Analysis of Types, Sources of Errors and Misconceptions in South African Algebra Cognition

Abstract

Due to the persistent nature of errors and misconceptions, through SOLO model, the current research was aimed at examining the types and the sources of errors and misconceptions committed by Grade 9 learners in Algebra cognition. Thus, in the current research, the model was applied to assess learners' learning outcomes and to classify the value of the response. Through a survey, the sample size for this study was 100 Grade 9 learners in KwaZulu-Natal province of South Africa. In response to the aim of the research, the themes comprised, algebraic fractions, graphs, expressions and equations, words problems. The results revealed that possible sources were lack of conceptual and procedural knowledge, a lack of factual knowledge, lack of connection between new knowledge and old knowledge, lack of interpretation, errors caused by translation. The major conclusion because of the SOLO theory revealed the level of thinking, indicating both one-structure and many-structures only in equations and expressions involving translation of equation to table and table to the graph. The practical implication is positioned on the need to improve understanding the sources of errors, classified as a lack of conceptual and procedural knowledge; lack of factual knowledge; lack of connection between new knowledge and old knowledge, lack of interpretation, inattentiveness and failure to read and understand; errors caused by translation. The theory applied revealed the need to emphasize other level of thinking as well as sources of errors.

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

“…This is because the SOLO model assisted us to monitor participants' cognitive development and levels of response. Thus, we were able to assess participants' levels of thinking with reference to the thinking structures of the SOLO model based on their levels of response [20]. According to [10] "the abstract structure of algebraic expressions poses many problems to students such as understanding or manipulating them according to accepted rules, procedures or algorithms".…”

Mitigating errors and misconceptions among Grade 11 learners in algebra through error analysis

“…The SOLO model developed by Briggs and Collis provides five hierarchical thinking levels. According to Mathaba and Bayaga (2021), the SOLO model is characterised by five structural levels:…”

“…The MS level corresponds to Newman's (1977) level 3 at which learners should transform ideas into mathematical operations. • Relational structure level (R): Mathaba and Bayaga (2021) describe this level as one that reveals much thought meaning a correct answer would have been produced. • Extra-extended level of the learning outcome (E): The same authors describe this level as one that represents exceptional responses.…”

“…The argument is that introducing erroneous worked examples in the learning process can force learners to reflect on what they know and then generate clearer and more complete explanations for their solutions (Rushton 2018). In addition, incorrect knowledge induces cognitive conflicts which when resolved culminate in coherent knowledge pieces (Mathaba & Bayaga 2021). Hence, this study seeks to establish the extent to which common errors and misconceptions among learners in algebra can be mitigated by increasing students' awareness of those misconceptions through learner-conducted error analysis.…”

Learners’ Misconceptions and Errors when Solving Inequalities

“…A number of studies have been conducted on learners' errors and misconceptions in the various branches of algebra (Almog & Ilany, 2012;Mathaba & Bayaga, 2019). Comparatively, few studies address the issue of learners' misconceptions in inequalities.…”