Responding to calls for studies on task design and enactment using technology in geometry classroom, this dissertation connects theoretical and empirical studies to instructional practices by designing, enacting, and revising a sequence of tasks using DGEs for college students in an axiomatic geometry course. First, I discuss a set of mathematical activities using DGEs that consist the core of the task sequence in this study. I illustrate a sequence of instructional tasks designed and enacted in an axiomatic geometry course where a DGE plays a crucial role in students' mathematical activities in class. The illustration of the task sequence consists of the mathematical activities intended in the design of each task as well as student reasoning. Student work collected in the actual classroom provides pedagogical implications to revise the task sequenceSecond, I report an empirical study on students' uses of DGEs and their engagement in mathematical reasoning and axiomatic reasoning while enacting three tasks in the sequence. Students used DGEs to communicate their mathematical ideas and to examine mathematical statements describing properties of geometric objects within axiomatic systems and models of hyperbolic geometry. The analyses of this study revealed case themes describing student use of DGEs, engagement in mathematical reasoning and axiomatic reasoning, and relationships thereof. The findings of the analysis provide practical implications to revise the task design as well as theoretical implications to better understand the nature of student engagement in advanced mathematical reasoning in such technology-rich environments.At last, not the least, I address theoretical consideration on understanding of epistemic aspects of student learning in axiomatic geometry supported by technology and appropriate mathematical activities exploiting pedagogical roles of technology. I address students' epistemological shifts that have been discussed in the existing literature of student learning of advanced geometry in connection with student work collected and analyzed in the empirical study reported above. First, students make a shift in the ontological view of geometric models from Euclidean to non-Euclidean geometry, in which the geometric models are considered conscious artifacts of mathematical design. Second, students make a shift in the epistemological view of mathematical proofs from absolutism to fallibilism, in which proofs can be characterized with a variety of functions and forms. Drawing on the prior literature, I argue that making successful shifts can benefit students in axiomatic geometry and that such shifts can be facilitated by engaging in mathematical activities with supports of dynamic geometry environments. In particular, I highlight examples of student work reported in the empirical study that illustrate those different views of geometric models and mathematical proofs captured observed from students who were on the process of such shifts.
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