4.2 Data presentation and discussion
4.2.2 Planning teaching and learning
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Yes, I know them. Eeerrr…! (Frowning) Triangle has three sides. Yaa! I think that’s how they differ.
Teacher Moliehi was also very uncertain as to how the shapes differ. She said:
They are not different. Yes, they may look different, but they are all shapes, maybe they may differ in terms of their sizes and colour.
The responses from all the teachers did not provide any satisfactory answer to the question, which revealed that the respondents had limited knowledge of the subject matter. Both teachers Ntsoaki and Moliehi lacked knowledge of the subject matter probably because of their lack of qualifications or from ignorance because the differences between those shapes are actually common content knowledge (CCK) which Ball et al. (2008, p.399) define as “the mathematical knowledge and skill used in settings other than teaching”. This implies that people may know the differences between those shapes even if they are not teachers. I expected the teachers to describe the differences in terms of their sides, corners and angles; as explained in the Curriculum for CECE programme (2007) for instance, a square differs from these other shapes because it has four straight sides with all sides equal. It also has four corners which are all right angles. A rectangle has four straight sides with opposite sides having the same length and corners, all right angles. A triangle has three straight sides which may be of equal or unequal lengths and its angles will be right, acute or obtuse angles (Curriculum for CECE programme, 2007).
The results based on the above question regarding the differences between the triangle, square and rectangle, clearly revealed that the majority of teachers lacked basic knowledge of the subject matter they were teaching. This implies that teachers are likely to experience challenges in terms of effective teaching of mathematics in Grade R, and that these challenges are consequently transferred to the learners. Shulman (1987,1986) insists that teachers should be competent in subject matter knowledge. They are required to go beyond the knowledge of the facts or concepts of a main content area and also understand the structures of the subject matter.
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teaching and learning of mathematics (Ginsburg et al., 2008). Lesson plans should indicate activities that are in line with educational theories such as those of Piaget, Vygotsky, Brunner and constructivism that describe and explain how learners learn.
To comprehend what teachers understand about the planning and teaching of mathematics in Grade R, I asked the respondents two questions. The first question asked them to share what they understood by the requirement to plan learning activities (i.e., lessons) in order to teach mathematics in Grade R. The second question required an explanation of how the classroom should be arranged in order to teach mathematics in Grade R.
The findings indicated that the teachers had similar understanding with regards to the planning of the teaching and learning of mathematics in Grade R. Teachers Itumeleng and Manyai understood that their planning had to incorporate concrete, semi-concrete and abstract materials. Teachers Ntsoaki and Tselane understood planning as incorporating sequential lesson activities that involved the use of concrete, semi-concrete and abstract materials. Teacher Moliehi understood it as planning activities that would involve all learners as well as concrete materials. For instance:
I plan my teaching in a way that it starts with concrete materials, then abstract like eeer… using pictures (teacher Itumeleng).
I think I should plan in a manner that my activities will be sequential. Like I start with activities that involves use of concrete objects first then abstract follows (teacher Ntsoaki).
I understand that activities which involve the use of concrete materials are done first, the semi abstract ones will follow. (teacher Manyai)
Mmm…! I think activities must involve all learners and my activities should make use of concrete materials (teacher Moliehi).
I think they should be developed sequentially and they should follow concrete and abstract level. For instance, eee…! At the beginning of the week I use concrete objects, towards the end of the week we use both concrete and semi-concrete materials (teacher Tselane).
The responses revealed that all the teachers seemed to know and understand that learners in Grade R learn through the use of concrete materials first, followed by the use of semi- concrete materials. This understanding portrayed by the teachers showed that they had knowledge of what theorist like Piaget and Bruner discovered about how learners should
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learn. Furthermore, it was revealed that the teachers had knowledge about the learners’
developmental stage and characteristics, as advocated by Shulman (1987
The planning of teaching and learning extends far beyond the planning of class activities only; it also involves the organisation and arrangement of the classroom in order to create an atmosphere which provokes spontaneous learning (Ginsburg et al., 2008; Clements, 2001).
Shulman (1987) states that teachers should possess general pedagogical knowledge, meaning that they should be knowledgeable of the strategies of classroom management such as being able to handle discipline issues in the classroom and to manage time by allocating it to lesson activities. Teachers should be creative in organising the teaching materials that will be needed during the teaching of mathematics and they should also design or obtain various posters with mathematical concepts and paste them on the walls of the classroom or notice boards (Shulman, 1987).
I asked the respondents to share what they understood by ‘arranging and organising the classroom for the teaching of mathematics’. The findings showed that all the teachers understood that the classroom has to be arranged in a manner that creates a positive teaching and learning atmosphere. They all shared that they would like to have a ‘maths corner’ in their classroom.
I do not have a special arrangement for mathematics in my class because it is too small but I understand that it should be arranged in the manner that it instil the love of mathematics in learners. There has to be a display of colourful maths posters, a beautiful counting box with colourful counters. I would love to have maths corner (teacher Itumeleng).
I have arranged my classroom by partitioning it into five corners but I do not have a special arrangement for mathematics. However I would like to have maths corner amongst other corners that I already have in my classroom (teacher Ntsoaki).
I believe that, eee…! The classroom should be arranged in a manner that indicates that there is mathematics lesson going on in that class. I would like to have maths corner. I have five corners in my classroom already (teacher Manyai).
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I do not have a special arrangement for mathematics but I wish to have maths corner even though my classroom is so small that it does not even allow me to accommodate even just one corner (teacher Moliehi).
To arrange a classroom is important more especially to have a maths corner where learners can do maths all the time. I like to teach maths outside at the playground where there is enough space. As a result I do not have a special arrangement for maths in my class (teacher Tselane).
From the above responses it is clear that all the teachers understood that when arranging the classroom, mathematics teaching and learning should be taken into consideration. The teachers revealed different reasons for not having such an arrangement in their classrooms.
For instance, teachers Itumeleng and Moliehi claimed that their classrooms were too small to accommodate more corners. Teacher Tselane pointed out that she liked to do mathematics outside on the playground where there was enough space; as a result she did not have a special arrangement for maths in her classroom. However, all the teachers wished to have a
“maths corner” in their classrooms. Teachers Ntsoaki and Manyai acknowledged that classroom arrangement is very important. They claimed that they had already arranged their classrooms by having five corners and wished to have a maths corner as well. However, they did not provide a reason why they did not have a maths corner.