Mathematics: a good beginning ; strategies for teaching children
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Pacific Grove, Calif.
Brooks/Cole
1987
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXI, 532 S. Ill., graph. Darst. |
| ISBN: | 0534069843 |
Staff View
MARC
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| 245 | 1 | 0 | |a Mathematics |b a good beginning ; strategies for teaching children |c Andria P. Troutman ; Betty K. Lichtenberg |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Pacific Grove, Calif. |b Brooks/Cole |c 1987 | |
| 300 | |a XXI, 532 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Mathématiques - Étude et enseignement (Primaire) | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematics |x Study and teaching (Elementary) | |
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Record in the Search Index
| _version_ | 1804119316050739200 |
|---|---|
| adam_text | Contents
0
Zero, Our Starting Point 1
¦ Some special features of this book 4
1
Getting Ready for a Good Beginning
Pre Number Concepts 9
¦ Objectives for the child 10
¦ Teacher goals 10
¦ Helping the child develop pre number
concepts 10
The child s view 11
Classifying 12
Finding the relation between two sets 14
xi
Conserving relations 16
Finding and using properties of relations 18
Classifying on the basis of the as many as relation 21
Ordering sets on the basis of the more than or less than relation 22
Summary 23
¦ Learning the numbers 1 through 10 24
Naming a family of sets with a number 24
What about 10 and 0? 26
¦ It s time to count 26
¦ Getting ready to add and subtract 28
¦ The computer corner 29
Computer tips 30
¦ Ideas for enrichment: Classification games 31
¦ In closing... 31
¦ It s think tank time 32
¦ Suggested readings 34
2
... 100s, 10s, Is ... The Best Yet
Our Base Ten Numeration System 35
¦ Objectives for the child 36
¦ Teacher goals 36
¦ Understanding numeration systems 36
Introduction 36
Early numeration systems 38
A base ten numeration system 39
Reading and writing with larger numbers 41
Extension to decimal fractions 41
Applications 42
A few advantages 43
¦ Helping children understand place value 43
Activities for teaching place value concepts 45
Place value activities for later grades 48
Beyond happy faces: Place value activities for numbers greater than
1000 50
Rounding numbers 52
A variety of interpretations for large numbers 53
¦ The computer corner 59
Computer tips 60
¦ Ideas for enrichment: Other bases 60
¦ In closing... 62
¦ It s think tank time 62
¦ Suggested readings 63
3
Better Ways to Use the Best
Addition and Subtraction of Whole Numbers 64
¦ Objectives for the child 65
¦ Teacher goals 65
¦ Addition of whole numbers 66
Interpretations 66
Learning the basic facts of addition 67
Sums less than 10 69
Sums that equal 10 71
Sums greater than 10 71
Developing an addition algorithm 78
¦ Subtraction of whole numbers 82
Interpretations 83
Relating subtraction sentences to the basic facts of addition 85
Developing a subtraction algorithm 89
Subtraction computation involving numbers greater than 100 93
Other computational ideas 94
¦ Using mental arithmetic 96
When to teach what 97
¦ The computer corner 98
Computer tips 98
¦ Ideas for enrichment: Integers 99
¦ In closing... 100
¦ It s think tank time 100
¦ Suggested readings 101
4
Better Ways to Use the Best
Multiplication and Division 103
¦ Objectives for the child 104
¦ Teacher goals 104
¦ Multiplication of whole numbers 105
Interpretations 105
Learning the basic facts of multiplication 110
Properties of multiplication 111
Activities for skill development 117
Products of multiples of 10 118
Developing a multiplication algorithm 121
When to teach what 123
¦ Division of whole numbers 124
Interpretations 125
Developing a division algorithm 132
¦ Estimation and whole numbers 138
¦ Using mental arithmetic 139
When to teach what 140
¦ The computer corner 140
Computer tips 141
¦ Ideas for enrichment: Finger multiplication 142
¦ In closing... 143
¦ It s think tank time 143
¦ Suggested readings 145
5
Some Theory about Numbers
Factors, Multiples, Primes, and Composites 146
¦ Objectives for the child 147
¦ Teacher goals 147
¦ Factors and multiples 148
Even numbers and odd numbers 148
Classifying on the basis of number of factors 150
