Students’ Development of Instrumented Action Schemes for Numerically Determining Limits Using Programming

Abstract Through educational reforms, programming has in recent years been integrated into school curricula in many countries, often in conjunction with mathematics education. Using programming in school mathematics presents new mathematical possibilities but also introduces challenges for both students and teachers. In this case study, we employ the Instrumental Approach as a theoretical lens to investigate how students’ perceptions of function limits are affected by their use of programming. The findings reveal how a careful design of lesson activities involving programming can enhance students’ ability to use programming as a mathematical tool. However, the study also demonstrates that using programming to numerically determine limits primarily fosters a dynamic process view of limits. In this view, students focus on the process in which the dependent variable approaches a specific value but struggle to coordinate this with the corresponding process of the independent variable approaching a given value. We contend that it is essential for mathematics teachers to thoughtfully integrate programming into their teaching and to consider how students’ use of programming might influence their perception of mathematical concepts such as limits.