Description 
1 online resource (xxiii, 364 pages) : illustrations 
Contents 
A 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 PartWhole 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 
Summary 
Children'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 reorganizingnot simply using or building upontheir whole number knowledge. This hypothesis is explained in detail using examples of actual gradeschoolers 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 reflectand which in the classroom may even suppressyoungsters' 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 partwhole, 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 upclose 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 
Bibliography 
Includes bibliographical references (pages 353357) and index 
Notes 
Print version record 
Subject 
Mathematics  Study and teaching (Elementary)  Philosophy.


Numeracy.


Fractions  Study and teaching (Elementary)  Case studies.


Learning, Psychology of.

Genre/Form 
Case studies.


Case studies.

Form 
Electronic book

Author 
Olive, John.

LC no. 
2009932112 
ISBN 
144190591X 

9781441905918 

(hbk.) 

(hbk.) 
