Abstract
In this chapter, we describe how two experienced and well-respected teachers grapple with a specific example of a problem that all teachers confront, helping students build more sophisticated understandings from more limited ones. And we illustrate how, in the context of their grappling, they have developed their own knowledge of the content for teaching and their own responses to student difficulties. While we do not have the means to evaluate the effectiveness of their responses, we are intrigued by the sensitivity to issues of student learning that their responses represent and to the evidence this sensitivity suggests for on-the-job learning by teachers. Though it is beyond the scope of our chapter, given the limited time available for initial teacher training, it seems important to explore ways of organizing the work of teaching to support such on-the-job learning by teachers (for some discussion of how the organization of the work of teaching is different in different cultures, see Britton, Paine, Raizen, & Pimm, 2003).
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Notes
- 1.
In what follows, we are concentrating on the solving of equations. When we use the phrase the “meaning of solve,” we intend in the context of solving equations.
- 2.
Our interview is based on earlier work by Chazan, Yerushalmy, and Leikin (2007; 2008).
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The research reported here was supported by NSF REC 0106709. This chapter represents the views of the authors and not the National Science Foundation.
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Marcus, R., Chazan, D. (2010). What Experienced Teachers Have Learned from Helping Students Think About Solving Equations in the One-Variable-First Algebra Curriculum. In: Leikin, R., Zazkis, R. (eds) Learning Through Teaching Mathematics. Mathematics Teacher Education, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3990-3_9
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