Math for Kids

Upon the request of a friend, I started this collection of "abstract maths" texts for K-12 students

All indented text represents quotes. None of this is my original work, but some quoted text was written in first person.

Elementary School

Joel David Hamkins: Math for Kids [Blog]

Academic Bio:

My main research interest lies in mathematical and philosophical logic, particularly set theory, with a focus on the mathematics and philosophy of the infinite. I have worked particularly with forcing and large cardinals, those strong axioms of infinity, and have investigated the interaction of these two central set-theoretic concepts. I have worked in the theory of infinitary computability, introducing (with A. Lewis and J. Kidder) the theory of infinite time Turing machines, as well as in the theory of infinitary utilitarianism and, more recently, infinite chess. My work on the automorphism tower problem lies at the intersection of group theory and set theory. Recently, I am preoccupied with various mathematical and philosophical issues surrounding the set-theoretic multiverse, engaging with the emerging debate on pluralism in the philosophy of set theory, as well as the mathematical questions to which they lead, such as my work on the modal logic of forcing and set-theoretic geology.

Discovering Category Theory with primary school children

A few years ago I ran a maths circle for primary school children experimenting with teaching category theory. The meetings were documented in a series of blog posts which were recently published as a series of articles by Mathematics Teaching, the journal of the Association of Teachers of Mathematics (issues 264-268).

Middle School

Graph Theory for the Middle School

Laura Ann Robinson, MSc Thesis, ‘06

After being introduced to graph theory and realizing how it can be utilized to solve real-world problems, the author decided to create modules of study on graph theory appropriate for middle school students. In this thesis, four modules were developed in the area of graph theory: an Introduction to Terms and Definitions, Graph Families, Graph Operations, and Graph Coloring. It is written as a guide for middle school teachers to prepare teaching units on graph theory.

High School

For the Teacher

Teaching and Learning Discrete Mathematics Worldwide: Curriculum and Research

The summary is not helpful, so I’ve included the book index below:

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