engleski

Comparison of students' understanding of graphs in mathematics, physics and other contexts

Students are introduced to graphs rather early in their education and through different school subjects. They acquire most of their knowledge about graphs through the study of mathematics and physics. However, students also encounter graphs in contexts other than those of mathematics and physics, such as biology, chemistry, everyday life, economy etc. The ability to interpret graphs is considered one of the important outcomes of high school mathematics and physics courses, and is often assumed by university faculty to be fully developed by the time that students enroll in university. This study investigates university students understanding of graphs accross three different domains: mathematics, physics (kinematics) and contexts other than physics (economy, biology, everyday life), which did not require any substantial context - dependent knowledge. Eight sets of parallel mathematics, physics and other context questions about graphs were developed by authors. Questions were parallel in the sense that the required mathematical procedure for solving the question was the same in each set of three items. However, depending on the domain, the interpretation of the meaning of the obtained solution differed among parallel questions. A test consisting ofthose eight sets of questions (24 questions) was administered to 385 first year students at University of Zagreb, who were either prospective physics/mathematics teachers or researchers. The test was administered at the beginning of the first semester. Four sets of questions were multiple choice, and four were open ended, but in all questions explanation of the answer was required. Data was analyzed with the Winsteps 3.66 software for Rasch analysis and linear measures for item difficulties were obtained. Average difficulties of items in different conceptual areas (graph slope, area under a graph) and in different domains (mathematics, physics, other contexts) were computed and compared. Analysis suggests that the concept of graph slope is of equal difficulty in all three domains, whereas the difficulty of the concept of area under a graph differs across domains. Mathematics was, for students in this study, the easiest of the three domains. It appears that addition of either physics or other context to mathematical items significantly increases difficulties of those items. No significant difference was found between average item difficulties in physics and in other contexts domain, suggesting that physics as a context was not easier for students than other contexts presented in the study, although all students had previously studied physics in high school. Students' reasoning on parallel problems in different domains will be illustrated by examples and discussed. The findings of the study suggest that students' mathematical knowledge is not the most important factor for students' success in solving graph problems in physics or other sciences, and point to important differences in student understanding of graph slope and area under a graph.

physics education research; graphs; Rasch modelling

nije evidentirano