Playing with Perpendicular Lines: The Case of Laura

Playing with Perpendicular Lines: The Case of Laura

Douglas A. Lapp (Central Michigan University, USA) and Dennis St. John (Central Michigan University, USA)
Copyright: © 2015 |Pages: 21
DOI: 10.4018/978-1-4666-6497-5.ch005
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This chapter has been designed to examine both the teaching and learning of algebraic concepts as well as the way in which representations play a role in the development of these concepts. The framework for the discussion of representational use is based on the Kaput, Blanton, and Moreno (2008) model for the development of symbolic meaning. The specifics of this model are elaborated toward the end of the chapter.
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As you read the case, we encourage you to think about the interactions between the students and teacher along two dimensions: (1) what are the relevant mathematical ideas involved and (2) what did the teacher do or not do to facilitate the development of these ideas? Keep in mind that mathematical ideas are not limited to specific concepts such as slope, but also include mathematical processes. The Common Core State Standards (CCSS) lay out Standards for Mathematical Practice such as “Construct viable arguments and critique the reasoning of others” that go beyond the mere teaching of concepts to include habits of the mind for thinking mathematically. The development of these practices is crucial for preparing students that are capable of adapting in a constantly changing world where the mathematics we teach is mediated by technological changes that are happening at ever increasing rates.

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