International Portal of Teacher Education

Source: Journal of Teacher Education 62(1), p. 8-22. (January/February 2011).
(Reviewed by the Portal Team)

In this article the authors analyze three episodes from an elementary mathematics teacher education class: two where students were positioned as children learning mathematics and a more extended one where students were positioned as teachers.

By addressing only the general categories of “teachers” and “children” the authors intended to highlight the way the models were drawn from and developed and how they interacted with figured worlds and constructions of mathematics.

The instructors presented the figured world of reform pedagogy in at least two ways over the course of the semester: by describing it and approximating it in class activities.
The instructors stressed the importance of posing problems that are mathematically meaningful and accessible to various levels of understanding so that students could reason with real quantities and share their solutions. They described the teacher’s role in orchestrating student explanations so as to promote efficiency, accuracy, and flexibility.
They enacted approximations of this world by posing such problems, modeling the teacher’s moves, and prompting students to both come up with solutions and imagine next pedagogical steps

In the spring of 2008, the class consisted of two instructors and 11 female students, 10 of whom were undergraduate sophomores and juniors preparing to teach in elementary classrooms.

Data Sources
The analysis is based on observations, field notes, and video of 18 of the 28 class sessions that occurred between January and April 2008. The authors also collected corresponding classroom artifacts, including handouts and course assignments. In addition, the authors conducted several informal interviews with the instructors over the course of the semester.

The findings reveal that there were shifts in the models of identity students drew on, the way they constructed mathematics in their talk, and their conceptions of the figured world of reform pedagogy. By midsemester, students had changed their minds and drew readily from a model of identity of children who reason in various ways about quantities.

A consideration of figured worlds of mathematical teaching and learning and models of identity necessarily has implications for how mathematics is socially constructed for teachers and children. This perspective can be productive for teacher education practice.
The instructors presented the new models of identity, constructions of mathematics, and figured world of reform mathematics with the world of traditional mathematics pedagogy as an inevitable backdrop. As students mixed elements from the two worlds, confusion or conflict emerged.

The authors conjecture that teacher educators might work with the confusion, deliberately leveraging the multiple models of identity students bring to university-based coursework to help them understand the people and practices of the figured worlds of mathematics that they will encounter in the field, and so more effectively manage and refine their repertoires.

Finally, the authors propose that by recognizing certain models of identity for children learning math, students in Mathematics for Elementary Teachers drew on corresponding models of identity for elementary mathematics teachers.