Part two of MGD test

Question 3: graph as a picture

Only one of the learners was interviewed on this question. In general, the learners' performance in this question was not alarming; Table 4.4 shows that 63 per cent of the learners obtained more than four out of eight for the question. In the interview, the one learner revised the concepts inherent to all the graphs given in this particular question. He answered the first part of each question correctly, stating whether the graphs were increasing or decreasing. The researcher then asked the learner to give more details:

Interviewer: These questions are not just about increasing or decreasing, but rather about how rapid those changes are. Looking at the first graph, finish the sentence - As x increases, y…

Learner: Increases

Interviewer: Can you use other words to further describe the type of increase? Learner: It increases constantly.

Interviewer: And after the dash.

Learner: It increases faster but an exponential rate.

After the request to the learner to use more words to describe the type of increase or decrease, the learner expounded on each question and used descriptions like “the graph is increasing constantly" and “the graph decreases rapidly". This indicates that learners often answer simplistically and have to be prompted to delve deeper into the interpretation of graphs. They are inclined to be satisfied with a superficial level of answer.

Question 6: height slope confusion

This question assessed the same concept as that of question 7 in part one of the MGD test. The intriguing aspect was how the learners performed in question 7 compared with question

136 6 of part two of the MGD test. Only 14 per cent of the learners obtained full marks for question 7 of part one while 24 per cent of the learners obtained full marks for question 6 (see Table 4.3 and Table 4.4).

The one learner interviewed on this question was a Mathematical Literacy learner who did not do well in question 7 of part one of the post-test. The learner first explained his understanding of the rate of change, noting that it is the difference in the y-values and the x- values. The researcher then asked about the definition of gradient and he noted y over x. The researcher then asked the learner about the graph with the greatest rate of change in the shaded areas. He immediately realised that he had made a mistake by originally writing A instead of B. For the second part of the question, when x is 25, he maintained his original answer which was correct. The conversation about this question was as follows:

Interviewer: Looking at the two graphs, using that same notion of the rate of change, which one has the greatest rate of change in that region?

Learner: I had originally said A, but now looking at it, I would not keep the same answer. I would say B because the rate of change is greater than that of A which is just a steady, showing little growth whereas line B, in that little area alone, it goes from about three till about nine, whereas the rate of change in A line goes from 14 to about 16 which is not correct.

Interviewer: And then the b section of the question: when x = 25, can you see that? Which of the two curves has the greatest rate of change?

Learner: I said A. Although it is decreasing, it still has a greater a dip, the gradient as compared to B. B has just a steady curve.

4.5 CONCLUSION

This study recorded and analysed data in three phases.

In phase one, the results of the MGD test and attitude questionnaire were recorded and analysed using descriptive statistics. The MGD test results and the attitude questionnaire

137 results were analysed separately and then the relation between learner performance and learner attitudes were analysed.

In phase two of the study, the results of the intervention worksheets were recorded and analysed, studying how the different groups of learners answered the worksheets. Also, excerpts from the reflective questionnaires that the learners completed after each intervention session were examined and different codes from these questionnaires examined in order to gain an understanding of learners’ view of the intervention.

In phase three, the 10 learners’ post-test results and their post-intervention attitude questionnaire results were studied, summarised and compared to their results in the pre-test and pre-intervention attitude questionnaire in order to gauge the effectiveness of the intervention in changing the learners’ attitude towards the subject and ability in the MGD test.

The next chapter summaries the main findings of the study, the limitations connected with this study and offers recommendations for further research on this topic.

138 CHAPTER FIVE

CONCLUSIONS AND RECOMMENDATION

5.1 INTRODUCTION

The main research question for this study was: ‘Does the use of Excel as a learning tool influence learners’ ability to interpret functions?’ This chapter provides a summary of the main findings of the study in line with the following four sub-questions that were derived in order to answer the main research question:

1) Is there any relationship between the achievement levels of learners and their attitudes towards the subject of Mathematics as a whole?

2) Is there any difference in attitude towards Mathematics between pure Mathematics learners and Mathematical Literacy learners?

3) Does using Excel have an effect on learners’ attitudes towards Mathematics?

4) Is there any difference between the achievement levels of pure Mathematics and Mathematical Literacy learners after an intervention using Excel?

The study was conducted in three phases and the instruments used in each phase are reiterated in Table 5.1 below:

Table 5.1 Summary of the phases and the instruments used in each phase Phase Participants Instruments

One 72 learners Pre-tests of MGD test and attitude questionnaire

Two 10 learners Intervention and reflective questionnaires

Three 10 learners

Post-test of MGD test and attitude questionnaire, and five interviews

139 Apart from discussing the main findings of this research, the limitations of the study are also considered, the findings linked to the seminal research that informs this study and some recommendations are made about possible further research on the role that Excel could play in helping learners interpret and understand concepts concerning functions.