CONTENTS -- Preface -- The Crisis We Face and How to Try to Deal with It J. Jerry Uhl and Debra Woods -- The Failure of Math Education in Our Schools -- References -- Mathematics Topics Foundational to Calculus at the Secondary Level Antonio R. Quesada -- 1. Introduction -- 2. Mathematics Instruction Before the Integration of Technology -- 3. Mathematics Instruction After the Integration of Technology -- 4. Goals of This Article -- 5. How the Integration of Technology Expands the Study of Functions in Precalculus -- 6. On the Role of Transformations with all Families of Functions -- 7. On Solving Equations and Inequalities -- 8. On the Relative Growth of Functions -- 9. On the Range and Local Extrema of Functions -- 10. On Factoring Real Polynomials -- 11. On the Local and Global Behavior of a Function -- 12. On Continuity -- 13. On Modeling -- 14. Conclusion -- References -- Hand-held Technology in Secondary Mathematics Education Barry Kissane -- 1. Introduction -- 2. Technology for Education -- 3. Hand-held Technologies -- 3.1. Advantages of Hand-Held Technology -- 3.2. A Hierarchy of Hand-Held Technologies -- 3.2.1. Arithmetic Calculators -- 3.2.2. Scienti c Calculators -- 3.2.3. Graphics Calculators -- 3.2.4. ClassPad 300 -- 4. Three Roles for Hand-held Technologies -- 4.1. Computational Role -- 4.2. Experiential Role -- 4.3. Inuential Role -- 4.3.1. Computation -- 4.3.2. Content -- 4.3.3. Sequence -- 5. Some Key Issues -- 5.1. Integration of Technology -- 5.2. Supporting Learning -- 5.3. Motivating Learning -- 5.4. The Role of the Teacher -- 5.5. Pedagogical E ects -- 5.6. Changing the Curriculum -- 6. Conclusions -- References -- College Algebra Change Robert L. Mayes, Vennessa L. Walker and Philip N. Chase -- Theoretical Framework -- Applied College Algebra Curricular Reform -- Fall 2004 -- Method -- Results -- Discussion -- Spring 2005.

Results -- Discussion -- References -- Mathematics Experiments - Learning and Investigating Mathematics with the Help of Computers Shangzhi Li -- Introduction -- 1. The Graphs of Functions -- 1.1. Taylor's Series -- 1.2. Fourier's Series -- 1.3. Graph of y = sin 1 near x = 0. -- 2. How to Calculate ¼? -- 2.1. Method of Numerical Integral -- 2.2. Method of Using Taylor's Series -- 3. Geometric Transformations -- 3.1. Invariant Properties Under a Linear Transformation -- 3.2. Eigenvectors -- 3.3. Projective Transformations -- Reference -- CreaComp: Experimental Formal Mathematics for the Classroom G unther Mayrhofer, Susanne Saminger and Wolfgang Windsteiger -- 1. Introduction -- 2. The CreaComp Project: An Overview -- 2.1. The Components MeetMath and Theorema -- 2.2. The Combination of MeetMath and Theorema -- 3. The Case Study: Equivalence Relations and Set Partitions -- 3.1. The Interface to Computer-Supported Experiments -- 3.2. The Interface to Automated Proving -- 3.3. The Entire Unit -- 4. Conclusion and Future Work -- References -- Free Software SSP for Teaching Mathematics Jing-Zhong Zhang, Hui-Min Xiong and Xi-Cheng Peng -- 1. Introduction: What Is SSP? -- 2. What Is the Special of SSP in Dynamic Drawing? -- 3. Symbolic Computation and Dynamic Measurement for Expression -- 4. Programming Environment in SSP -- 5. More Examples -- 6. Prospect -- References -- Bringing More Intelligence to Dynamic Geometry by Francisco Botana -- 1. Introduction -- 2. Continuity and Discontinuity -- 3. Loci Computations -- 4. Automatic Discovery -- 5. Finding Elementary Extrema -- 6. Conclusion -- Acknowledgments -- References -- Combining CAS and DGS - Towards Algorithmic Thinking Ulrich H. Kortenkamp -- 1. Introduction -- 1.1. Spreadsheets -- 1.2. Computer Algebra Software -- 1.3. Dynamic Geometry Software -- 2. Using DGS in Teaching.

