Proportional reasoning: The effect of two context variables, rate type, and problem setting

Abstract

This study investigated the effects of two context variables, ratio type and problem setting, on the performance of seventh-grade students on a qualitative and numerical proportional reasoning test. Six forms of the qualitative and numerical-tests were designed, each form using a single context (one of two settings for each of three ratio types). Different ratio types appear to have a stronger impact on the difficulty of the qualitative and numerical proportional reasoning problems than small differences in problem setting. However, the familiarity of problem setting did show an increasingly large effect on qualitative reasoning as the difficulty of ratio type increased. We also investigated the nature of the relationships between rational number skills, qualitative reasoning about ratios, and numerical proportional reasoning. Qualitative reasoning appears to be sufficient, but not necessary for numerical proportional reasoning. The evidence for the requisite nature of rational number skills for proportional reasoning was equivocal. The implications of these findings for science education are discussed.

Mathematical Dimensions of Students' Use of Proportional Reasoning In High School Physics

“…Conceptual understanding of physics concepts and information processing is important for students to successfully employ meaningful proportional reasoning strategies during problem solving. Several studies in the past have shown that the subject matter content of problems may influence students' reasoning skills or level of problem‐solving performance (e.g., Heller et al, 1989; Lawton, 1993; Linn, Pulos, & Gans, 1981). The use of proportional reasoning strategy has also been found to depend on the context of the given ratio task (Kuchemann, 1991).…”

“…School science is increasingly permeated by mathematics (Heller, Ahlgren, Post, Behr, & Lesh, 1989), and this suggests a need for the strengthening and integration of mathematics and science instruction. However, more needs to be understood about students' facility with mathematics in their science classes before an integrated mathematics‐ science curriculum can be developed (Fleener, 1993a).…”

“…Proportional reasoning, an essential scheme for developing formal operational thought (Inhelder & Piaget, 1958) and a form of mathematical reasoning (Cramer & Post, 1993), has been described as the key to the door that currently exists between high school and college mathematics and science (Fleener, 1993a). It is one of the most ancient and fundamental connections between science and mathematics (Heller et al, 1989).…”

“…School science is increasingly permeated by mathematics (Heller, Ahlgren, Post, Behr, & Lesh, 1989), and this suggests a need for the strengthening and integration of mathematics and science instruction.…”

“…Proportional reasoning, an essential scheme for developing formal operational thought (Inhelder & Piaget, 1958) and a form of mathematical reasoning (Cramer & Post, 1993), has been described as the key to the door that currently exists between high school and college mathematics and science (Fleener, 1993a). It is one of the most ancient and fundamental connections between science and mathematics (Heller et al, 1989). This form of mathematical reasoning is essential for students' success in high school science courses (Akatugba, 1995;Fleener, 1993a;Guckin&Morrison, 1991;Harel, Behr, Post, & Lesh, 1992) and is highly correlated with achievement in science (Mitchell & Lawson, 1988).…”