Knowledge building in mathematics: Supporting collaborative learning in pattern problems

While it has been suggested that patterning activities support early algebra learning, it is widely acknowledged that the shift from perceiving patterns to understanding algebraic functions- and correspondingly, from reporting empirical patterns to providing explanations-is difficult. This paper reports on the collaborations of grade 4 students (n = 68) from three classrooms in diverse urban settings, connected through a knowledge-building environment (Knowledge Forum), when solving mathematical generalizing problems as part of an early algebra research project. The purpose of this study was to investigate the underlying principles of idea improvement and epistemic agency and the potential of knowledge building-as supported by Knowledge Forum-to support student work. Our analyses of student-generated collaborative workspaces revealed that students were able to find multiple rules for challenging problems and revise their own conjectures regarding those rules. Furthermore, the discourse was sustained over 8 weeks and students were able to find similarities across problem types without the support of teachers or researchers, suggesting that these grade-4 students had developed a disposition for evidence use and justification that eludes much older students.