Professors in proof-based mathematics courses often intend that the feedback they provide on students' flawed proofs will promote proof comprehension. In this theoretical article, we investigate how such feedback can be formulated. Drawing on Lakatos's process of proof and refutation, we propose the notion of "heuristic refutation…

There is a growing body of evidence suggesting that secondary mathematics teachers may not be drawing significant benefit from the tertiary mathematics courses they take in preparation programs or in-service for professional development. While there are some theory-driven attempts to re-design or complement such courses for teachers, empirical…

With the emergence of e-textbooks, along with expectations to integrate technology in instruction, teachers are becoming significant co-designers of the curriculum. Informed selection and sequencing of learning resources requires sensitivity to didactic nuance, and tools to support development and application of such sensitivity. Teachers'…