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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.
The Landscape of Discrete Mathematics in the School Curriculum
Discrete Mathematics Is Essential Mathematics in a 21st Century School Curriculum
The Absence of Discrete Mathematics in Primary and Secondary Education in the United States… and Why that Is Counterproductive
Discrete Mathematics in Lower School Grades? Situation and Possibilities in Italy
Discrete Mathematics and the Affective Dimension of Mathematical Learning and Engagement
Combinatorics and Combinatorial Reasoning
Combinatorial Reasoning to Solve Problems
Children’s Combinatorial Counting Strategies and their Relationship to Conventional Mathematical Counting Principles
Reinforcing Mathematical Concepts and Developing Mathematical Practices Through Combinatorial Activity
Complex Mathematics Education in the 21st Century: Improving Combinatorial Thinking Based on Tamás Varga’s Heritage and Recent Research Results
Recursion and Recursive Thinking
Discrete Dynamical Systems: A Pathway for Students to Become Enchanted with Mathematics
How Recursion Supports Algebraic Understanding
Networks and Graphs
Food Webs, Competition Graphs, and a 60-Year Old Unsolved Problem
Graph Theory in Primary, Middle, and High School
Fair Decision-Making and Game Theory Fairness
Mathematical Research in the Classroom via Combinatorial Games
Machines Designed to Play Nim Games (1940–1970): A Possible (Re)Use in the Modern French Mathematics Curriculum?
Logic and Proof
Mathematics and Logic: Their Relationship in the Teaching of Mathematics