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Computational Experiment Approach to Advanced Secondary Mathematics Curriculum [[electronic resource] /] / by Sergei Abramovich
| Computational Experiment Approach to Advanced Secondary Mathematics Curriculum [[electronic resource] /] / 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
Computer mathematics Education—Data processing Computer software Learning Instruction Mathematics Education Computational Mathematics and Numerical Analysis Computers and Education Mathematical Software Learning & Instruction |
| 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 | ||
| ||
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 |
|
Abramovich Sergei
|
||
| New York, : Nova Science Publishers, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
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 |
| Edizione | [1st ed.] |
| 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-9910824550103321 |
|
Abramovich Sergei
|
||
| New York, : Nova Science Publishers, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Developing deep knowledge in middle school mathematics : a textbook for teaching in the age of technology / / Sergei Abramovich and Michael L. Connell
| Developing deep knowledge in middle school mathematics : a textbook for teaching in the age of technology / / Sergei Abramovich and Michael L. Connell |
| Autore | Abramovich Sergei |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (451 pages) |
| Disciplina | 510.71 |
| Collana | Springer Texts in Education |
| Soggetto topico |
Mathematics - Study and teaching (Middle school)
Mathematics - Study and teaching Ensenyament de la matemàtica Educació secundària |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-68564-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910483522503321 |
|
Abramovich Sergei
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| Cham, Switzerland : , : Springer, , [2021] | ||
| 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 / / Sergei Abramovich and Viktor Freiman
| Fostering Collateral Creativity in School Mathematics : Paying Attention to Students' Emerging Ideas in the Age of Technology / / Sergei Abramovich and Viktor Freiman |
| Autore | Abramovich Sergei |
| Edizione | [First edition.] |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer Nature Switzerland AG, , [2023] |
| Descrizione fisica | 1 online resource (141 pages) |
| Disciplina | 510.71071 |
| Collana | Mathematics Education in the Digital Era Series |
| Soggetto topico |
Creative teaching
Mathematics - Study and teaching - Canada Mathematics - Study and teaching - United States |
| ISBN | 3-031-40639-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- References -- Contents -- 1 Theoretical Foundation and Examples of Collateral Creativity -- 1.1 Introduction -- 1.2 Theories Associated with Collateral Creativity -- 1.3 Collateral Creativity and the Instrumental Act -- 1.4 Three More Examples of Collateral Creativity -- 1.4.1 A Second Grade Example of Collateral Creativity -- 1.4.2 A Fourth Grade Example of Collateral Creativity -- 1.4.3 Collateral Creativity in a Classroom of Secondary Mathematics Teacher Candidates -- 1.5 Collateral Creativity as Problem Posing in the Zone of Proximal Development -- 1.6 Forthcoming Examples of Collateral Creativity Included in the Book -- References -- 2 From Additive Decompositions of Integers to Probability Experiments -- 2.1 Introduction -- 2.2 Artificial Creatures as a Context Inspiring Collateral Creativity -- 2.3 Iterative Nature of Questions and Investigations Supported by the Instrumental Act -- 2.4 The Joint Use of Tactile and Digital Tools Within the Instrumental Act -- 2.5 Tactile Activities as a Window to the Basic Ideas of Number Theory -- 2.6 Historical Account Connecting Decomposition of Integers to Challenges of Gambling -- References -- 3 From Number Sieves to Difference Equations -- 3.1 Introduction -- 3.2 On the Notion of a Number Sieve -- 3.3 Theoretical Value of Practical Outcome of the Instrumental Act -- 3.4 On the Equivalence of Two Approaches to Even and Odd Numbers -- 3.5 Developing New Sieves from Even and Odd Numbers -- 3.6 Polygonal Number Sieves -- 3.7 Connecting Arithmetic to Geometry Explains Mathematical Terminology -- 3.8 Polygonal Numbers and Collateral Creativity -- References -- 4 Explorations with the Sums of Digits -- 4.1 Introduction -- 4.2 About the Sums of Digits -- 4.3 Years with the Difference Nine -- 4.4 Calculating the Century Number to Which a Year Belongs.
4.5 Finding the Number of Years with the Given Sum of Digits Throughout Centuries -- 4.6 Partitioning n into Ordered Sums of Two Positive Integers -- 4.7 Interpreting the Results of Spreadsheet Modeling -- References -- 5 Collateral Creativity and Prime Numbers -- 5.1 'Low-Level' Questions Require 'High-Level' Thinking -- 5.2 Twin Primes Explorations Motivated by Activities with the Number 2021 -- 5.3 Students' Confusion as a Teaching Moment and a Source of Collateral Creativity -- 5.4 Different Definitions of a Prime Number -- 5.5 Tests of Divisibility and Collateral Creativity -- 5.6 Historically Significant Contributions to the Theory of Prime Numbers -- 5.6.1 The Sieve of Eratosthenes -- 5.6.2 Is There a Formula for Prime Numbers? -- References -- 6 From Square Tiles to Algebraic Inequalities -- 6.1 Introduction -- 6.2 Comparing Fractions Using Parts-Within-Whole Scheme -- 6.3 Collateral Creativity: Calls for Generalization -- 6.4 Collaterally Creative Question Leads to the Discovery of "Jumping Fractions" -- 6.5 Algebraic Generalization -- 6.6 Seeking New Algorithms for the Development of "Jumping Fractions" -- References -- 7 Collateral Creativity and Exploring Unsolved Problems -- 7.1 Exploring Palindromic Number Conjecture in the Middle Grades -- 7.2 The 196-Problem as a Possible Counterexample to Palindromic Number Conjecture -- 7.3 Formulation of Collatz Conjecture and Its History -- 7.4 Introducing the Rule: Initial Steps in Conjecturing -- 7.5 Deepening Investigation: Some Possible Paths Using a Spreadsheet -- 7.6 Fibonacci Numbers Emerge -- 7.7 More on the Role of a Teacher in Supporting Problem Posing by Students -- References -- 8 Egyptian Fractions: From Pragmatic Uses of Technology to Epistemic Development and Collateral Creativity -- 8.1 Introduction -- 8.2 Brief History of Egyptian Fractions. 8.3 Egyptian Fractions as a Context for Conceptualizations of Fractional Arithmetic -- 8.4 The Greedy Algorithm and Some Practice in Proving Fractional Inequalities -- 8.5 Pizza as a Context for Introducing Egyptian Fractions -- 8.6 Semi-fair Division of Pizzas -- 8.7 The Joint Use of Wolfram Alpha and a Spreadsheet -- References -- Appendix -- Part 1: Answers to Challenging Questions Introduced in the Chapters of the Book -- Part 2 (for Chap. 8): Constructing Fraction Circles Using the Geometer's Sketchpad -- Part 3: Programming of Spreadsheets. |
| Record Nr. | UNINA-9910746956203321 |
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Abramovich Sergei
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| Cham, Switzerland : , : Springer Nature Switzerland AG, , [2023] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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