Generating functions: a topic for post-AP test study

Abstract

Many teachers of AP Calculus find themselves facing a dilemma at the end of the school year. The AP Exam, the event for which their students have spent the year preparing, is completed, but the school year is not. In our district, students typically have two more weeks of school after the AP Exam before graduation. I've spent several years searching for a meaningful and engaging Calculus topic for students to study during this time. For this paper, I developed a set of lessons that would introduce students to some of the power series concepts studied in a Calculus II course, to some discrete math concepts, and finally, to the topic of generating functions. The students in my Advanced Placement Calculus class completed these lessons in the time between the AP test and graduation. Their knowledge was assessed before the lessons began and after they finished their study of these topics. They were also given a survey to evaluate their interest in the topic and their self-assessed level of understanding. Based on the end of unit assessment, the surveys completed by the students, and my observation of the level of student engagement during the lessons, I felt this was a topic of study that held the interest of the students, would be adaptable to take more or less time depending on the schedule at the end of the year, and seemed to be a good introduction to some advanced math concepts. It is definitely a series of lessons that I would enjoy teaching again.