Children's Fractional Knowledge:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2010
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXIII, 364 S. graph. Darst. |
| ISBN: | 9781441905901 |
Internformat
MARC
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| 100 | 1 | |a Steffe, Leslie P. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Children's Fractional Knowledge |c Leslie P. Steffe ; John Olive |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2010 | |
| 300 | |a XXIII, 364 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Philosophie | |
| 650 | 4 | |a Fractions |x Study and teaching (Elementary) |v Case studies | |
| 650 | 4 | |a Learning, Psychology of | |
| 650 | 4 | |a Mathematics |x Study and teaching (Elementary) |x Philosophy | |
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Datensatz im Suchindex
| _version_ | 1804139196848275456 |
|---|---|
| adam_text | CONTENTS 1 A NEW HYPOTHESIS CONCEMING CHILDREN S FRACTIONAL KNOWLEDGE I
THE INTERFERENCE HYPOTHESIS 2 THE SEPARATION HYPOTHESIS 5 A SENSE OF
SIMULTANEITY AND
SEQUENTIALITY................................................. 6
ESTABLISHING TWO AS
DUAL......................................................................
7 ESTABLISHING TWO AS UNITY 8 RECURSION AND
SPLITTING..................................... 9 DISTRIBUTION AND
SIMULTANEITY LO SPLITTING AS A RECURSIVE
OPERATION........................................................ 11
NEXT STEPS ,.... 12 2 PERSPECTIVES ON CHILDREN S FRACTION
KNOWLEDGE.................................... 13 ON OPENING THE
TRAP..........................................................................
......... 14 INVENTION OR CONSTRUCTION? 15 FIRST-ORDER AND SECOND-ORDER
MATHEMATICAL KNOWLEDGE 16 MATHEMATICS OF
CHILDREN......................................................................
. 16 MATHEMATICS FOR CHILDREN 17 FRACTIONS AS SCHEMES 18 THE PARTS OF A
SCHEME........................................................................
... 20 LEARNING AS ACCOMMODATION 21 THE SUCKING
SCHEME........................................................................
..... 21 THE STRUCTURE OF
ASCHEME....................................................................
22 SERIATION AND ANTICIPATORY
SCHEMES..................................................... 24
MATHEMATICS OF LIVING RATHER THAN
BEING................................................. 25 3 OPERATIONS
THAT PRODUCE NUMERICAL COUNTING SCHEMES 27 COMPLEXES OF DISCRETE UNITS
27 RECOGNITION TEMPLATES OF PERCEPTUAL COUNTING SCHEMES 29 COLLECTIONS
OF PERCEPTUAL HEMS 29 PERCEPTUAL
LOTS..........................................................................
............ 30 RECOGNITION TEMPLATES OF FIGURATIVE COUNTING SCHEMES 32
NUMERICAL PATTERNS AND THE INITIAL NUMBER SEQUENCE 35 XV XVI CONTENTS
THE TACITLY NESTED NUMBER
SEQUENCE........................................................ 38 THE
EXPLICITLY NESTED NUMBER
SEQUENCE................................................... 41 AN
AWARENESS OF NUMEROSITY: A QUANTITATIVE
PROPERTY............................. 42 THE GENERALIZED NUMBER
SEQUENCE............................................................ 43
AN OVERVIEW OF THE PRINCIPAL OPERATIONS OF THE NUMERICAL COUNTING
SCHEMES 45 THE INITIAL NUMBER SEQUENCE 45 THE TACITLY NESTED AND THE
EXPLICITLY NESTED NUMBER SEQUENCES.. 45 FINAL COMMENTS 47 4 ARTICULATION
OF THE REORGANIZATION HYPOTHESIS......................................
49 PERCEPTUAL AND FIGURATIVE LENGTH 50 PIAGET S GROSS, INTENSIVE, AND
EXTENSIVE QUANTITY...................................... 51 GROSS
QUANTITATIVE COMPARISONS 52 INTENSIVE QUANTITATIVE COMPARISONS 52 AN
AWARENESS OF FIGURATIVE PLURALITY IN COMPARISONS 53 EXTENSIVE
QUANTITATIVE COMPARISONS 55 COMPOSITE STRUCTURES AS TEMPLATES FOR
FRAGMENTING 57 EXPERIENTIAL BASIS FOR FRAGMENTING 58 USING SPECIFIC
ATTENTIONAL PATTERNS IN FRAGMENTING...................................
