Connecting Real-World and In-School Problem-Solving Experiences

Abstract

In this article, we address the challenge of supporting students in real-world problem solving as a vibrant part of their in-school experience of mathematics. On one hand, we describe the issues associated with using traditional schooling approaches to prepare students for success in a world that is increasingly characterized by complexity and rapid disciplinary change. Today’s STEM professionals need to adapt the knowledge they have learned in school in creative ways to use them effectively; thus it is desirable to provide learners with activities that offer a more realistic simulation of problem-solving settings beyond school. On the other hand, we argue that the schooling context does offer unique opportunities for reflecting on problem-solving experiences and for unpacking, extending, and formalizing ideas that emerge in students’ solutions to realistic problems. To balance these two needs, we describe Model-Eliciting Activities (MEAs) as authentic problem-solving settings, and we describe Model-Development Sequences (MDSs) as a framework for extension activities that help students to process the conceptual work they have done on MEAs and that help classroom groups to develop shared understandings that are consistent with disciplinary norms and conventions. With this frame in place, we then present a teaching episode extracted from ongoing design research, in which the first author elaborated and adapted an MDS in response to student needs that surfaced in the moment. We describe the instructional decisions that guided this work, and we articulate a set of six design principles for MDS sequences, which emerged through the author group’s reflective analysis of this implementation episode.