Examination of Thai freshmen’s understanding on vectors using a model analysis technique

Abstract

This study focused on an investigation of Thai students’ comprehension of vectors using the model analysis technique, which is based on the matrix representation of quantum physics. This technique displays students’ knowledge states and the probability of applying each mental model to solve a given vector concept. A well-known vector concept test in physics education research named the Test of Understanding of Vectors (TUV) was translated into Thai language and validated by a group of physics lecturers. It was administered to 651 first-year engineering students at Prince of Songkla University via the online system at the beginning of the first semester. The three common mental states of vectors were identified as correct, popular incorrect, and other models. Model estimation of the model analysis revealed that although 54% of the students correctly answered vector addition, they still had difficulty with vector subtraction. Theoretically, both topics are considered as identical concepts. The students had inconsistent ideas on vector subtraction as reported by eigenvalues < 0.65. Moreover, they demonstrated equal distribution in using the three mental models to solve the dot product of vectors. The most common incorrect idea was that a dot product resultant was a vector quantity. The initial knowledge states of the cross product were in an incorrect model region involving confusion between calculating magnitudes of the cross product and the dot product, and incorrectly applying the right-hand rule to locate a direction of the cross product. Overall, the findings will guide instructors which common vector ideas should be revised and how. The vector concept plays an important role in physics learning since it is embedded in several physics topics as a learning mechanism.