Understanding the structure of elementary school mathematics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston u.a.
Allyn and Bacon
1987
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 488 S. graph. Darst. |
| ISBN: | 020508821X |
Staff View
MARC
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| 245 | 1 | 0 | |a Understanding the structure of elementary school mathematics |c Daniel M. Fendel |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Chapter 1 BASIC CONCEPTS .,
Section 1 INEQUALITIES 2
Section 2 IN-OUT MACHINES 5
Ordered Pairs 7
Missing Input 7
Section 3 OTHER PRELIMINARIES 10
Use of Parentheses, Order of Operations 10
Sets 13
Number Line 14
FURTHER IDEAS FOR THE CLASSROOM 15
CALCULATOR ACTIVITIES 16
Chapter 2 OPEN SENTENCES 18
Section 1 THE GENERAL IDEA 18
Section 2 MORE THAN ONE BOX 22
Section 3 EQUIVALENT SENTENCES 26
Division with Zero 30
Expanded Form for Multiplication 32
* Algebra with Equivalent Sentences 33
Section 4 GRAPHING OPEN SENTENCES 37
Section 5 WORD PROBLEMS AND OPEN SENTENCES 43
Forward Word Problems 46
Backward Word Problems 49
More Than One Solution 55
An Over-Determined Problem 56
From Open Sentences to Word Problems 57
FURTHER IDEAS FOR THE CLASSROOM 59
CALCULATOR ACTIVITIES 59
Chapter 3 OPERATIONS AND FUNCTIONS 61
Section 1 OPERATIONS—SOME INVENTED EXAMPLES 61
Juxtaposition 62
Backward Juxtaposition 65
Perimeter Operation 67
Section 2 OPERATIONS ON SETS 69
Section 3 PROPERTIES OF OPERATIONS 74
Identity Elements 76
Section 4 MORE ABOUT FUNCTIONS 79
Composition 80
Domain and Range 82
*Some Special Functions 84
FURTHER IDEAS FOR THE CLASSROOM 85
CALCULATOR ACTIVITIES 86
Chapter 4 EXPONENTIATION 87
Section 1 A NEW OPERATION 87
Properties of Exponentiation 89
Standard Notation and Special Terminology 91
Order of Operations 92
Section 2 COUNTING FACTORS AND ADDENDS 92
Distributive Law 94
Two Variations 95
Section 3 ZERO AS AN EXPONENT 96
0°: A Special Case 98
Section 4 OTHER LAWS OF EXPONENTS 99
One More Pair of Formulas 101
Section 5 FRACTIONS AS EXPONENTS 103
Some Further Developments 106
FURTHER IDEAS FOR THE CLASSROOM 108
CALCULATOR ACTIVITIES 108
Chapter 5 NUMBER THEORY 109
Section 1 MULTIPLES AND DIVISORS 109
Section 2 PRIMES AND PRIME FACTORIZATION 113
Interesting Things About Primes 115
Section 3 USING PRIME FACTORIZATION 117
*Counting Divisors 119
FURTHER IDEAS FOR THE CLASSROOM 122
CALCU LATO R ACTIVITIES 123
Chapter 6 BASE NUMERATION SYSTEMS 125
Section 1 A SECRET CODE 125
Section 2 OTHER BASES 12g
Avoiding Confusion 130
Arbitrary Bases 132
A Very Important Example 132
?Bases Bigger than Ten 133
Section 3 WORKING WITH BASE NUMERATION
SYSTEMS 135
Section 4 ARITHMETIC USING BASE NUMERATION:
ADDITION 141
Adding in Columns 144
Adding With Improper Numerals 145
Comparing Base Ten to Other Bases -j 47
Basic Addition Facts 148
Meanings of Counting and Addition—Pedagogical Discussion 149
Completing the Addition Algorithm 151
Section 5 ARITHMETIC USING BASE NUMERATION:
SUBTRACTION 155
Meanings of Subtraction 155
Subtraction Algorithm 156
Section 6 ARITHMETIC USING BASE NUMERATION:
MULTIPLICATION 158
Basic Facts 159
Distributive Law 160
Multiplication Using Powers of the Base 161
Putting It All Together 162
Analyzing the Multiplication Algorithm—Pedagogical Discussion 163
Concepts of Multiplication 165
Section 7 ARITHMETIC USING BASE NUMERATION:
DIVISION 167
Intuitive Division 168
A Division Algorithm 170
