INTUITIVE PHYSICS KNOWLEDGE AND MATHEMATICAL FORMALISM

BUTELER, LAURA; COLEONI, ENRIQUE

Jyväskylä

Congreso; GIREP-EPEC 2011 International Conference; 2011

GIREP-EPEC Local Organising Committee

The mathematical formalization of physical situations is a fundamental process in the development of Physics. For this very reason, it constitutes an inevitable goal in Physics instruction. Mastering this process is both a difficult goal for students and a greatly valued objective for teachers. At the same time, little is known about how it is learned or how it is best taught. This report attempts to contribute to better understand the meaning that students assign to mathematical equations when solving a Physics problem. More specifically, it addresses the role of equations in progressively modifying students? previous knowledge as they solve Physics problems. This previous knowledge is referred to as physical intuition (diSessa, 1993) and is understood as the ?principles? students use to understand and solve Physics problems. Some particular traits of this knowledge include: a) it is neither purely normative, nor purely experiential, nor is it necessarily wrong, but rather a mixture of all these; b) it is a type of knowledge found not only in novices, but also in experts, since the latter have not abandoned their intuitions, but rather they have modified it so that it can be explained in terms of formal physical knowledge; and c) it is a knowledge which is necessary for future learning, that is, it is useful knowledge. Assuming that progressive modification of physical intuition occurs largely during problem solving, the question that oriented the present study was: ?How do mathematical equations contribute to this modification during problem solving?? Two pairs of third-year university students were interviewed as they solved a problem on hydrostatics. Students had covered this topic during the previous year. The study is of an exploratory and interpretive nature, and is based on case analysis. Therefore, conclusions are restricted to the cases. Its goal is not to test any hypothesis, but rather to construct one. Interviews are approximately 1 hour long and the interviewer participated only to ask for clarification or to promote interaction between subjects. Interviews were registered in audio and video for their analysis. Cases are compared and analyzed in regards to the role of mathematical equations in modifying ? or not modifying ? students? physical intuitions during the solving process. Given the exploratory nature of the study, results are tentative and restricted to the cases studied. They are, however, valuable in providing an onset to formulate hypothesis. The hypothesis suggested is that the mathematical formalism not always helps students to question or refine their physical intuitions. In particular, this formalism is not helpful when it does not involve their intuitions (whether correct or incorrect) in a way evident to students. This hypothesis goes beyond the one proposed by Sherin (2006), according to which mathematical equations decide among competing physical intuitions, and thus allow for the refinement of intuitive physics knowledge. This hypothesis is extended, and a more binding relation is proposed for physical intuition and mathematics, in which equations are subordinated to physical intuitions. In this extended hypothesis, students? intuitions seem to define which mathematical equations are accepted as plausible and which are not.