Teaching fractions and ratios for understanding: essential content knowledge and instructional strategies for teachers
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Routledge
2012
|
| Ausgabe: | 3. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes index. |
| Beschreibung: | XIII, 266 S. Ill., graph. Darst. |
| ISBN: | 9780415886123 9780203803165 |
Internformat
MARC
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| 245 | 1 | 0 | |a Teaching fractions and ratios for understanding |b essential content knowledge and instructional strategies for teachers |c Susan J. Lamon |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Routledge |c 2012 | |
| 300 | |a XIII, 266 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes index. | ||
| 650 | 4 | |a Fractions |x Study and teaching (Elementary) | |
| 650 | 4 | |a Ratio and proportion |x Study and teaching (Elementary) | |
| 650 | 0 | 7 | |a Unterrichtsführung |0 (DE-588)4187078-5 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804148641055637504 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
PRIFACE
1. PROPORTIONAL REASONING: AN OVERVIEW STUDENT STRATEGIES1 INTRODUCTION2
THE CONSTANT C1 PROPORTIONALITY3 REASONING:BEYOND MECHANIZATION 4
INVARIANCEAND COVARIANCE5 SOLVINGPROPORTIONSUSING K 7
MULTIPLICATIVETHINKING 9 CRITICALCOMPONENTS C1 POWEIFUL REASONING 9
GETTING STARTED 10 ANALYZING CHILDREN S THINKING 13 ACTIVITIES 14
2. FRACTIONS AND RATIONAL N UMBERS STUDENT STRATEGIES20 NEW UNITS AND A
NEW NOTATIONAL SYSTEM 21 THE PSYCHOLOGY C1 UNITS 22
NEW OPERATIONSAND QUANTITIES 23 INTEIFERENCE C1 MOLE NUMBER IDEAS 24
PROBLEMSWITH TERMINOLOGY 26 DEVELOPMENT C1 SETS C1 NUMBERS 26 KINDS C1
FRACTIONS 28
MAT AREFRACTIONS?29 RATIONALNUMBERS 29 FRACTIONSAS NUMBERS 30
FRACTIONS,RATIOS AND RATES 31
MANY SOURCES C1 MEANING 32 MULTIPLE INTERPRETATIONS C1 THE FRACTION~ 33
ACTIVITIES 35
3. RELATIVE THINKING AND MEASUREMENT STUDENT STRATEGIES39 TWO
PERSPECTIVES ON CHANGE 40 RELATIVETHINKING AND UNDERSTANDINGFRACTIONS42
XI
1
20
39
IMAGE 2
VLLL CONTENTS
ENCOURAGINGMULTIPLICATIVETHINKING 43
TWO MEANINGSFOR MORE 45 THE IMPORTANCEOF MEASUREMENT 46 THE
COMPENSATORYPRINCIPLE 47
THE APPROXIMATION PRINCIPLE 48 RECURSIVEPARTITIONINGPRINCIPLE 49
MEASURINGMORE ABSTRACTQUALITIES 50 OTHER STRATEGIES52 ACTIVITIES 55
4. QUANTITIES AND COVARIATION STUDENT STRATEGIES63 BUILDING ON
CHILDREN S INFORMAL KNOWLEDGE 64 QUANTITIES UNQUANTIFIED 64
QUANTIFIABLECHARACTERISTICS66 DISCUSSINGPROPORTIONALRELATIONSHIPSIN
PICTURES 68 VISUALIZING, VERBALIZING,AND SYMBOLIZING CHANGING
RELATIONSHIPS70 COVARIATIONAND INVARIANCE 71
CUISENAIRESTRIPS 73 SCALEFACTORS 75 SIMILARITY 76 INDIRECTMEASUREMENT 80
TESTINGFOR S IMILARITY 81 MOCKUPS AND PUDGY PEOPLE 83 ACTIVITIES 85
5. PROPORTIONAL REASONING STUDENT STRATEGIES96 THE UNIT 97 UNITS DTFTNED
IMPLICITLY 99
USING UNITS IFU1RIOUS TYPES 100 REASONING UP AND DOWN 102 UNITS AND
UNITIZING 103 UNITIZING NOTATION 105
FLEXIBILITY IN UNITIZING 105 CHILDREN S THINKING 107
CLASSROOMACTIVITIESTO ENCOURAGEUNITIZING 108 VISUALACTIVITIES 109
REASONINGWITH RATIO TABLES 110
PROBLEM TYPES 112 RATIO TABLES 114 INCREASINGTHE DFFFICULTY 116
ANALYZING RELATIONSHIPS 117 PERCENT 119
63
96
IMAGE 3
CONTENTS LX
PERCENTSAS AN INSTRUCTIONALTASK 120
REASONINGWITH PERCENTS 120 ACTIVITIES 121
6. REASONING WITH FRACTIONS 133
STUDENT STRATEGIES133 VISUALIZINGOPERATIONS 133 EQUIVALENTFRACTIONSAND
UNITIZING 135 COMPARINGFRACTIONS 136
FRACTIONSIN BETWEEN 140 ACTIVITIES 142
7. FRACTIONS AS PART-WHOLE COMPARISONS 144
STUDENT STRATEGIES144 PART-MOLE FRACTIONS:THE BIG IDEAS 145 UNITIZING
AND EQUIVALENCE 146 PROBLEMSIN CURRENT INSTRUCTION 148
FRACTIONMODELS 149 FRACTIONSTRIPS 150 COMPARINGPART-MOLE FRACTIONS 151
DISCRETEUNITS 152
MULTIPLICATION 155 PARTITIVEAND QUOTATIVEDIVISION 156 DIVISION 157 OTHER
RATIONALNUMBER INTERPRETATIONS160 ACTIVITIES 161
8. FRACTIONS AS QUOTIENTS 170
STUDENT STRATEGIES170 QUOTIENTS 171 PARTITIONINGAS FAIR SHARING 172
PARTITIONINGACTIVITIES 173
CHILDREN SPARTITIONING 174 EQUIVALENCE177 SHOULD * REDUCE? 178
UNDERSTANDINGFRACTIONSAS QUOTIENTS 179 MOREADVANCEDREASONING 180
SHARINGDIJJERENTPIZZAS 181 ACTIVITIES 184
9. FRACTIONS AS OPERATORS 190
STUDENT STRATEGIES190 OPERATORS 191 EXCHANGEMODELS 194 COMPOSITION 196
IMAGE 4
X CONTENTS
AREA MODELFOR MULTIPLICATION 198
AREA MODELFOR DIVISION 200 COMPOSITIONSAND PAPERFOLDING 201
UNDERSTANDINGOPERATORS203 ACTIVITIES 203
