Abstract
Error analysis has been considered indispensable in teaching mathematics in classrooms worldwide. One of the greatest skills in mathematics teaching has been recognised as the ability to model learners’ misconceptions through error analysis. The use of error analysis in the classroom has therefore made tremendous contribution to mathematics teacher knowledge. However, despite the acclaims about error analysis in teaching mathematics, researchers and teachers lack a detailed understanding of mathematics teacher knowledge as it is used in error analysis and the use of error analysis is still regarded as challenging for most teachers. This qualitative study therefore explored eight purposively selected pre-service teachers’ ability to identify, interpret and remediate learners’ error patterns as a result of misconceptions in differential calculus. The pre-service teachers’ analyses were re-analysed by the researcher to ascertain their ability to handle learners’ errors in mathematical calculus. The study established that though some pre-service teachers portrayed knowledge of the differentiation content as reflected by their ability to identify the errors made, most of them failed to identify the possible causes of the errors as well as provide appropriate instructional strategies that could be used to remediate learners’ error patterns. This finding illustrates that the pre-service teacher’s ability to diagnose, interpret and correct errors in learners’ work, with targeted instruction is an essential and necessary skill for good mathematics teaching.
Highlights
Error analysis has been recognised by teachers and scholars as an inseparable part of the routine of teaching mathematics [1]
The analysis of literature and the data collected established that learners sometimes make conceptual errors in differential calculus because they lack basic knowledge of pre-requisite concepts such as algebra to solve problems on differentiation
Though some of the pre-service teachers were well acquainted with the content knowledge of differential calculus and could identify the errors made by learners, they could hardly provide appropriate instructional strategies that could be used to remediate the learners’ error patterns [17]
Summary
Error analysis has been recognised by teachers and scholars as an inseparable part of the routine of teaching mathematics [1] It has been preferred by most researchers as an instructional strategy that assists mathematics learners to retain their learning [2]. Russell et al [3] agree with this statement and affirm that the most powerful learning experiences often result from making errors, which are highlighted, analysed and remediated by the teacher. This is because if an individual discovers her errors, it is rare to repeat that error, which becomes a break-through in learning mathematics. The immediate remedy to the errors made by learners is essential and this dictates the need to analyse errors as part of teaching mathematics
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