This teacher educator explains the fundamental nature of representation and describes how technology can be used to support the development of mathematical understanding in students.
Teachers often struggle to find ways to help their students understand very abstract notions.
In addition, there is a call for the teaching of algebra in middle school and algebraic concepts even earlier. As we face this challenge, we must think about how best to help children form understandings of mathematical abstractions. In contemporary educational theory, this challenge translates into a quest to help children construct internal representations of the abstract concepts embodied in external representations. Internal representations are cognitive abstractions of mathematical concepts that are developed through experience. It is the job of the teacher to help students internalize concepts presented in mathematical symbols or in graphs and other external representations of these concepts.