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…

In this paper, we elaborate the "seeds of algebraic thinking" perspective, drawing upon Knowledge in Pieces as a heuristic epistemological framework. We argue that students' pre-instructional experiences in early childhood lay the foundation for algebraic thinking and are a largely untapped resource in developing students' algebraic…

This paper pushes beyond current debates over what is being called the science of reading to articulate a multidimensional complex conception of what is entailed in reading comprehension. Reading comprehension entails not only cognitive processes, but equally important is how issues of identity along multiple dimensions, perceptions of tasks and…