6.4 ANSWERS TO RESEARCH QUESTION 3
6.4.4 The teachers instinctively used principles of RME in their
engage learners into small group work activities. Their philosophy of learner- centred teaching was that of a guide. During their observed lessons the teachers implicitly used Treffers’ (1987) notions of horizontal and vertical mathematization which are within the principles of the Dutch’s RME tradition.
In his introduction, Sabelo narrated a story to the learners and started asking learners questions about the story. He used a contextual problem in his introduction in an attempt to link it to Polya’s approach of problem solving.
Dickinson et al. (2010) had noted that Mathematics teachers must start with a meaningful context which will serve as a basis for the learning process.
However, during Sabelo’s introduction, none of his learners was able to respond to the questions he had asked them about the story. They could not see the links probably because it was farfetched. Sabelo’s context could have been out of the learners’ experiences (Bansilal, 2009) as such they could not make meaning to it. His intention was that the context was the learners’ experiences. It was also possible that they struggled to answer his questions because the story was narrated to them in English hence the context ended up being an English barrier.
In my interview with Sabelo he did acknowledge his learners have a problem with English Language when solving Mathematics problems. Sabelo eventually solved the problem himself when he wanted it to be solved by the learners.
In his main lesson, Sabelo gave his learners a contextual problem on commercial arithmetic to work on which I believe was within the notion of horizontal mathematization. Below is the problem that he gave to the learners:
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Wamkelwe bought 25 apples at E1.20 each. He was then given a discount of E2.00. How much did he pay for the apples?
The problem seemed to be familiar to the learners and was activity based. Of note about Sabelo’s problem was that it was located in a real-life situation (Treffers, 1987) and learners were expected to use their mathematical tools to solve it. The problem was in fact within the idea of horizontal mathematization wherein, according to Treffers, learners mathematize a problem from real life situation.
Out of Sabelo’s seven groups who were working on the problem, only three got a correct solution to it. Recall that during Sabelo’s lesson some groups did discuss the given problem whilst in other groups there was one learner doing the problem. Possibly during Sabelo’s lesson either one learner had difficulty in solving the given problem or all members of a group had a difficulty working it out. Or rather it could have happened that the design of the task and/or the context being biased, made it difficult for the learners to get a correct solution (Bansilal, 2009). In other words, learners can get confused by a contextualised problem if it is not actually their context. This issue would have been averted had Sabelo made some meaningful interventions during the group activities.
Whilst Sabelo used a contextual problem in his lesson, Themba and Milton used problems where learners were supposed to use aspects of mathematical content within the mathematical system itself (Treffers, 1987). Treffers referred to such use of mathematical problems as vertical mathematization because with this notion of mathematization concepts are used within mathematics to build on others. Themba gave his learners a problem where he asked them to calculate one of the missing interior angles in a quadrilateral. Clearly learners had to use their relevant prior mathematical ideas to work out the solution of the problem.
As for Milton, he wanted his learners to do a geometrical construction of a triangle where all its dimensions were given. Similarly, his problem was located within the RME’s vertical mathematization as pointed out by Treffers because it required learners to navigate within the system of Mathematics.
Both Themba and Milton seemed to be introducing their lessons by attempting to use aspects of mathematical content that the learners have learnt whilst Sabelo
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made use of a real-life situation. Thus, it is encouraging to note that these novice teachers are actively finding ways to try to put the RME ideas into their teaching practices implicitly. My argument is that they used the principles of RME in their lessons instinctively in order to enable meaningful learning.
6.4.5 The teachers made their own personal enactment of learner-centred lessons in the absence of direction from the department
Both the curriculum and subject syllabus documents of Eswatini Ministry of Education and Training advocate for learner-centred teaching methods when teaching Mathematics at Primary school level in Eswatini. However, none of the two documents unpack approaches on how the Primary school teachers should teach Mathematics within the learner-centred framework. Furthermore, the two documents do not provide any explanation or clarification of the meaning of learner-centred practices. When I quizzed the teachers on the type of teaching method that was used by their lecturers at college, they responded by saying that it was the lecture method. Hence the teachers seemed not to be empowered with some of the skills to attend to the fundamentals of facilitating learner-centred practices in their teaching of Mathematics. This is simply because their lecturers at college did not model the substantive elements of learner-centred practices during lectures.
