000 03596nam a22004935i 4500
001 978-0-387-98132-1
003 DE-He213
005 20140220084457.0
007 cr nn 008mamaa
008 100702s2010 ne | s |||| 0|eng d
020 _a9780387981321
_9978-0-387-98132-1
024 7 _a10.1007/978-0-387-98132-1
_2doi
050 4 _aLC8-6691
072 7 _aJNU
_2bicssc
072 7 _aPB
_2bicssc
072 7 _aEDU029010
_2bisacsh
082 0 4 _a370
_223
100 1 _aMaher, Carolyn A.
_eeditor.
245 1 0 _aCombinatorics and Reasoning
_h[electronic resource] :
_bRepresenting, Justifying and Building Isomorphisms /
_cedited by Carolyn A. Maher, Arthur B. Powell, Elizabeth B. Uptegrove.
264 1 _aDordrecht :
_bSpringer Netherlands,
_c2010.
300 _aXVIII, 224 p. 35 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aMathematics Education Library ;
_v47
505 0 _aIntroduction, background, and methodology -- The Longitudinal Study -- Methodology -- Foundations of proof building (1989-1996) -- Representations as Tools for Building Arguments -- Towers: Schemes, Strategies, and Arguments -- Building an Inductive Argument -- Making Pizzas: Reasoning by Cases and by Recursion -- Block Towers: From Concrete Objects to Conceptual Imagination -- Making connections, extending, and generalizing (1997-2000) -- Responding to Ankur’s Challenge: Co-construction of Argument Leading to Proof -- Block Towers: Co-construction of Proof -- Representations and Connections -- Pizzas, Towers, and Binomials -- Representations and Standard Notation -- So Let’s Prove It! -- Extending the study, conclusions, and implications -- “Doing Mathematics” from the Learners’ Perspectives -- Adults Reasoning Combinatorially -- Comparing the Problem Solving of College Students with Longitudinal Study Students -- Closing Observations -- Erratum.
520 _aCombinatorics 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.
650 0 _aEducation.
650 0 _aCombinatorics.
650 0 _aMathematics.
650 1 4 _aEducation.
650 2 4 _aMathematics Education.
650 2 4 _aCombinatorics.
700 1 _aPowell, Arthur B.
_eeditor.
700 1 _aUptegrove, Elizabeth B.
_eeditor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387981314
830 0 _aMathematics Education Library ;
_v47
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-387-98132-1
912 _aZDB-2-SHU
999 _c109888
_d109888