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
• Pubblicazione: Cham, Switzerland : , : Springer Nature Switzerland AG, , [2023]; ©2023
• Edizione: First edition.
• Descrizione fisica: 1 online resource (141 pages)
• Disciplina: 510.71071
• Soggetto topico: Creative teaching; Mathematics - Study and teaching - Canada; Mathematics - Study and teaching - United States
• Persona (resp. second.): FreimanViktor
• Nota di bibliografia: Includes bibliographical references.
• 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.
• Titolo autorizzato: Fostering Collateral Creativity in School Mathematics
• ISBN: 3-031-40639-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910746956203321
• Lo trovi qui: Univ. Federico II
• Serie: Mathematics education in the digital era ; ; Volume 23.