking skills necessary to pass algebra. The National Mathematics Advisory Panel (2008) identifies the skills that demonstrate algebra readiness as: (1) whole number computation, (2) fraction and decimal proficiency, (3) number concepts (including percents), (4) general concepts, proportions, and geometry, (5) problem-solving, and (6) basic understanding of integers, variables, and simple equations.

Fraction and decimal proficiency is often developed with the use of pizza and pie charts as the introductory piece. Visually, this allows students to see one “whole” partitioned into equal parts, which in turn, helps students understand the part-whole idea of fractions. However, this leaves out the idea that fractions are numbers with magnitude that can be compared (Siegler et al, 2010).

If students are to be truly algebra-ready, visual representations must extend to model fraction concepts that teach the part-whole relationship, as well as, fractions as a distance and magnitude. The IES practice guide recommends the use of number lines as the “central representational tool” to help students recognize fractions as numbers and expand student thinking beyond whole numbers (Siegler et al, 2010, p. 19).

The use of number lines can help students visualize and understand the magnitude of fractions, the relationship between fractions and whole numbers, and the relationship between fractions, decimals, and percents (Siegler et al, 2010). This conceptual understanding is foundational to understanding algebra (Siegler et al, 2010). Based on the recommendations put forth in the IES practice guide, teachers should center fraction instruction around the number line model and support that instruction with other models that include (but are not limited to) fraction circles and strip diagrams. If number lines are recommended as the “central representational tool” for fraction and decimal proficiency, then teachers must consider moving beyond pizza and pie charts in their instruction and assessments to prepare students for mastery of this component of algebra readiness.

National Mathematics Advisory Panel (Spring 2008). Final report, Washington, D.C. 

Siegler, R., Carpenter, T., Fennell, F., Geary, D., Lewis, J., Okamoto, Y., Thompson, L., & Wray, J. (2010). Developing effective fractions instruction for kindergarten through 8th grade (NCEE 2010-4039). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from 

U.S. Department of Education. (2006). Math now: Advancing math education in elementary and middle school. February 2006. Retrieved from: 

Williams, T. G. (2011). Reaching algebra readiness (RAR): Preparing middle school students to succeed in algebra – the gateway to career success. Rotterdam, The Netherlands: Sense Publishers.

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