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"