Transfer and measures of transfer in introductory physics

Instructors of introductory physics courses expect that students will be able to apply what they have learned in previous mathematics courses to what they are learning in introductory mechanics, and that once they have completed introductory mechanics they will be able to apply the conceptual and procedural knowledge developed in mechanics to the learning of electricity and magnetism. Fulfillment of these expectations requires that students transfer knowledge obtained in previous courses to different contexts in subsequent courses. However, there is little agreement among education researchers about the mechanism of transfer from one context to another and about how to measure transfer. This dissertation describes an initial investigation into transfer across contexts in introductory physics, and into the measurement of transfer.;The first part of this dissertation describes an investigation we have conducted to better understand the extent to which students transfer knowledge from math to physics, concentrating on the mathematics of proportional reasoning that is ubiquitous in introductory physics courses. We have analyzed students responses to a diagnostic intended to measure student fluency with proportional reasoning. This diagnostic includes questions designed to assess student proficiency with a variety of components of proportional reasoning that instructors of introductory physics will expect. Our results suggest that many students do not have the level of preparation expected by their instructors, and that it may be necessary to provide additional scaffolding for students to apply the procedural knowledge typically taught in mathematics classes to help them understand the ways that proportions are used by physicists.;The second part of this dissertation, describes our attempt to measure the degree to which students are able to transfer concepts acquired in introductory classical mechanics courses to a subsequent electricity and magnetism course. We have analyzed students' responses to an assessment tool, intended to measure whether relevant concepts learned in mechanics are used by students when they take electricity and magnetism. The results show that transfer from mechanics to electrostatics concepts depends on the context, the students' mathematical preparation, the elements of the design of the questions, and the knowledge of mechanics concepts.