Research in mathematics education constantly oscillates between theoretical or 'Is' questions and practical or 'Ought' questions: Researchers are not only pursuing theoretical questions by investigating what those involved in the teaching and learning of mathematics do, but they are also working on practical recommendations for what they ought to…

This article addresses the learning paradox, which obliges researchers to explain how cognition can advance from a lower level of reasoning to a higher one. Although the question is at least as old as Plato, two major flaws have inhibited progress in developing solutions: the assumption that learning is an inductive process, and the conflation of…

When asked to give a talk at a mathematics teacher conference that focused on research in mathematics education, Ruhama Even viewed the invitation as an opportunity to address the meta-question: what can teachers learn from research in mathematics education? The reason for her view was her way of feeling, as a researcher and teacher educator, that…