Investigates the effects of two context variables on the performance of seventh-grade students on a qualitative and numerical proportional reasoning test. Explores the nature of the relationships between rational number skills, qualitative reasoning about ratios, and numerical proportional reasoning. (Author/YP)

Discusses a study which compared differences in ratio construction made by high school freshman and junior students. Reports that more freshmen than juniors selected solutions involving one variable, whereas juniors chose solutions that coordinated two variables in a mathematical or verbal rule. Reviews implications in problem solving and concept…

Defines the mathematical concept of proportionality. Uses graphs of linear relationships to explore and make generalizations about the characteristics of proportional situations to help students critically evaluate problems involving proportions. (MDH)

Higher order cognitive development and success in the study of high school mathematics and science require an understanding of rational number concepts and facility with proportional reasoning and computation. Proportional reasoning is an essential schema for developing formal operational thought. This study involving 16 ninth-grade students was…