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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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書目名稱Combinatorics and Reasoning
副標(biāo)題Representing, Justif
編輯Carolyn A. Maher,Arthur B. Powell,Elizabeth B. Upt
視頻videohttp://file.papertrans.cn/231/230048/230048.mp4
概述Unique Longitudinal research over 20 years.Presents compelling evidence of the advantages to using combinatorics in mathematics education.Extensive discussion of mathematical tasks
叢書名稱Mathematics Education Library
圖書封面Titlebook: Combinatorics and Reasoning; Representing, Justif Carolyn A. Maher,Arthur B. Powell,Elizabeth B. Upt Book 2011 Springer Netherlands 2011 Co
描述Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms is based on the accomplishments of a cohort group of learners from first grade through high school and beyond, concentrating on their work on a set of combinatorics tasks. By studying these students, the editors gain insight into the foundations of proof building, the tools and environments necessary to make connections, activities to extend and generalize combinatoric learning, and even explore implications of this learning on the undergraduate level.This volume underscores the power of attending to basic ideas in building arguments; it shows the importance of providing opportunities for the co-construction of knowledge by 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.
出版日期Book 2011
關(guān)鍵詞College Mathematics; Combinatorics Learning; Isomorphism; Longitudinal Studies; Proof Building; combinato
版次1
doihttps://doi.org/10.1007/978-94-007-0615-6
isbn_softcover978-94-007-3495-1
isbn_ebook978-94-007-0615-6Series ISSN 0924-4921 Series E-ISSN 2214-983X
issn_series 0924-4921
copyrightSpringer Netherlands 2011
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Nataliia Vergunova,Sergey VergunovIn this chapter, we discuss how data were collected and analyzed, and we brieflydescribe some results, which will be more fully explored in later chapters. Wesummarize student work on fundamental problems and note how this work led toexceptional growth in the students’ mathematical understanding.
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Smart Technologies in Urban EngineeringIn previous chapters, we followed the students in Kenilworth as they worked on theshirts and jeans task and the towers problems in the second through fifth grades. Inthis chapter, we discuss five sessions during which these students worked to make sense of the pizza problems.
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Pizzas, Towers, and BinomialsIn the previous chapter, we observed a cohort of tenth-grade students as theyinvestigated the connections among the pizza problems, the towers problems, thebinomial coefficients, and Pascal’s Triangle, leading to their increased understandingof the meaning of the numbers in Pascal’s Triangle and how the triangle grows.
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