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However, within me I know I will talk about integers because that is where learners will make errors …
Anele: Yes, but I do not write it down in ink in the lesson plan how so it is that I am teaching mathematics Grade 8 and Grade 9 or let’s say mathematics. And you will agree with me that mathematics is a continuation of what was done in the previous grade. So, in Grade 9 I am continuing from where the Grade 8 teacher left off. So, when I am preparing my lesson I do consider the common errors in this task. For my past years of teaching as a teacher and as a learner at some stage, I can say that these are some of the common errors that I expect or anticipate from my learners. So yes, when I am preparing my lesson, I do anticipate some common errors and some common misconceptions learners may carry from the previous grade.
Zafira: Yes, I do sir, you know in mathematics it is difficult to see the error that a learner will make without you as the educator doing the sum yourself, so you are trying to get the error that the learner can make in the particular topic. I do the sums that I will do in class and then when I do those sums, maybe when I do the sums as fast as possible I get to see that a learner can confuse the signs here or a learner can make an error there. And then when I get to class then I will have to clarify that you mustn’t confuse the signs there, you mustn’t do this error here, so I can just put it this way, when doing lesson plans I first do the sums aforetime before I get to the class, so that I can try to predict the errors that learners will make.
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Anele’s response:
… When I am bringing it to our context, remedial teaching, that is teaching that is aimed at assisting our learners to understand a concept (Learner support) or a topic and most importantly to ensure that the anticipated skills of that objective of that topic are achieved. So basically I will say it is that teaching that comes after you have taught and you have assessed, because after that assessment you can see that my students still lack A, B, C and D. These skills or objectives have not been met yet and now you start remedial teaching (redress of learning gap), you try to correct the errors and misconceptions or anything that the learners may have portrayed after you have assessed them.
Figure 5.1 Coding from Anele’s response on the extent to which teachers engage with errors
This process was repeated in all sections for all responses generated from all of the participants in the study. Figure 5.2 shows an extract from Zafira’s comments on how she engages with learners’ errors and how her response was coded.
Zafira’s response:
Precisely yes, because I am of the view that my learners need to know as to how they did (feedback) and where are their strong points and their weak points and what to improve and what to do to ensure that they pass eventually. The analysis of errors helps me to give correct feedback to learners after assessment, to give the feedback for me to return the scripts back to them, and after they have seen what they did, correct or incorrect then after I will provide correction (correction) again outlining step by step what was expected of them from that particular question asked (remedial teaching)
Figure 5.2 Coding from Zafira’s responses on how teachers engage with learners’ errors Throughout the coding process the researcher assigned colour codes to specific categories, which assisted in generating themes to answer the research questions on the extent to which and how teachers engage with learners’ errors. The process followed three phases: phase one shows how data was coded from the interview as presented in Table 5.1. Phase two presents how the coded data was categorise into meaningful theme in Table 5.2 and finally phase three show the final theme were generated. Data was then analysed in three sections using the three final themes generated in Table 5.3.
5.3.1 Inductive analysis of qualitative interview data
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Table 5.1 Coding and explanation of codes from interview data
Participants Codes Codes/ explanation
MRT EAS ICCK MRT: Meaning of remedial
teaching.
EAS: Error analysis strategies ICCK: Importance of common content knowledge
Kwaku EoL C, R T, F KFT, MFL EoL: Emphasis on learning C: Correction
RT: Remedial teaching F: Feedback
KFT: Knowledge for teaching MFL: Motivation for learning
Anele DMT F, RT,C,
PL KTIE, KFT, KFL DMT: Different methods of teaching C: Correction
RT: Remedial teaching F: Feedback
PL: Peer learning
KFT: Knowledge for teaching KFL: Knowledge for learning KTIE: Knowledge to identify errors
Zafira LS,
RLG RT, IS, C,
F KFT, KFL LS: Learner support
RLG: Redress of learning gap C: Correction
RT: Remedial teaching F: Feedback
IS: Individual support
KFT: Knowledge for teaching KFL: Knowledge for learning
In phase 2 of the analysis a constant comparative method was used and codes which were similar were collapsed to generate themes. In all, three themes were generated based on the categories, as presented in Table 5.2.
Table 5.2: Categories and themes generated from interview data coding
Codes Categories Themes
EOL
LS / RLG
Emphasis of learning
Learner support, Redress of learning gaps
Teachers’ conception of remedial teaching C, F, RT Correction, Feedback, Remedial teaching Strategies for error analysis KFT, KFIE,
MFL
Knowledge for teaching, Knowledge for identifying errors, Motivation for learning
Usefulness of content knowledge
Phase 3 speaks to Table 5.3, which is a summary of the final themes after the recategorisation of the themes from the semi-structured interviews.
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Table 5.3: Final themes generated from interview data FINAL THEMES Theme 1: Usefulness of teachers’ content knowledge Theme 2: Teachers’ conception of remedial teaching Theme 3: Strategies for dealing with learners’ errors