An actor-oriented transfer perspective on high school students’ development of the use of procedures to solve problems on “rate of change”.

This article reports on a longitudinal observation study about students’ development in their use of procedures to calculate instantaneous rate of change. Different procedures for solving tasks on rate of change are taught in mathematics and physics classes, and together they form a repertoire. Our study took an actor-oriented perspective, which we operationalized as a search for students’ personal constructions of relations between (1) learning from mathematics and physics classes and (2) interview tasks. We followed ten students for two years (from grade 10 to 12), during which we administered four task-based interviews. We analyzed the breadth and connectedness of students’ repertoire of procedures and report on the long-term development thereof. We conclude that often procedures are not part of students’ repertoire shortly after the first introduction of this procedure in class. Students need time to acquire single procedures, and much more time to develop a broad and connected repertoire. In the development of their repertoire there are major differences between students. From an actor-oriented perspective many personal constructions are visible between learning and interview tasks. Students often use procedures that differ from procedures that are most appropriate from an expert’s perspective. We also observed from an actor-oriented perspective, that words such as ‘velocity’, ‘steepness’ or ‘slope’ act as bridge for creating relations between situations and procedures.