Using Ratio Tables to Encourage Proportional Reasoning

ABSTRACT USING RATIO TABLES TO ENCOURAGE PROPORTIONAL REASONING by © Rita M. Nutsch 2009 Master of Science in Mathematics Education California State University, Chico Fall 2009 It is essential that proportional reasoning is developed at the middle-school level to allow students access to higher mathematics. Because of the importance of proportional reasoning, every effort should be made to assure its careful development. A quick scan of textbooks on the California state adoption list for middle schools shows little emphasis placed on understanding proportionality beyond showing the use of the cross-multiplication algorithm. Proportional reasoning is a sophisticated thinking process that goes far beyond the ability to solve routine proportion problems using crossmultiplication. The purpose of this study was to explore the relationship between student use of ratio tables and their conceptual understanding of proportional reasoning. A ratio table is a chart of two or more rows that is used as a tool to help record and organize equivalent ratios. This study addressed the following questions: How does the use of ratio tables affect the conceptual understanding of routine and non-routine proportional reasoning problems? and How does the use of ratio tables influence the quality of verbalization, written or oral, of a student’s proportional thinking? All students were given a pretest and seven randomly chosen students were interviewed to assess conceptual understanding of proportional reasoning. Each problem required a written explanation of the student’s thinking while solving the problem. After conducting a unit on proportional reasoning in which ratio tables were introduced as an organization tool, a posttest and subsequent interviews were administered to the same pre-algebra students to answer the stated research questions.