59 NUMBER SEQUENCES AND SUBDIVIDING A LINE 64 PARTITIONING AND ITERATING
67 LEVELS OF FRAGMENTING 68 FINAL COMMENTS 70 OPERATIONAL SUBDIVISION
AND PARTITIONING 72 PARTITIONING AND SPLITTING 73 5 THE PARTITIVE AND
THE PART-WHOLE SCHEMES............................................ 75
THE EQUIPARTITIONING SCHEME 75 BREAKING A STICK INTO TWO EQUAL PARTS
................................................. 75 COMPOSITE UNITS AS
TEMPLATES FOR PARTITIONING 76 SEGMENTING TO PRODUCE A CONNECTED NUMBER
78 EQUISEGMENTING VS.
EQUIPARTITIONING.................................................... 78
THE DUAL EMERGENCE OF QUANTITATIVE OPERATIONS 80 MAKING A CONNECTED
NUMBER SEQUENCE..................................................... 80
AN ATTEMPT TO USE MULTIPLYING SCHEMES IN THE CONSTRUCTION OF COMPOSITE
UNIT
FRACTIONS.....................................................................
.. 83 PROVOKING THE CHILDREN S USE OF UNITS-COORDINATING SCHEMES 83 AN
ATTEMPT TO ENGENDER THE CONSTRUCTION OF COMPOSITE UNIT
FRACTIONS.....................................................................
................... 86 CONFLATING UNITS WHEN FINDING FRACTIONAL PARTS OF
A 24-STICK 87 OPERATING ON THREE LEVELS OF
UNITS...................................................... 89 NECESSARY
ERRORS 90 CONTENTS XVII LAURA S SIMULTANEOUS PARTITIONING SCHEME 92 AN
ATTEMPT TO BRING FORTH LAURA S USE OF ITERATION TO FIND FRACTIONAL PARTS
95 JASON S PARTITIVE AND LAURA S PART-WHOLE FRACTION
SCHEMES...................... 98 LACK OF THE SPLITTING
OPERATION.............................................................
98 JASON S PARTITIVE UNIT FRACTION SCHEME ;................. 100 LAURA S
INDEPENDENT USE OF PARTS 102 LAURA S PART- WHOLE FRACTION SCHEME 107
ESTABLISHING FRACTIONAL MEANING FOR MULTIPLE PARTS OF A
STICK................... 110 A RECURRING INTERNAL CONSTRAINT IN THE
CONSTRUCTION OF FRACTION OPERATIONS 112 CONTINUED ABSENCE OF FRACTIONAL
NUMBERS 113 AN ATTEMPT TO USE UNITS-COORDINATING TO PRODUCE IMPROPER
FRACTIONS 114 A TEST OF THE ITERATIVE FRACTION
SCHEME................................................ 116 DISCUSSION OF
THE CASE
STUDY......................................................................
118 THE CONSTRUCTION OF CONNECTED NUMBERS AND THE CONNECTED NUMBER
SEQUENCE 118 ON THE CONSTRUCTION OF THE PART- WHOLE AND PARTITIVE
FRACTION SCHEMES 119 THE SPLITTING
OPERATION.....................................................................
.... 121 6 THE UNIT COMPOSITION AND THE COMMENSURATE
SCHEMES...................... 123 THE UNIT FRACTION COMPOSITION
SCHEME..................................................... 124 JASON S
UNIT FRACTION COMPOSITION SCHEME 125 CORROBORATION OF JASON S UNIT
FRACTION COMPOSITION SCHEME 126 LAURA S APPARENT RECURSIVE PARTITIONING
128 PRODUCING COMPOSITE UNIT
FRACTIONS.......................................................... 129
LAURA S RELIANCE ON SOCIAL INTERACTION WHEN EXPLAINING COMMENSURATE
FRACTIONS 133 FURTHER INVESTIGATION INTO THE CHILDREN S EXPLANATIONS AND
PRODUCTIONS...................................................................
