Construction is a defining characteristic of geometry classes. In a traditional classroom, teachers and students use physical tools (i.e. a compass and straight-edge) in their constructions. However, with modern technology, construction is possible through the use of digital applications such as GeoGebra and Geometer’s SketchPad.
Many other studies have researched the benefits of digital manipulatives and digital environments through student completion of tasks and testing. This study intends to research students’ use of the digital tools and manipulatives, along with the students’ interactions with the digital environment. To this end, I conducted exploratory teaching experiments with two calculus I students.
In the exploratory teaching experiments, students were introduced to a GeoGebra application developed by Fischer (2019), which includes instructional videos and corresponding quizzes, as well as exercises and interactive notepads, where students could use digital tools to construct line segments and circles (corresponding to the physical straight-edge and compass). The application built up the students’ foundational knowledge, culminating in the construction and verbal proof of Euclid’s Elements, Proposition 1 (Euclid, 1733).
The central findings of this thesis are the students’ interactions with the digital environment, with observed changes in their conceptions of radii and circles, and in their use of tools. The students were observed to have conceptions of radii as a process, a geometric shape, and a geometric object. I observed the students’ conceptions of a circle change from a geometric shape to a geometric object, and with that change, observed the students’ use of tools change from a measuring focus to a property focus.
I report a summary of the students’ work and classify their reasoning and actions into the above categories, and an analysis of how the digital environment impacts the students’ conceptions. I also briefly discuss the impact of the findings on pedagogy and future research.