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Teaching and Learning Discrete Mathematics Worldwide: Curriculum and Research

  • Book
  • © 2018

Overview

Editors:
  1. Eric W. Hart

    1. Mathematics Department, Grand View University, Des Moines, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. James Sandefur

    1. Department of Mathematics and Statistics, Georgetown University, Washington, USA

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    You can also search for this editor in PubMed   Google Scholar

  • Presents extended papers from the Topic Study Group on Discrete Mathematics at the 13th International Congress on Mathematical Education (ICME-13), which was held in Hamburg, Germany from July 24 to 31, 2016
  • Includes practical examples from the classroom
  • Puts forward suggestions for future research
  • Provides an overview of discrete mathematics from an international perspective

Part of the book series: ICME-13 Monographs (ICME13Mo)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xii
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  3. Combinatorics and Combinatorial Reasoning

    1. Front Matter

      Pages 67-67
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    2. Combinatorial Reasoning to Solve Problems

      • Tom Coenen, Frits Hof, Nellie Verhoef
      Pages 69-79

    3. Children’s Combinatorial Counting Strategies and their Relationship to Conventional Mathematical Counting Principles

      • Karina Höveler
      Pages 81-92

    4. Reinforcing Mathematical Concepts and Developing Mathematical Practices Through Combinatorial Activity

      • Elise Lockwood, Zackery Reed
      Pages 93-110

    5. Complex Mathematics Education in the 21st Century: Improving Combinatorial Thinking Based on Tamás Varga’s Heritage and Recent Research Results

      • Ödön Vancsó, Eliza Beregszászi, Hana Burian, György Emese, Eleonóra Stettner, Judit Szitányi
      Pages 111-134

  4. Recursion and Recursive Thinking

    1. Front Matter

      Pages 135-135
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    2. Discrete Dynamical Systems: A Pathway for Students to Become Enchanted with Mathematics

      • Robert L. Devaney
      Pages 137-144

    3. How Recursion Supports Algebraic Understanding

      • James Sandefur, Kay Somers, Rosalie Dance
      Pages 145-162

  5. Networks and Graphs

    1. Front Matter

      Pages 163-163
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    2. Food Webs, Competition Graphs, and a 60-Year Old Unsolved Problem

      • Margaret (Midge) Cozzens, Pratik Koirala
      Pages 165-181

    3. Graph Theory in Primary, Middle, and High School

      • Daniela Ferrarello, Maria Flavia Mammana
      Pages 183-200

  6. Fair Decision-Making and Game Theory

    1. Front Matter

      Pages 201-201
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    2. Fairness

      • Sol Garfunkel
      Pages 203-213

    3. Mathematical Research in the Classroom via Combinatorial Games

      • Ximena Colipan
      Pages 215-227
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Keywords

About this book

This book discusses examples of discrete mathematics in school curricula, including in the areas of graph theory, recursion and discrete dynamical systems, combinatorics, logic, game theory, and the mathematics of fairness. In addition, it describes current discrete mathematics curriculum initiatives in several countries, and presents ongoing research, especially in the areas of combinatorial reasoning and the affective dimension of learning discrete mathematics. 

Discrete mathematics is the math of our time.' So declared the immediate past president of the National Council of Teachers of Mathematics, John Dossey, in 1991. Nearly 30 years later that statement is still true, although the news has not yet fully reached school mathematics curricula. Nevertheless, much valuable work has been done, and continues to be done. This volume reports on some of that work. It provides a glimpse of the state of the art in learning and teaching discrete mathematics around the world, and it makes the case once again that discrete mathematics is indeed mathematics for our time, even more so today in our digital age, and it should be included in the core curricula of all countries for all students.

 

Editors and Affiliations

  • Mathematics Department, Grand View University, Des Moines, USA

    Eric W. Hart

  • Department of Mathematics and Statistics, Georgetown University, Washington, USA

    James Sandefur

Bibliographic Information

  • Book Title: Teaching and Learning Discrete Mathematics Worldwide: Curriculum and Research

  • Editors: Eric W. Hart, James Sandefur

  • Series Title: ICME-13 Monographs

  • DOI: https://doi.org/10.1007/978-3-319-70308-4

  • Publisher: Springer Cham

  • eBook Packages: Education, Education (R0)

  • Copyright Information: Springer International Publishing AG 2018

  • Hardcover ISBN: 978-3-319-70307-7Published: 18 January 2018

  • Softcover ISBN: 978-3-319-88921-4Published: 06 June 2019

  • eBook ISBN: 978-3-319-70308-4Published: 09 December 2017

  • Series ISSN: 2520-8322

  • Series E-ISSN: 2520-8330

  • Edition Number: 1

  • Number of Pages: XII, 276

  • Number of Illustrations: 84 b/w illustrations

  • Topics: Mathematics Education, Learning & Instruction, Teaching and Teacher Education, Curriculum Studies, Discrete Mathematics

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