Abstract
This article situates comic-based representations of teaching in the long history of tensions between theory and practice in teacher education. The article argues that comics can be semiotic resources in learning to teach and suggests how information technologies can support experiences with comics in university mathematics methods courses that (a) help learners see the mathematical work of teaching in lessons they observe, (b) allow candidates to explore tactical decision-making in teaching, and (c) support preservice teachers in rehearsing classroom interactions.
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Notes
These characterizations are admittedly simple and for the sake of defining the following attributes. We realize that in actuality there are widely different ways of using each of those media forms, video or writing, to narrate practice.
The notion of practical rationality (Herbst & Chazan 2003) encapsulates the categories of perception and value that organize the stories in the teaching of a mathematics domain, such as geometry or algebra.
This and other stories can be watched in http://grip.umich.edu/themat.
In the main trunk of this story, the teacher gives lines with points of tangency that are not equidistant from the intersection of the lines, thus making the problem unsolvable.
The tangent segments theorem says that a circle tangent to two intersecting lines has its points of tangency equidistant from the point of intersection.
These possibilities include to give two intersecting lines with two tangent points, one on each line, that are (1) apparently equidistant to the point of intersection and (2) not equidistant to the point of intersection.
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Acknowledgments
Work described in this paper has been done with support of the USA's National Science Foundation grant ESI-0353285 to Herbst and Chazan. Opinions are those of the authors and do not necessarily represent the views of the Foundation.
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Herbst, P., Chazan, D., Chen, CL. et al. Using comics-based representations of teaching, and technology, to bring practice to teacher education courses. ZDM Mathematics Education 43, 91–103 (2011). https://doi.org/10.1007/s11858-010-0290-5
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DOI: https://doi.org/10.1007/s11858-010-0290-5