Date of Award
Mathematics and Statistics
This work is an attempt to accomplish two main objectives. First is to encourage secondary students to engage in the kinds of mathematical reasoning skills that will be necessary to them when they move to college math classes. My experience in college, along with that of many others is that "school math," with its obsession with calculations and memorization, is dreadfully insufficient in preparing students for the proof and reasoning-based classes they will face in high school. This is an attempt to integrate some of those reasoning skills into high school courses using graph theory as a vehicle.
The second objective is to give more students greater access to this kind of mathematical thinking. This is accomplished by using several alternative teaching methods and strategies that are designed to engage students in learning as well as providing enough variety to the students that they are able to remain interested in the mathematics they are doing. Graph theory is an excellent vehicle with which to do this principally because it is hardly used in schools today. The thought of being able to do math that none of their colleagues has done before is motivating to students. Furthermore it is empowering to those students who are traditionally portrayed as being "unable to do math." Putting these students on the cutting edge should have the result of giving these students a second chance to fall in love, or at least fall out of hate, with mathematics and have a higher chance of success in school and college. This same strategy will also have the same result of boosting the skills and performance of those students who are considered to be excellent students, further preparing them in new ways for their college courses.
In the end, it is my goal not only to show how graph theory can help teachers help their student succeed, but also to show them that teaching in this way is simple and something teachers can do without taking up too much of their precious time and patience. I believe that teachers will find that these resources will be valuable in boosting academic performance for more students and better preparing them for college.
Buhler, Michael, "Spock, Euler, and Madison: Graph Theory in the Classroom" (2013). Undergraduate Honors Capstone Projects. 143.
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Lawrence O. Cannon