Testing relationships between Mathematics performance and learner level

Table 4.11 provides an overview of the distribution of the variables, type of variables (discrete or continuous) as well as the type of analysis used to test if relationships exist between the Mathematics score (dependent) and the independent variables. In cases where independent variables are discrete simple ANOVAs are used and in the case of continuous independent variables, correlations are used.

Table 4.11: Outline of learner level variables included in the analysis Learner level

variables Distribution Type of variable Type of analysis

Age Normal Continuous Pearson correlation

Population group Non-normal Discrete (Nominal) ANOVA Language of learning

and teaching (LoLT) Non-normal Discrete (Nominal) ANOVA Family structure Non-normal Discrete (Nominal) ANOVA

Family SES Normal Continuous Pearson correlation

Home educational

resources Non-Normal Discrete (Nominal) ANOVA

Adult involvement in

student learning Non-normal Continuous

Spearman correlation Learner being bullied Non-Normal Discrete (Nominal) ANOVA Learner perception of

school climate Non-normal Continuous

Spearman correlation Learner likes

Mathematics

Non-Normal Discrete (Nominal) ANOVA

Learner values Mathematics

Non-Normal Discrete (Nominal) ANOVA

Learner confidence in learning Mathematics

Non-Normal Discrete (Nominal) ANOVA  

93 | P a g e 4.2.3.1 Correlations

Correlations are used to describe the strength of relationships between two variables. The correlation coefficient ranges from -1 to 1 with correlations closer to zero signifying weak relationships and strong relationships occurring when values are closer to one or minus one. A positive (+) or negative (-) sign before a correlation indicates the direction of the relation where a positive sign means a positive relationship, indicating that an increase in one variable results in an increase in the other variable or a decrease in one variable results in a decrease in the other variable. However, a negative relationship means an increase in one variable result in a decrease in the other variable. Table 4.12 (Hinkle, Wiersma, & Jurs, 2003) provides a rule of thumb that enables one to interpret the results of the correlations.

Table 4.12: Rule of thumb for analysis of correlation results

Size of Correlation Interpretation

.90 to 1.00 (-.90 to –1.00) Very high positive (negative) correlation .70 to .90 (-.70 to -.90) High positive (negative) correlation .50 to .70 (-.50 to -.70) Moderate positive (negative) correlation .30 to .50 (-.30 to -.50) Low positive (negative) correlation .00 to .30 (.00 to -.30) Little if any correlation

Table 4.13: Correlations of the continuous variables

Math Performance R2 Age Pearson Correlation -0.382 14.6 Sig. (2-tailed) 0.000 N 11818 Family SES Pearson Correlation 0.504 25.4 Sig. (2-tailed) 0.000 N 11889

Adult Involvement Pearson -0.08 0.64

Sig. (2-tailed) 0.000 N 11703        

94 | P a g e

School Climate Pearson 0.049 0.24

Sig. (2-tailed) 0.000

N 11790

** Correlation is significant at the 0.01 level (2-tailed).

There is a significant negative relationship between Mathematics performance and age with a Pearson correlation r= -0.382, p-value (2-tailed) < 0.001. Age accounts for 14.6% of the variability in Mathematics performance. This variability was calculated using R2 which is the coefficient of determination. The results show that a low positive association exists between age and Mathematics performance (see Table 4.13).

A statistically significant relationship is observed between family SES and performance with Pearson correlation r = 0.504, p-value (2-tailed) < 0.001 which is higher than that for learner age. This result shows that moderate positive association exists between family SES and Mathematics performance. SES accounts for 25.4% of the variability in Mathematics performance (see Table 4.13).

Adult involvement shows a significant relationship with Mathematics performance; r (Spearman correlation) = -0.08; p-value (two tailed) < 0.001. The correlation shows that there is very little association between adult involvement and Mathematics with adult involvement only explaining close to 1% of the variance in Mathematics performance (see Table 4.13).

There appears to be a very low significant relationship between school climate and Mathematics performance (r = 0.049; p-value (two tailed) < 0.001) School climate only accounts for 0.24% of the variation in Mathematics performance (see Table 4.13).

4.2.3.2 One-way Analysis of Variance (ANOVA)

An analysis of variance is a way to test the equality of means at one time by using variances. The assumptions of ANOVA are as follows:

95 | P a g e

 The population from which the sample was drawn is normally distributed;

 The samples are independent;

 The variances of the population are equal. The general hypothesis that is tested in an ANOVA is:

Ho: There is no difference in the mean level of Mathematics performance among the different population groups (African versus Other).

Ha: There is a difference in the mean level of Mathematics performance among the different population groups (African versus Other).

Table 4.14: Anova: relationship between Mathematics and the discrete variables ANOVA output

Variable Category Mean F Sig.

