So Let’s Prove It!



In previous chapters, we observed students throughout middle school and high school working on and making sense of two isomorphic problems in combinatorics – the towers problems and the pizza problems. In this chapter, we see how students just finishing high-school work on another isomorphic problem, demonstrating the application of techniques and ways of thinking that they developed throughout their previous years in the study. We further address the challenge that Davis (1992a) proposes to mathematics education researchers to investigate the emergence among learners of what lies at the core of mathematics: mathematical ideas. Here, a cohort of four high-school seniors – Brian, Jeff, Mike, and Romina – elaborates mathematical ideas and reasoning through work on the Taxicab Problem. They display criteria and techniques for justifying claims and an awareness of the power of generalizing, particularly as an aid to respond to special cases.


Short Route Mathematical Work Isomorphic Problem Efficient Route Problem Task 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Urban EducationRutgers UniversityNewarkUSA

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