From Counting to Computing
eBook - ePub

From Counting to Computing

Ideas for Mathematics Education in Information Age

  1. English
  2. ePUB (mobile friendly)
  3. Available on iOS & Android
eBook - ePub

From Counting to Computing

Ideas for Mathematics Education in Information Age

About this book

From Counting to Computing demonstrates the powerful integration of formal mathematical reasoning, hands-on educational experiments, and digital computation to solve problems. It focuses on numeric tables shaped as squares, equilateral and isosceles triangles, offering ample opportunities for algebraic generalization in the digital age. Activities are grounded in addition and multiplication tables, polygonal numbers, and Pascal's triangle. Based on the idea that counting objects arranged in geometric shapes leads to the development of numeric patterns, this book extends this concept to digital computing. Using technology-immune/technology-enabled didactical framework, it blends formal reasoning with digital computation in problem solving and provides a conceptual shortcut to achieving mathematically significant computational outcomes.

From Counting to Computing covers classic topics from arithmetic, number theory, combinatorics, and probability theory. Many historical and cultural origins of mathematical concepts are highlighted, featuring figures like Pythagoras, Aristotle, Heron of Alexandria, Theon, Fibonacci, Gersonides, Pacioli, Cardano, Galilei, Kepler, Descartes, Fermat, Pascal, Spinoza, Leibniz, Jacob Bernoulli, Binet, de Moivre, Lamé, and Lucas.

The final chapter includes problems on the proof of divisibility of integer variable polynomials, motivated by digital computations. Ideal for mathematics teacher education programs and discrete mathematics courses, this book showcases the use of simple algorithms and tools like spreadsheets, Wolfram Alpha, Maple, and Graphing Calculator to achieve sophisticated computational results.

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Yes, you can access From Counting to Computing by Sergei Abramovich in PDF and/or ePUB format, as well as other popular books in Education & Education Administration. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. Contents
  5. About the Author
  6. Preface
  7. Acknowledgments
  8. 1. From Concepts to Conceptual Shortcuts to the Use of Technology
  9. 2. Exploring the Addition and the Multiplication Tables
  10. 3. Exploring Equilateral Triangles Filled With Integers
  11. 4. Exploring Isosceles Triangles Filled With Integers
  12. 5. Exploring Squares Filled With Integers
  13. 6. Pascal’s Triangle as a Bridge From Combinatorics to Probability
  14. 7. From Pascal’s Triangle to Fibonacci-Like Polynomials
  15. 8. Problems Motivated by Digital Computing
  16. References