目次

Part I: The Landscape of Discrete Mathematics in the School Curriculum Discrete Mathematics is Essential Mathematics in a 21st 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 ?c and Why that is Counterproductive Joseph G. Rosenstein Discrete Mathematics in Lower School Grades? Situation 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?fs Combinatorial Counting Strategies and their Relationship to Mathematical Counting Principles Karina Hoveler 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 Tamas Varga's Heritage and Recent Research Results Odon Vancso, Eliza Beregszaszi, Hana Burian, Gyorgy Emese, Eleonora Stettner, and Judit Szitanyi 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