.................. 136 PRODUCING FRACTIONS COMMENSURATE WITH
ONE-HALF................................... 138 PRODUCING FRACTIONS
COMMENSURATE WITH ONE- THIRD 142 PRODUCING FRACTIONS COMMENSURATE WITH
TWO- THIRDS 147 AN ATTEMPT TO ENGAGE LAURA IN THE CONSTRUCTION OF THE
UNIT FRACTION COMPOSITION SCHEME 148 THE EMERGENCE OF RECURSIVE
PARTITIONING FOR LAURA 151 LAURA S APPARENT CONSTRUCTION OF A UNIT
FRACTION COMPOSITION SCHEME 153 PROGRESS IN PARTITIONING THE RESULTS OF
A PRIOR PARTITION 157 DISCUSSION OF THE CASE
STUDY......................................................................
161 THE UNIT FRACTION COMPOSITION SCHEME AND THE SPLITTING
OPERATION................................. 162 INDEPENDENT MATHEMATICAL
ACTIVITY AND THE SPLITTING OPERATION 163 XVIII CONTENTS INDEPENDENT
MATHEMATIEAL AETIVITY AND THE COMMENSURATE FRAETION
SEHEME........................................................................
............ 163 AN ANALYSIS OF LAURA S CONSTRUETION OF THE UNIT
FRAETION COMPOSITION SEHEME 164 LAURA S APPARENT CONSTRUETION OF
RECURSIVE PARTITIONING AND THE UNIT FRAETION COMPOSITION SEHEME 169 7
THE PARTITIVE, THE ITERATIVE, AND THE UNIT COMPOSITION SCHEMES 171 JOO S
ATTEMPTS TO CONSTRUET COMPOSITE UNIT
FRAETIONS.............................. 172 ATTEMPTS TO CONSTRUET A UNIT
FRAETION OF A CONNECTED NUMBER................. 174 PARTITIONING AND
DISEMBEDDING OPERATIONS 176 JOO S CONSTRUETION OF A PARTITIVE FRAETION
SEHEME 180 JOO S PRODUETION OF AN IMPROPER
FRAETION................................................... 185
PATRICIA S RECURSIVE PARTITIONING OPERATIONS 188 THE SPLITTING
OPERATION: CORROBORATION IN JOO AND CONTRAINDIEATION IN PATRICIA 188 A
LAEK OF DISTRIBUTIVE
REASONING...............................................................
191 EMERGENEE OF THE SPLITTING OPERATION IN PATRIEIA 193 EMERGENEE OF
JOO S UNIT FRAETION COMPOSITION SEHEME............................ 195
JOO S REVERSIBLE PARTITIVE FRAETION SEHEME 197 FRACTIONS BEYOND THE
FRAETIONAL WHOLE: JOO S DILEMMA AND PATRIEIA S CONSTRUETION 199 JOO S
CONSTRUETION OF THE ITERATIVE FRAETION SEHEME 204 A CONSTRAINT IN THE
CHILDREN S UNIT FRAETION COMPOSITION SEHEME........... 208 FRAETIONAL
CONNECTED NUMBER SEQUENEES 211 ESTABLISHING COMMENSURATE
FRAETIONS........................................................ 214
DISEUSSION OF THE CASE
STUDY......................................................................
