A Mathematical Medley

When students share their mathematical creations with us--their proofs, their models, their algorithms and techniques--how do we respond as educators? I consider two common responses: the giving of feedback, and the event of critique. The terms feedback and critique are often used interchangeably in education to describe a kind of formative assessment. Here, I propose they offer distinctly different educational possibilities for our encounters with students' mathematical creations, and with the students themselves.