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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.

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Part I: The Landscape of Discrete Mathematics in the School Curriculum
Discrete Mathematics is Essential Mathematics in a 21 st Century School Curriculum (and introduction to this volume)

Eric W. Hart and W. Gary Martin

The Absence of Discrete Mathematics from Primary and Secondary Education in the United States ... and Why that is Counterproductive

Joseph G. Rosenstein

Discrete Mathematics in Lower School Grades? S ituation and Possibilities in Italy

Aaron Gaio and Benedetto Di Paola

Discrete Mathematics and the Affective Dimension of Mathematical Learning and Engagement

Gerald A. Goldin

Part II: Combinatorics and Combinatorial Reasoning

Combinatorial Reasoning to Solve Problems

Tom Coenen, Frits Hof, and Nellie Verhoef

Children´s Combinatorial Counting Strategies and their Relationship to Mathematical Counting Principles

Karina Höveler

Reinforcing Mathematical Concepts and Developing Mathematical Practices through Combinatorial Activity
Elise Lockwood and Zack Reed

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, and Judit Szitányi

Part III: Recursion and Recursive Thinking

Discrete Dynamical Systems: A Pathway for Students to Become Enchanted with Mathematics

Robert L. Devaney

How Recursion Supports Algebraic Understanding

James Sandefur, Kay Somers, and Rosalie Dance

Part IV: Networks and Graphs

Food Webs, Competition Graphs, and a 60-year-old Unsolved Problem

Margaret (Midge) Cozzens and Pratik Koirala

Graph Theory in Primary, Middle and High School

Daniela Ferrarello and Maria Flavia Mammana

Part V: Fair Decision-Making and Game Theory

Fairness

Sol Garfunkel

Mathematical Research in the Classroom via Combinatorial Games

Ximena Colipan

Machines designed to play Nim games (1940-1970): A possible (re)use in the modern French mathematics curriculum?Lisa Rougetet

Part VI: Logic and Proof

Mathematics and Logic: Their Relationship in the Teaching of Mathematics

Vladimir I. Igoshin

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