Reasoning by Cases While Exploring Fractions as Numbers

Esther Winter; Dina Yankelewitz

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Reasoning by Cases While Exploring Fractions as Numbers

In: Children's Reasoning While Building Fraction Ideas

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Esther Winter

Esther Winter
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Dina Yankelewitz

Dina Yankelewitz
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Type:: Chapter

Pages:: 35–41

DOI:: https://doi.org/10.1007/9789463510080_006

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In this chapter, we explore various forms of reasoning employed by students as they work on another “non-existence” task given the available rods. The task, which was presented to the students towards the end of the second session and which does not have a correct solution using the rods that are included in the set, prompted the students to use multiple forms of reasoning to justify their claims. The arguments posed by the students were structured as both direct and indirect arguments. One form of reasoning which appeared several times in the context of this task was exhaustive reasoning, or reasoning by cases. The episodes in this chapter have been described previously (Steencken, 2001; Yankelewitz, 2009), and this chapter describes the way students reasoned using cases as they solved a task with no solution using the actual rods. This chapter references events from the analytic entitled “Fourth Graders Reason by Cases as They Explore Fraction Ideas” (http://dx.doi.org/doi:10.7282/T3Q2420N).

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Children's Reasoning While Building Fraction Ideas

Series: Mathematics Teaching and Learning, Volume: 3

E-Book ISBN:: 9789463510080

Publisher:: Brill

Print Publication Date:: 01 Jan 2017

Subjects
- Education
  - Children Education
  - Mathematics Education

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Reasoning by Cases While Exploring Fractions as Numbers

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Children's Reasoning While Building Fraction Ideas

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