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Computational Experiment Approach to Advanced Secondary Mathematics Curriculum / / by Sergei Abramovich
| Computational Experiment Approach to Advanced Secondary Mathematics Curriculum / / by Sergei Abramovich |
| Autore | Abramovich Sergei |
| Edizione | [1st ed. 2014.] |
| Pubbl/distr/stampa | Dordrecht : , : Springer Netherlands : , : Imprint : Springer, , 2014 |
| Descrizione fisica | 1 online resource (333 p.) |
| Disciplina | 510.78 |
| Collana | Mathematics Education in the Digital Era |
| Soggetto topico |
Mathematics - Study and teaching
Mathematics - Data processing Education - Data processing Computer software Learning, Psychology of Mathematics Education Computational Mathematics and Numerical Analysis Computers and Education Mathematical Software Instructional Psychology |
| ISBN | 94-017-8622-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- 1. Theoretical foundations of computational experiment approach to secondary mathematics -- 2. One-variable equations and inequalities: the unity of computational experiment and formal demonstration -- 3. Computationally supported study of quadratic functions depending on parameters -- 4. Computational experiment approach to equations with parameters -- 5. Inequalities with parameters as generators of new meanings -- 6. Computational experiments in trigonometry -- 7. Advancing stem education through temp: Geometric probabilities -- 8. Exploring topics in elementary number theory through a computational experiment -- References. . |
| Record Nr. | UNINA-9910299964803321 |
Abramovich Sergei
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| Dordrecht : , : Springer Netherlands : , : Imprint : Springer, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Computer-enabled mathematics [[electronic resource] ] : integrating experiment and theory in teacher education / / Sergei Abramovich
| Computer-enabled mathematics [[electronic resource] ] : integrating experiment and theory in teacher education / / Sergei Abramovich |
| Autore | Abramovich Sergei |
| Pubbl/distr/stampa | New York, : Nova Science Publishers, c2011 |
| Descrizione fisica | 1 online resource (275 p.) |
| Disciplina | 510.71 |
| Collana | Education in a competitive and globalizing world |
| Soggetto topico |
Mathematics teachers - Training of
Mathematics - Study and teaching (Secondary) - Data processing Mathematics - Computer-assisted instruction Electronic data processing - Study and teaching (Secondary) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-61209-031-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910458022003321 |
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Abramovich Sergei
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| New York, : Nova Science Publishers, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Computer-enabled mathematics [[electronic resource] ] : integrating experiment and theory in teacher education / / Sergei Abramovich
| Computer-enabled mathematics [[electronic resource] ] : integrating experiment and theory in teacher education / / Sergei Abramovich |
| Autore | Abramovich Sergei |
| Pubbl/distr/stampa | New York, : Nova Science Publishers, c2011 |
| Descrizione fisica | 1 online resource (275 p.) |
| Disciplina | 510.71 |
| Collana | Education in a competitive and globalizing world |
| Soggetto topico |
Mathematics teachers - Training of
Mathematics - Study and teaching (Secondary) - Data processing Mathematics - Computer-assisted instruction Electronic data processing - Study and teaching (Secondary) |
| ISBN | 1-61209-031-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | The multiplication table from an advanced standpoint -- Algebraic equations with parameters -- Inequalities and spreadsheet modeling -- Geometric probabilities -- Combinatorial explorations -- Historical perspectives -- Computational experiments and formal demonstration in trigonometry -- Developing models for computational problem solving -- Programming details. |
| Record Nr. | UNINA-9910781868003321 |
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Abramovich Sergei
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| New York, : Nova Science Publishers, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Fostering Collateral Creativity in School Mathematics : Paying Attention to Students’ Emerging Ideas in the Age of Technology / / by Sergei Abramovich, Viktor Freiman
| Fostering Collateral Creativity in School Mathematics : Paying Attention to Students’ Emerging Ideas in the Age of Technology / / by Sergei Abramovich, Viktor Freiman |
| Autore | Abramovich Sergei |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (141 pages) |
| Disciplina | 510.71071 |
| Collana | Mathematics Education in the Digital Era |
| Soggetto topico |
Mathematics - Study and teaching
Art - Study and teaching Educational technology Mathematics Education Creativity and Arts Education Digital Education and Educational Technology |
| ISBN |
9783031406393
3031406397 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Chapter 1: Theoretical foundation of collateral creativity -- Chapter 2: From additive decompositions of integers to probability experiments -- Chapter 3: From number sieves to difference equations -- Chapter 4: Prime numbers -- Chapter 5: From dividing shapes in equal parts to the Four-color theorem -- Chapter 6: From purchasing flowers to minimax mathematics -- Chapter 7: From comparing chances to algebraic inequalities -- Chapter 8: Recreational mathematics (8-Queens, Tower of Hanoi) -- Chapter 9: Exploring unsolved problems (e.g., 4, 2, 1, sequence) -- Chapter 10: The Golden Ratio -- Chapter 11: Monty Hall Dilemma -- Chapter 12: Playing with calendar -- Chapter 13: Egyptian fractions. Appendix. Bibliography. Index. |
