ANALYSIS OF SEMI-STRUCTURED INTERVIEWS

Planning is an integral part of teaching and learning. Besides understanding the concept of planning, it is essential that the pre-service teachers know and understand the steps involved in planning a mathematics lesson. Planning is an ideal starting point to prepare the mathematical content and adapt teaching methodologies to engage the learners in the classroom. When asked are you offay with the steps in planning a mathematics lesson all of the respondents indicated they knew the steps involved in planning a lesson.

According to du Toit (du Toit, Louw and Jacobs, 2016:140) the following questions are imperative during the planning process, namely, “what do I teach?; who are my learners?, why am I teaching this?, how can I teach this?” and “how successfully do I teach?” The pre-service teachers were asked: Name some aspects that that you will consider when planning a lesson. Some of their responses were:

Learner diversity; Prior knowledge; Language; Misconceptions; Integration;

Content – what you will do with the lesson; Aspect of time;

Various levels of understanding.

These responses provided the relevant responses to the questions posed by du Toit. The classrooms in South Africa are a cauldron of diversity. In addition to the language challenges facing learners there are other academic impediments teachers have to take into consideration. Some of the issues are mentioned above have to be by the pre-service teachers to meet the educational needs of the learners. The pre-service teachers, when drawing up a lesson plan, have to consider all of these aspects. All of learner diversity, prior knowledge, language and misconceptions can be classified together. Learners bring their own understanding of concepts due to the language they speak and the environment they live in. This forms their prior knowledge that they bring into the classroom. Therefore the pre-service teachers need to build from what the learners share as common knowledge. The correct use of language when explaining mathematical concepts can clear any misconceptions that the learners may have and the pre-service teachers need to be aware of these factors when they go out for their practice teaching so that the learners are catered for the in the different activities.

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The pre-service teachers had to explain how they used some of the aspects used in planning. They are expected to use the lesson plan provided by the higher education institution they attend in all their teaching preparation. Provision is made for routine information, namely, topic, time; objectives for the lesson and resources to be used to support the lesson. The majority of the interviewees indicated that they follow the given headings to complete the aspects on the lesson plan.

In the lesson preparation there is an interrelationship between the introductory, teaching and conclusion phases. This interrelationship allows for the free flow of the content material during teaching. Determining learner‟s prior knowledge, catering for diversity in the classroom, managing misconceptions, content to be taught and language of learning and teaching must be considered in the planning stage. All of these are of the utmost importance to meet the needs of the learners. In the introductory phase the lesson is introduced in such a manner that the teacher is able to determine the learners‟ prior knowledge so that the teacher will „know how to go about teaching the rest of the lesson‟. The teacher, by having an open discussion with the learners, will also be in a position to manage misconceptions by clearly explaining the vocabulary specific to the language of mathematics. By selecting the correct grade, the pre- service teachers would be able to determine the lesson objectives and „curriculum content‟ to be taught. In order to do so they need to understand curriculum progression material for the relevant grades in the CAPS policy document. The CAPS document lists the key elements and content that needs to be considered when preparing a lesson therefore the pre-service teachers need to be trained to use this document. The pre-service teachers must take the initiative and plan the objectives, select the „content‟ material to suite the grade, time needed for the lesson, determine which teaching strategy or strategies will be appropriate to accommodate the learner‟s learning style. To successfully engage in all aspects mentioned above the pre-service teachers must have pedagogical content knowledge (how to make the subject matter accessible to all learners irrespective of their learning challenges).

I am very critical of the lesson plan used by the pre-service teachers during their teaching practice. The lesson plan used still has resemblances to the one used during Outcomes Based Education (OBE). It involved a lot of writing out of information not relevant to the planning and teaching process. The Department of Education has made changes, since the introduction of CAPS, to the lesson plans in all subjects and has provided templates of the lesson plans to all schools. These lesson plans are currently in use. The pre-service teachers are expected to be mentored by subject teachers when they are out at schools doing their teaching practice and this includes been exposed to using the lesson plan used in the schools. Proper mentoring does not take place because teachers are not willing to check the long lesson plans used during teaching

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practice. The teachers consider it a laborious and tedious process. Therefore it is imperative that the institution implement changes to the existing prescribed lesson plan. These pre-service teachers need to be exposed to the current trends in lesson planning hence they should use what is already in practice at schools in order to equip them with the proper skills needed for teaching and learning .