Remainders and Checking 172
FURTHER IDEAS FOR THE CLASSROOM 173
CALCU LATO R ACTIVITIES 174
Chapter 7 EXTENDING THE NUMBER SYSTEM 175
Section 1 INVENTING NEW NUMBERS 176
Introducing Negative Numbers 176
A Similar Invention 179
Section 2 INVERSES 180
Mutuality of Inverses 181
Section 3 EXTENDING ARITHMETIC 185
Combining Inverses 188
Section 4 ANOTHER VIEW OF DIVISION NUMBERS 191
What Is a Fraction? 193
Section 5 WHAT IS A NEGATIVE NUMBER? 196
Other Ideas about Negative Numbers 198
Integers: Sign and Absolute Value 198
Section 6 THE TWO SYSTEMS MEET 199
Section 7 THE RATIONAL NUMBERS 202
FURTHER IDEAS FOR THE CLASSROOM 203
CALCULATOR ACTIVITIES 203
Chapter 8 INTEGERS 204
Section 1 SUBTRACTION 204
Section 2 COMPLETING INTEGER ARITHMETIC 207
Multiplication 207
Exponentiation 210
Division 211
Section 3 ORDERING THE INTEGERS 212
Section 4 GRAPHING 214
FURTHER IDEAS FOR THE CLASSROOM 216
CALCULATOR ACTIVITIES 217
Chapter 9 FRACTIONS 218
Section 1 MORE ON ADDITION AND MULTIPLICATION 218
Addition of Like Fractions 218
Multiplication: By Splitting 219
Multiplication: Using Area 220
Reciprocals 221
Exponentiation 222
Section 2 EQUIVALENT FRACTIONS 224
Section 3 IMPROPER FRACTIONS AND MIXED NUMBERS 228
Section 4 ADDITION AND SUBTRACTION 230
Subtraction 231
Section 5 DIVISION 232
Section 6 ARITHMETIC OF MIXED NUMBERS 236
Addition 237
Subtraction 238
Multiplication 239
Division 241
Section 7 COMPARISON OF FRACTIONS 241
*Further Developments 243
Section 8 ARITHMETIC OF RATIONAL NUMBERS 245
FURTHER IDEAS FOR THE CLASSROOM 249
CALCULATOR ACTIVITIES 250
Chapter 10 DECIMALS IN BASE NUMERATION SYSTEMS 251
Section 1 EXTENDING BASE NUMERATION 251
Section 2 DECIMAL ARITHMETIC 257
Addition and Subtraction 257
Multiplication and Division 258
Comparison of Decimals 262
Section 3 FRACTIONS AS REPEATING DECIMALS 263
Section 4 PERCENTS 267
Section 5 REAL NUMBERS 269
FURTHER IDEAS FOR THE CLASSROOM 271
CALCULATOR ACTIVITIES 271
Chapter 11 GEOMETRY—FUNDAMENTALS 272
Section 1 TOPOLOGICAL IDEAS 273
Networks 280
Section 2 BASIC TERMINOLOGY 284
Polygons and Circles 287
Congruence 289
Using Congruence 291
Section 3 MEASUREMENT 296
Length 298
?Other Kinds of Length 300
Area 300
Angle Measurement 305
Units for Angles 306
Section 4 METRIC UNITS OF MEASUREMENT 307
Length 307
Area 308
Volume 308
Mass and Weight 308
Temperature 309
Conversion between English and Metric Measurement 309
FURTHER IDEAS FOR THE CLASSROOM 310
Chapter 12 GEOMETRY—FURTHER DEVELOPMENTS 312
Section 1 CONSTRUCTION 312
Section 2 SIMILARITY 318
Section 3 SYMMETRY 323
Line Symmetry 324
Rotational Symmetry 325
Section 4 ANGLE SUM AND RIGHT TRIANGLES 326
Angle Sum 327
Pythagorean Theorem 329
Section 5 AREA FORMULAS AND UNDERSTANDING n 336
Using Similarity 336
Area: From Rectangles to Polygons 336
From Polygons to Circles 340
Section 6 FORMAL GEOMETRY: NONCOORDINATE 342
Noncoordinate Geometry 342
Congruence— Traditional Approach 343
*Congmence— Transformational Approach 344
*Transformations and Similarity 347
Section 7 COORDINATE GEOMETRY 347
Length 350
Congruence 351
Algebra and Geometry 352
FURTHER IDEAS FOR THE CLASSROOM 352
Chapter 13 COMPUTERS IN THE CLASSROOM 355
Section 1 COMPUTER AS INSTRUCTIONAL DEVICE 357
Snoopy and Blackjack 357
Balloon and Beans 358
Postal and Mugwump 360
Hammurabi and Racetrack 361
The Factory and Rocky*s Boots 362
Discussion 363
Section 2. PROCEDURAL THINKING 364
Following Instructions 365