¦ Primes and composites 153
Finding factors of whole numbers 154
Greatest common factor 158
Least common multiple 160
¦ The computer corner 164
Computer tips 164
¦ Ideas for enrichment: Patterns in nature 164
¦ In closing... 165
¦ It s think tank time 165
¦ Suggested readings 167
6
Mot All Numbers Are Whole Numbers
Representing, Adding, and Subtracting Rational
Numbers 168
¦ Objectives for the child 169
¦ Teacher goals 169
¦ The need for rational numbers 170
Describing parts 172
Describing ratios 175
¦ Learning to use rational numbers 176
Exploratory experiences 176
A more structured approach for developing key concepts 177
¦ Emphasizing meaning 184
Developing algorithms 185
¦ A better way to work with rational
numbers 191
Exploratory experiences 193
Addition and subtraction with decimals 198
Addition and subtraction: Expanded form 199
¦ Percent 201
¦ Estimation 203
¦ The computer corner 204
Computer tips 204
¦ Ideas for enrichment: Scientific notation 205
¦ In closing... 205
¦ It s think tank time 206
¦ Suggested readings 207
7
Security Is Knowing Why
Multiplying and Dividing Rational Numbers 209
¦ Objectives for the child 210
¦ Teacher goals 210
¦ Multiplication of rational numbers 211
The additive interpretation for multiplication with fractions 211
The area interpretation for multiplication with fractions 213
Algorithms for multiplication with fractions 216
Multiplication with decimals 218
¦ More about percent 220
¦ Reciprocals 221
¦ Division of rational numbers 221
Interpretations for division with fractions 221
An algorithm for division with fractions 223
Extending the equivalent fraction rule 224
Division with decimals 225
Developing an algorithm 226
¦ Estimating 232
Products 232
Quotients 232
¦ When to teach what 234
¦ The computer corner 235
Computer tips 235
¦ Ideas for enrichment: Terminating and repeating
decimals 236
¦ In closing ... 237
¦ It s think tank time 238
¦ Suggested readings 239
8
Diagnosis, Before and After
Common Mathematical Difficulties 240
¦ Teacher goals 241
¦ Getting ready to diagnose 242
What is diagnosis? 242
What learner characteristics can be diagnosed? 243
What skills must teachers have? 243
What methods are used for diagnosing? 244
¦ Common mathematical difficulties involving whole
numbers and suggestions for remediation 248
What kind of difficulties are there? 248
Problem solving 263
¦ Common difficulties involving fractions and
decimals and suggestions for remediation 263
Difficulties associated with fractions 263
Difficulties using decimals 269
¦ Reading and writing difficulties 271
I
¦ The computer corner 276
Computer tips 276
¦ In closing... 277
¦ It s think tank time 278
¦ Suggested readings 279
9
Putting It All Together
Problem Solving 280
¦ Objectives for the child 281
¦ Teacher goals 281
¦ What is problem solving? 282
Routine problems 282
Unusual problems 283
¦ Solving routine problems 283
Translating word problems involving one operation 284
Solving number sentences 288
Dealing with more than one operation 289
Dealing with problems involving two variables 292
¦ Solving unusual problems 297
¦ Encouraging problem solving in the
classroom 302
¦ The computer corner 305
Computer tips 306
¦ In closing... 306
¦ It s think tank time 307
¦ Suggested readings 308
10
The Shape of Things
Geometric Figures and Relationships 309
¦ Teacher goals 310
¦ Geometric figures 311
Points, lines, segments, and rays 311
Plane figures 312
Space figures 315
¦ Congruence and similarity 318
Congruence 318
Similarity 320
¦ Motions and symmetry 322
Motions 322
Symmetry 324
¦ In closing... 326
¦ It s think tank time 326
¦ Suggested readings 330
11
Seeing Is Believing
Children s Development of Geometric Ideas 331
¦ Objectives for the child 332
¦ Teacher goals 332
¦ Before age 4 334
¦ From ages 4 to 7 335
Geometry concepts for kindergarten through second grade 337
¦ From ages 7 to 9 343
Geometry concepts for the second through fourth grades 345
¦ From ages 9 to 11 351
Geometry concepts for grades four through six 352
¦ Ideas for enrichment: Constructions 356
¦ The computer corner 357
Computer tips 358
¦ In closing... 358
¦ It s think tank time 359
¦ Suggested readings 360
12
Before You Teach Measurement
Attributes of Measurement... The Metric System ...
