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.

Day 1 (9/18/13)

River Dell Regional High School

(7:30-12:00)

            During this first day of my internship at the River Dell Regional High School, I met Mr. Sincak and the other teachers within both the mathematics and science departments. After introductions with various teachers and procedural activities, Mr. Sincak provided me with an office within the school for me to work in throughout the day. He and I discussed possibilities with utilizing the program Geogebra within his classroom, and he asked me to construct a program file that would interactively diagnose which students required assistance throughout his Honors Geometry class. Specifically, my task was to construct a program that would create random line segments on a coordinate grid, provide spaces for students to submit answers based on questions regarding those segments, and create an indicator on the screen to reveal which students are doing well and which students are struggling.

            Throughout the day, I worked on learning the Geogebra program and its association with JavaScript. I found it difficult to connect my experience with mathematics with my basic knowledge of computer science and programming, but I enjoyed it tremendously. I realized that the range of tools available for teaching purposes was larger than I ever expected, as I soon discovered how useful this application would be for the average classroom. These tasks, as well as my conversations with Mr. Sincak, have begun to inspire me into a career choice that connects to both technology and education, with the underlying factor still being mathematics; and although I still need to improve on my programming abilities, they nonetheless improved significantly on this first day. In the end, I was partly successful in performing my tasks regarding GeoGebra, but I fully associated myself with the other faculty members here. In addition, I also helped create challenging problems for Mr. Sincak’s Honors Geometry course. Overall, I plan to learn more about JavaScript in order to produce more fruitful results in the future.

Fairleigh Dickinson University

(12:56-3:00)

            On this first official day of the internship at Fairleigh Dickinson University, I discussed with my mentor, Professor Mark Farag, about my tasks throughout the semester: auditing the course, organizing class notes, preparing solutions to assignments, and other works related to mathematics. I also met with Professor Alfredo Tan, the director of the engineering department at the university, who was friendly and generous enough to speak with me during his busy schedule, albeit briefly. In addition, Professor Farag allowed me to explore the various sections and departments of the school, encouraging me to also consider careers related to applied mathematics (such as regarding finances), instead of solely focusing on theoretical mathematics.

            The class, for a course called “Abstract Algebra,” was very small in population, as only five students excluding me had shown up. Professor Farag explained that this phenomenon was due to the fact that the course was among the highest level classes provided at the university. Nonetheless, such a small class helped me fit in and become adjusted to the environment. I felt like an actual university student throughout the day.

            After the course, Professor Farag provided me with space to work on my assignments regarding class notes and solutions. Although I had a somewhat extensive knowledge of the mathematical typing program LaTeX before I began the internship, it allowed me to master my skills in the program. Because I had to practice typing notes throughout the class, in the format required by LaTeX, I became fluent, to the point where I can type in LaTeX as fast as I can type regularly. I also learned a significant amount of abstract algebra, even though it has only been one class so far. I discovered how college life and studies would feel, and I plan to use these learned skills throughout both high school and beyond.