Computer algebra systems and dynamic geometry for mathematical thinking

For more than three decades, the use of Computer Algebra Systems (CAS) and Dynamic Geometry Environments (DGE) has introduced new possibilities in Mathematics Education. Ontological, epistemic, educational, and social perspectives, and their theoretical and empirical approaches, have described the cognitive processes that students go through when faced with the use of these technologies. Given the diversity of the knowledge that has been generated through international research, there is a need to systematize it to understand the different roles of these technologies in Mathematics Education and their effects on mathematics learning. In this chapter, we review the literature produced in the last 8 years on CAS and DGE. We focus on identifying the contributions of these technologies in the development of mathematical processes such as mathematical modeling and reasoning and in the learning of geometry, algebra, and calculus. Within each topic, we identify relevant research and provide feedback on their contributions. We end the chapter with comments on those contributions and raise issues for discussion and future directions of research.