217 COMPOSITE UNIT FRAETIONS:
JOO.............................................................. 217
JOO S PARTITIVE FRAETION SEHEME 218 EMERGENEE OF THE SPLITTING OPERATION
AND THE ITERATIVE FRAETION SEHEME: JOO 219 EMERGENEE OF RECURSIVE
PARTITIONING AND SPLITTING OPERATIONS: PATRIEIA 220 THE CONSTRUETION
OFTHE ITERATIVE FRAETION SEHEME 221 STAGES IN THE CONSTRUETION OF
FRAETION SEHEMES................................... 222 8
EQUIPARTITIONING OPERATIONS FOR CONNECTED NUMBERS: THEIR USE AND
INTERIORIZATION 225 MELISSA S INITIAL FRAETION SEHEMES 225
CONTRAINDIEATION OF REEURSIVE PARTITIONING IN MELISSA 227 REVERSIBILITY
OF JOO S UNIT FRAETION COMPOSITION SEHEME 228 A REORGANIZATION IN
MELISSA S UNITS-COORDINATING SEHEME 231 MELISSA S CONSTRUETION OF A
FRAETIONAL CONNEETED NUMBER SEQUENEE....... 236 TESTING THE HYPOTHESIS
THAT MELISSA COULD CONSTRUET A COMMENSURATE FRAETION
SEHEME.............................................................. 241
CONTENTS XIX MELISSA S USE OF THE OPERATIONS THAT PRODUEE THREE LEVELS
OF UNITS IN RE-PRESENTATION 247 REPEATEDLY MAKING FRAETIONS OF
FRAETIONAL PARTS OF A RECTANGULAR BAR 247 MELISSA ENAETING A PRIOR
PARTITIONING BY MAKING A DRAWING 251 A TEST OF AEEOMMODATION IN
MELISSA S PARTITIONING OPERATIONS 254 A FURTHER AEEOMMODATION IN
MELISSA S REEURSIVE PARTITIONING OPERATIONS 256 A CHILD-GENERATED
FRAETION ADDING SEHEME 260 AN ATTEMPT TO BRING FORTH A UNIT FRAETION
ADDING SCHEME...................... 263 DISEUSSION OF THE CASE
STUDY......................................................................
266 THE ITERATIVE FRAETION SEHEME 268 MELISSA S INTERIORIZATION OF
OPERATIONS THAT PRODUEE THREE LEVELS OF
UNITS.........................................................................
... 269 ON THE POSSIBLE CONSTRUETION OF A SEHE ME OF RECURSIVE
PARTITIONING OPERATIONS 271 THE CHILDREN S MEANING OF FRAETION
MULTIPLIEATION 273 A CHILD-GENERATED VS. A PROCEDURAL SEHEME FOR ADDING
FRAETIONS.....................................................................
........ 275 9 THE CONSTRUCTION OF FRACTION SCHEMES USING THE
GENERALIZED NUMBER SEQUENCE :........................ 277 THE CASE OF
NATHAN DURING HIS THIRD GRADE 277 NATHAN S GENERALIZED NUMBER
SEQUENEE.............................................. 278 DEVELOPING A
LANGUAGE OF FRAETIONS 279 REASONING NUMERIEAL1Y TO NAME COMMENSURATE
FRAETIONS................. 284 CORROBORATION OF THE SPLITTING OPERATION
FOR CONNEETED NUMBERS 286 RENAMING FRAETIONS: AN AEEOMMODATION OF THE
IFS: CN 288 CONSTRUETION OF A COMMON PARTITIONING SEHEME 289
CONSTRUETING STRATEGIES FOR ADDING UNIT FRAETIONS WITH UNLIKE
DENOMINATORS 291 MULTIPLIEATION OF FRAETIONS AND NESTED
FRAETIONS....................................... 295 EQUAL FRAETIONS 298
GENERATING A PLURALITY OF FRAETIONS 299 WORKING ON A SYMBOLIE
LEVEI............................................................... 301
CONSTRUETION OF A FRAETION COMPOSITION SEHEME 303 CONSTRAINING HOW
ARTHUR SHARED FOUR-NINTHS OF A PIZZA AMONG FIVE PEOPLE...... 304 TESTING
THE HYPOTHESIS USING TIMA:
BARS........................................... 307 DISEUSSION OF THE
CASE
STUDY......................................................................
310 THE REVERSIBLE PARTITIVE FRAETION SEHEME 310 THE COMMON PARTITIONING
SEHEME AND FINDING THE SUM OF TWO FRAETIONS 311 THE FRAETIONAL
COMPOSITION SCHEME....................................................
313 XX CONTENTS 10 THE PARTITIONING AND FRACTION SCHEMES 315 THE
PARTITIONING SCHEMES 315 THE EQUIPARTITIONING SCHEME 315 THE
SIMULTANEOUS PARTITIONING SCHEME 316 THE SPLITTING
SCHEME........................................................................
317 THE EQUIPARTITIONING SCHEME FOR CONNECTED NUMBERS 319 THE SPLITTING
SCHEME FOR CONNECTED NUMBERS 320 THE DISTRIBUTIVE PARTITIONING
SCHEME............................................... 321 THE FRACTION
SCHEMES.......................................................................
