ABSTRACT
The problem-solving process in many of the most important 21st century contexts involves teamwork, as illustrated in chapter 12 by Oakes and Rud. However, this point of view is not typically reflected in school mathematics, where students generally work in isolation, especially at the middle and high school levels. It is difficult for schools to change this pattern because parents, administrators, and even teachers find small group learning activities suspect. They ask question such as: What do the “smart” kids learn if all they do is teach the other kids what they already know? What do the “not so smart” kids learn if the smart kids do all of the work? The purpose of this chapter is to examine the role of small group work with model-eliciting activities in order to understand its potential value, and to provide initial guidance for implementing these types of activities. The type of tasks that form the basis of the problem solving experiences discussed are model-eliciting activities, which we believe are most like the kinds of problems that students of today will be solving in the workplace tomorrow. This chapter begins by describing how the design of the tasks embeds social aspects into the activities. We then explore the mathematical power that students as a group have when working on such problems. Cognitive development is then addressed from two different perspectives. First we examine how the group’s mathematical model, which underlies their final product, develops during a problem-solving episode. We assume that groups’ interpretations of a problem evolve from unstable to increasingly coordinated and stable models. Based on this assumption, we then discuss the potential for small group interactions to ameliorate the problems associated with unstable models, which are common during early phases of model-eliciting activities. The chapter ends with helpful hints for implementing model-eliciting activities with small groups, based on their experiences and observations of the authors.
