How Much Do Pre-Service Teachers Know About Some of the Key Operations in Vector Analysis?

Abstract

The primary purpose of this study is to find out how accurately pre-service teachers use gradient, divergence and curl, which are key operations in vector analysis, and also how well they know the correct meanings of those operations. The secondary purpose of the research is to determine at what level they use scalar product and vector product, which are key algebraic operations that form a basis for the use of the aforementioned differential operations. The research was conducted with 90 pre-service physics teachers who have all passed the “Mathematical Methods in Physics I-II Courses”. Students' understanding and usage level of the operations mentioned above were tested using a Paper-and-Pencil Test (including eight tasks). The analyses of the collected data were based on the quantitative and qualitative techniques. Results indicate that pre-service physics teachers have specific and considerable comprehension difficulties with the physical meanings of vector differentialoperations. In the paper, the conclusions of the study and implications for physical mathematics teaching are discussed.