Fostering students' multivariational reasoning through technology-enhanced learning environments

The study aimed to investigate students' multivariational reasoning regarding the concept of two-variable functions in a technology-enhanced learning environment. This study provided two main contributions. The first was to identify students' mental actions in multivariational reasoning through technology-enhanced learning environment, and the second was to how their mental actions evolve in this environment. The participants of the study involved 15 university students enrolled in a mathematics education programme. The data collection tools included audio and video recordings of students, screenshots, dynamic mathematics software GeoGebra files, and written products. The collected data were analysed based on the framework of mental actions of multivariational reasoning. As a result of the data analysis, it was found that the technology-enhanced learning environments encouraged students' multivariational reasoning by supporting their processes of creating graphs of two-variable functions, mathematically interpreting contour lines, and interpreting the intersection of a plane with a surface function in three-dimensional space. The use of GeoGebra tools in the stages of collaborative learning, scientific debate, and self-reflection (ACODESA method) promoted students' mental actions in reasoning about multivariation.