A variety of researchers in the last fifteen years have described how people learn and use mathematics in out-of-school situations. These researchers have found that mathematics learning and practice in and out of school differ in a number of ways. In this paper we examine and discuss these differences while maintaining the position that while some differences may be inherent, many differences can be narrowed so that mathematics learning and practice in school and out of school can build on each other and be connected. Before discussing a framework that we think sheds some light on connecting these experiences, we present some research from several of our studies that illustrates some of the differences between in-school and out-of-school mathematics practice and lays the groundwork for the discussion of the framework. We then discuss Saxe's (1991) research framework for 'gaining insight into the interplay between sociocultural and cognitive development processes through the analysis of practice participation' (p. 13). Although Saxe's framework is a method for studying the interplay between sociocultural and cognitive development processes, we propose that it may be helpful in working towards connecting in-school and out-of-school mathematics learning and practice. Thus, we discuss the framework with illustrations from our own research, and then elaborate on ways to make this interplay between in-school and out-of-school contexts more deliberate.
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