Exploring Non-Mathematics Students’ Reasoning in Solving Function Continuity Problems in Calculus Courses

Sri Suryanti; Clinton Chidibere Anyanmwu

doi:10.31764/jtam.v10i2.36864

Exploring Non-Mathematics Students’ Reasoning in Solving Function Continuity Problems in Calculus Courses

Sri Suryanti, Clinton Chidibere Anyanmwu

Abstract

Understanding the concept of function continuity is one of the main conceptual challenges for non-mathematics students in learning calculus, as they tend to rely on algorithmic procedures rather than reasoning conceptually. This study aims to explore and compare the types of mathematical reasoning used by non-mathematics students in solving function continuity problems in basic calculus courses, using Lithner's reasoning framework. Using qualitative descriptive, this study compares two first-year calculus classes from two non-mathematics study programs using Lithner's framework. The research instruments comprised three written assignments on function continuity, developed according to the categories of Imitative Reasoning (IR) and Creative Reasoning (CR), in addition to task-based interviews (think-aloud) conducted to investigate students' cognitive processes. Data were analyzed by categorizing mathematical reasoning into Memorized Reasoning (MR), Algorithmic Reasoning (AR), Local Creative Reasoning (LCR), and Global Creative Reasoning (GCR), accompanied by an inter-rater reliability assessment. The results indicate differences in reasoning patterns between engineering and general education students, especially regarding their propensity to employ imitative reasoning (IR) or creative reasoning (CR) when confronted with continuity-of-function problems. These results offer a significant critique of the utilization of Lithner's framework in the analysis of calculus tasks especially the continuity of functions and propose minor adjustments to enhance the categorization of reasoning, making it more suitable for non-mathematics students.

Keywords

Mathematical reasoning; Non-mathematics students; Continuity of functions; Lithner framework; Calculus.

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DOI: https://doi.org/10.31764/jtam.v10i2.36864