“You’re Not Allowed to Give Us the Solution, but Can You Guide Us towards It?”

Abstract

In task-based mathematics classes, where several solution approaches may be valid, diagnosing students’ solution processes and adaptively supporting them is a significant challenge for teachers. The question arises as to how mathematics teachers can successfully support students in solving these mathematical tasks and which aspects constitute adaptive teaching interventions. However, few studies have analyzed adaptive teaching interventions in the context of mathematics didactics. This paper first presents a detailed model of adaptive teaching interventions. Based on this model, the interventions of four secondary school mathematics teachers were analyzed using two methodological approaches. The applicability of the model was analyzed, and factors that hinder the adaptivity of teachers’ interventions were identified. The results show that 41–63 % of all identified teaching interventions were adaptive. Up to 55 % of the teachers’ interventions took place even though the students were not facing barriers within their learning processes. The sampled teachers faced major difficulties in diagnosing and in addressing the barriers in students’ solution processes. Furthermore, up to 65 % of all teaching interventions analyzed did not enable students to overcome barriers in their solution processes.

Keywords

• adaptive teaching interventions
• adaptivity
• mathematical problem solving
• student-teacher interactions
• adaptiver Unterricht
• mathematische Kompetenz