Building connections between sociomathematical norms and cognitive demand to improve the quality of whole class mathematics conversations.

摘要

Mathematical discussions support and promote student learning as an integral part of the contexts in which students learn mathematics. Yet, American school practices often focus on teachers disseminating knowledge to students and students acquiring that knowledge through rote rehearsal rather than higher order thinking. One barrier to change in these practices is teachers' lack of training or practice in facilitating discourse.;This research hypothesized that the quality of classroom mathematics discussions as measured by the level of cognitive demand of statements could be improved by providing teachers with professional development focused on the characteristics of high quality conversations. A professional development program (PDP) was designed around the key characteristics of social norms, sociomathematical norms, and cognitive demand. During the PDP, social norms that govern the participation of students during whole class discussion were contrasted with the sociomathematical norms that raise the level of cognitive demand of the discussion in order to provide teachers with knowledge that would change teacher questioning beliefs and behaviors. These changes in beliefs and behaviors were believed to influence the development of norms among students.;Data were collected from participants' pre- and post-PDP video recordings of mathematics instruction, their written course work, and the instructor's logs and journal. Teachers reported perceived changes in practice in their written work which included general references to increased use of higher order questions and specific references to increased use of justification questions. Wilcoxon Signed Ranks test indicated a statistically significant increase in the percent of high level questions asked by grade K-8 teachers.;It was also hypothesized that the quality of classroom conversations and the effectiveness of the PDP in changing teachers' knowledge and practices would be related to the teachers' mathematical knowledge for teaching (MKT). Differences between teachers with low levels of MKT and those with high MKT included: (a) low MKT teachers primarily set goals focused on changing their own behaviors while high MKT teachers also set goals for changing student behaviors, (b) low MKT teachers applied their learning by identifying places for change while high MKT teachers noted more actual changes in behaviors and understandings, and (c) low MKT teachers increased use of justification questions while high MKT teachers increased use of both justification and comparison questions.