Incorporating programming into mathematics education : How using programming shapes upper-secondary students’ mathematical understanding

This thesis comprises two studies investigating upper-secondary students’ use of programming as a mathematical tool. It aims to examine both the intertwined relationship between students’ use of programming and their mathematical understanding, and how the design of learning activities can support the incorporation of programming into mathematics education. The first study adopts a design-based research approach centred on a problem-solving activity involving programming. The second study examines a teacher’s design of programming activities for numerical calculations and its influence on students’ understanding of limits. The Instrumental Approach provides the theoretical lens for analysing students’ instrumental genesis, describing the relationship between their use of programming and their mathematical understanding. The findings indicate that, as programming is not designed as a mathematical or educational tool, its technical handling may be less intuitive for students than that of digital tools explicitly developed for mathematical purposes. A theoretical contribution of the thesis is that the analysis of students’ instrumental genesis, when programming functions as a mathematical tool, must encompass not only mathematical conceptual aspects but also those required for learning to program. The findings further suggest that using programming as a mathematical problem-solving tool, particularly when students construct their own algorithms, places considerable demands on those with limited programming experience. Conversely, providing pre-designed algorithms for numerical computations, to ease students’ use of programming, may limit the development of deeper mathematical understanding. A practical contribution of the thesis is that teachers designing mathematical learning activities involving programming must balance scaffolding students’ use of programming with allowing them autonomy to use the tool in ways that support their mathematical understanding.