2.1. Reasons to Use DGS at All -- 2.1.1. Pedagogical Aspects -- 2.1.2. Mathematical Aspects -- 2.2. E-Learning/E-Teaching Scenarios -- 2.2.1. Assessment and Guidance -- 3. Automatic Theorem Proving -- 4. Combining DGS and CAS -- 4.1. Continuity vs. Discreteness -- 4.1.1. Principle of Continuity -- 4.2. Usage Paradigms for Math Software -- 4.3. Successful Interaction Between CAS and DGS -- 4.3.1. CAS as a User -- 4.3.2. Make CAS Results Available to Geometry -- 4.3.3. Discretization: Event-based Calculation -- 4.4. CindyScript and Other Scripting Languages -- 5. Consequences for Educational Setups -- 5.1. Algorithmic Thinking -- 5.1.1. Example: Discrete Mathematics -- 5.2. Creating Things to Think About -- 5.3. Bringing Teachers Back into Charge -- 6. Further Integration and Other Approaches -- 6.1. OpenMath -- 6.2. Extended Use of Symbolic Computation for the Geometry Kernel -- 6.3. Geometry Expressions -- 6.4. Feli-X -- Acknowledgements -- References -- Integrating Rule-based and Input-based Approaches for Better Error Diagnosis in Expression Manipulation Tasks Rein Prank, Marina Issakova, Dmitri Lepp, Eno Tonisson and Vahur Vaiksaar -- 1. Introduction -- 2. What Type of Learning Environment Do We Need? -- 3. Solution Step Dialogue in T-algebra -- 4. What Can We Diagnose in A-O-I-Interface? -- 4.1. What Can Be Decided About the Selected Operation? -- 4.2. Checking the Operation and Marking of Operands Together -- 4.3. Checking Entered Result of Conversion -- 5. Conclusions -- Acknowledgments -- References -- Automated Generation of Readable Proofs for a Class of Limits of Sequences and Functions Jing Ruan and Zhengyi Lu -- 1. Introduction -- 2. Algorithms for Proofs of Limits -- 2.1. Proofs for Limits of Sequences -- 2.2. Proofs for Limits of Functions -- 3. Future Work -- References.

Computer Algebra Meets an Ancient Egyptian Problem Yiu-Kwong Man -- 1. Introduction -- 2. The Fibonacci-Sylvester Algorithm -- 3. A New Improved Fibonacci-Sylvester Algorithm -- 4. Implementation in Computer Algebra Systems -- 5. Final Remarks -- References -- Finite Series Expansions for Powers of Sine and Cosine Functions via Mathematica Tilak de Alwis -- 1. Introduction -- 2. Finite Series Expansions for Cosnx Where n Is a Positive Even Integer -- 3. Finite Series Expansions for Cosnx Where n Is a Positive Odd Integer -- 4. Pascal Type Properties for the Coe±cients in the Expansion of Cos2kx -- 5. Conclusion -- References -- Solving the Heat and Wave Equations with the (Fast) Discrete Fourier Transform Alkiviadis G. Akritas, Panagiotis S. Vigklas and J. Jerry Uhl -- 1. Introduction -- 2. FFT Is the Basis of Fast Fourier Fit (FFF) -- 3. FFF in Deriving the Heat and Wave Equations -- 3.1. Preliminaries -- 3.2. The Heat Equation 2temp(x -- t) x2 = temp(x -- t) t -- 3.3. The Wave Equation 2position(x -- t) x2 = 2position(x -- t) t2 -- 4. Conclusions -- References -- Author Index.