Coordinating Multiple Representations in Mechanics: A Mixed-Methods Analysis of Prospective Physics Teachers

This exploratory case study investigates the multiple representational skills of prospective physics teachers in solving mechanics problems within a specific institutional context. The study employed a mixed-method approach to obtain both quantitative and qualitative insights into students’ representational skills. The participants were 17 second-semester students enrolled in a Physics Education program at a public university in Langsa City, Indonesia, representing a bounded institutional case. Data were collected using a validated test comprising 11 mechanics problems across four types of representations (tabular, graphical, diagrammatic, and mathematical). Follow-up semi-structured interviews were conducted with three randomly selected participants to explore their reasoning processes and representational difficulties. Quantitative data were analyzed using descriptive statistics and the Friedman test to examine differences across representation types. Qualitative data from interviews were analyzed using thematic analysis to identify recurring patterns of challenges and reasoning strategies. The findings revealed statistically significant differences in students’ performance across representation types (. Students demonstrated the highest skill in tabular representations, followed by mathematical and diagrammatic representations, while graphical representations emerged as the weakest area. Qualitative findings indicated that students relied heavily on formula-based problem-solving, experienced difficulty interpreting graphs and diagrams, and struggled to translate and coordinate across representations. The results suggest that prospective physics teachers possess uneven representational skills, characterized by procedural strength in symbolic manipulation but weaknesses in visual interpretation and representational coordination. These findings highlight the need for explicit training in multiple representations, collaborative learning, and scaffolded instruction in physics teacher education. However, the conclusions should be interpreted cautiously due to the small sample drawn from a single institution. Future research with larger and more diverse samples is recommended. Keywords: multiple representation, prospective physics teacher, mechanics, mix-methods analysis.