5.2 MILTON’S TEACHING
5.2.4 Interview with Milton…
5.2.4.2 Learning practices
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Milton: There are because most of the time child-centred teaching, it needs you to make the groups in the class.
From the above conversation, Milton acknowledged that during learner-centred teaching, learners should sit in small groups. But in his class learners were not working with one another. Instead Milton was seen assisting one learner whilst the whole class was watching.
Milton insisted that learners should work in pairs and told them that they should discuss with each other and communicate. What I observed was that though the learners were sitting next to each other but they were doing individual work and were not discussing or communicating with one another. Throughout the lesson, Milton took the role of telling, explaining and giving directions.
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I think what made the learning meaningful was the articulation of the facts meaning it was clear to the learners that’s why they were able to follow through all the steps involved in constructions.
Here, Milton means that since the learners could do all the steps that he demonstrated about constructing a triangle, then he had accomplished meaningful learning. However, in the previous extract he mentioned that meaningful learning was accomplished since learners were able to solve the problems that he had given to them. Basically, he had two conceptions about meaningful learning. They are the learners’ abilities to solve problems and the learners’ abilities to follow steps. Actually, it seemed Milton was not clear of the exact meaning of meaningful learning.
Milton was also asked about possible strategies he could make in his lessons so that there was meaningful learning during his lesson. He responded by saying that:
Mathematics is a technical subject. It has to do with a lot of practice. It is a lot of hands-on working. The pupils should practice it and the teacher should make it more practical and if possible concrete object can be used. Those things make the picture on how to work out problems. The picture last for a long time.
By the word, picture, Milton meant concrete objects. In my interview with him he acknowledged that he normally uses concrete objects in most of his lessons.
According to him, the use of practical activities and concrete objects enable meaningful learning because they help learners work out problems and the image stays in their minds.
Interviewer: So you were talking about concrete objects, how often do you use concrete objects when teaching Mathematics?
Milton: I use them a lot. As I said earlier on concrete objects make the picture in the mind of the child. The picture lasts longer than words.
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Apart from the chalkboard and a piece of chalk, Milton used only a metre ruler and a pair of compasses. He used these materials as physical tools to help learners make accurate construction of triangles. The metre rule and a pair of compasses were important resource materials used by Milton to support the construction of a triangle. Without them it would be a big challenge for him to do the construction of a triangle. Basically he did not use them to connect a representation of a mathematical idea with some concrete materials e.g. the use of Dienes Blocks to represent whole numbers when teaching addition. In other words, Milton did not use the metre rule and the pair of compasses as manipulatives to facilitate conceptual understanding. Below is an excerpt in his attempt to teach learners on how to construct a triangle using a metre rule and a pair of compasses?
Milton: We have to open the chalk board compass and measure a radius of 50 cm on the rule. After measuring the 50 cm, we have to make what is called an arc. Because we are measuring AC, our compass by the sharper side should lie at exactly on A because we are looking for the side AC, at the beginning of the line at A.
Milton did not use opportunities to engage in discussion with learners such as how do we know that the line from any part of the arc to A will always be 50cm?
Furthermore, he did not explain to learners why at the point of intersection, we can be certain that at the point of intersection of the arcs AC will be 50 and CB will be 70 (see Figure 5.5). He just asked the class to clap hands for the learner who had constructed the triangle successfully.
However, Milton did acknowledged the value of manipulatives as an enabler of meaningful learning during my interview with him. He said that manipulatives are useful when teaching Mathematics because they make the lessons meaningful so that there is meaningful learning.
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Milton was also asked to shed some light on the use of prior knowledge in the teaching of Mathematics. He seemed to articulate the significance of prior knowledge when teaching but to him, it had nothing to do with meaningful learning.
Interviewer: Why do you use prior knowledge?
Milton: It is important because you have to take the known to the unknown. In fact, prior knowledge as I used it earlier on these pupils are not empty vessels they have knowledge that they have acquired. It shapes what they have to do to something. You add to what they are having.
Milton believed that some knowledge must exist in the mind of a learner before he learns other ideas. During the introduction of the lesson he taught, he did attempt to review with the learners on what they learnt previously which had a bearing on the current topic. The lesson topic was about constructing a triangle hence Milton first conducted a question-and-answer session with the leaners to find out about their understanding of constructing and meaning of a triangle. According to him, the learners’ knowledge of these two constructs would help them in making a drawing of a triangle. The interviewer then wanted to find out from him the frequency at which he used prior knowledge in his teaching of Mathematics.
Interviewer: How often do you use it?
Milton: I use it a lot. For instance in the lesson I asked them about a triangle. They know what a triangle is. They are able to define its qualities. Others went to the extent of describing the qualities of triangles. Now what was new was how to construct it using certain measurements, a pair of compasses.
From the above conversation, Milton seemed to know the value of prior in the teaching of Mathematics. However, one striking observation is that Milton’s use of prior ideas did not seem to be associated with meaningful learning. In the lesson that I observed, Milton did use prior knowledge in his introduction.
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But when I interviewed him about the use of prior knowledge he did not necessarily mention that it had anything to do with meaningful learning. To him, it was a way of facilitating conceptual understanding among the learners.
Clearly, Milton’s construction of meaningful learning did not correlate with the notion of linking learner’s prior ideas to existing ideas.