........ 322 THE PART- WHOLE FRACTION SCHEME 322 THE PARTITIVE FRACTION
SCHEME 323 THE UNIT FRACTION COMPOSITION
SCHEME........................................... 328 THE FRACTION
COMPOSITION SCHEME...................................................
330 THE ITERATIVE FRACTION SCHEME 333 THE UNIT COMMENSURATE FRACTION
SCHEME 335 THE EQUAL FRACTION SCHEME 336 SCHOOL MATHEMATICS VS. SCHOOL
MATHEMATICS 337 11 CONTINUING RESEARCH ON STUDENTS FRACTION
SCHEMES......................... 341 RESEARCH ON PART- WHOLE CONCEPTIONS
OF FRACTIONS 342 TRANSCENDING PART- WHOLE
CONCEPTIONS..................................................... 344 THE
SPLITTING OPERATION.......... 345 STUDENTS DEVELOPMENT TOWARD ALGEBRAIC
REASONING 348 REFERENCES 353 INDEX 359
|
| any_adam_object | 1 |
| author | Steffe, Leslie P. Olive, John |
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| building | Verbundindex |
| bvnumber | BV035551691 |
| callnumber-first | Q - Science |
| callnumber-label | QA137 |
| callnumber-raw | QA137 |
| callnumber-search | QA137 |
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| callnumber-subject | QA - Mathematics |
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| classification_tum | PSY 215f |
| ctrlnum | (OCoLC)501390034 (DE-599)DNB993423221 |
| dewey-full | 372.72 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 372 - Primary education (Elementary education) |
| dewey-raw | 372.72 |
| dewey-search | 372.72 |
| dewey-sort | 3372.72 |
| dewey-tens | 370 - Education |
| discipline | Pädagogik Psychologie |
| format | Book |
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| indexdate | 2024-07-09T21:40:15Z |
| institution | BVB |
| isbn | 9781441905901 |
| language | English |
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| record_format | marc |
| spelling | Steffe, Leslie P. Verfasser aut Children's Fractional Knowledge Leslie P. Steffe ; John Olive New York [u.a.] Springer 2010 XXIII, 364 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematik Philosophie Fractions Study and teaching (Elementary) Case studies Learning, Psychology of Mathematics Study and teaching (Elementary) Philosophy Numeracy Lerntechnik (DE-588)4074168-0 gnd rswk-swf Schüler (DE-588)4053369-4 gnd rswk-swf (DE-588)4522595-3 Fallstudiensammlung gnd-content Lerntechnik (DE-588)4074168-0 s Schüler (DE-588)4053369-4 s DE-604 Olive, John Verfasser aut Digitalisierung UB Erlangen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017607584&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Steffe, Leslie P. Olive, John Children's Fractional Knowledge Mathematik Philosophie Fractions Study and teaching (Elementary) Case studies Learning, Psychology of Mathematics Study and teaching (Elementary) Philosophy Numeracy Lerntechnik (DE-588)4074168-0 gnd Schüler (DE-588)4053369-4 gnd |
| subject_GND | (DE-588)4074168-0 (DE-588)4053369-4 (DE-588)4522595-3 |
| title | Children's Fractional Knowledge |
| title_auth | Children's Fractional Knowledge |
| title_exact_search | Children's Fractional Knowledge |
| title_full | Children's Fractional Knowledge Leslie P. Steffe ; John Olive |
| title_fullStr | Children's Fractional Knowledge Leslie P. Steffe ; John Olive |
| title_full_unstemmed | Children's Fractional Knowledge Leslie P. Steffe ; John Olive |
| title_short | Children's Fractional Knowledge |
| title_sort | children s fractional knowledge |
| topic | Mathematik Philosophie Fractions Study and teaching (Elementary) Case studies Learning, Psychology of Mathematics Study and teaching (Elementary) Philosophy Numeracy Lerntechnik (DE-588)4074168-0 gnd Schüler (DE-588)4053369-4 gnd |
| topic_facet | Mathematik Philosophie Fractions Study and teaching (Elementary) Case studies Learning, Psychology of Mathematics Study and teaching (Elementary) Philosophy Numeracy Lerntechnik Schüler Fallstudiensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017607584&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT steffelesliep childrensfractionalknowledge AT olivejohn childrensfractionalknowledge |