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.