Solving rate of change tasks with a graphing calculator: A case study on instrumental genesis

In an increasing number of mathematics classes throughout the world, technology is being used for the teaching and learning of mathematics. But knowledge is limited about the long-term development of students’ mathematical thinking when learning mathematics with the use of technology. This article reports on the development of a student and the role of the graphing calculator (GC) in his learning about derivatives and instantaneous rate of change. This case is compelling, because the student is an intensive user of the GC and develops flexible problem-solving techniques – techniques which differ from those of his peers and from what he was taught in mathematics class. We used the framework of instrumental genesis to investigate how this student’s mathematical thinking was affected by the use of the GC. Over a 2-year period, we administered four task-based interviews involving problems on instantaneous rate of change situated in contexts. We found that the use of the GC may facilitate a learning process in which instrumentation schemes involving symbolical representations develop separately from those for the graphical and numerical use of the GC.