| Record Nr. | UNINA-9910746956203321 |
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Abramovich Sergei
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Revisiting Fibonacci numbers through a computational experiment / / Sergei Abramovich and Gennady A. Leonov
| Revisiting Fibonacci numbers through a computational experiment / / Sergei Abramovich and Gennady A. Leonov |
| Autore | Abramovich Sergei |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | New York : , : Nova Science Publishers, Incorporated, , [2019] |
| Descrizione fisica | 1 online resource (264 pages) |
| Disciplina | 512.72 |
| Collana | Education in a competitive and globalizing world series |
| Soggetto topico | Fibonacci numbers |
| ISBN |
9781536149067
1536149063 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Revisiting Fibonacci Numbers through a Computational Experiment -- Revisiting Fibonacci Numbers through a Computational Experiment -- Contents -- Preface -- Acknowledgments -- Chapter 1 -- Theoretical Background: Fibonacci Numbers as a Framework for Information vs. Explanation Cognitive Paradigm -- 1.1. Introduction -- 1.2. Goals of the Book -- 1.3. A Pedagogy of the Book -- 1.4. Collateral Learning and Hidden Mathematics Curriculum -- 1.5. TITE Problems as a Framework for the Information vs. Explanation Paradigm -- 1.6. Summary -- Chapter 2 -- From Fibonacci Numbers to Fibonacci-Like Polynomials -- 2.1. The Binary Number System and Fibonacci Numbers -- 2.2. Different Representations of Fibonacci Numbers -- 2.3. Fibonacci Numbers and Pascal's Triangle -- 2.4. Hidden Mathematics Curriculum of Pascal's Triangle -- 2.5. Binomial Coefficients and Fibonacci Numbers -- 2.6. From Pascal's Triangle to Fibonacci-Like Polynomials -- 2.7. Other Classes of Polynomials Associated with Fibonacci Numbers -- 2.8. Summary -- Chapter 3 -- Different Approaches to the Development of Binet's Formulas -- 3.1. Fibonacci-Like Numbers -- 3.2. Parameterization of Fibonacci Recursion -- 3.3. Deriving Binet's Formulas for Recurrence (3.8) Using The Machinery of Matrices -- 3.4. Generating Function Approach to the Derivation of Binet's Formulas -- 3.4.1. The Case of Fibonacci Numbers -- 3.4.2. The Case of Lucas Numbers -- 3.4.3. The Case of Matijasevic Numbers -- 3.4.4. The Case of Jacobsthal Numbers -- 3.5. Characteristic Equation Approach -- 3.5.1. The Case of Fibonacci Numbers -- 3.5.2. The Case of Lucas Numbers -- 3.5.3. The Case of Matijasevic Numbers -- 3.5.4. The Case of Jacobsthal Numbers -- 3.6. Continued Fractions and the Golden Ratio -- 3.7. Leibniz Diagrams as Level Lines for Eigenvalues.
3.8. Limiting Behavior of the Ratios , - + ./, - . -- 3.9. Summary -- Chapter 4 -- Fibonacci Sieves and Their Representation through Difference Equations -- 4.1. Fibonacci Sieve of Order K and Its Difference Equation -- 4.2. Connecting Fibonacci Sieves to Modern Mathematics -- 4.3. Constructing (r, k)-Section of Fibonacci Numbers as a TITE Exploration -- 4.4. The Golden Ratio as an Invariant for Fibonacci-Like Sequences -- 4.4.1. The Case of Fibonacci and Lucas Number Sequences -- 4.4.2. The Case of Fibonacci-Like Number Sequences -- 4.5. Computational Experiments with Fibonacci-Like Sieves -- 4.6. Summary -- Chapter 5 -- TITE Explorations of Generalized Golden Ratios -- 5.1. Introduction -- 5.2. Convergence to a Generalized Golden Ratio -- 5.3. Disappearance of the Golden Ratio -- 5.4. Constructing Cycles of Higher Periods -- 5.5. Summary -- Chapter 6 -- Exploring Cycles Using a Combination of Digital Tools -- 6.1. Verifying Theory Through Experiment -- 6.2. Recursive Computing of Coefficients of Fibonacci-Like Polynomials -- 6.3. Generating Fibonacci-Like Polynomials Using Maple -- 6.4. On the Existence of a Cycle of an Arbitrary Large Period -- 6.5. Summary -- Chapter 7 -- Method of Iterations and Fibonacci-Like Polynomials -- 7.1. Developing Iterative Formulas in the General Case -- 7.2. Connecting Iterative Formulas to Some Known Sequences of Numbers -- 7.3. Geometric Interpretation of the Method of Iterations -- 7.4. Building Connections to Other Sequences Included into the OEIS( -- 7.5. Method of Iterations in the Case of the Polynomials , - ., . and , - ., . -- 7.6. Method of Iterations in the Case of a Fibonacci-Like Polynomial of Degree Four -- 7.7. Summary -- Chapter 8 -- Identities for Fibonacci-Like Polynomials -- 8.1. Introduction -- 8.2. Additive Identities Among Fibonacci-Like Polynomials. 8.3. Multiplicative Identities Among Fibonacci-Like Polynomials -- 8.4. Polynomial Generalizations of Cassini's Identity -- 8.5. Conjecturing Polynomial Forms of Catalan's Identity -- 8.6. Summary -- Chapter 9 -- Uncovering Hidden Patterns in the Oscillations of Generalized Golden Ratios -- 9.1. On The Roots of Fibonacci-Like Polynomials -- 9.2. Permutations with Rises/Falls and the Directions of Cycles -- 9.3. Recognizing the Nature of Permutations of the Elements of a Three-Cycle -- 9.4. Permutations of the Elements of a Four-Cycle -- 9.5. Permutations of the Elements of a Five-Cycle -- 9.6. Generalizing from Observations -- 9.7. Proof of Proposition 9.3 -- 9.8. Circular Diagrams and Oscillations Associated with the Largest Root -- 9.9. Summary -- References -- About the Authors -- Index -- Blank Page -- Blank Page. |
| Record Nr. | UNINA-9911026160603321 |
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Abramovich Sergei
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| New York : , : Nova Science Publishers, Incorporated, , [2019] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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