The pre-service teachers must also factor contextual factors, namely, „language levels of the learners; learner‟s ability and reading‟ into their planning and preparation which might impact on their teaching. The Department of Education admission requirements states that the learners cannot be denied admission based on their understanding of a language. Learners in South African schools are expected to be taught in their mother tongue in their formative years at schools. The migration of learners between provinces, especially the rural areas, forces the parents to seek out schools that have English as their LOLT. The general consensus is that obtaining schooling in an English medium school bolsters the learner‟s chances of achieving academic success to gain entry into tertiary institutions and inevitably in the job market. Thus schools are forced to accommodate learners who do not have the schools LOLT as their mother tongue. These learners inability to communicate effectively in the classroom will impact on teaching and learning. Reading will become a barrier to these learners. This will inevitably have an impact on the learner‟s ability to learn to read and solve problems during the teaching and learning process.

It is expected that the pre-service teachers have the expertise in preparing teaching and learning activities. If the pre-service teachers answered yes to using certain aspects in planning then they had to explain how they used them.

Pre-service teacher: I look at the learner‟s text book for material for my lesson.

This response indicated the pre-service teacher‟s reliance on the textbook as the primary source of material for teaching. Low level of readiness to source sufficient teaching and learning material on the part of the pre-service teacher can impact on the learner‟s learning experience. It is expected that the teacher content knowledge is higher than that of the learner knowledge. Pre-service teacher: I check for the resources at the school to prepare for my lesson because I don‟t really know how to teach the subject without it.

This indicated that the lack of reference resources at schools will impede the creation of knowledge for teaching. The pre-service teacher will be in a predicament if the he lacked the basic pedagogical content knowledge to teach the subject.

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Mathematics teaching has become technologically revolutionised to such an extent that being a highly qualified teacher means being able to use technology effectively to support teaching learning in the classroom. According to National Council of Teachers of Mathematics (2000) technology is an absolute necessity in supporting teaching and learning as it influences the manner how mathematics is taught. It also supports how the learners learn the subject effectively as it engages the varying learning styles of the learners. It is therefore important, never mind the location of the school, to utilize whatever resources is available. The pre-service teachers were asked: do you use any of the following in your lessons: worksheets/charts/OHP/laptop/other creative media. The majority of them indicated that they used „charts, laptop and worksheets‟ to support their teaching. These are readily available at most schools. Majority of the South African schools have the relevant technological equipment to support teaching and learning. Certain technological companies in South Africa have formed partnerships with the Department of Basic Education and have provided schools with tablets loaded with mathematics learning material. Teachers have not made any real effort to utilise them in their teaching as they lack the basic technological pedagogical knowledge to utilise technology as part of their teaching programme. The pre-service teachers are in an advantageous learning situation since they are exposed to Information Communication Technology (ICT) as one of their modules at the university. This is proof enough that they are techno-savvy and knowledgeable in the field of technology. Whilst studying ICT as a learning module they need to acquire technological pedagogical knowledge to be able to use technology efficiently and effectively in their teaching. The effectiveness of using technology as a support to visualization will rely heavily on their readiness in implementing the visual aspect in teaching the subject. They need to demonstrate how this technological pedagogical knowledge can be used to show how innovative learning environments can be created in the classrooms. One of the pre-service teachers indicated that they will also use games. Games, especially board games, are inherently visual and support the learning of mathematics. Integrating the lesson using games can drive active engagement amongst the learners. As they strive to win they are also learning valuable techniques from each other. This valuable technique can help learners develop their language and problem solving skills.

The pre-service teachers had to provide reasons why they used these technological resources to support their teaching.

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To make the language of mathematics more understandable, providing the learners with visual support develops their understanding of mathematical concepts. Problem solving strategies produced diagrammatically can prove a valuable guide for future problem solving activities. Pre-service teacher: these aspects will make the learners remember and gain a better understanding of the content.

In order for learners to understand better, the learning activities need to be visually aesthetic and relevant to learners. The visual medium will engage their level of thinking allowing them to learn and understand in a fun way. This kind of learning improves their understanding of mathematical content.

Pre-service teacher: accommodate inclusive education all types of learners, learning needs and styles.

Various aspects affect the learner‟s ability to grasp the steps involved in solving problems. The pre-service teachers need to be aware that South African classrooms have learners of mixed academic ability and amongst them are learners who learn visually. These learners learn best by drawing diagrams. To further accommodate the learners, they should be exposed to diverse opportunities for speaking, explaining, reading and writing to construct meaning of the mathematical problem.

Pre-service teacher: it keeps the learners focussed in the lesson and it is more engaging as well. Knowledge creation has a starting point when learners are exposed to working with concrete material, seeing or listening to things in the immediate environment. The pre-service teachers were asked: Which visuals are used when solving mathematical problems? Majority of the respondents mentioned that they mostly used mostly charts. These visual learning resources are readily available at most schools as schools buy subject related and content related charts from their learning and teaching supplementary material (LTSM) allocation. Teachers are also expected to supplement their teaching with additional resources and the most common of them all is the use of charts.

