Freshman STEM students' misconceptions in a basic limit theorem of [Formula: see text]

Hailu Nigus Weldeana; Desta Berhe Sbhatu; Gebreslassie Tesfay Berhe

doi:10.1016/j.heliyon.2023.e22359

Freshman STEM students' misconceptions in a basic limit theorem of $\lim_{x \to 0} (\sin x / x)$

Heliyon. 2023 Dec 1;9(12):e22359. doi: 10.1016/j.heliyon.2023.e22359. eCollection 2023 Dec.

Authors

Hailu Nigus Weldeana¹, Desta Berhe Sbhatu², Gebreslassie Tesfay Berhe¹

Affiliations

¹ Mekelle University, College of Natural and Computational Science, Department of Mathematics, P. O. Box: 231, Ethiopia.
² Mekelle University, Mekelle Institute of Technology, P. O. Box: 1632, Ethiopia.

Abstract

This study examined learning difficulties among three consecutive cohorts of freshmen engineering and technology students (n = 251; 17 females) in solving problems in the basic limit theorem. The students were enrolled in a four-credit hour calculus course delivered in 16 weeks. Then, they completed a 1-h six-item test after they covered the topics of the basic limit theorem. Answer papers were scored using an explicit guide. Interviews were also conducted after the test with 15 randomly selected students without and with cognitive supports (cues) in topics related to the test. The study demonstrated that the students have difficulties understanding the surface structure of the problems, identifying the mathematical heuristics to solve the problems, and solving the problems by properly employing procedures, rules, and conventions. Examination of students' test results showed that for every student earning a correct answer via valid problem-processing pathways, there were about two students earning two correct answers via invalid pathways. Interview results showed the students were incapable of fixing their limitations without cognitive support and cues. They needed an average of 7.7-9.3 question-response dialogues to fix their limitations. Such learning difficulties were due to lack and misapplication of solid prior knowledge. Identifying and compiling lessons that cause learning difficulties due to misapplication of prior knowledge can help to adopt better instructional approaches. Cognitive supports and cues can be used as research tools to extract the reasons and sources of students' learning difficulties and devise innovative instructional methods for better learning.

Keywords: Basic limit theorem; Cognitive support; Misconception; Problem processing pathway.