A Mathematics-Science Community of Practice: Reconceptualising Transfer in Terms of Crossing Boundaries.

Over the last three years we have been involved in an interdisciplinary research project whose general aim was to study what has been called in the educational literature 'transfer of knowledge', in this case between mathematics and science school practices. Tiris project has been developed in a basic (elementary and secondary) school where Cristina teaches mathematics and Selma teaches science. During the first year of the project, Cristina and Selma acted as teacherresearchers of one of the Year 9 classes (approx 15-yearolds) that they both taught The three of us have spent the last two years making sense of the data We have also set out to offer a contribution to the discussion of transfer from what Engestrom (1999a) refers to as a 'strong' situated point of view that is, using ideas of community of practice as our starting point Beyond our intellectual committuent to the situated character of learning, two significant observations have encouraged us to develop this project: first, the controversial notion of transfer within situated learning perspectives; second, the elem diversity of views of transfer in the mathematics education literature relating to these perspectives. In the educational literature, transfer of knowledge refers in general to the use or application in one context of knowledge learned in another. It is suggested by some researchers (e.g., Greeno, 1997; Lave, 1993) that those choosing a strongly cognitive perspective on learning see knowledge as something relatively stable, generalizable to different situations and characterized by personal attributes in the sense that, once acquired, the subject carries it from one place to another. As Boaler (2002a) points out, situated learning perspectives offer an interpretation of knowledge that is radically different: a representation of knowledge as activity, as something that is shared or distributed by persons; something that emerges between persons, the environments in which they are inserted, and in developing activities. From these perspectives it is not that cognitive structures are not considered, but that they cannot be detached or abstracted from learning contexts The epistemological assumptions that accompany situated perspectives of learning have challenged, among other things, the interpretation of transfer mentioned above; they have also led some mathematics educator researchers to rethink the issue in terms of these assmnptions. However, we still find much variation among the approaches to transfer of mathematics educators taking a situated perspective. Ibis raises theoretical and methodological difficulties for those who aim to research the issue of transfer of knowledge from a situated perspective At the beginning of our research, we strongly believed that we could plan a collaborative school project between mathematics and science, theorizing it in terms of a community of practice But we had no clear idea about the direction to take to elaborate a theoretical contribution to the discussion of uansfer from a strongly situated point of view During the planning phase, the teacher-researchers' struggles to share both their scientific discourses and their disciplinary expetiences led us to think about transfer in Bernstein's (1996) terms, as the transfer of knowledge between two insulated domains or vertical discourses Our situated account of transfer represents, more specifically, a reconceptualization of transfer within the school context in terms of boundary crossing between two apparently insulated practices We suggest that, where transfer between practices is thought to be observed, it can be usefully conceptualised in terms of a community of practice that overlaps these practices In doing so we take as our major challenge a response to Lerman's (1999) question, "how can children learn to be conscious of contexts and cross the boundaries of practices successfully? " (p. 94)