Titlebook: Combinatorics and Reasoning; Representing, Justif Carolyn A. Maher,Arthur B. Powell,Elizabeth B. Upt Book 2011 Springer Netherlands 2011 Co

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Milton Ruiz,Esteban Inga,Silvio Simani original towers problem (building towerswhen selecting from two colors of Unifix cubes) and extensions (with more thantwo colors of cubes), using methods including controlling for variables, justificationby cases, and inductive reasoning.

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Virtual Reality for Social Phobia Treatment course of the semester. From aperspective of conceptualizing reasoning in terms of solving open-ended problems,it was of interest to learn whether students in a liberal-arts college mathematicscourse could be successful in providing arguments to support their reasoning and inmaking connections in a problem-solving-based curriculum.

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Representations and Connectionsde use of their understanding of the structure of those problems to form preliminary ideas about the meaning of Pascal’s Identity. We show how their development and use of a sophisticated general representation scheme helped them make these connections and generalize their knowledge.

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Book 2011s the value of careful construction of appropriate tasks. Moreover, it documents how reasoning that takes the form of proof evolves with young children and discusses the conditions for supporting student reasoning.

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Smart Technologies in Urban Engineeringow those students and others in the longitudinal study build on those representations and strategies in their work on some towers problems. (A towers problem involves determining how many towers can be built of a given height from a specified number of colors of Unifix cubes, small plastic cubes that can be stacked together.

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Towers: Schemes, Strategies, and Argumentsow those students and others in the longitudinal study build on those representations and strategies in their work on some towers problems. (A towers problem involves determining how many towers can be built of a given height from a specified number of colors of Unifix cubes, small plastic cubes that can be stacked together.

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0924-4921 y groups of learners; and it demonstrates the value of careful construction of appropriate tasks. Moreover, it documents how reasoning that takes the form of proof evolves with young children and discusses the conditions for supporting student reasoning.978-94-007-3495-1978-94-007-0615-6Series ISSN 0924-4921 Series E-ISSN 2214-983X

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