Instructional videos on ill-structured mathematical problem-solving processes: The cases of mathematical modeling and proof construction

Wirth, L

Abstract

The dissertation deals with mathematical modeling and proof construction as problem-solving processes and their support through instructional videos. Based on the current state of research on heuristic worked examples and principles of instructional video design, design criteria for instructional videos on mathematical problem-solving processes are developed and empirically investigated in three studies. The results show that learners find the videos particularly helpful for structuring their own solution processes. Elements such as segmentation along process steps and self-explanation prompts promote process-related knowledge. In addition, the findings indicate that instructional videos can effectively support both modeling in a school context and proof construction at the undergraduate level. The work thus contributes to the integration of instructional videos into mathematics education at school and university.