5.3 THEMBA’S TEACHING
5.3.4 Interview with Themba
5.3.4.2 Learning practices
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From my interview with Themba I noticed that he believed in learner-centred teaching. However, his actual teaching methods did not model a learner-centred approach. In his teaching, he used the demonstration method which involved demonstrating an example while his learners watched him. According to Themba, the demonstration method is consistent with learner-centred teaching because the teacher had to guide the learners. Furthermore, his question-and- answer technique was used to get the specific answer that he was looking for.
Although he made the effort to arrange his learners in groups, he did not use this arrangement to encourage learner engagements within the groups. He continued teaching to them and dominated the discussions whilst learners were in their small groups. When he asked them to work on problems in his first activity, the learners worked as individuals within their groups and did not communicate with one another in their groups. Whilst in the second activity there was discussion among learners.
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real life. I further asked him what he meant about real life and he responded by saying that:
I said geometry sir, so now we are calculating angles this thing is meaningful in real life because he does it in Primary level. When they grow up everybody is not going to be a doctor or a lawyer. So when you are dealing with angles some will be a builder or carpenter so we are dealing with angles, dealing with calculations. It is meaningful learning because we face these things in the outside world.
From the above extract, it emerged that Themba connected meaningful learning with learners’ future careers. His notion about meaningful learning is that Mathematics concepts should be linked with everyday life. However, Themba never mentioned the connection between the topic and everyday life experiences in his teaching. He made explanations of some concepts and explained how to find missing interior angles of quadrilaterals (see Figures 5.21 and 5.23).
Basically Themba believed that if learners could apply the concepts then there was meaningful learning.
Themba was also asked about whether he knew anything about concrete materials in the teaching of Mathematics and he responded by saying that he knew what they were. I then asked him the frequency at which he used concrete materials when teaching Mathematics.
Interviewer: Do you actually use concrete material when you are teaching your Math lessons?
Themba: I use them.
Interviewer: How often do you use them?
Themba: Most of the time.
In his lesson Themba brought a chart with pre-drawn quadrilaterals (Figure 5.14). He used it to help learners to mark interior angles of the quadrilaterals.
In that way he was assisting them to connect an idea of an interior angle with interior angles of quadrilaterals. His intention of using the chart was to facilitate
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conceptual understanding. I further wanted him to tell me more about concrete materials by asking him the following question.
Interviewer: Why do you use concrete materials?
Themba: It brings reality to the learners. My topic was about quadrilaterals in the previous class I was also teaching them.
They know what a quadrilateral is. They know a square, a parallelogram and a kite. They know and it makes sense.
Themba seemed to have an understanding of concrete materials as he mentioned that they bring reality to learners. But in practice he believed that the shapes he had drawn on his chart were concrete materials because he had taught his learners about them the previous day hence they knew what quadrilaterals were.
His theoretical understanding of concrete materials was in conflict with his practical aspect of what concrete materials were.
According to Ausubel (1962), in any educational classroom setting, meaningful learning will take place when there are connections between learner’s prior knowledge and new knowledge. In my interview with Themba I asked him about his knowledge about prior knowledge.
Interviewer: Do you know anything about prior knowledge in the teaching of Mathematics? What is prior knowledge?
Themba: According to my understanding it is the information they have before they get into the new concepts. The one that they have based on mapping. Information they had before I gave them the new information.
From the above conversation with Themba it can be pointed out that Themba had a firm understanding of prior knowledge. His response about it is in line with its literature definition. Indeed in his introduction he confirmed the idea of prior knowledge with his learners. He asked them the definition of a
‘quadrilateral’, the meaning of ‘sum’, and the meaning of ‘interior angles’. And all these have a fundamental bearing on learners’ understanding of the new topic. Here, he was attempting to link what the learners knew which was related to the idea of “The sum of interior angles of a quadrilateral”. However, during
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the interview he did not mention the fact that linking learners’ prior ideas and the new idea constitute meaningful learning. I also wanted to find out more about Themba’s understanding of meaningful learning. Below is my conversation with him.
Interviewer: Why do you use prior knowledge when teaching mathematics?
Themba: I am just stimulating their thoughts. So that they easily link the old concepts with the new concepts. It is easy for them.
Interviewer: How often do you incorporate prior knowledge when teaching Mathematics? Do you always use prior knowledge?
Themba: I used it so many times sir. I use them as my introduction most of the time so that they link and so it’s easy for them. It is easy to apply to their concepts.
The above conversation confirms his position about prior knowledge in his teaching of Mathematics. He articulated it very well and asserted that he used it often. Of course, even when learners had difficulty with a task, he would use their prior ideas that would help them solve the current problem. His teaching also demonstrated that he valued the role of prior knowledge as shown when he reminded the learners about the adjacent angles being supplementary when they formed a line as in Figure 5.25. The learners needed to apply that known result to the new situation of working with interior angles of quadrilaterals when finding the value of G in Figure 5.23. That in itself was prior knowledge to finding the interior angel of the quadrilateral when the other angle in the straight line was known.
Despite Themba’s articulation of prior knowledge, he never related it to meaningful learning as articulated by Ausubel. In my interview with him he associated meaningful learning with connecting Mathematics to real life situations. Basically, his conceptual understanding of meaningful learning never connected with the view of linking learner’s prior knowledge to existing knowledge.
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