How can upper secondary school mathematics teachers use programming in teaching in an effective way? And how can the use of programming develop students’ mathematical understanding? These are questions examined by Andreas Borg, PhD in Educational Work at Karlstad University.
The aim of this dissertation is to investigate how learning activities can be designed to integrate programming into mathematics education in a meaningful way, and how upper secondary students’ use of programming affects their mathematical understanding.
The dissertation consists of two studies. The first focuses on students solving mathematical problems where programming is required. The second examines how a teacher designs programming tasks for numerical calculations and how these tasks influence students’ understanding of mathematical concepts.
“The first study was based on how programming, according to the mathematics curriculum, is intended to be used as a tool for mathematical problem solving,” says Andreas Borg, PhD in Educational Work. The results show that the use of programming in mathematics education is complex and often too challenging for students, as they frequently have limited experience with programming. The role of programming as a mathematical problem-solving tool was unclear, which led students to fall back on trying to solve the problems using pen and paper. When they attempted to use programming, they had difficulties translating mathematical algorithms into functioning programming algorithms. The study therefore shows that programming should first be integrated into other parts of mathematics education, and that students need to understand the role of programming as a mathematical tool before it is used for problem solving.
“In the second study, the focus was on how programming could be used as a tool for applying numerical methods. Here, I studied a teacher who taught students the meaning of mathematical concepts by allowing them to use programming in mathematics. The teacher had designed how programming could be integrated into mathematics instruction and had a clear plan along with ready-made code examples to facilitate the use of programming algorithms. This made it easier for students to use programming for mathematical purposes when they only needed to make adjustments to existing code. However, the results of the study indicate that students’ understanding of mathematical concepts was not necessarily strengthened through the use of programming.”
More time needed to introduce programming as a mathematical tool
A practical contribution of the dissertation is that teachers need to find a balance: they must support students in how programming can be used as a mathematical tool, while also allowing space for students to use the tool in ways that deepen their mathematical understanding.
“Nearly a decade after the reform, there is reason to question whether teachers were given the right conditions to integrate programming into school mathematics. Teachers have very limited time to teach students how to use programming in mathematics, which raises the question of what the goal of instruction is and how programming should be used as a digital tool to strengthen students’ understanding of mathematics.”
