Current conceptualizations of knowing and learning tend to separate the knower from others, the world they know, and themselves. In this article, we offer "relationality" as an alternative to such conceptualizations of mathematical knowing. We begin with the perspective of Maturana and Varela to articulate some of its problems and our alternative.…

Investigated problem- and solution-related activity of (n=28) fourth and fifth graders in ill-defined and open-ended settings. In the course of their negotiations, students demonstrated an uncanny competence to frame and reframe problems and solutions and to decide courses of actions of different complexities in spite of the ambiguous nature of…

Investigates variations in students' responses to lever problems across multiple assessment contexts and formats. Data sources include students' semantic maps, written responses to questions, and modeled solutions to practical problems. Contains 40 references. (DDR)