Creating Instructions 371
Section 3 PROGRAMMING 376
What Is a Program? 376
General Features 376
LOGO vs. BASIC 377
LOGO 378
Naming a Procedure 381
Cleaning Up the Procedure 382
Repetition and Variables 383
Recursion 386
Angles of Polygons—From a Turtle s Point of View 387
BASIC 390
Improvements 391
FURTHER IDEAS FOR THE CLASSROOM 395
Chapter 14 PROBABILITY AND STATISTICS 397
Section 1 PROBABILITY 397
Section 2 COMBINATIONS OF EXPERIMENTS 401
Conditional Probability 402
Union of Events 404
Section 3 PERMUTATIONS AND COMBINATIONS 405
Pascal s Triangle 410
Section 4 NOT EQUALLY LIKELY OUTCOMES 411
Unbalanced Coins 413
Section 5 STATISTICS 414
Presenting Information 414
Measures of Central Tendency 416
Measures of Dispersion 418
Normal Distribution 419
FURTHER IDEAS FOR THE CLASSROOM 421
Appendix A PROBLEMS AND PROBLEM SOLVING 422
WHAT IS A PROBLEM? 422
SOLVING PROBLEMS 423
I UNDERSTANDING THE PROBLEM 424
II DEVISING A PLAN 426
III CARRYING OUT THE PLAN 427
IV LOOKING BACK 432
FINAL CONCLUSIONS 434
Appendix B EXAMPLES OF THE PROBLEM-SOLVING STAGES 435
I UNDERSTANDING THE PROBLEM 436
II DEVISING A PLAN 437
III CARRYING OUT THE PLAN 438
IV LOOKING BACK 439
Appendix C CALCULATORS 442
CHOOSING A CALCULATOR 443
Type of Logic 443
Display 443
Keyboard 443
Practicalities 444
GETTING TO KNOW YOUR MACHINE 444
PRINCIPLES FOR THE CLASSROOM 445
Appendix D INFORMATION ON SOFTWARE 447
Appendix E ANSWERS TO SELECTED EXERCISES 448
Index 475
|
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| discipline | Pädagogik Mathematik |
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| spelling | Fendel, Daniel M. Verfasser aut Understanding the structure of elementary school mathematics Daniel M. Fendel Boston u.a. Allyn and Bacon 1987 XX, 488 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathématiques Mathematik Mathematics Mathematikunterricht (DE-588)4037949-8 gnd rswk-swf Grundschule (DE-588)4022349-8 gnd rswk-swf USA (DE-588)4078704-7 gnd rswk-swf USA (DE-588)4078704-7 g Mathematikunterricht (DE-588)4037949-8 s Grundschule (DE-588)4022349-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003683451&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fendel, Daniel M. Understanding the structure of elementary school mathematics Mathématiques Mathematik Mathematics Mathematikunterricht (DE-588)4037949-8 gnd Grundschule (DE-588)4022349-8 gnd |
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| title | Understanding the structure of elementary school mathematics |
| title_auth | Understanding the structure of elementary school mathematics |
| title_exact_search | Understanding the structure of elementary school mathematics |
| title_full | Understanding the structure of elementary school mathematics Daniel M. Fendel |
| title_fullStr | Understanding the structure of elementary school mathematics Daniel M. Fendel |
| title_full_unstemmed | Understanding the structure of elementary school mathematics Daniel M. Fendel |
| title_short | Understanding the structure of elementary school mathematics |
| title_sort | understanding the structure of elementary school mathematics |
| topic | Mathématiques Mathematik Mathematics Mathematikunterricht (DE-588)4037949-8 gnd Grundschule (DE-588)4022349-8 gnd |
| topic_facet | Mathématiques Mathematik Mathematics Mathematikunterricht Grundschule USA |
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