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Emmanuel Olawale  \nUniversity of Waikato [bolawale@waikato.ac.nz](bolawale@waikato.ac.nz)  \nSaidat Adeniji  \nUniversity of Southern Queensland [Saidat.Adeniji@unisq.edu.au](Saidat.Adeniji@unisq.edu.au)  \nZizipho Mabhoza  \nUniversity of Fort Hare  \n[ziziphomabhoza@gmail.com](ziziphomabhoza@gmail.com)  \nThis paper analyses learners’ common errors in simplifying algebraic problems. 102 Grade 10 learners from three rural schools in South Africa participated in the study.  \nFollowing a quantitative approach, content analysis of learners’ responses to algebraic tests revealed that while learners commit several errors in algebraic problems, encoding and transformation errors were the most prominent. These errors are mainly due to the inability to utilise correct methods, misapplication and overlooking algebraic rules, and failure to provide final answers to problems. The study highlights the need for remedial intervention, which has implications for improving mathematics teaching and learning.  \nAlgebra is a discipline characterised by its abstract nature and governed by a set of rules, principles, and theories. However, errors and misconceptions arise when these rules, principles, and theories are disregarded or improperly implemented. In the South Africa’s Further Education and Training phase (Grade 10 - 12), solving algebraic expressions and equations typically requires the understanding and integration of various mathematical concepts, including equations, factorisation, division, and exponents (Baidoo, 2019) . As such, it is important to recognise that understanding algebra is beneficial for simplifying and solving mathematical problems in various subjects, including functions, calculus, trigonometry, financial mathematics, and others (Luneta & Makonye, 2010) . This is because proficiency in algebra is essential for achieving success in higher-level mathematics.  \nNotwithstanding the South Africa National Diagnostic Report (2022) stating that algebra and equations make up 30% of the curricula for Grade 10, 25% for Grade 11, and 17% for Grade 12, learners exhibit deficiency in solving algebra. In fact, Grade 10-12 learners sometimes struggle to demonstrate fundamental and elementary algebraic skills that should have been gained in the early years of education, resulting in difficulties responding to algebraic problems (National Diagnostic Report, 2022) . Similarly, researchers across several countries have reported that learners have challenges in comprehending the simplification of algebraic problems (Adeniji & Baker, 2023; Luneta & Makonye, 2010) . This could be due to the requirement of performing multiple mathematical algorithms concurrently and utilising additional concepts such as exponents, factorisation, and division. The inability to remember algebraic rules or the inappropriate application of the rules forms the basis for encountering difficulties in solving algebraic problems, leading to several errors or misconceptions (Luneta & Makonye, 2010; Mamba, 2012; Pournara et al., 2016). The present study examines the causes of learners’ errors in algebra and the possible solutions to avoid them. Specifically, this paper answers the following research question: Which errors are the most prevalent when solving algebraic expressions among Grade 10 learners?  \nLiterature Review  \nThe role mathematics plays in our everyday lives and in understanding other subjects of the curriculum cannot be overemphasised (Ndemo & Ndemo, 2018) . Algebra is the bedrock of advanced mathematics, and it is related to all branches of mathematics (Department of Education, 2011; Moru & Mathunya, 2011) . Agustyaningrum et al. (2018) stated that algebra  \nconsists of axiomatic theories that provide opportunities to consider various mathematical systems, whether special cases or not. In addition, Adeniji and Baker (2023) stated that solving algebraic equation","cbCaih7cFTPRl9jx","https://ap.wps.com/l/cbCaih7cFTPRl9jx","pdf",483175,"English","# Introduction\n## Background and importance of algebra\n## Problem statement and research question\n# Literature Review\n## Algebra and learners’ performance\n## Newman’s Error Analysis (NEA) and error types\n## Systematic errors\n## Transformation errors","[{\"question\":\"What is the focus of the study?\",\"answer\":\"The study focuses on identifying common errors Grade 10 learners make when simplifying algebraic problems, especially during algebraic expressions tasks.\"},{\"question\":\"Which error types are most prominent in learners’ responses?\",\"answer\":\"Encoding and transformation errors are the most prominent error categories revealed through content analysis of learners’ algebra test responses.\"},{\"question\":\"Why do learners make these errors according to the paper?\",\"answer\":\"Errors are mainly linked to inability to apply correct methods, misapplication or overlooking algebraic rules, and failing to provide final answers, reflecting difficulties with algebraic procedures and rules.\"}]","Analysis of Common Errors in Simplifying Algebraic Problems among Grade 10 Learners | PDF"]