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Problems with students’ performance in Mathematics at tertiary level are common in South Africa − as it is worldwide. Pass rates at the university of technology where the researcher is a lecturer, are only about 50%. At many universities it has become common practice to refer students who do not have a reasonable chance to succeed at university level, for additional support to try to rectify this situation. However, the question is which students need such support? Because the Grade 12 marks are often not perceived as dependable, it has become common practice at universities to re-test students by way of an entrance exam or the "National Benchmark Test"- project. The question arises whether such re-testing is necessary, since it costs time and money and practical issues make it difficult to complete timeously. Many factors have an influence on performance in Mathematics. School-level factors include articulation of the curriculum at different levels, insufficiently qualified teachers, not enough teaching time and language problems. However, these factors also affect performance in most other subjects, but it is Mathematics and other subjects based on Mathematics that are generally more problematic. Therefore this study focused on the unique properties of the subject Mathematics. The determining role of prior knowledge, the step-by-step development of mathematical thinking, and conative factors such as motivation and perseverance were explored. Based on the belief that these factors would already have been reflected sufficiently in the Grade 12 marks, the correlation between the marks for Mathematics in Grade 12 and the Mathematics marks at tertiary level was investigated to assess whether it was strong enough for the marks in Grade 12 Mathematics to be used as a reliable predictor of success or failure at university level. It was found that the correlation between the marks for Mathematics Grade 12 and Mathematics I especially, was strong (r = 0,61). The Mathematics marks for Grade 12 and those for Mathematics II produced a correlation coefficient of rs = 0,52. It also became apparent that failure in particular could be predicted fairly accurately on the basis of the Grade 12 marks for Mathematics. No student with a Grade 12 Mathematics mark below 60% succeeded in completing Mathematics I and II in the prescribed two semesters, and only about 11% successfully completed it after one repetition. The conclusion was that the reliability of the prediction based on the marks for Grade 12 Mathematics was sufficient to refer students with a mark of less than 60% to receive some form of additional support. / MEd, Learning and Teaching, North-West University, Vaal Triangle Campus, 2011

Problems with students’ performance in Mathematics at tertiary level are common in South Africa − as it is worldwide. Pass rates at the university of technology where the researcher is a lecturer, are only about 50%. At many universities it has become common practice to refer students who do not have a reasonable chance to succeed at university level, for additional support to try to rectify this situation. However, the question is which students need such support? Because the Grade 12 marks are often not perceived as dependable, it has become common practice at universities to re-test students by way of an entrance exam or the "National Benchmark Test"- project. The question arises whether such re-testing is necessary, since it costs time and money and practical issues make it difficult to complete timeously. Many factors have an influence on performance in Mathematics. School-level factors include articulation of the curriculum at different levels, insufficiently qualified teachers, not enough teaching time and language problems. However, these factors also affect performance in most other subjects, but it is Mathematics and other subjects based on Mathematics that are generally more problematic. Therefore this study focused on the unique properties of the subject Mathematics. The determining role of prior knowledge, the step-by-step development of mathematical thinking, and conative factors such as motivation and perseverance were explored. Based on the belief that these factors would already have been reflected sufficiently in the Grade 12 marks, the correlation between the marks for Mathematics in Grade 12 and the Mathematics marks at tertiary level was investigated to assess whether it was strong enough for the marks in Grade 12 Mathematics to be used as a reliable predictor of success or failure at university level. It was found that the correlation between the marks for Mathematics Grade 12 and Mathematics I especially, was strong (r = 0,61). The Mathematics marks for Grade 12 and those for Mathematics II produced a correlation coefficient of rs = 0,52. It also became apparent that failure in particular could be predicted fairly accurately on the basis of the Grade 12 marks for Mathematics. No student with a Grade 12 Mathematics mark below 60% succeeded in completing Mathematics I and II in the prescribed two semesters, and only about 11% successfully completed it after one repetition. The conclusion was that the reliability of the prediction based on the marks for Grade 12 Mathematics was sufficient to refer students with a mark of less than 60% to receive some form of additional support. / MEd, Learning and Teaching, North-West University, Vaal Triangle Campus, 2011

Thesis (Mcom)--University of Stellenbosch, 2003. / ENGLISH ABSTRACT: The field of human resources involves continuous decision-making regarding the matching of the workforce with the workplace, since this match determines individuals' motivation to perform the actions associated with the workplace. If, at the time of the decision, the decision maker could obtain information on end performance, the chances of achieving the desired results would be increased. However, personnel selection is complicated by the obvious fact that information on end performance is not available at the time of the selection decision. All such decisions thus involve predictions about people's performance. The classic validity model forms the foundation of all prediction in as far as the strength of the relationship between the predictor of performance and the actual performance determines the accuracy of the predictor. Over time, numerous possibilities have been considered on how to increase the magnitude of this relationship as experienced through the validity coefficient, mostly involving modifications and/or extensions to the standard regression model. An interesting