Coordinated variation across semiotic modes: an analysis of teaching and learning in university physics education

Abstract This article examines coordinated variation across semiotic modes in the teaching and learning of circular motion in a vertical plane in a second-year university physics course. Using illustrative empirical cases, we analyse a lecture episode and a student group-work tutorial from the same course as two educational settings addressing overlapping critical aspects of vertical circular motion. The analysis combines variation theory and social semiotics by identifying patterns of variation—contrast, generalisation and fusion—and the semiotic resources through which these patterns are enacted. The analysis illustrates how physics meaning-making depends on coordinating and remaking representations such as diagrams, equations, gestures and speech in ways that bring relevant disciplinary relationships into focus. In the lecture episode, persistent modes such as diagrams and equations were coordinated with dynamic modes such as speech and gesture, making relationships among speed, position, acceleration and force available for discernment. In the tutorial, speech and equations dominated, while sketches and force representations were less used and developed. The students explicitly recognised that speed varied with position but did not successfully formulate and use the limiting condition at the top of the circular track. The two settings are juxtaposed to illustrate how the same disciplinary relations can be made available and coordinated differently across teaching and student problem-solving activity. The study clarifies how variation theory and social semiotics can be coordinated as complementary analytical lenses and discusses implications for designing university physics activities that support representational coordination across critical aspects.