CHAPTER 6 FINDINGS
6.1 ANSWERS TO RESEARCH QUESTION 1: HOW DID THE TEACHER MEDIATE THE CTA?
The analysis of the data revealed that the teacher sometimes: did not prepare beforehand;
provided incorrect information to the learners; accepted learners' incorrect responses;
provided answers to her learners as they appeared in the memorandum and marked learners' work in an inconsistent manner. These findings were revealed in Chapter Five under the description of the lesson observations. Because of the large amount of supporting evidence to back my claims, I have decided to annotate these categories in a table. This is done so as to facilitate the reading and to take less space. So below is a table with two columns, the first of which are my claims about the teacher's responses. The second column provides the evidentiary basis for my claims in a summarised form.
Table 6.1 Claim
Claims about the teacher supported with evidence Supporting Evidence
The teacher did not prepare beforehand.
The teacher often provided incorrect information.
The teacher provided answers from the memorandum.
The teacher accepted learners' incorrect responses.
The teacher's marking was inconsistent.
I. The teacher continually read from the CTA.
2. While engaging with the CTA, she realised that activity 1.1 had no marks.
3. Told learners to number activity 1.2 as 1.2.1 etc and then noticed the activity was already numbered.
4. For question 1.2.3 the line measure varied. The teacher was not aware of that because she accepted a learner's response and did not provide further information.
5. For question 2.3.2 she told learners to measure the distance on the map on page 8 and during the discussion, realised a distance table was provided.
6. On day 3 she told learners to complete activity ].4 as homework but at the end of the lesson discussed activity 1.4 and completes question] .4.1 with them.
I. For question 1.3.2 she told learners that in order to convert IOOOcm to metres they needed to divide by 10000.
2. Question 1.4.5 was a question to be answered on its own but told learners that they needed 1.4.4 to answer 1.4.5.
3. For question 2.2.1, she was not aware that the numbers were rounded off because the rate used varied from two to four decimal places but replied to a learner "478 is an odd number so it's rounded off to 480".
4. For question 2.3.1, the opening time was for the month of July but conveyed to learners that it was October, the month
in which they were engaging with the CTA.
5. For question 2.3.2 told learners that in order to convert distance divided by speed into hours, they should divide by 60. Distance was in kilometres and speed was in kilometres per hour, so the answer obtained would have been in hours already.
6. For 2.3.1 told learners that if "40 mm had to be converted to kilometres then it would have to be multiplied by 16". A comment that was irrelevant to the task.
For question 2.2.1 the teacher provided the learners with the solution. This was evident in Sihle, Thabani and Cleo's responses. This was also evident from the observation because the teacher provided headings and columns that were not given in the instructions provided for this question.
1. For question 1.2.3 a learner stated that 'x', the measurement to be used in the scale conversion, was 20, which she accepted, however 'x' was equal to 15 mm.
2. The scale of I: 200 000 does not convert 20mm to 40km but accepted a learner's response that it converted to 40 km.
3. For question 1.2.3 a learner responded with an answer of2, 25 and the teacher accepted the response.
4. For the question "What is additional rates?" a learner responded with "give you an extra room". The teacher responded with a "yes".
I. Haphazardly placed ticks which were evident in Sihle's response to activity 1.2.
2. For Question 1.3.1 Sihle received 3 marks for a table that
fulfilled some requirements.
3. For activity 2.1 Sihle provided a table as his solution and critical values such as 18 boys and 22 girls were left out yet he received 2 marks.
4. Thabani demonstrated a deeper understanding to question 1.3.1 and only received 2 marks.
5. Thabani extracted critical information for activity 2.1.but his response was marked as incorrect.
6. A learner's response to activity 1.2 was not marked.
7. Cleo's response to question 1.3.1 made no sense yet she received 4 marks for this question instead of 1 mark.
8. Cleo's response to question 1.4.3 was not marked.
9. For activity 2.1, Cleo received 2 marks for her response but another learner with the identical response received no marks.
Prestage & Perks (2001) stated that problems that are set in context usually pose the biggest challenges to educators. In this CTA setting, the roleof the teacher was made more crucial because of the stipulation by the Department of Education that the teacher was allowed to intervene in order to "help learners succeed" (DoE, 2002, p.12). Unpacking the CTA became the problem of the teacher, who had to unpack the problems in the different contexts and to help learners answer the mathematical questions embedded within the context. This is a huge responsibility on the part of the teacher. An interview with Sihle established that he would have preferred more intervention from the teacher.
From the descriptions of the classroom observations, which appeared in Chapter Five, it is evident that the teacher continually read from the CTA. The teacher rarely paused to explain or to enquire from learners about matters pertaining to the different activities. The CTA contained large amounts of textual material. Most of the words were not part of learners' everyday vocabulary, therefore they would have benefited from regular explanations. The teacher needed to provide more guidance to learners on what was expected from each activity. A lack of guidance and assistance was evident from the video observation.
The teacher interventions were often harmful, rather than helping her learners 'to succeed'.
For example in Cleo's case, we saw two instances where Cleo seemed to have been directly influenced by the teacher's misguided instructions. Cleo used 350 and 60 from question 1.4.3 as a basis for her calculations in question 1.404. This seemed to have been influenced by the teacher's direction that they should "use question 104.3 for question 10404
and question 1.4.4 for question 1.4.5". Furthermore in lesson 4, the teacher told learners (incorrectly) that they should divide the result (question 2.3.2) by 60. It is likely that the teacher's instruction led Cleo to divide her answer by 60 for noapparent reason.
The teacher's actions, when she marked inconsistently and accepted incorrect responses, also negatively affected her learners. Although in certain instances when she gave the learners the exact answers appearing in the memorandum, this could be seen as an attempt to help her learners succeed, in line with the CTA requirement. Although the teacher was one of the contributing factors on how the learners experienced the CTA, the teacher cannot be held to be entirely responsible for their poor results. Learners should also take responsibility for their own learning, as this is one of the principles of C200S. Sihle conveys the impression that he is one of those learners who needs constant guidance and assistance. Therefore when left to continue on his own, Sihle is not capable to answer the required work, he blames the teacher. Also the fact that the tasks were set in context also contributed to the poor results.
The Common Tasks for Assessment in Mathematical Literacy, Mathematics and Mathematical Sciences contribute 25% to the final mark a learner obtains in mathematics at the end of grade 9. Since it is an important undertaking, it is imperative that the provincial departments monitor that the CTA is being written by all grade 9 learners and that the marking of the CTA is moderated. In this study, the CTA was not monitored or the marking moderated as indicated by the Government Gazette (DoE, 2003). In my study the teacher did not view the CTA as an important assessment activity and marked the CTA haphazardly, which was evident with red ticks being placed any where on the written response of the learners. This inevitably disadvantaged the learners and is an illustration of Cooper's (1992) statement that "the children, potentially, become the confused victims"
between the state and the educational profession (p. 242).