Over half of all students enrolling at a particular university in KwaZulu-Natal fail to complete a degree. This article aims to determine to what extent the marks they obtain for English and Mathematics at school impact on their probability of graduation at this university. In addressing this problem, other student specific factors associated with their gender, race and the type of school they attended need also to be properly accounted for. To provide answers for this study, the performance of 24 392 students enrolling at the university over the period 2004 to 2012 was followed until they graduated or dropped out from their studies. A structural equation model was fitted because it allows one to separate a direct effect from that of an indirect effect. Gender, race and school background were found to be very significant with men, Black Africans and students coming from a less privileged school background having a smaller probability associated with eventually graduating from this university. Men tend to perform better than women in Mathematics, with women performing better men in English. More importantly, however, a single percentage point increase in one’s mark for English increases the probability associated with graduating from this university far more than would be the case if their Mathematics mark were to increase by a single percentage point. In light of these mediated results, perhaps this university should be directing their efforts more towards improving the English (rather than mathematical) literacy of students entering the university.

Prior to 2008 students completing their school-leaving Grade 12 examinations in South Africa could take subjects at a higher or a standard grade level. In 2008 all subjects were collapsed into a single grade with Mathematical Literacy being offered as an alternative for students who would have preferred to take Mathematics at a standard grade level prior to 2008. Entry into a particular programme at a specific university in KwaZulu-Natal in South Africa (hereafter the university) depends on an appropriate level of marks (called a

Support for some of the factors that we will be including in our structural equation based prediction model come from a variety of international and locally based studies. Naylor and Smith (

Wealthier schools will be able to appoint better qualified teachers. Added to this mix is a powerful teacher’s union whose policies attempt to entrench the job security of teachers in the less wealthy schools irrespective of whether they can teach their subjects or not. In a recent study, Murray (

Bohlmann and Pretorius (

Studies by Feast (

Do women perform better than men at university?

Do women perform better than men even after an appropriate adjustment has been made for other predictive factors associated with race, school background, college of enrolment and the receipt of residence-based accommodation?

How do women who have done well in English at school compare with those who have not done well in English with respect to their performance at university?

The data that have been used for this study comes from a university situated in KwaZulu-Natal. A total of 24 392 students enrolled for a degree at this university over the period 2004 to 2012. For each student, the mark (expressed as a percentage) that they obtained for Mathematics and English in their school-leaving examinations was collected together with some of the other more important predictor variables that have been highlighted in the previous section of this article. University specific variables indicating whether or not they received some form of residence-based accommodation while studying at university were also included together with the college in which they chose to study.

Variables that were included in the analysis.

Variable name | Definition |
---|---|

Male | 1 = male student |

National Senior Certificate | 1 = wrote the National Senior Certificate examination |

Residence | 1 = given residence-based accommodation |

Black African | 1 = Black African student |

Agriculture, Engineering & Science | 1 = student enrolled in College of Agriculture, Engineering & Science |

Law & Management | 1 = student enrolled in College of Law & Management |

Health Sciences | 1 = student enrolled in College of Health Sciences |

Humanities | 1 = student enrolled in College of Humanities |

Quintile 5 | 1 = student went to a quintile 5 school |

The results in

Performance measures for English and Mathematics over the period 2004–2012.

Subject | Definition | Mean (%) | Standard deviation |
---|---|---|---|

English | Percentage mark obtained for English in the school-leaving examination | 69.51 | 10.21 |

Mathematics | Percentage mark obtained for Mathematics in the school-leaving examination | 64.06 | 17.49 |

All public schools in South Africa are given a ranking based on the level of poverty that exists within the community in which the school is located. This ranking takes into account the average level of income that is earned by someone in the area surrounding that school, the unemployment rate and the level of education within that community. Schools falling in the bottom 20% of this ranking (i.e. the poorest schools) are then classified as being quintile 1 schools. Schools falling within the top 20% of this ranking are said to be quintile 5 schools. In

Two sample test results for comparing the Mathematics and English results of quintile 5 schools with quintile 1–4 schools (assuming unequal variances in the grouped populations).

Subject | Population groups | Number of observations | Mean | Standard error | Two sample |
---|---|---|---|---|---|

English | Quintile 5 school |
14 957 |
71.66 |
0.19 |
41.32 |

Mathematics | Quintile 5 school |
14 957 |
64.98 |
0.13 |
10.19 |

denotes significance at 5% level.