10. FRACTIONS AS MEASURES STUDENT STRATEGIES209 MEASURES CF DISTANCE 209
STATIC AND DYNAMIC MEASUREMENT 210
THE GOALS CF SUCCESSIVEPARTITIONING211 UNDERSTANDINGFRACTIONSAS MEASURES
213 UNITS, EQUIVALENT FRACTIONS,AND COMPARISONS214 FRACTIONOPERATIONS
216 ACTIVITIES 217
11. RATIOS AND RATES STUDENT STRATEGIES224 WHAT IS A RATIO? 225 NOTATION
AND 7CRMINOLOGY227 EQUIVALENCEAND COMPARISON CF RATIOS 228
RATIOS AS AN INSTRUCTIONALIASK 232 WHAT IS ARATE? 235 OPERATIONSWITH
RATES AND RATIOS 237 LINEAR GRAPHS 238
COMPARINGRATIOS AND RATES GRAPHICALLY 240 SPEED: THE MOST IMPORTANT RATE
242 CHARACTERISTICS CF SPEED 243 STUDENTS MISCONCEPTIONSABOUT SPEED 244
AVERAGESPEED 245
DISTANCE-SPEED-TIME AND GRAPHS 246 ACTIVITIES 248
12. CHANGING INSTRUCTION STUDENT COMMENTS 255 WHY CHANGE? 255 A SUMMARY
CF FRACTIONINTERPRETATIONS256
CENTRAL STRUCTURES 258 CHARACTERISTICS CF PROPORTIONALTHINKERS 258
OBSTACLESTO CHANGE 260 SEQUENCINGTOPICS261 DIRECTIONS JOR CHANGE 261
INDEX
209
224
255
263
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| author | Lamon, Susan J. 1949- |
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| dewey-full | 372.7/2 |
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| dewey-ones | 372 - Primary education (Elementary education) |
| dewey-raw | 372.7/2 |
| dewey-search | 372.7/2 |
| dewey-sort | 3372.7 12 |
| dewey-tens | 370 - Education |
| discipline | Pädagogik |
| edition | 3. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T00:10:21Z |
| institution | BVB |
| isbn | 9780415886123 9780203803165 |
| language | English |
| lccn | 2011019888 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024597159 |
| oclc_num | 772905337 |
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| physical | XIII, 266 S. Ill., graph. Darst. |
| publishDate | 2012 |
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| publishDateSort | 2012 |
| publisher | Routledge |
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| spelling | Lamon, Susan J. 1949- Verfasser (DE-588)173467962 aut Teaching fractions and ratios for understanding essential content knowledge and instructional strategies for teachers Susan J. Lamon 3. ed. New York [u.a.] Routledge 2012 XIII, 266 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes index. Fractions Study and teaching (Elementary) Ratio and proportion Study and teaching (Elementary) Unterrichtsführung (DE-588)4187078-5 gnd rswk-swf Unterrichtsführung (DE-588)4187078-5 s DE-604 V:DE-604 application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024597159&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lamon, Susan J. 1949- Teaching fractions and ratios for understanding essential content knowledge and instructional strategies for teachers Fractions Study and teaching (Elementary) Ratio and proportion Study and teaching (Elementary) Unterrichtsführung (DE-588)4187078-5 gnd |
| subject_GND | (DE-588)4187078-5 |
| title | Teaching fractions and ratios for understanding essential content knowledge and instructional strategies for teachers |
| title_auth | Teaching fractions and ratios for understanding essential content knowledge and instructional strategies for teachers |
| title_exact_search | Teaching fractions and ratios for understanding essential content knowledge and instructional strategies for teachers |
| title_full | Teaching fractions and ratios for understanding essential content knowledge and instructional strategies for teachers Susan J. Lamon |
| title_fullStr | Teaching fractions and ratios for understanding essential content knowledge and instructional strategies for teachers Susan J. Lamon |
| title_full_unstemmed | Teaching fractions and ratios for understanding essential content knowledge and instructional strategies for teachers Susan J. Lamon |
| title_short | Teaching fractions and ratios for understanding |
| title_sort | teaching fractions and ratios for understanding essential content knowledge and instructional strategies for teachers |
| title_sub | essential content knowledge and instructional strategies for teachers |
| topic | Fractions Study and teaching (Elementary) Ratio and proportion Study and teaching (Elementary) Unterrichtsführung (DE-588)4187078-5 gnd |
| topic_facet | Fractions Study and teaching (Elementary) Ratio and proportion Study and teaching (Elementary) Unterrichtsführung |
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