Children's Fractional Knowledge
(Sprache: Englisch)
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...
Leider schon ausverkauft
versandkostenfrei
Buch
163.50 €
81 DeutschlandCard Punkte
sammeln
- Lastschrift, Kreditkarte, Paypal, Rechnung
- Kostenlose Rücksendung
- Ratenzahlung möglich
Produktdetails
Produktinformationen zu „Children's Fractional Knowledge “
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 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.
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.
Klappentext zu „Children's Fractional Knowledge “
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 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 beingOperations that produce numerical counting schemesCase studies: children's part-whole, partitive, iterative, and other fraction schemesUsing the generalized number sequence to produce fraction schemesRedefining 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.
Inhaltsverzeichnis zu „Children's Fractional Knowledge “
Chapter I. A New Hypothesis Concerning Children's Fractional KnowledgeThe Interference HypothesisThe Separation HypothesisNext Steps Chapter II. Perspectives on Children's Fraction KnowledgeOn Opening the TrapFractions as SchemesMathematics of Living Rather Than Being Chapter III. Operations that Produce Numerical Counting SchemesComplexes of Discrete UnitsRecognition Templates of Perceptual Counting SchemesRecognition Templates of Figurative Counting SchemesNumerical Patterns and the Initial Number SequenceThe Tacitly Nested Number SequenceThe Explicitly Nested Number SequenceAn Awareness of Numerosity: A Quantitative PropertyThe Generalized Number SequenceAn Overview of the Principal Operations of the Numerical Counting SchemesFinal Comments Chapter IV: Articulation of the Reorganization HypothesisPerceptual and Figurative LengthPiaget's Gross, Intensive, and Extensive QuantityComposite Structures as Templates for FragmentingPartitioning and IteratingFinal Comments Chapter V: The Partitive and the Part-Whole SchemesThe Equi-Partitioning SchemeSegmenting to Produce a Connected NumberMaking a Connected Number SequenceAn Attempt to Use Multiplying Schemes in the Construction of Composite Unit FractionsLaura's Simultaneous Partitioning SchemeJason's Partitive and Laura's Part-Whole Fraction SchemesEstablishing Fractional Meaning for Multiple Parts of a StickContinued Absence of Fractional NumbersAn Attempt to Use Units-Coordinating to Produce Improper FractionsDiscussion of the Case Study Chapter VI. The Unit Composition and the Commensurate SchemesThe Unit Fraction Composition SchemeProducing Composite Unit FractionsProducing Fractions Commensurate with One-HalfProducingFractions Commensurate With One-ThirdProducing Fractions Commensurate With Two-ThirdsAn Attempt to Engage Laura in the Construction of the Unit FractionComposition SchemeDiscussion of the Case Study Chapter VII. The Partitive, the Iterative, and the Unit Composition SchemesJoe's Attempts to Construct
... mehr
Composite Unit FractionsAttempts to Construct a Unit Fraction of a Connected NumberPartitioning and Disembedding OperationsJoe's Construction of a Partitive Fraction SchemeJoe's Production of an Improper FractionPatricia's Recursive Partitioning OperationsThe Splitting Operation: Corroboration in Joe and Contraindication in PatriciaA Lack of Distributive ReasoningEmergence of the Splitting Operation in PatriciaEmergence of Joe's Unit Fraction Composition SchemeJoe's Reversible Partitive Fraction SchemeJoe's Construction of the Iterative Fraction SchemeA Constraint in the Children's Unit Fraction Composition SchemeFractional Connected Number SequencesEstablishing Commensurate FractionsDiscussion of the Case Study Chapter VIII. Equi-Partitioning Operations for Connected Numbers: Their Use and InteriorizationMelissa's Initial Fraction SchemesA Reorganization in Melissa's Units-Coordinating SchemeMelissa's Construction of a Fractional Connected Number SequenceTesting the Hypothesis that Melissa Could Construct a CommensurateFractional SchemeMelissa's Use of the Operations that Produce Three Levels of Units in Re-presentationA Child-Generated Fraction Adding SchemeAn Attempt to Bring Forth a Unit Fraction Adding SchemeDiscussion of the Case StudyChapter IX. The Construction of Fraction Schemes Using the Generalized Number SequenceThe Case of Nathan During his 3rd GradeMultiplication of Fractions and Nested FractionsEqual
... weniger
Bibliographische Angaben
- Autoren: Leslie P. Steffe , John Olive
- 2009, 364 Seiten, Maße: 16,4 x 24,4 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 1441905901
- ISBN-13: 9781441905901
Sprache:
Englisch
Kommentar zu "Children's Fractional Knowledge"
0 Gebrauchte Artikel zu „Children's Fractional Knowledge“
| Zustand | Preis | Porto | Zahlung | Verkäufer | Rating |
|---|
Schreiben Sie einen Kommentar zu "Children's Fractional Knowledge".
Kommentar verfassen