A 0/1 variable indicating whether a student has eventually been able to graduate from this university has been used as a response variable Y for this article. Students who were still busy with their studies when the study period ended were deleted from the data set. The results given in

Observed graduation rates at the university over the period 2004–2012.

Outcome | Frequency (%) |
---|---|

Did not graduate | 56.73 |

Did graduate | 43.27 |

A demographic breakdown of graduation rates at this university.

Covariate | Outcome | Proportion of students being represented in the sample | Percentage who graduated |
---|---|---|---|

Male | Yes | 0.423 | 0.384 |

No | 0.577 | 0.439 | |

Black African | Yes | 0.425 | 0.341 |

No | 0.575 | 0.501 | |

Quintile 5 | Yes | 0.613 | 0.454 |

No | 0.387 | 0.334 | |

National Senior Certificate | Yes | 0.404 | 0.231 |

No | 0.596 | 0.687 | |

Residence | Yes | 0.273 | 0.427 |

No | 0.727 | 0.383 | |

College | Agriculture, Engineering and Science | 0.282 | 0.345 |

Humanities | 0.077 | 0.471 | |

Health Sciences | 0.366 | 0.425 | |

Law and Management | 0.275 | 0.459 |

All the results given in

Parameter estimates associated with covariates affecting the probability of graduation at the university.

Covariates | Parameter estimate | Standard error | [95% confidence interval] | Odds ratio |
---|---|---|---|---|

English | 0.021 |
0.002 | [0.017; 0.024] | 1.021 |

Mathematics | 0.009 |
0.001 | [0.007; 0.011] | 1.009 |

Quintile 5 | 0.111 |
0.047 | [0.017; 0.205] | 1.117 |

Quintile 5 × Black African | 0.097 | 0.067 | [−0.034; 0.229] | 1.102 |

Male | −0.237 |
0.031 | [−0.297; –0.177] | 0.789 |

Black African | −0.427 |
0.059 | [−0.543; –0.312] | 0.652 |

Residence | 0 260 |
0.048 | [0.165; 0.355] | 1.297 |

Agriculture, Engineering and Science | −0.637 |
0.037 | [−0.711; –0.565] | 0.529 |

Humanities | 0.078 |
0.038 | [0.003 0.154] | 1.081 |

Health | 0.624 | 0.075 | [0.477; 0.771] | 1.866 |

National Senior Certificate | −1.144 |
0.030 | [−1.203; –1.085] | 0.319 |

Constant | −0.797 |
0.142 | [−1.075; –0.519] | - |

denotes significance at 5% level.

Parameter estimates that are significantly positive in value indicate covariates that will help to increase the probability associated with graduating from the university. For example, the parameter estimate –0.237 associated with being male implies that men have a smaller probability associated with eventually graduating than women. In terms of an odds ratio, the above estimate implies that the probability associated with a man graduating is 0.789 times the probability associated with a woman graduating; i.e.

Using a 5% level of significance, the results in

In this section, we will focus on the marks that students obtained for Mathematics and English when writing their school-leaving examinations. Given that these subjects are compulsory for all school leavers we want to identify whether obtaining a particular mark for Mathematics improves one’s probability of graduating from this university more than obtaining the same mark for English. At the same time, we want to separate the total effect that race, gender and school background have on graduation into an indirect effect that is mediated by the type of mark obtained at school for Mathematics and English and a direct effect representing the residual effect of these three factors on graduation that results after having controlled for the mediation effects of Mathematics and English. By doing this, we can now address other issues that may be of interest such as whether the university should look at offering an extra course in English or Mathematics (or both) to help students bridge the gap between what they actually know and what they need to know in order to improve their chances of graduating at this university.

Structural equation based models allow one to estimate direct and indirect effects for a given problem. Referring to the diagram given in

A structural equation model for graduation with direct and indirect mediated effects.

Path-based estimates associated with the fitting of a logistic model to that part of the path model in

Direct effect estimates associated with graduation for the model structure given in

Path | Parameter estimate | Standard error | [95% Confidence interval] | Odds ratio |
---|---|---|---|---|

Quintile 5 → Graduate | 0.113 |
0.047 | [0.017; 0.204] | 1.119 |

Quintile 5 × Black African → Graduate | 0.097 | 0.067 | [−0.034; 0.229] | 1.101 |

Male → Graduate | −0.237 |
0.031 | [−0.297; –0.178] | 0.789 |

Black African → Graduate | −0.427 |
0.059 | [−0.543; –0.312] | 0.652 |

Residence → Graduate | 0.260 |
0.048 | [0.165; 0.355] | 1.297 |

Agriculture, Engineering and Science → Graduate | −0.637 |
0.037 | [−0.710; –0.564] | 0.529 |

Humanities → Graduate | 0.078 |
0.039 | [0.002; 0.153] | 1.081 |

Health Sciences → Graduate | 0.624 |
0.075 | [0.477;0.770] | 1.866 |

National Senior Certificate → Graduate | −1.144 |
0.030 | [−1.203; –1.085] | 0.318 |

Constant → Graduate | −0.797 |
0.142 | [−1.075; –0.519] | - |

denotes significance at 5% level.

