An Instrumental Approach to Developing Mathematics Teachers' TPACK Using Dual Technological Environments

This mixed-method case study examines how the technological pedagogical and content knowledge (TPACK) of primary school mathematics teachers develops when they are tasked with designing inquiry-based geometry tasks that integrate two dynamic technological environments: Origametria, a digital platform based on paper-folding, and GeoGebra, a dynamic geometry environment. This study was conducted over 13 weeks during an academic course that was part of an MEd program for teaching primary school mathematics. Teachers designed inquiry-based geometry tasks utilizing both Origametria and GeoGebra and documented their reflections about the mathematical discourse that accompanied their collaborative work in their personal teachers' journal. They also answered dedicated pre- and post-study questionnaires. Our paper focuses on one group of four representative mathematics teachers and uses their submitted inquiry-based tasks as part of the data. The quantitative findings suggest that engaging in the design of inquiry-based tasks in geometry using dual technological applications led to a noticeable improvement in the teachers’ TPACK: after completing the activities, the respondents reported higher levels of confidence in integrating technological tools, higher overall TPACK, and specifically higher knowledge in the technological‑pedagogical component. This study expands on the theoretical concept of the “instrumental approach” framework by proposing three distinct patterns of multi-tool instrumental genesis: Sequential Instrumental Genesis, Complementary Instrumental Genesis, and Integrated Instrumental Genesis. This affords a more nuanced understanding of how teachers can develop proficiency using dual technological environments and contributes to understanding how to better train teachers to integrate technology into mathematics education.