000			03427nam a22005055i 4500
001			978-94-007-0615-6
003			DE-He213
005			20140220083830.0
007			cr nn 008mamaa
008			101124s2011 ne | s |||| 0|eng d
020			_a9789400706156 _9978-94-007-0615-6
024	7		_a10.1007/978-94-007-0615-6 _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.
250			_a1.
264		1	_aDordrecht : _bSpringer Netherlands, _c2011.
300			_aXVIII, 226 p. _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 -- The Longitudinal Study -- Methodology -- Representations as a Tool for Building Arguments -- Building Towers: Justifications Leading to Proof Making -- Making Pizzas: Reasoning by Cases and recursion -- Responding to Ankur's Challenge: Co-construction of Argument Leading to Proof -- Co-construction of Proof -- The Case of Stephanie -- Representations and Connections -- Pizzas, Block Towers, and Binomials -- Generalizing from Pizzas, Towers, Binomial Expansion, and Pascal's Triangle -- Extending and Generalizing the Isomorphism: Towers, Pizzas, Pascal's Triangle, and the Taxicab Problem -- College Students Building Towers and Making Pizzas -- Comparing the Problem Solving of College Students with Longitudinal Study Students -- Conclusions and Suggestions for Practice.
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: _z9789400706149
830		0	_aMathematics Education Library ; _v47
856	4	0	_uhttp://dx.doi.org/10.1007/978-94-007-0615-6
912			_aZDB-2-SHU
999			_c109334 _d109334