When considering the study of graphs, many of us in education would first think of bar graphs, line graphs, or pie graphs to chart and compare a set of data. Few would consider the discrete mathematics concept of graph theory as an area of study for elementary students. Although this concept may be fundamentally too complex for a majority of students, using it to study a portion of discrete mathematics can be very powerful for gifted students.
Graph theory is the study of graphs representing a set of dots connected by lines or arcs. It is beneficial for students to learn how to construct and interpret these graphs as they have a strong correlation between discrete mathematics and the real world. Graph theory has proven to be crucial for solving problems in urban planning, choosing the most efficient flight path routes for airplanes, computer network design, and molecular biology. Showing gifted students the connection between discrete mathematics and other areas of study is powerful as it encourages them to connect their learning to real world applications.
Adventurous teachers who wish to begin the study of graph theory with gifted students have multiple options when planning instruction:
- Instead of beginning by introducing students to the fundamental theory or a set of defined vocabulary words, teachers have found it valuable to start with fun math challenges. The students often don't even realize they are solving a mathematical problem! One activity teachers can start with is giving the students a set of five points that are connected to form a five point star. Teachers ask the students if they can draw the star without lifting the pencil or repeating the same line twice. Then, using the same set of points, students can be challenged to connect the shape using the shortest route possible. This challenge can be repeated multiple times with a variety of shapes representing certain sets of points and lines.
- Teachers can also extend the learning begun in the simple math challenges by introducing more complicated problem-solving opportunities centered on graph theory. Each of these problem-solving opportunities focus on a story related to a real world application. Students are challenged to thoroughly investigate and study the scenario in order to solve the problem. Although the options for developing these problems are endless, there are multiple stories, games, and puzzles available on the Internet to get teachers started. Two sites in particular to visit are "More Games on Graphs" and "Graph Theory Activities".
- This YouTube video, Graph Theory - Child's Puzzle, does a great job of explaining graph theory in relation to a classic child's puzzle.
- As students become more comfortable with the concepts and problem-solving opportunities, teachers may begin introducing parts of the larger graph theory. The challenge for teachers is how to make the higher level discrete mathematics concepts relatable for children. This website does an excellent job of defining the core concepts of graph theory in a way that is accessible for children. It also contains multiple links to other sites that teachers will find helpful for exploring the graph theory concept with children.
- Additionally, there are books that have been published that present graph theory problems for children. One such book, More Math Games & Activities, is a book designed for children that is full of math games from around the world. There is an entire section devoted to games related to graph theory. Helping Children with Mathematics, a text written for teachers or parents, has a section on geometry and measurement that relates to the concepts of graph theory.
The bottom line is, have fun with the concept and your gifted students will appreciate an early introduction to discrete mathematics.