Mathematical knowledge and practices resulting from access to digital technologies

Through an extensive review of the literature we indicate how technology has influenced the contexts for learning mathematics, and the emergence of a new learning ecology that results from the integration of technology into these learning contexts. Conversely, we argue that the mathematics on which the technologies are based influences their design, especially the affordances and constraints for learning of the specific design. The literature indicates that interactions among students, teachers, tasks, and technologies can bring about a shift in empowerment from teacher or external authority to the students as generators of mathematical knowledge and practices; and that feedback provided through the use of different technologies can contribute to students’ learning. Recent developments in dynamic technologies have the potential to promote new mathematical practices in different contexts: for example, dynamic geometry, statistical education, robotics and digital games. We propose a transformation of the traditional didactic triangle into a didactic tetrahedron through the introduction of technology and conclude by restructuring this model so as to redefine the space in which new mathematical knowledge and practices can emerge