Citlalli Villegas and Dr. Ivona Grzegorczyk
Abstract
Many undergraduates have difficulty with the principle of mathematical induction (PMI). This project seeks to understand the common struggles associated with this topic and how it relates to students’ overall performance in their course. Additionally, it explores how educators can transform their standard approach to teaching mathematical induction in a way that builds on students’ prior knowledge to create a strong foundation for this type of proof writing. This project gathered data from 80 students, a majority of whom were freshmen. We analyze their response to a midterm question on mathematical induction requiring knowledge of series. We also gathered data from a group of 20 seniors to analyze their performance on a similar induction question and compare their results to the freshmen. Our data explored several correlations between student understanding of checking for small numbers, formulating k + 1 correctly, identifying the induction hypothesis, performing the induction step and arriving at correct conclusions.
Excellent presentation and good explanations. Good data presentation.
From personal experience, this is a very crucial topic that needed much attention. It was interesting to learn that the correlation coefficient was insignificant between a student’s understanding of checking for small numbers and them performing the induction steps correctly. Furthermore, from personal experience, I do agree that formulating k+1 steps correctly greatly increases the chances of performing the induction step correctly. Great presentation!