ABSTRACT
In this chapter, we describe an approach to design research1 that we have refined while conducting a series of design research projects in mathematics education over a ten-year period. Our intent in doing so is to highlight a number of issues that we believe it is essential to consider when conducting a design experiment regardless of the specific approach followed. For the purpose of this chapter, we define design research as a family of methodological approaches in which instructional design and research are interdependent.2 On the one hand, the design of learning environments serves as the context for research, and, on the other hand, ongoing and retrospective analyses are conducted in order to inform the improvement of the design. This type of research involves attempting to support the development of particular forms of learning and studying the learning that occurs in these designed settings. The learning of interest might be that of individual students who interact one-on-one with a researcher in a series of teaching sessions (Cobb & Steffe, 1983; Steffe & Thompson, 2000), a group of students in a classroom (Cobb, 2000a; Confrey & Lachance, 2000; Gravemeijer, 1994b), preservice teachers in a university course (Simon, 2000), or practicing teachers who collaborate with researchers as members of a professional teaching community (Kazemi & Franke, 2004; Stein et al., 1998). In each of these cases, design research enables us to investigate simultaneously both the process of learning and the means by which it is supported and organized. As we will argue later in the chapter, the potential contributions of the methodology become particularly apparent when the current research base is thin and provides only limited guidance for the design of learning environments.
