Relationship between semiotic representations and student performance in the context of refraction

Social semiotic discussions about the role played by representations in effective teaching and learning in areas such as physics have led to theoretical proposals that have a strong common thread: in order to acquire an appropriate understanding of a particular object of learning, access to the disciplinary relevance aspects in the representations used calls for the attainment of representational competence across a particular critical constellation of systematically used semiotic resources (which are referred to as modes, see more on this later). However, an affirming empirical investigation into the relationship between a particular object of learning and different representational formulations, particularly with large numbers of students, is missing in the literature, especially in the context of university -level physics education. To start to address, this research shortfall the positioning for this article is that such studies need to embrace the complexities of student thinking and application of knowledge. To achieve this, both factor and network analyses were used. Even though both approaches are grounded in different frameworks, for the task at hand, both approaches are useful for analyzing clustering dynamics within the responses of a large number of participants. Both also facilitate an exploration of how such clusters may relate to the semiotic resource formulation of a representation. The data were obtained from a questionnaire given to 1368 students drawn from 12 universities across 7 countries. The questionnaire deals with the refraction of light in introductorylevel physics and involves asking students to give their best prediction of the relative visual positioning of images and objects in different semiotically constituted situations. The results of both approaches revealed no one-to-one relationship between a particular representational formulation and a particular cluster of student responses. The factor analysis used correct answer responses to