Practices of questioning and explaining in learning to model

Conceptual learning in mathematics involves more than getting to the right answer. Recent efforts in math education reform have focused on having students work in groups on open-ended projects that are based in realistic contexts. We extend previous analyses with hypotheses about conceptual and interactional aspects of understanding and solving problems by groups. The conceptual hypothesis focuses on integration of information in the group's situation model and its problem model. The interactional hypotheses involve patterns of interaction that make it easy or hard for the group to open up a discussion of assumptions in its reasoning, and that make the group accountable to a wider audience for explaining relations between the situations and mathematical operations involved in their solutions. Regarding educational practice, these findings highlight a way in which student groups must coordinate their conceptual and interactional work to arrive at satisfactory solutions to the problems posed. The present study suggests the importance of students in these environments not only connecting the contextual situation and the attending mathematics, but also reconsidering the situation in light of their new mathematical understanding (bringing the mathematics back into play in their understanding of the situation). Interactional patterns in a group make this relatively easier or harder, and this must be accounted for in implementing new curricula and conducting teacher education.