Can Problem Solving Affect the Understanding of Rational Numbers in the Middle School Setting?

Abstract

In this study, problem solving provided deeper meaning and understanding through the implementation of a structured problem solving strategy with the teaching of rational numbers. This action-research study was designed as a quasi-experimental model with a control closely matched to an experimental group using similar demographics and number of economically disadvantaged students. In comparison to the control group, the experimental group received their instruction in rational numbers with the addition of a structured problem solving strategy, and a pre/posttest on problem solving with proportionality between similar geometric figures, converting fractions to percents, proportionality with a given ratio, expression of a ratio, and appropriate application of ratios. The study indicates that a structured problem solving strategy can improve the mathematical accuracy, approach and the explanation of rational numbers that are focused on rates, ratio, proportion, and percents. Results showed a statistically significant difference in the performance of these two groups. Effect sizes and 95% confidence intervals (CIs) were reported to support the findings. When examining subgroups, the study showed the structured problem solving stratey not only improved students' ability to understand and use rational numbers but also improved students' problem solving skills and their attitude towards problem solving. The experimental group showed the most improvement in the approach to solving problems with rational numbers indicating deeper understanding of rates, ratios, proportions and percents.