Pre-service teacher: definitely writing on the board.

This is one of the oldest of all educational media but still the most valuable medium to teach. Chalkboards are a permanent fixture in all classrooms and can be used creatively by the teacher to teach and consolidate mathematical concepts. Leaners thoughts, as mentioned by them, can be written down as the lesson develops. Whatever is written or illustrated on the board can be seen by all learners. The teacher can create a visual medium at an appropriate time to highlight

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significant points of the lesson and an explanation can be provided alongside to draw learner‟s attention to what is being studied.

Pre-service teacher: Videos, provided that the videos must be appropriate to the content you are teaching.

Teachers and schools have become technologically advanced and have the necessary equipment to source material to teach mathematics. The availability of videos to enhance teaching has enabled teachers to engage in a wide variety of content related material as a visual means to solving mathematical problems. Teachers, pre-service teachers to be included here, must ensure that the video material sourced on how to teach learners to solve problems must not lead them or their learners to become dependent on watching the material to solve problems. Twenty first century education demands that we provide learners with a sound academic education together with skills that will prepare them for a full and productive life. There must be a shift away from the traditional teaching to ensuring our learners can read, write and become critical thinkers. Authentic learning needs to occur in the classroom and visualization gives the learners an opportunity to organise their knowledge acquisition by creating and their communicating intellectual though. Teachers at all levels, sometime or the other have used visualization in their lessons. The pre-service teachers were asked: what is your understanding about visualization?

Pre-service teacher: visualization is something that the learners are able to see and create a picture of their own to understand.

Visualization creates a situation for the learners to see the process in their minds when they read the problem. They are able to structure the mathematical process mentally and then produce a written structure of it. This written structure is a representation of steps used during the problem solving strategies.

To visualise to create a picture stretches the learners thinking abilities as they use visual, physical and oral aspects to better show or interpret a problem which leads to knowledge building.

Pre-service teacher: Visualization is when the learners conceptualize in their mind the problem. Learners develop their conceptual and content knowledge by bringing their prior knowledge into the classroom. Visualization anchors these concepts in their minds for use when confronted with mathematical issues in their lives.

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Pre-service teacher: Visualization allows them to build their knowledge on it.

According to Kolb and Kolb (2011:61) people construct new knowledge and understanding from what they already know. This is based on their previous experience. The learners come to school from various cultural backgrounds and socio-economic conditions. They bring with them to school their own ideas of certain mathematical concepts and construct their own meaning of them. Their understanding of the concepts in the problem will show in their working of the problem thus visualization becomes the medium to consolidate their existing knowledge and creation of new knowledge.

The curriculum demands on teachers are such that they have got into the routine of „chalk and talk.‟ Visualization offers an alternate change away from the traditional teaching and learning where the teacher taught and the learners solved problems using a set method. The use of visualization in solving problems is a shift away for learners from learning through memorization and swotting rules to understanding concepts better. Memorization of rules does a disservice to mathematics because learner‟s risks forgetting a sequential step in the problem solving process thus getting the problem wrong. Conceptualizing the problem in their minds and using prior knowledge to support understanding leads to further concretizing of concepts. This brings forth their understanding and creativity to solve the problem.

In order to become adept in their teaching in the classroom the pre-service teachers need to adopt an on-going attitude to using visualization in problem solving. Instead of teaching learners mathematics in the traditional manner, pre-service teachers need to learn on how to encourage learners to solve the problem in a manner that makes sense to them. The use of diagrams and pictures was at one stage a dominant feature in mathematics lessons and pre- service teachers themselves have learnt the importance of using such visual mediums during their teaching practice.

Pre-service teacher: Visualization is when one will use illustrations to present to the learners so that they can see how certain mathematical concepts are explained.

This indicated that visualization plays an important role in mathematics. Visualization is used to explain concepts in an illustrative manner thus making it easier for learners to understand them. As learners are able to visualize concepts differently they are in a position to use their own methods to show how the maths problems are solved. When using visualization, the learners actively engage with the concepts to make sense of the problem and this intensifies their understanding of mathematics. They are able to represent the concepts, explain the methods and communicate all of this simultaneously as they are able to picture the

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mathematical process. This is authentic learning in practice as they are in a space to express their solutions differently. When learners convey their ideas through means of diagrams and pictures it indicates their cognitive responses to the problem as visualization assists in the depiction to convey ideas, concepts or methods.

The responses provided above by the pre-service teachers indicated that they understood the concept visualization.

Using visualization allows the learners to proficiently transfer their acquired knowledge to new situations. When asked, do you think your learners perform better when the lesson is supported by the above (visualization), the respondents were all in agreement that learner‟s performance improve with visualization.