Indirect effect estimates that are mediated through Mathematics and English.

Path | Parameter estimate | Standard error | [95% confidence interval] | Odds ratio |
---|---|---|---|---|

Black African → English | −10.016 |
0.197 | [−10.404; –9.629] | - |

Quintile 5 → English | 0.466 |
0.186 | [0.101; 0.830] | - |

Quintile 5 × Black African → English | 1.546 |
0.255 | [1.045; 2.046] | - |

Male → English | −3.440 |
0.113 | [−3.663; –3.216] | - |

Constant → English | 74.283 |
0.172 | [73.945; 74.621] | - |

Male → Mathematics | 3.720 |
0.219 | [3.291; 4.149] | - |

Black African → Mathematics | −7.299 |
0.379 | [−8.042; –6.556] | - |

Quintile 5 → Mathematics | −0.510 | 0.359 | [−1.214; 0.194] | - |

Quintile 5 × Black African → Mathematics | 0.437 | 0.498 | [−0.539; 1.413] | - |

Constant → Mathematics | 65.716 |
0.332 | [65.066; 66.368] | - |

English → Graduate | 0.021 |
0.002 | [0.017; 0.024] | 1.021 |

Mathematics → Graduate | 0.009 |
0.001 | [0.007; 0.011] | 1.009 |

denotes significance at 5% level.

Focusing on the direct effect estimates that are given in

Focusing on the path-based estimates that appear in

Focusing on gender and its mediated effect on graduation based on the type of mark recorded for Mathematics and English, the results given in

Two sample test results comparing the Mathematics and English results of men with women (assuming unequal variances in the grouped populations).

Subject | Gender | Number of observations | Mean | Standard error | Two sample |
---|---|---|---|---|---|

Mathematics | Male |
10 341 |
66.04 |
0.17 |
15.26 |

English | Male |
10 341 |
67.08 |
0.10 |
−32.23 |

denotes significant at 5% level.

Focusing on race and its mediated effect on graduation based on the type of mark recorded for Mathematics and English, the results given in

Two sample test results comparing the Mathematics and English results of Black African with non-Black African students (assuming unequal variances in the grouped populations).

Subject | Race | Number of observations | Mean | Standard error | Two sample |
---|---|---|---|---|---|

Mathematics | Black African |
10 373 |
60.26 |
0. 17 |
−29.36 |

English | Black African |
10 373 |
64.09 |
0.09 |
−78.47 |

denotes significant at 5% level.

Focusing on school background, the inclusion of an interaction term (Quintile 5 × Black African) that denotes a Black African who attended a quintile 5 school allows one to isolate the direct and mediated effect on graduation of this cohort from that of other non-Black African students who also attended a more privileged quintile 5 school. The results in

In this article, we have been concerned primarily with constructing an appropriate prediction model for graduation at the university. By making use of a structural equation model we have been able to model not only the direct effects associated with graduation but also the indirect effects that have been appropriately mediated by the marks that students obtain for English and Mathematics in their school-leaving examinations. Focusing on the direct effects that were observed, gender and race play a significant role with men having a smaller probability of graduating (when compared to women) and Black African students not doing as well as their non-Black African counterparts. Students coming from a more privileged school background have a greater probability of eventually graduating from the university.

Focusing on the indirect effects, a strong gender bias emerges with men tending to perform better in Mathematics than women and women better than men in English. More importantly, however, a single percentage increase in one’s mark for English serves to increase the probability of graduating from the university by an amount which far exceeds what would be the case with a single percentage point increase in one’s Mathematics mark.

In light of these mediated results, when it comes to holding a discussion around bridging and the type of courses that should be developed for struggling students, more attention should be given towards improving the English (rather than mathematical) literacy of students entering this institution.

The author declares that he has no financial or personal relationships that may have inappropriately influenced him in writing this article.