The mathematics education field, including prospective teacher education program, has seen a continuous effort to change teaching practices to be more cognitively demanding, conceptually oriented and student centred. Our goal in this study was to examine how certain underlying assumptions about mathematical learning, as reflected in a skilled instructor's discourse, align with opportunities to learn. The data included a set of fully transcribed 11 lessons from an introductory algebra course. The method of analysis was built upon the communicational (commognitive) framework and included discerning between the instructor's mathematizing and identifying talk. This framework was extended to quantify the instructor's identifying talk over the whole set of lessons. Our findings showed that at the surface level, the instruction in the class seemed to align with ''explorative'' goals. On a deeper level, however, it was more aligned with ''ritual'' goals that are concerned with producing narratives about people, not about mathematics.
This paper examines the methodological issues pertaining to study group facilitation assisted by representations of teaching. The study groups, which comprised high school geometry teachers, aimed at achieving two goals: enhancing professional development among teachers and studying the practical rationality of geometry teaching. Therefore, session facilitation involved playing two roles that were often contradictory. A specific co-facilitation model was developed to achieve both goals. This paper examines the characteristics of the discourse of each of the facilitators. The results of this study are used to explain how the facilitators' discourse created a relevant environment for achieving both goals.
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