An investigation of pre-service elementary mathematics teachers' learning processes of fundamental linear algebra

This study was conducted to examine the learning processes of pre-service mathematics teachers regarding fundamental linear algebra concepts. The research was carried out in the computer laboratory of the Faculty of Education at a university located in the Central Anatolia region. The study group consisted of ten volunteer pre-service mathematics teachers from the same university during the 2024–2025 academic year. The participants were given worksheets containing questions involving various sets. They were asked to predict the underlying linear algebra concepts represented by these sets, explain them mathematically, and share their observations on the GeoGebra screen. A qualitative data analysis method was employed in the study. The results revealed that the participants most accurately predicted and mathematically explained the concepts of linear dependence and independence. On the GeoGebra interface, it was observed that the concept of span (germe) was the most accurately identified and interpreted.