Misconceptions of mathematical concepts vis-à-vis how they pose as barriers to developing students’ conceptual understanding

Abstract

This paper is a report of a qualitative case study conducted in South Africa that sought to identify students’ misconceptions and how those misconceptions hinder students’ conceptual understanding of mathematical concepts, with a focus on algebraic expressions. The Structure of the Observed Learning Outcomes (SOLO) theory was adopted as the theoretical framework. The media for data collection were: classroom observations, activities, unstructured interviews and standardized tests. Participants were required to explain their solutions to the standardized test via unstructured interviews. This guided the researchers to identify students’ misconceptions and how they hindered their conceptual understanding of mathematical concepts. Content analysis was carried out on participants’ written and oral responses by applying the SOLO theory. From this study, the researchers established that conceptual misunderstandings are the main students’ misconception in algebraic expressions. This misconception serves as barriers to students developing conceptual understanding as it does not invoke students’ rational reasoning.

Investigating lower secondary school students’ geometric argumentation structure using Toulmin model

“…Errors in using concepts can also occur if students incorrectly recognize a problem, resulting in inappropriate application of rules, this can also be called a misconception (Al-Mutawah et al, 2019;Mishra, 2020). Research conducted by Abakah and Brijlall (2024) states that misunderstandings in mathematical concepts are more dominant, due to students' inability to remember and understand mathematical concepts. This often happens in the warrant section, students are wrong in using formulas and theories that are not by the prerequisite conditions of the problem (Andriani et al, 2017).…”