Misconceptions among Undergraduate Students in Determining Sequence Limits

Panyawat Haarsa

doi:10.33830/hexagon.v4i1.10108.

Panyawat Haarsa
Department of mathematics, Srinakharinwirot University, Bangkok

Keywords: misconceptions, sequence limits, calculus education, undergraduate students, error analysis

Abstract

Misconceptions related to limits remain a significant challenge in undergraduate calculus learning and may hinder students’ understanding of advanced mathematical concepts. Although misconceptions in calculus have been widely studied, research focusing specifically on sequence limits among science undergraduates remains limited. This study aimed to identify and classify students’ misconceptions when determining sequence limits. A qualitative document analysis approach was employed involving 126 undergraduate science students enrolled in a Calculus course at Srinakharinwirot University, Thailand. Data was collected from students’ written responses to a midterm examination question and analyzed using content analysis guided by an error analysis framework. The findings revealed five major categories of misconceptions: misapplication of limit theorems, improper algebraic cancellation, incorrect use of dominant-term strategies, symbolic transcription errors, and inappropriate application of the Ratio Test. These misconceptions reflect deeper conceptual difficulties related to convergence, infinity, algebraic structure, and the distinction between sequences and series. Interpreted through the Concept Image and Concept Definition framework, the findings suggest that conflicts between intuitive reasoning and formal mathematical definitions contribute to students’ errors. The study highlights the importance of strengthening conceptual understanding alongside procedural competence in calculus instruction and provides implications for addressing misconceptions in learning sequence limits

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