| This dissertation involved an 8-week investigation in a high school classroom to explore how students' prior experiences with dynamic graphs of linear equations supported their efforts to understand systems of linear equations. The researcher and the classroom teacher developed two technology-intensive instructional sequences that were taught by the classroom teacher. The daily collaborative meetings of the researcher and the teacher informed revisions to the instructional sequence.;This study used the situated perspective to analyze the collective mathematical development of the class and to compare the ways in which individuals participated in the collective development. According to theorists of the situated perspective, knowing mathematics is considered an aspect of participation in social practices. In order to describe the collective development, the construct of a practice was used to examine the structure, responsibilities, and common activities of the mathematics classroom. I describe four target students' individual growth in terms of a trajectory of participation in the practices of mathematical thinking.;Our conjectures about the means of supporting student learning, in the form of curriculum and software, were empirically tested. By providing insight into the process by which a group of students collectively develop understandings of important mathematical ideas, analyses such as this can help teachers and instructional designers anticipate possible ways other groups of students will develop meaning.;This work also informs classroom teachers in that situated research such as this embraces the complexity of the classroom. It accounts for what students contribute and what teachers can do to support student learning. This analysis is not prescriptive in the sense of theory informing educational practice. Instead, in this theoretical framework a reflexive relationship exists between theory and practice. Teachers can see how ideas emerged and student conceptions developed within a particular context. |
