Development of Proportional Reasoning Through the Study of Speed, an Intensive Quantity

This presentation reports the findings of a study that shows the effectiveness of targeted intervention on the ability of high school students to reason proportionally. Proportional reasoning, including its applications in science and other everyday tasks, is a skill that few people are comfortable with and fewer people master. Students that lack this ability have more difficulty with most higher math and science concepts; however, the ability to reason through a problem of proportionality or through a problem involving ratios is a skill that can be taught successfully. It has been proposed in a study by Modestou and Gagatsis (2010) that mastery of proportional reasoning is a result of strength in three cognitive and metacognitive aspects. The present study endeavors to show that knowing in which of these aspects a student is deficient can indicate to an instructor where to target instruction or intervention which leads to more complete mastery of proportional reasoning. Through an analysis of the comparative strengths of these three aspects in case studies of four high school students and focused intervention on the weakest area, this study proposes that an increase in the students\u27 ability to reason proportionally will result. After taking a three pronged pre-test, the students are tutored in the one aspect of understanding in which they are most deficient. The results of the pre- and post-test are then analyzed to determine what progress has been mad