Graph Coloring and Chromatic Numbers for Second Graders

Math professor and philosopher Joel David Hamkins gave a guest lesson to his daughter’s second grade class. How does someone dedicated to “the philosophy of the infinite” present a math lesson to a group of seven-year-olds? By coloring pages!

We began with vertex coloring, where one colors the vertices of a graph in such a way that adjacent vertices get different colors. We started with some easy examples, and then moved on to more complicated graphs, which they attacked.

The aim is to use the fewest number of colors, and the chromatic number of a graph is the smallest number of colors that suffice for a coloring. The girls colored the graphs, and indicated the number of colors they used, and we talked as a group in several instances about why one needed to use that many colors.

They went on to map coloring, in which odd shapes must be colored so that touching border have different colors, using the fewest possible colors. Then he wrapped it up with Eulerian paths and circuits. In these lessons the fun part comes first, and the concepts underlying them follow as they go.

The high point of the day occurred in the midst of our graph-coloring activity when one little girl came up to me and said, “I want to be a mathematician!” What a delight!

Read how the lessons went at Hamkins’ blog. Hamkins also provides a printable version of the booklet he gave each child. -via Digg

Young kids quite quickly pick up some of the basic aspects of things like graph theory, set theory, and even abstract algebra in the right contexts. I've seen multiple mathematicians speculate that teaching such topics more and at much younger ages could raise both kids interests in math and their long term prospects in pure math. The issue is that for 99% of people these math subjects have no direct practical use (still great mental exercises in multiple ways though), and some efforts to teach such subjects in the past did so at the expense of more practical arithmetic and applied math that people need in today's world. While I'm all for kids exploring topics for sake of interests or to help improve abstract thinking, the basics still need to be covered.

But with the way math is taught in most schools now, the closest most get to pure math is a proof-centric geometry course (which some like much more than a cookbook algebra course), and those that trying to go more heavily into math in university hit a wall with an abstract algebra course that weeds out a large number of people from math programs.

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