Word-problem and multiple-choice tests

Word-problem and multiple-choice tests (see appendices Q, R, S & T) were administered to both the experimental and control group at the beginning and the end of the intervention.

Pre-tests N Minimum % Maximum % Mean % Std. deviation Experimental group

multiple choice pre-test 28 36.00 66.00 52.53 7.99 Experimental group

word-problem pre-test 28 39.00 64.00 51.40 7.10 Control group multiple-

choice pre-test 29 32.00 68.00 52.07 10.31 Control group word-

problem pre-test 29 34.00 67.00 54.64 8.38

Table 4. 11 Descriptive statistics for pre- word-problem and multiple-choice tests for

both the experimental and control groups

The mean scores for each test were slightly different such that one might think that the performance of the control group was better than that of the experimental group in the word-problem pre-test or that the performance of the experimental group was better than that of the control group in the multiple-choice pre-test. It is therefore imperative to use statistical techniques to determine whether or not there was a significant difference in the mean scores of these groups. A t-test for independent data was run to test the hypothesis:

H0: There are no significant differences between the pre-test mean

scores of the learners in the experimental and the control groups, that is, the population means are the same.

The calculated t-value for the pre-word-problem test was 0.78 and the calculated t-value for the post-multiple-choice test was 0.41. The calculated t- values for both the word-problem and multiple-choice tests were less than the critical t-value for a 2-tailed test at the p < 0.05 level of significance. Hence the null hypothesis was accepted. This implies that there was no statistically significant difference in the mean scores between the control group and experimental group in the pre- word-problem and multiple-choice tests.

4.3.4.1

Descriptive statistics for the post- word problem and

multiple-choice tests of the experimental and control groups

The post- word-problem and multiple-choice tests were different in the wording of the items but similar in the level of difficulty and all respects to the pre- word-problem and multiple-choice tests and were administered to both groups after the intervention, which was 10 weeks, after learners had written the pre-tests. Below is a table that helped the researcher to compare the performance of the two groups in the post- word-problem and multiple-choice tests.

Post-tests N Minimum % Maximum % Mean % Std. deviation Experimental group multiple-choice post- test 28 50.00 88.00 71.40 9.96 Experimental group word-problem post- test 28 60.00 86.00 74.67 9.31

Control group multiple-

choice post-test 29 46.00 67.00 63.29 8.99 Control group word-

problem post-test 29 45.00 70.00 65.07 7.81

Table 4. 12 Descriptive statistics for post- word-problem and multiple-choice tests for

both the experimental and control groups

The mean scores of the experimental group were higher than the mean scores of the control groups in both the post-word-problem and multiple- choice tests. The minimum and maximum scores of the experimental group were also higher than those of the control group. A t-test for independent data was run to compare the means of the experimental and control groups for both the post-word-problem and multiple-choice tests. The following null hypothesis was tested:

H0: There is no significant difference between the post-test mean

scores of the learners in the experimental and the control groups, that is, the population means are the same.

The calculated t-value for the post-word-problem test was 5.68 and the calculated t-value for the post-multiple-choice test was 4.96. These two values are both larger than the critical t-value for a 2-tailed test at the p < 0.05 level of significance. Hence the null hypothesis was rejected and the researcher concluded that the experimental group learners performed better than control group learners in the post- word-problem and multiple-choice tests. It was therefore reasonable to conclude that the development of mathematical problem solving had a positive effect on grade 8 learners’ performance and achievement in mathematics.

4.3.4.2

Descriptive statistics for the pre- and post- word-problem

and multiple-choice tests for the experimental group

Learners in the experimental group’s performance in the pre- and post- word- problem and multiple-choice tests were analysed in table 4.13.

Pre- and post-tests N Minimum % Maximum % Mean %

Std. deviation Experimental group multiple-

choice pre-test 28 36.00 66.00 52.53 7.99 Experimental group word-problem

pre-test 28 39.00 64.00 51.40 7.10

Experimental group multiple-

choice post-test 28 50.00 88.00 71.40 9.96 Experimental group word-problem

post-test 28 60.00 86.00 74.67 9.31

Table 4. 13 Descriptive statistics for the pre- and post- word-problem and multiple-

choice tests for the experimental group

Table 4.13 indicates a tremendous performance by experimental group learners in their post-tests. The mean scores of post-tests are higher than those of the pre-tests. The minimum and maximum values for the post-tests are higher than the minimum and maximum values for the pre-tests. A t-test was run to test whether or not the mean scores obtained in the pre- and post- word-problem and multiple-choice tests were significantly different. The following null hypothesis was tested:

H0: There is no significant difference between the mean scores of the

experimental group in the pre- and post- word-problem and multiple-choice tests.

The calculated t-value for the word-problem test was 5.53 and for the multiple- choice test was 5.10. The calculated t-values are larger than the critical t- values for a 2-tailed test at the p < 0.05 level of significance and the null hypothesis was thus rejected. The researcher concluded that there was a significant difference between the mean scores of the experimental group in the pre- and post- word-problem and multiple-choice tests. The experimental group’s learners performed and achieved better in their post-test compared to their pre-tests. The researcher confidently concluded that the development of mathematical problem solving skills had a positive effect on the experimental group learners’ performance and achievement in mathematics.