International Portal of Teacher Education

Source: Journal of Mathematics Teacher Education, Volume 19, Issue 6, (2016) 547–574
(Reviewed by the Portal Team)

This study aimed to examine how certain underlying assumptions about mathematical learning, as reflected in a teacher educator’s discourse in whole-classroom discussions, align with opportunities to mathematize either ritually or exploratively.

Methods
This study described 11 lessons from an introductory algebra course.
The authors also collected students’ written work field notes were taken by two of the authors that were present at all lessons.

Discussion
The authors argue that the findings showed that at the surface level, the instruction in the class seemed to align with ‘‘explorative’’ goals. For example, the authors found that the instructor attempts to conciliate between motives of mathematical activity and identity considerations was to minimize opportunities for erring.
The authors also argue that the instruction, however, was more aligned with ‘‘ritual’’ goals that are concerned with producing narratives about people, not about mathematics. For example, the authors saw that the instructor repeatedly identified her students as teachers to be. The authors hypothesized that this was a strategy for engaging her students in an activity.

The authors argue that the present study shows that identity considerations in the provision of Opportunity to learn (or OTL), both in a prospective teachers’ classroom and perhaps also in school classrooms, are a result of a certain set of assumptions. The authors argue that the challenge for teachers, and especially for teacher educators, is changing these underlying assumptions in such a way that the mathematical discourse will be foregrounded and explorative engagement will be encouraged. They found that in this case study, the instructor, together with her students, aligning herself with the prevalent cultural norms of what mathematics is all about.