Volume 3 - Number 3 - Learner Errors and Misconceptions in Elementary Analysis

Oct 15, 2026

Uploaded by Rizky

The paper analyses Grade 12 learner errors and misconceptions in calculus in a secondary school in South Africa’s Limpopo Province. It characterizes the nature of mathematics errors and misconceptions, using a typological framework to code learners’ mistakes. Results indicate that many errors stem from gaps in basic algebra and from over-reliance on procedural knowledge without conceptual grounding, while some correct answers conceal missing linked procedures. Educational implications for mathematics education are discussed.

LanguageEnglish

CategoryExam

FormatPDF

Pages12

Reading Time30 min

AccessFree to download

Abstract

Introduction

The anatomy of learner errors and misconceptions

Statement of the problem

Purpose of the study

Theoretical framework and literature review

Volume 3, Number 3, 2010 LEARNER ERRORS AND MISCONCEPTIONS IN ELEMENTARY ANALYSIS: A CASE STUDY OF A GRADE 12 CLASS IN SOUTH AFRICA Kakoma Luneta, Paul J. Makonye Abstract: The paper focuses on analysing grade 12 learner1 errors and the misconceptions in calculus at a secondary school in Limpopo Province, South Africa. As part of the analysis the paper outlines the nature of mathematics errors and misconceptions. Coding of learners’ errors was done through the lens of a typological framework. The analysis showed that most of the errors and misconceptions were due to knowledge gaps in basic algebra. Also noted was that errors and misconceptions in calculus were related to learners’ over-dependence on procedural knowledge which had no conceptual basis. On the other hand, learners sometimes had sound conceptual knowledge for which they had not acquired allied procedural knowledge needed to perform in particular questions. Implications of the study to the wider mathematics education community are highlighted. Keywords: Errors, misconceptions, differential calculus Introduction Curriculum reform perspectives in mathematics education articulated in many research papers and policy documents aim at deepening and increasing each learner’s mathematical learning and achievement (National Curriculum Statement (NCS), 1998; National Mathematics Advisory Panel (NMAP), 2008) . The perspectives suggest shifts from teacher-centred to learner-centred approaches. The learner-centred approaches imply that teaching must also be directly responsive to the difficulties experienced by learners on the learning platform, such as the mathematical errors and misconceptions they experience. In a workshop organised for mathematics teachers by the South African Department of Education, teachers were required to outline the topics that they found problematic to teach. The teachers revealed that among others calculus was one of them. One wonders why to a large extent the teaching and learning of mathematics is so difficult and ineffective. To this quest, we suspected that poor performance in mathematics is correlated to learner errors and misconceptions. The anatomy of learner errors and misconceptions Although errors and misconceptions are related, they are different. An error is a mistake, slip, blunder or inaccuracy and a deviation from accuracy. According to Riccomini (2005), unsystematic errors are unintended, non-recurring wrong answers which learners can readily correct by themselves. Systematic errors though, are recurrent wrong responses methodically constructed and produced 1 In this study the terms learner and student are treated synonymously. In practice the term learner is reserved for one who studies at primary or secondary school and student for one older who studies at a higher education institution Received 17 April 2010, accepted 25 June 2010, published 30 September 2010. across space and time. Systematic errors are symptomatic of a faulty line of thinking causing them referred to as a misconception (Green, Piel & Flowers, 2008; Nesher, 1987; Riccomini, 2005) . Characteristically, misconceptions are intuitively sensible to learners and can be resilient to instruction designed to correct them (Smith, DiSessa & Roschelle, 1993) . Errors are visible in learners’ artefacts such as written text or speech. However misconceptions are often hidden from the undiscerning observer. Sometimes misconceptions can even be hidden in correct answers (Smith, DiSessa & Roschelle, 1993), when correct answers are accidental. Educators need to listen carefully to determine why learners give answers they give so that they can correctly follow learners’ reasoning. Statement of the problem The application of calculus in solving multitudes of theoretical and practical problems in diverse areas of human expertise represents its immense utility. The most crucial courses in higher education are calculus driven. Despite the demostrable importan

FAQs

What is the study’s main focus?

The study investigates Grade 12 learner errors and misconceptions in differential calculus and explains how errors relate to underlying misconceptions.

How are learner errors coded and analyzed?

Learners’ errors are coded using a typological framework to support classification and interpretation of misconceptions.

What did the analysis show about the sources of errors?

Many errors and misconceptions were linked to knowledge gaps in basic algebra and to learners’ over-dependence on procedural knowledge without conceptual basis.

Oct 15, 2026

Uploaded by Rizky