Proving and refuting are fundamental aspects of mathematical practice that are intertwined in mathematical activity in which conjectures and proofs are often produced and improved through the back-and-forth transition between attempts to prove and disprove. One aspect underexplored in the education literature is the connection between this…

Listening to students in productive ways seems to be at the core of teaching practices aligned with the basic tenets of the constructivist world view. We present a definition for productive ways of listening, discuss the challenges involved in implementing it, and propose a way to support the "decentering" needed to learning to listen for teacher…

Distinguishes two conceptions of sample and sampling that emerged in the context of a teaching experiment conducted in a high school statistics class. Suggests that the conception of a sample as a quasi- proportional, small-scale version of the population is a powerful one to target for instruction. (Author/KHR)

Presents an exploration of conversation in a single episode of a 12th grade girls' calculus class. Analyzes Habermasian communicative competence which requires students to show critical thinking and the ability to express their views. Explains learning outcomes by teachers' mode of questioning, cooperative endeavor by students, instructional…