This study will follow a group of 14 æfocus studentsÆ through two years of secondary school mathematics, using in-class observation, clinical interviewing, and audio/video recordings of after-school working sessions to document and analyze changes in the way these students make and explain proofs. A subset of these students were participants in an earlier longitudinal study of mathematical thinking (grades 1 - 8). This will allow detailed documentation of the intellectual histories of these students.
The goals of the project are (1) provide in-depth case studies of the development of proof making in high school students; (2) to investigate the relationship of studentsÆ earlier ideas and insights to later justifications and proof building; (3) to trace the origin, development and use of representations of student ideas, explorations, insights relating to explanation, justification and proof building. Within the context of the learning community, additional goals are: (4) to investigate the nature of teacher intervention in the growth of student mathematical ideas and (5) to study individual cognition in the context of the movement of ideas within the community of learners.
