Using an Analytic Model to Gauge the Potential of Innovative Pedagogies of Approximation in Mathematics Teacher Education



Approximations, StoryCircles, Preactive, Interactive, Mathematics teacher education research, Teacher education, Practice-based pedagogies, Methodological models


In order to leverage pedagogies of approximation to improve teacher education, educational researchers must first tackle the methodological question “How can we determine the potential of pedagogies of approximation for supporting the growth of prospective teachers’ knowledge and practices for teaching?” In this paper, we offer a model called the Dual Action Cycles of Approximations of Practice for identifying the pedagogical practices made available to pre-service teachers within various approximations of practice and describe its use to empirically investigate the potential of StoryCircles—a facilitated process of collaboratively representing a lesson using a multimedia storyboarding tool. We illustrate ways that the Dual Action Cycles Model was used to make observations of pre-service teachers during StoryCircles. A key feature of the model is that it provides a bi-focal perspective on both the preactive and interactive phases of teaching, which help bring into focus the interdependent nature of these two phases. We close by suggesting that the development of new forms of approximation needs to be accompanied by research frameworks capable of investigating the potential of these various innovations.

Author Biographies

Patricio Herbst, University of Michigan

Educational Studies, Professor

Kristi Hanby, Wayne Regional Educational Service Agency

Mathematics Consultant


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