Race Other 388.45 56797.56 0.000

African 341.83

Test language vs. home language LoLt

Test lang NOT same as home lang 339.18 167159.80 0.000 Test lang SAME as home lang 428.71

Family structure 2 parent 363.88 15134.66 0.000

Other 343.35 Home educational resources Many resources 487.37 56880.90 0.000 Some resources 362.33 Few resources 333.34 Bullying Almost never 392.55 54879.66 0.000 About monthly 361.82 About weekly 322.05

Like learning Maths

Like learning Maths 378.11 24042.16 0.000

Somewhat like learning Maths 338.61 Do not like learning Maths 347.73

Value Maths

Value Maths 363.98 17125.43 0.000

Somewhat value Maths 340.71

Do not value Maths 308.64

Confidence in doing Maths Confident 427.48 44720.91 0.000 Somewhat confident 349.15 Not confident 344.37        

96 | P a g e

Table 4.15: Bonferroni tests to evaluate between group differences

Variables I J Mean Difference (I-J) Std. Error Home Educ. Resources

Many Resources Some Resources 125.04 *

0.72

Few Resources 154.04* 0.72

Some Resources Few Resources 29.00* 0.15

Bullying Almost never

About monthly 30.72* 0.21

About weekly 70.50* 0.22

About monthly About weekly 39.77* 0.19

Like learning Maths Like learning Maths Somewhat like learning Maths 39.50 * 0.18

Do not like learning

Maths 30.38

*

0.25

Somewhat like learning Maths

Do not like learning

Maths -9.12 * 0.25 Value Maths Value Mathematics Somewhat value Maths 23.26 * 0.21

Do not value Maths 55.34* 0.34 Somewhat value Do not value Maths 32.08* 0.38

Confidence in doing Maths Confident in learning Mathematics Somewhat confident 78.33* 0.28 Not confident 83.12* 0.29 Somewhat

confident Not confident 4.79

*

0.18 * mean difference is significant at the 0.001 level

Table 4.14 shows that population group has a significant effect on Mathematics performance; hence the Ho is rejected in favour of the Ha and it is concluded that there is a significant difference among the mean levels of Mathematics performance, (F = 56797.6; p-value <0.001). The mean Mathematics value for Africans is 341.83 and for the “Other” population groups combined is 388.45 (which is significantly higher).

A similar result is observed for language of instruction and learning. The Ho is rejected in favour of the Ha and it is concluded that there is a significant difference in the means; (F= 167159.8; p-value < 0.001). The mean Mathematics values for the test language being the same as the home language is 428.71, which is

97 | P a g e

significantly higher than when the language of testing and the home language differ (339.18).

Table 4.14 shows that family structure has a significant effect on Mathematics performance and hence the Ho is rejected in favour of the Ha; this indicates that there is a significant difference among the mean levels of Mathematics performance, (F = 15134.66; p-value <0.001). The mean Mathematics value for 2- parent households is significantly higher at 368.88 compared to the other group at 343.35.

When looking at the mean Mathematics scores between categories of the educational resources in the home an improvement in mean Mathematics scores is observed between those learners who said they had many resources (having more than 100 books in the home, Internet, own room and either parent with a degree or higher qualification) and those who said they had few (fewer than 25 books, no Internet, no own room, neither parent has a secondary school qualification). There is a 154 point difference between learners who have many resources and those who said they had few. The ANOVA results in Table 4.14 show that a significant difference is observed; F = 56880.9; p-value <0.001. The Bonferroni test shows that significant differences occur between all the pairwise comparisons of this variable (see Table 4.15).

It is clear from Table 4.14 that bullying has an effect on learner Mathematics performance. The Ho is rejected in favour of the Ha and the conclusion thus is that there are differences between the mean Mathematics levels (F =54879.66; p-value <0.001). The Bonferroni strengthens this result and in Table 4.15 it is shown that there are significant differences between all levels of the bullying variable. Learners who are almost never bullied had an average score of 393 which is significantly higher than learners who are bullied on a weekly basis (322) as well as those bullied once or twice a month (362).

The composite constructs that measure a learner’s perception of Mathematics (liking and valuing Mathematics as well as confidence in doing Mathematics) are all significant (see Table 4.14) and hence the Ho is rejected in favour of the Ha; it

98 | P a g e

is concluded that there are significant differences in the Mathematics scores between the categories of these variables (see Table 4.15). Learners who like learning Mathematics have an average Mathematics score of 378 (F = 24042, p- value< 0.001) which is higher than learners who say they somewhat like learning Mathematics and have an average score of 339. Strange, however, is the fact that learners who say they do not like learning Mathematics had an average Mathematics score that is higher than those learners who said they somewhat like learning Mathematics.

Similarly learners who value Mathematics had an average Mathematics score of 364 which is higher than those who said they somewhat valued Mathematics.