The post-test was administered immediately after the intervention with the experimental group, which was aproximately six weeks after the pre-test.
Questions in this test were similar to those in the pre-test. Questions in both tests were matched. e.g. question 1 of pre-test was similar to question 1 of post-test. The same marking rubric that was used for the pre-test was also used for the post-test.
Table 5 shows statistical analysis of results for the pre-and post-tests for the two groups. This analysis assisted in making comparisons on the general performance of these two groups in the tests.
Experimental group Control group
Pre-test Post-test Pre-test Post-test
Total score 40 40 40 40 X 7,13 12,57 6,93 8,44 SD 4.45 4.80 4.19 3.31 Maximum score 17 27 18 17 Minimum score 1 3 1 2 Range 16 24 17 15 N 45 45 45 45
Table 5 Summary of results of both groups in the two tests
4.3.1
The mean scores
It can be seen from Table 5 that in the pre-test, the mean score of the experimental group (7,13) was slightly higher than that of the control group (6,93) therefore, to compensate for this difference, the mean scores in the post-test were adjusted. This was done to minimize the possibility that selection based on mathematical ability will be a threat to this study (Schumacher & Macmillan 1997:376).
The means were adjusted by 0,1 because the mean of the experimental group in the pre-test was 0,1 higher than the mean of both groups in a pre-test.
The mean score of the control group in the post-test was increased by 0,1 and that of the experimental group was lowered by 0,1.
The adjusted means are shown below:
Table 6 Adjusted means of post-test
4.3.2
Frequencies of scores
Figure 5 below shows that the lowest scores were 2 and 3 for the control and experimental groups respectively. The highest score for the control group was 17 while that of the experimental group was 27.
The scores of both groups in the post-test are represented in the following bar chart
Figure 5 Bar-chart showing frequency of scores in a post-test.
These results revealed that most of the learners in the control group obtained ten marks and lower, whereas in the experimental group numbers of learners obtaining different marks were evenly distributed.
Groups Mean before it was
adjusted Mean after it was adjusted
Control 8,44 8,54
4.3.3
The mean score per question
The mean scores for each question in the post-test are shown in the following table:
Question 1 2 3 4 5 6 7 8
Experimental
group 2.96 1.6 1.80 1.09 0.7 1.38 2.98 0.51
Control group 1.87 1.04 1.16 0.87 0.78 0.6 1.04 0.93 Table 7 Mean score per question in a post-test
Table 7 shows that the experimental group performed better than the control group in six out of eight questions. The group that received instruction in problem solving strategies performed better than the group that did not. These findings support Ramnarain’s (1999:143) conclusion that explicit instruction in problem solving strategies improves learners’ performance in mathematics.
4.3.4
Strategies revealed in learners’ work
From learners’ work in the post-test, it was apparent that learners in the experimental group were now aware of different strategies because they tried to use those strategies in the test. Their work revealed that they used tables, drew diagrams, used trial and error, arranged numbers systematically and looked for patterns.
Here are few examples of some strategies that learners used to solve No. 5: (a)
(c)
However, it is interesting to point out that learners avoided algebraic methods to solve problems. It is also important to point out that very few learners left out the working details of the problem. One would believe that learners were now aware of the importance of writing out the whole solution process and not only the answer. I believe the explanations that were required during class discussions contributed to this behaviour. According to Lester (1985:47) post problem sessions in which learners share and discuss reasons for their choices during problem solving reveal the importance of writing out the solution process.
The control groups’ use of strategies was still very limited.
In questions five and eight, the control group performed slightly better than the experimental group, however, one cannot say much because for both groups, the mean score is less than 1 in these questions, which is still a very unsatisfactory performance. One concludes by pointing out that although the mean scores per question had increased in most of the questions for the experimental group, the overall performance was generally still low. According to Kantowski (Lester 1985:43), students’ ability in problem solving increases gradually over time and numerous skills and procedures involved develop at different rates. The results of the post-test also revealed what was said earlier that improved performance in problem solving does not only depend on the knowledge of problem solving strategies but also on many other factors (Lester 1985:44).
Learners’ solutions indicated that in some instances, their content knowledge was limited and in others it was clear that learners were unsure of which strategies to use.
4.3.5
Comparison of mean scores
A t-test for independent data was calculated to compare the means and to test the null hypothesis:
There is no significant difference in the mean scores of both control and experimental groups in the post-test.
The calculated value was 4,4706 which is larger than the critical value for two-tailed test at both 5 % and 1 % level of confidence. Since the calculated value was larger than the critical value at both of these levels, null hypothesis was rejected (see 4.2). Therefore the following conclusion was made:
There is a significant difference in the mean scores of the control and experimental groups.
It can be deduced from the above conclusion that the experimental group performed better than the control group in the post-test.