Knowledge for teaching mathematical problem-solving with technology: An exploratory study of a mathematics teacher’s proficiency

Abstract

This paper presents the results of an exploratory case study that examined a veteran secondary teacher’s knowledge for teaching non-routine mathematical problem-solving with digital technologies. Data was collected through the observation of a veteran mathematics teacher, in real time, solving a mathematical problem with the digital tools of his choice. The descriptive model Mathematical Problem-Solving with Technology (MPST) was used to analyse the teacher’s utterances and actions while solving a mathematical problem, with GeoGebra and a spreadsheet, and expressing his reasoning also with technology. Our findings reveal the complexity of expert problem-solving with technology, through regulation processes and several micro-cycles that mainly involve the processes integrate and explore. Mathematical problem solving with technology entails relevant mathematical knowledge as well as knowledge about the mathematical affordances of the digital tools available, and the ability to combine them to develop a conceptual model of the solution to the problem. Thus, the teacher’s techno-mathematical fluency seems crucial to successfully solve the problem and express the reasoning with technology. Based on the findings, we discuss the teachers’ knowledge for teaching mathematical problem-solving with technology as including a particular kind of proficiency, techno–mathematical fluency for solving-and-expressing problems with technology. The limitations of the study, further research topics and implications for professional development and teacher education programmes are discussed.