000			03879nam a22004575i 4500
001			978-1-4419-0591-8
003			DE-He213
005			20140220084502.0
007			cr nn 008mamaa
008			100301s2010 xxu| s |||| 0|eng d
020			_a9781441905918 _9978-1-4419-0591-8
024	7		_a10.1007/978-1-4419-0591-8 _2doi
050		4	_aLC8-6691
072		7	_aJNU _2bicssc
072		7	_aPB _2bicssc
072		7	_aEDU029010 _2bisacsh
082	0	4	_a370 _223
100	1		_aSteffe, Leslie P. _eauthor.
245	1	0	_aChildren’s Fractional Knowledge _h[electronic resource] / _cby Leslie P. Steffe, John Olive.
264		1	_aBoston, MA : _bSpringer US : _bImprint: Springer, _c2010.
300			_aXX, 358p. 50 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aA New Hypothesis Concerning Children’s Fractional Knowledge -- Perspectives on Children’s Fraction Knowledge -- Operations That Produce Numerical Counting Schemes -- Articulation of the Reorganization Hypothesis -- The Partitive and the Part-Whole Schemes -- The Unit Composition and the Commensurate Schemes -- The Partitive, the Iterative, and the Unit Composition Schemes -- Equipartitioning Operations for Connected Numbers: Their Use and Interiorization -- The Construction of Fraction Schemes Using the Generalized Number Sequence -- The Partitioning and Fraction Schemes -- Continuing Research on Students’ Fraction Schemes.
520			_aChildren’s Fractional Knowledge elegantly tracks the construction of knowledge, both by children learning new methods of reasoning and by the researchers studying their methods. The book challenges the widely held belief that children’s whole number knowledge is a distraction from their learning of fractions by positing that their fractional learning involves reorganizing—not simply using or building upon—their whole number knowledge. This hypothesis is explained in detail using examples of actual grade-schoolers approaching problems in fractions including the schemes they construct to relate parts to a whole, to produce a fraction as a multiple of a unit part, to transform a fraction into a commensurate fraction, or to combine two fractions multiplicatively or additively. These case studies provide a singular journey into children’s mathematics experience, which often varies greatly from that of adults. Moreover, the authors’ descriptive terms reflect children’s quantitative operations, as opposed to adult mathematical phrases rooted in concepts that do not reflect—and which in the classroom may even suppress—youngsters’ learning experiences. Highlights of the coverage: Toward a formulation of a mathematics of living instead of being Operations that produce numerical counting schemes Case studies: children’s part-whole, partitive, iterative, and other fraction schemes Using the generalized number sequence to produce fraction schemes Redefining school mathematics This fresh perspective is of immediate importance to researchers in mathematics education. With the up-close lens onto mathematical development found in Children’s Fractional Knowledge, readers can work toward creating more effective methods for improving young learners’ quantitative reasoning skills.
650		0	_aEducation.
650		0	_aNumber theory.
650		0	_aMathematics.
650	1	4	_aEducation.
650	2	4	_aMathematics Education.
650	2	4	_aNumber Theory.
700	1		_aOlive, John. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781441905901
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4419-0591-8
912			_aZDB-2-SHU
999			_c110220 _d110220