Serpinksi’s Triangle
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In the IB Diploma Program (DP) students are tasked with writing their Extended Essay (EE) which is a 4000-word research paper where DP candidates construct arguments and conclusions based on their research. Although it is a lengthy and stressful process, it teaches students how to organize their thoughts to get ready for college-level writing and in-depth research skills. Historically speaking, at Lincoln Community School (LCS), writing an EE in Mathematics has not been so much of a hot topic for a variety of reasons, be it general interest, preconceptions, and sometimes fear (4000-words of mathematics does sound intimidating). As a member of the LCS Mathematics Department, I set a goal a few years ago to change this culture and I can say that after three years, many of the misconceptions about mathematical writing are being faced, challenged, and changed.
There are three grade 12 students currently finishing their EE in mathematics. These students do not fit the traditional mathematical student profile. They have a passion for mathematics, specifically for problem solving, and that is derived from their hard work and dedication to the subject, not some magical innate ability. Their research questions are about the volume and surface area of a spherical-corked napkin ring, making conjectures to Trinomial Theorem through Binomial Theorem, and investigating area and perimeter for Serpinksi’s Triangle as the number of iterations approaches infinity. Even though these topics have limited application, each of these students have said, more or less, “It is just a fun problem to think about and solve.” They have all told me that writing their Mathematics Extended Essay has been either one of the favorite parts if not THE favorite part of the DP. To me, this is one of the best comments a student can make.
As I reflect on LCS’s Learning Principles and the processes these students have gone through, I have been given the opportunity to witness student-driven inquiry, concept-based learning, and an awareness of socio-emotional wellbeing. These students have linked their findings to something that has been taught in class. Even while in class, I am finding these three students offering shameless plugs for their EE because the excitement they have for their individual inquiry is the driving force behind the research. When working with these students, I get to witness them develop empathy as they attempt to explain to others and me their thinking in a way that is connected to the listeners’ previous experiences. And, when given the opportunity, listening to students using metaphors and similes to compare the major concepts of their problems is fascinating. I consider myself fortunate to observe the Learning Principles intertwined into the learning process through independent college-level mathematical research papers from 16, 17, and 18-year-old students.
It is very satisfying that I get to work in an environment and a culture where students promoting their mathematical thinking is encouraged and welcomed. The culture of mathematical writing and the EE has changed drastically in my three years of teaching at LCS. I have chosen to share this experience with the greater community because working in a school where this culture exists has not been the norm in other
international schools where I have worked. I would like to thank the students for their hard work and congratulate them on the pleasure they find in the art of problem solving as well as the artistic nature of mathematics in the International Baccalaureate Organization.
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William Pamperin is a math teacher and enthusiast at the Lincoln Community School in Ghana.