The teachers in the study were left to decide on their own on how they could personally enact this notion of learner-centred lessons, based on their own incomplete understandings. Furthermore, the education department did not provide any curriculum workshops about how these ideas could be put into practice. It would be expected that curriculum workshops would empower teachers with some elements of learner-centred teaching such as group work as a strategy to enable learner participation and engagement (Brodie et al., 2002b) in order to facilitate meaningful learning. Umugiraneza et al. (2017) have pointed out that classroom teachers need some professional support in trying to move to more modern teaching such as group work as a teaching strategy to enable effective learning. Through professional development support, teachers may be given practical advice on how to attend to the substance of learner-
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centred practices on how to facilitate the progressive group work strategies in order to enable meaningful learning.
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CHAPTER 7
CONCLUSIONS AND RECOMMENDATIONS 7.1 INTRODUCTION
This chapter presents the researcher’s conclusions and recommendations from this empirical study. The aim was to explore teachers’ constructions and enactments of learner-centred practices, focusing on three urban schools in the Shiselweni region of Eswatini. The findings, conclusions and recommendations of this study were based on data gathered from two data collection instruments;
semi-structured interviews with three Grade Six teachers and classroom observations of these three teachers during their Mathematics lessons.
7.2 SUMMARY OF FINDINGS
Based on these research questions the study yielded the following findings:
Research Question 1: What are Primary school Mathematics teachers’
understandings of learner-centred teaching?
The teachers’ perceptions of their learner-centred teaching is that the teacher takes on the role of a guide.
The teachers’ understanding of the role of the learner in learner-centred teaching approaches.
The teachers believed that group work was an important component of learner-centred teaching.
Research Question 2: How do the teachers’ understandings of learner-centred teaching influence their instructional practice?
The teachers’ personal philosophy of learner-centred teaching did not match their actual practices.
Teachers used ‘hybrid’ group work management strategies.
The teachers’ actions were modelled on how they were taught at college.
Research Question 3: To what extent do the teachers enable meaningful learning in their personal enactments of “learner-centred” practices?
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The teachers displayed narrow conceptions of meaningful learning which they tried to implement.
The teachers tried to emphasize the role of prior knowledge in their teaching.
The teachers emphasised the use of group work in their teaching.
The teachers instinctively used principles of RME in their teaching.
The teachers made their own personal enactment of learner-centred lessons in the absence of direction from the department.
7.3 CONCLUSION FROM THE EMPIRICAL STUDY
In this chapter, I have provided conclusions and recommendations drawn from the findings of the present study that sought to explore Mathematics teachers’
constructions of learner-centred practices and the extent to which their personal enactments of “learner-centred” practices enabled meaningful learning at Grade 6 level in Eswatini. I have also discussed the limitations of the study, the recommendations for action and further research which I noted as I conducted this study. There were two key findings in the study on which I drew my conclusion.
The study showed that teachers’ understandings of their learner-centred teaching are that the teacher takes on the role of a guide without clearly demonstrating the extent to which they offered the guidance to the learners. The teachers in the study shared some common understanding on this concept. I concluded that teachers have a vague knowledge of the concept of learner- centred teaching. Their construction just sees the role of the teacher as a guide and lacked explicit understanding of the theories and approaches that are involved in learner-centred teaching.
The teachers believed that learner-centred teaching was about the teacher guiding learners as they engage into a task. They engaged the learners into some small group work activity. To the teachers, guiding learners basically involved walking around class and watching the groups working on a problem or a task without making some meaningful interventions and encouraging them to participate.