The three lesson observations will be discussed in detail in order to capture the visual strategies used by these educators of pre-service teachers. It was necessary to scrutinize all actions with the intention of understanding how their words, actions and diagrams were used pedagogically to promote greater understanding. There was also the prospect that, the activities and strategies modeled by these lecturers influenced pre-service teachers in their practice as future educators.
These observations were conducted in conjunction with the materials that the educators used, the gestures they utilized to emphasize concepts, the activities given to the students, the artefacts they produced and all other visual items they thought were useful in the classroom.
Each lesson will be discussed separately in order to present a deeper understanding of what individual lecturers did. Hence, a discussion of its comparisons will then follow. The three lessons have been recorded over a period of one month. Multiple representations of visual
strategies were carefully observed by video recordings. The educators’ use of visual strategies and students’ development of mathematical concepts by means of visual strategies used were observed by the use of video recordings. The three educators will be represented as lecturer A, B and C as per table 3.2.1 in Chapter Three. The pictures depicted in images 4.3 are snap shots taken from the video recordings which analysed the visual strategies used, such as gestures, artefacts, classroom set, use of the chalkboard or whiteboard and booklets. An analysis of the semiotics used was scrutinized as this was one of the theoretical frameworks adopted in this research study. In the next section there will be a discussion on the overall analyses of the lessons taught by the three lecturers.
4.4.1. Analyses of lessons:
4.4.1.1. Lesson by Lecturer A
Lecturer A taught a lesson based on unifying ideas to a class of 2nd year primary mathematics education 210 students. During this lesson, numerous visual strategies were observed. The visual strategies used in this lesson appeared to arouse interest amongst students and appeared to have played a positive role in developing the mathematical understanding and thinking of students. Lesson one showed that an adequate number of visual strategies was used in the classroom. The use of visuals used as a pedagogical strategy in lesson one contributed to a vast amount of knowledge gained by students. Additionally, it was observed that, the use of words and the manner in which explanations occur, plays a pivotal role. The visual strategies used in lesson one constituted of artefacts such as paper, beans, the chalkboard and overhead projector.
Observation of lesson one demonstrates meaningful explanations which worked hand in hand with the artefacts used and all other visual strategies. Lecturer A used semiotics abundantly, which were used well since she did not overpower the lesson with their purpose yet was using them meaningfully. Students showed dislike when viewing many symbols in mathematics but lecturer A gained their confidence in the use of semiotics by carefully explaining at each point what each symbol was used for. Regarding other visual strategies used in the classroom, she used just enough, and mastered their role in the classroom. Next I discuss lesson B by lecturer B.
4.4.1.2. Lesson B by Lecturer B
Lecturer B taught a lesson based on ‘set models and recursive sequences’ to a class of 4th year FET mathematics student teachers. Lesson two did exhibit visual strategies, but not as many in comparison to lessons A and C. The uses of visual strategies were very limited during the study of this lesson and were not pre-meditated. Visual strategies were not a prioritized pedagogical element used in this lesson and were in no way used to arouse interest amongst students and appeared to have played a negative role in developing the mathematical understanding and thinking of students. The use of words and the manner in which explanation occurs play an essential role. In view of this, explanation appeared to have been poorly done and students seemed very uneasy. The lack of visual strategies used in this lesson showed students disinterest in the mathematics lesson. The visual strategies used in lesson two constituted of a whiteboard, data projector, chalkboard and booklets. Gestures were also a very prominent part in this lesson. Observation of lesson two also demonstrated that meaningful explanation, works hand in hand with artefacts. Lecturer B used many semiotics. Students showed dislike when viewing symbols in mathematics and were not confident enough to fully expose themselves to semiotics. By means of observation this was probably, owing to students’
misunderstanding of mathematical symbols and their function in the lesson. There were too many semiotics used thereby overpowering the lesson. Representing mathematics with a bare minimum of visuals strategies appeared to be empty and dull. A section such as recursive sequences where it is largely semiotics based can be regarded as a challenging section for students to assimilate. The use of some sort of visual strategies should be needed to assist in teaching a section like this. It was also noted that a simple visual strategy such as writing on a chalkboard, ‘effectively’ is crucial in a lesson. The presentation of mathematics when teaching is integral, and it is the core of any lesson. The gesture of the lecturer is also crucial in teaching.
Students need eye contact, yet lecturer B continuously looked and referred to her notes, consequently focus was not on teaching which had a negative impact on students. Semiotics cannot solely be represented especially in a section like recursive sequences. The use of semiotics is heavy on students and many do not understand the meaning behind these symbols being used together, it is therefore necessary to teach and explain simply especially if the lesson is predominantly semiotic in nature. It was observed that many students have a tendency of giving up when confronted by too many symbols.
4.4.1.3. Lesson C by Lecturer C
Lecturer C taught a lesson based on ‘Number relations and operations’ to 2nd year primary mathematics education student teachers. A great number of visual strategies were observed during this lesson. Lesson three presented many interesting and exciting visual strategies used to arouse interest amongst students and played a positive role in developing the mathematical understanding and thinking of students. Lesson three showed that visual strategies constitute a crucial part with potential to easily attract students’ attention and channel a weighted amount of mathematical knowledge to them. Additionally, the tone of the lecturer and the manner in which explanation occurs plays an essential role. The visual strategies used in lesson three constituted of artefacts such as coloured pegs, number line and Russian dolls. An overhead projector, data projector and booklets and worksheets were also used as visual strategies in this lesson. By means of observation, these artefacts and other visual strategies played the most attractive role in capturing students’ attention. Observation of lesson three demonstrated meaningful explanation which worked hand in hand with artefacts. Lecturer C used many semiotics. Students showed dislike when viewing symbols in mathematics but lecturer C gained their confidence in the use of semiotics by carefully explaining at each point what each symbol was used for. She used semiotics but she did not overpower the lesson by their function and role in mathematics. She used few visual strategies and mastered their role in the classroom positively.