From Counting to Computing: Ideas for Mathematics Education in Information Age

by Sergei Abramovich

Overview

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.

Product Details

ISBN-13:	9781837089017
Publisher:	Emerald Publishing Limited
Publication date:	11/03/2025
Pages:	200
Product dimensions:	6.14(w) x 9.21(h) x 0.42(d)

About the Author

Sergei Abramovich (PhD, Mathematics) has over 30 years of experience teaching more than 4,000 prospective K-12 mathematics teachers and has published 13 books and around 250 journal articles, book chapters, and conference proceedings on mathematics education and mathematics.

Table of Contents

Chapter 1. From Concepts to Conceptual Shortcuts to the Use of Technology
Chapter 2. Exploring the Addition and the Multiplication Tables
Chapter 3. Exploring Equilateral Triangles Filled with Integers
Chapter 4. Exploring Isosceles Triangles Filled with Integers
Chapter 5. Exploring Squares Filled with Integers
Chapter 6. Pascal’s Triangle as a Bridge from Combinatorics to Probability
Chapter 7. From Pascal’s Triangle to Fibonacci-Like Polynomials
Chapter 8. Problems Motivated by Digital Computing