With 14 chapters written by leading experts and educators, this book covers a wide range of topics from teaching philosophy and curriculum development to symbolic and algebraic manipulation and automated geometric reasoning, and to the design and implementation of educational software and integrated teaching and learning environments. The book may serve as a useful reference for researchers, educators, and other professionals interested in developing, using, and practising methodologies and software tools of symbolic computation for education from the secondary to the undergraduate level.
Author(s): Dongming Wang
Publisher: World Scientific Publishing Company
Year: 2007
Language: English
Pages: 256
Preface......Page 6
CONTENTS......Page 8
The Failure of Math Education in Our Schools......Page 10
References......Page 12
1. Introduction......Page 13
3. Mathematics Instruction After the Integration of Technology......Page 14
4. Goals of This Article......Page 15
5. How the Integration of Technology Expands the Study of Functions in Precalculus......Page 16
6. On the Role of Transformations with all Families of Functions......Page 17
7. On Solving Equations and Inequalities......Page 19
8. On the Relative Growth of Functions......Page 21
9. On the Range and Local Extrema of Functions......Page 24
10. On Factoring Real Polynomials......Page 25
11. On the Local and Global Behavior of a Function......Page 28
12. On Continuity......Page 32
13. On Modeling......Page 33
14. Conclusion......Page 37
References......Page 38
1. Introduction......Page 40
2. Technology for Education......Page 41
3.1. Advantages of Hand-Held Technology......Page 43
3.2.1. Arithmetic Calculators......Page 44
3.2.3. Graphics Calculators......Page 45
3.2.4. ClassPad 300......Page 46
4.1. Computational Role......Page 47
4.2. Experiential Role......Page 51
4.3.1. Computation......Page 57
4.3.2. Content......Page 60
4.3.3. Sequence......Page 62
5.1. Integration of Technology......Page 63
5.2. Supporting Learning......Page 64
5.4. The Role of the Teacher......Page 65
5.6. Changing the Curriculum......Page 66
References......Page 67
College Algebra Change Robert L. Mayes, Vennessa L. Walker and Philip N. Chase......Page 69
Theoretical Framework......Page 70
Applied College Algebra Curricular Reform......Page 74
Method......Page 76
Results......Page 78
Discussion......Page 79
Results......Page 80
Discussion......Page 81
References......Page 83
1. The Graphs of Functions......Page 86
1.1. Taylor's Series......Page 87
1.2. Fourier's Series......Page 89
1.3. Graph of y = sin 1/x near x = 0.......Page 91
2. How to Calculate π......Page 93
2.1. Method of Numerical Integral......Page 94
2.2. Method of Using Taylor's Series......Page 96
3.1. Invariant Properties Under a Linear Transformation......Page 97
3.2. Eigenvectors......Page 98
3.3. Projective Transformations......Page 100
Reference......Page 102
1. Introduction......Page 103
2.1. The Components MeetMath and Theorema......Page 106
2.2. The Combination of MeetMath and Theorema......Page 107
3. The Case Study: Equivalence Relations and Set Partitions......Page 110
3.1. The Interface to Computer-Supported Experiments......Page 111
3.2. The Interface to Automated Proving......Page 113
3.3. The Entire Unit......Page 115
4. Conclusion and Future Work......Page 121
References......Page 122
1. Introduction: What Is SSP?......Page 124
2. What Is the Special of SSP in Dynamic Drawing?......Page 127
3. Symbolic Computation and Dynamic Measurement for Expression......Page 132
4. Programming Environment in SSP......Page 134
5. More Examples......Page 138
6. Prospect......Page 142
References......Page 143
1. Introduction......Page 145
2. Continuity and Discontinuity......Page 147
3. Loci Computations......Page 148
4. Automatic Discovery......Page 152
5. Finding Elementary Extrema......Page 155
6. Conclusion......Page 156
References......Page 157
1. Introduction......Page 159
1.2. Computer Algebra Software......Page 160
2.1. Reasons to Use DGS at All......Page 161
2.1.2. Mathematical Aspects......Page 162
2.2. E-Learning/E-Teaching Scenarios......Page 163
3. Automatic Theorem Proving......Page 164
4. Combining DGS and CAS......Page 165
4.1.1. Principle of Continuity......Page 166
4.2. Usage Paradigms for Math Software......Page 167
4.3.1. CAS as a User......Page 168
4.3.2. Make CAS Results Available to Geometry......Page 169
4.4. CindyScript and Other Scripting Languages......Page 170
5. Consequences for Educational Setups......Page 172
5.1.1. Example: Discrete Mathematics......Page 173
5.2. Creating Things to Think About......Page 174
5.3. Bringing Teachers Back into Charge......Page 175
6.1. OpenMath......Page 176
6.3. Geometry Expressions......Page 177
6.4. Feli-X......Page 178
References......Page 179
1. Introduction......Page 183
2. What Type of Learning Environment Do We Need?......Page 184
3. Solution Step Dialogue in T-algebra......Page 188
4.2. Checking the Operation and Marking of Operands Together......Page 193
4.3. Checking Entered Result of Conversion......Page 196
5. Conclusions......Page 198
References......Page 199
1. Introduction......Page 201
2.1. Proofs for Limits of Sequences......Page 202
2.2. Proofs for Limits of Functions......Page 206
3. Future Work......Page 210
References......Page 214
1. Introduction......Page 215
2. The Fibonacci-Sylvester Algorithm......Page 216
3. A New Improved Fibonacci-Sylvester Algorithm......Page 219
4. Implementation in Computer Algebra Systems......Page 222
5. Final Remarks......Page 224
References......Page 226
1. Introduction......Page 227
2. Finite Series Expansions for Cosnx Where n Is a Positive Even Integer......Page 229
3. Finite Series Expansions for Cosnx Where n Is a Positive Odd Integer......Page 234
4. Pascal Type Properties for the Coefficients in the Expansion of Cos^{2k}x......Page 236
References......Page 237
1. Introduction......Page 239
2. FFT Is the Basis of Fast Fourier Fit (FFF)......Page 240
3.1. Preliminaries......Page 245
3.2. The Heat Equation θ^2 temp(x,t) / θx^2 = θ temp(x,t) / θt......Page 248
References......Page 254
Author Index......Page 256