Expectations 361
¦ Teacher goals 362
¦ Attributes of measurement 362
i
¦ Using metric units of measure 364
¦ Getting ready to measure 370
Levels of development 373
Measuring area 374
Measuring volume 376
Deciding on measurement experiences 377
¦ The computer corner 377
Computer tips 378
¦ In closing... 379
¦ It s think tank time 379
¦ Suggested readings 381
13
Superstitious? Mot Us ... 382
14
Sizing It Up
The Measurement of Attributes 383
¦ Objectives for the child 384
¦ Teacher goals 384
¦ Measuring length 385
¦ Measuring area 396
¦ Measuring volume 403
¦ Measuring weight 405
¦ Measuring angles 406
¦ Measuring time and temperature 408
Time 408
Temperature 410
¦ Estimation 411
¦ Money 413
¦ Ideas for enrichment: tt 416
¦ The computer corner 416
Computer tips 417
¦ In closing... 417
¦ It s think tank time 418
¦ Suggested readings 419
15
Making Numbers Count
Organizing, Representing, and Interpreting
Data 420
¦ Objectives for the child 421
¦ Teacher goals 421
¦ Statistics 422
Collecting and organizing data 423
Drawing inferences 426
¦ Probability 429
Using familiar language 430
Determining possible outcomes 431
The probability of an event 433
¦ Ideas for enrichment: Interesting data 436
¦ The computer corner 436
Computer tips 437
¦ In closing... 437
¦ It s think tank time 438
¦ Suggested readings 439
16
Computers and Mathematics Instruction
Status and Direction 440
¦ Teacher goals 441
¦ What is a microcomputer? 442
¦ Using computers to improve instruction 444
¦ Computer Directed Instruction 444
ARRAY, ARRAY: A program for concept development 445
AUTHOR: A program that can be customized 447
The Rule Genie: A program for thinking 450
TOYSTORE: A program of simulation 451
¦ Computer Directed Instruction: A wrap up 452
¦ Computer Enhanced Instruction 454
Models for fractions: A program that draws pictures 455
CERTIFICATE: A program for rewarding 458
The Item Database: A program for storing 458
MASTER MAKER: Another tool for the teacher 461
DATA: A student utility 462
4
¦ Computer Managed Instruction 464
Instructional management: Bits and pieces 465
LIST: A generic tool 465
MINI GRADER: A specific tool 466
¦ Putting the pieces together 467
¦ Important potpourri 468
¦ In closing... 469
¦ It s think tank time 470
¦ Suggested readings 472
17
The End ... Your Beginning
Toward Efficient Instruction 473
¦ Decide on a plan 475
Keeping records 475
¦ Arranging and managing the classroom 476
¦ The computer corner 478
Computer tips 479
¦ In closing ... 479
¦ Suggested readings 480
Appendix A Instructional Objectives Chart 483
Appendix B Selected Answers for Think Tank Time Exercises 486
Appendix C Material Sheets 499
Index 529
|
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| dewey-tens | 370 - Education |
| discipline | Pädagogik Mathematik |
| edition | 3. ed. |
| format | Book |
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| indexdate | 2024-07-09T16:24:15Z |
| institution | BVB |
| isbn | 0534069843 |
| language | English |
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| physical | XXI, 532 S. Ill., graph. Darst. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Brooks/Cole |
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| spelling | Troutman, Andria P. Verfasser aut Mathematics a good beginning ; strategies for teaching children Andria P. Troutman ; Betty K. Lichtenberg 3. ed. Pacific Grove, Calif. Brooks/Cole 1987 XXI, 532 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathématiques - Étude et enseignement (Primaire) Mathematik Mathematics Study and teaching (Elementary) Mathematikunterricht (DE-588)4037949-8 gnd rswk-swf Mathematikunterricht (DE-588)4037949-8 s DE-604 Lichtenberg, Betty K. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003189714&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Troutman, Andria P. Lichtenberg, Betty K. Mathematics a good beginning ; strategies for teaching children Mathématiques - Étude et enseignement (Primaire) Mathematik Mathematics Study and teaching (Elementary) Mathematikunterricht (DE-588)4037949-8 gnd |
| subject_GND | (DE-588)4037949-8 |
| title | Mathematics a good beginning ; strategies for teaching children |
| title_auth | Mathematics a good beginning ; strategies for teaching children |
| title_exact_search | Mathematics a good beginning ; strategies for teaching children |
| title_full | Mathematics a good beginning ; strategies for teaching children Andria P. Troutman ; Betty K. Lichtenberg |
| title_fullStr | Mathematics a good beginning ; strategies for teaching children Andria P. Troutman ; Betty K. Lichtenberg |
| title_full_unstemmed | Mathematics a good beginning ; strategies for teaching children Andria P. Troutman ; Betty K. Lichtenberg |
| title_short | Mathematics |
| title_sort | mathematics a good beginning strategies for teaching children |
| title_sub | a good beginning ; strategies for teaching children |
| topic | Mathématiques - Étude et enseignement (Primaire) Mathematik Mathematics Study and teaching (Elementary) Mathematikunterricht (DE-588)4037949-8 gnd |
| topic_facet | Mathématiques - Étude et enseignement (Primaire) Mathematik Mathematics Study and teaching (Elementary) Mathematikunterricht |
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