Day 2 (9/25/13)

River Dell Regional High School

(7:30-12:00)

            Today, Mr. Sincak and I began to plan out the curriculum and lesson plans for his chapter on Boolean logic. We first devised several mathematical examples of statements involving Boolean functions such as “and,” “or,” or “not,” which we also related to previously learned topics such as basic algebra and geometry. We also devised a project for the students that involve constructing circuits with dominoes based on the various forms of logical statements—both simple and compound. And throughout the process, Mr. Sincak taught me various techniques within the realm of teaching that would be useful for engaging students who are struggling and “entertain” (as Mr. Sincak describes) those who are excelling at the topic. Such methodologies included demonstrations of reversals of two-column proofs and the inclusion of engaging technological tools such as Geogebra. Furthermore, I began to realize more and more how intricate and enjoyably complex each lesson plan for highs school students could be, as I learned numerous strategies and potential methods that could be applied for teaching (not only for high school students, but for students in general).

            After constructing the curriculum, lesson plans, and projects for students for the unit, I continued to work on the Geogebra program that would reveal which students are excelling and which students are not as proficient. For today’s specific program, I constructed a Java-based program through Geogebra that would create random lines and ask students to input the segment’s distance. Each correct answer would make the background of the screen greener, thus helping in revealing which students retained a solid understanding of the topic. Mr. Sincak could see all of the students’ screens through a screen-sharing program, and he was able to assign helpers for struggling students efficiently. My mini-project for the day had been completed successfully, as I became more fluent in the languages of Java and Geogebra scripts.

            Hence overall, not only did I enhance my abilities to program basic applications for classroom settings, but I also learned various techniques and methodologies for teaching more efficiently and entertainingly. The domino demonstration especially struck out to me, as I never imagined that certain objects such as the little toys could ever be used for teaching mathematics. I have attained a more open, creative, and enlightened mindset for teaching, and I hope to utilize these skills as much as possible throughout my life and future careers.

Fairleigh Dickinson University

(1:00-3:00)

            During today’s lecture, Professor Farag shifted from teaching about groups to explaining the properties of their subgroups. We discussed and solved various selected problems from the textbook, and learned various theorems regarding cyclic subgroups, among others. Although I had missed the two previous classes (as the class runs on Mondays, Wednesdays, and Fridays), I was still able to follow the lecture comfortably, while typing notes.

            After the course, I moved to my regular, weekly responsibilities of typing and organizing class notes and solutions to homework problems. With my proficient skills in typing mathematical texts using the program LaTeX, I was able to type all of today’s class notes during the class itself. I then quickly typed up notes from the classes that I had missed throughout the past week, which were provided to me by a fellow student in the class, who attends Fairleigh Dickinson University and is also a staff member in BCA’s Math Team program. Afterwards, because the assigned homework problems were basic and elementary, I was able to type up the solutions as I solved them in my head simultaneously. While I perfected my knowledge in elementary Group Theory, I also discovered even more implications, extending to Number Theory and other branches of mathematics. In addition, I realized that I needed to study more about other forms of abstract mathematical structures to attain an even bigger grasp of abstract mathematics.