Inventory of Galilean Transformation of uniform linear motion in position-time graphs

When describing motion in physics, the selection of a frame of reference is crucial. The graph of a moving object can look quite different based on the frame of reference. In recent years, various tests have been developed to assess the interpretation of kinematic graphs, but none of these tests have specifically addressed differences in reference frames. Moreover, existing tests that explore differences in reference frame typically focus on the equivalence principle through written answers, interviews, or simple calculations and vector addition; however, none of these tests evaluate position-time graphs. To address this gap in the research, we developed and evaluated the Inventory of Galilean Transformation of uniform linear motion in position-time graphs (IGT). The IGT consists of 15 multiple-choice items that systematically use position-time graphs of linear uniform motion to assess the understanding of 3 types of Galilean transformations: the identity transformation, the transformation between two (opposing) stationary displaced frames of reference, and the transformation from a stationary into a uniformly moving frame of reference. Herein, we presented the development and validation of the IGT. A total of 532 upper secondary school students in the advanced track participated in the multistage development process. We evaluated the psychometric properties via classical test theory and item response theory. The degree of item discrimination and reliability were within the desired range. The IGT demonstrated good internal consistency, and confirmatory factor analysis supported the intended structure of the test. Rasch analysis revealed that the item difficulties were consistent with the increasing complexity of the three different transformations. The IGT also revealed several alternative student conceptions about frames of references, such as confusion between two scenarios of cars crossing versus overtaking, as well as misunderstandings regarding the changing shape of a graph when a uniformly moving object is transformed into a moving frame of reference. In its current form, the IGT serves as a new instrument for assessing students’ ability to interpret position-time graphs under the influence of the Galilean transformation, making it suitable for formative or summative assessment in advanced upper secondary education.