Visualizing Convergence or Divergence: Exploring Applied Mathematics Students’ Understanding of Infinite Series Using Direct Comparison Test


Infinite series is one of the topics that most undergraduate students find difficult to understand. Due to its abstract nature, students have difficulty visualizing and manipulating them. As part of an ongoing dissertation project, the current research focuses on students’ understanding of the convergence or divergence of infinite series using direct comparison test (DCT). Specifically, it aims to investigate how students utilize their prior constructs to build a new mathematical construct about the concept of convergence or divergence using DCT. The study employs a qualitative research methodology, where three Applied Mathematics students were separately interviewed and asked to verbally express their thought processes as they solve the task. Preliminary results showed that students who possess the ability to visualize graphs tend to grasp the idea more efficiently compared to those who cannot visualize. Moreover, those students who had the ability to visualize the graphs of the functions found it easier to handle algebraic manipulations of comparing infinite series and demonstrated deeper understanding of the concept. This paper can provide insights into the role of visual representations and algebraic manipulations in the students’ understanding of the convergence or divergence of infinite series.

Author Information
Guinever Vera, Ateneo De Manila University, Philippines
Catherine Vistro-Yu, Ateneo De Manila University, Philippines

Paper Information
Conference: ERI2023
Stream: STEAM (Science Technology Engineering Arts & Math) Education

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Posted by James Alexander Gordon