### Abstract:

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.