Pre-service teachers’ analysis and handling of student errors in outdoor modelling and its relation to beliefs about teaching and learning

Mathematical modelling, whether conducted indoors or outdoors, poses substantial challenges for learners and therefore multiple difficulties and errors can arise in the solution process. Supporting students in overcoming their errors requires (prospective) teachers to diagnose such errors accurately and respond appropriately. These skills have been well documented for classroom situations and indoor modelling, but scarcely researched in the context of outdoor modelling. This study employs a mixed-methods design to characterize mathematics pre-service teachers’ perceptions, analysis of and reactions to different error situations in the context of outdoor modelling. We also examine relations between error-diagnostic competences and pre-service teachers’ affective dispositions (beliefs), as it can be assumed that beliefs about teaching and learning of mathematics shape the way how teachers deal with errors. Findings indicate that the investigated diagnostic processes can be characterized by context-specific aspects of the outdoor modelling, since participants proposed outdoor-specific error causes and physical activities were used as interventions, which extends the variability of error handling strategies in this context in comparison to interventions during indoor modelling. Relations between error-diagnostic competence and beliefs were rather weak. It was also evident that some pre-service teachers viewed non-standard or typical outdoor strategies as “errors” and discouraged students from using these, which suggests incorporating outdoor modelling and its unique characteristics in teacher training.