and challenging alternative to the usual multiple-regression based attempts may be found in the work of Ghise11i (1956, 1960a, 1960b). He has chosen to improve prediction directly through the development of a composite predictability index that explains variance in the prediction errors resulting from an existing prediction model. It would, however, appear as if the procedure has found very little, if any, practical acceptance, partly attributed to the fact that the predictability index failed to significantly explain unique variance in the criterion when added to a model already containing one or more predictors. Resultantly, based on the Ghiselli idea, this research investigates the possibility of modifying such a predictability index so that it does significantly explain unique variance in the criterion when added to a model already containing one or more predictors. In addition, the study investigates whether the expansion of the prediction model is warranted by examining the effect the increase in subject predictability has on the predictive validity of the selection procedure, as well as the monetary effect it has on the utility of the procedure. Hypotheses are tested to determine the possibility of developing an index from a personality measurement that shows a strong and significant correlation with the residuals computed from the regression of the criterion on an ability predictor; to determine if the addition of the index to an ability predictor significantly explains variance in the criterion measurement that is not yet explained by the ability predictor relationships, and to determine whether this ability is affected by the direction in which the index has been developed. Furthermore, hypotheses are tested to determine the increment on validity and selection utility. The data for the analysis was obtained from Psytech (SA), where a validation study was performed at the Gordon Institute of Business Science using the Apil-B ability test, the Critical Reasoning Test Battery and the Organisational Personality Profile measurements to predict the performance of 100 MBA students. The results of the analysis confirmed Ghiselli' s earlier findings that the traditional predictability index does not significantly explain variance in the criterion residual when added to the selection battery. However, by modifying the Ghiselli procedure, the study found that the index was able to significantly explain variance when added to a battery already containing the predictor. When the index is based on the real values of the residuals, the addition of the predictability index to the model significantly explains unique variance in the criterion, but not so when based on the absolute values of the residuals. It also indicated that the inclusion of the predictability index to the prediction model created a substantial increase in the validity of the selection procedure and that the increase in validity translated into a noteworthy improvement in utility. Conclusions are drawn from the obtained results and recommendations are made for future research. / AFRIKAANSE OPSOMMING: 'n Psigometriese Ondersoek na die Gebruik van 'n Aanpassing van die Ghiselli Voorspellingsindeks in Personeelkeuring: Die veld van menslike hulpbronne sluit 'n aaneenlopende besluitnemingsproses aangaande die passing van die arbeidsmag met die werkplek in, aangesien hierdie passing die individu se motivering met betrekking tot optredes wat met die werkplek geassossieer word, bepaal. lndien die besluitnemer ten tye van die besluitneming alreeds oor inligting rakende die eindprestasie van die individu beskik, sal die moontlikheid verhoog word om die gewenste resultate uit die besluitneming te verkry. Personeelkeuring word egter gekompliseer deur die voor die hand liggende feit dat inligting rakende die eindprestasie nie beskikbaar is ten tye van die keuringsbesluit nie. Alle besluite van hierdie aard sluit dus voorspellings oor individue se prestasie in. Die klassieke geldigheidsmodel vorm die basis van alle voorspellings gebaseer op die sterkte van die verwantskap tussen die voorspeller van prestasie en die werklike prestasie van die individu. Oor die jare is verskeie moontlikhede oorweeg om die sterkte van die hierdie verwantskap soos uitgedruk deur die geldigheidskoëffisiënt te verhoog, hoofsaaklik deur middel van aanpassings en/of verlengings van die standaardregressiemodel. 'n Interessante en uitdagende alternatief vir die pogings gebaseer op meervoudige regessie kan gevind word in die werk van Ghiselli (1956, 1960a, 1960b). Hy poog om voorspelling direk te verbeter deur die ontwikkeling van 'n saamgestelde voorspellingsindeks wat variansie verklaar in die voorspellingsfoute verkry uit 'n bestaande voorspellingsmodel. Dit wil egter voorkom asof die voorspellingsindeks gefaal het om unieke variansie in die kriterium te verklaar wanneer dit toegevoeg word tot 'n model wat alreeds een of meer voorspellers bevat. Gebaseer op die Ghiselli-idee, ondersoek hierdie navorsing dus die moontlikheid om die voorspellingsindeks aan te pas sodat dit beduidend unieke variansie in die kriterium verklaar wanneer dit toegevoeg word tot 'n model wat alreeds een of meer voorspellers bevat. Die studie ondersoek enersyds ook die regverdiging van die uitbreiding van die voorspellingsmodel deur die impak van die verbetering in voorspelling op die voorspellingsgeldigheid van die keuringsprosedure, en andersyds bestudeer dit ook die monetêre effek op die nutwaarde van die prosedure. Hipoteses word getoets om die moontlikheid van 'n indeks, wat uit 'n persoonlikheidsmeting ontwikkel, is en wat sterk en beduidend met die residue wat uit die regressie van die kriterium op die vermoënsvoorspeller bereken is, te bepaal. Daar word ook getoets of die toevoeging van die indeks tot 'n vermoënsvoorspeller beduidende variansie in die kriteriummeting verklaar wat nie alreeds deur die vermoënsvoorspeller verklaar word nie. Daar word verder bepaal of hierdie vermoë geaffekteer word deur die rigting waarin die indeks ontwikkel is. Verder word hipoteses getoets aangaande die impak op beide die geldigheid en die nutwaarde van die keuringsprosedure. Die data vir die analises is verkry by Psytech SA, waar 'n valideringstudie uitgevoer is by die Gordon Institute of Business Science deur die gebruik van die Apil-B vermoënstoets, die Critical Reasoning Test Battery en die Organisational Personality Profile metings om die prestasie van 100 MBA studente te voorspel. Die resultate van die analise bevestig Ghiselli se vroeëre bevindings dat die tradisioneel ontwikkelde indeks nie beduidend variansie in die kriteriumresidue verklaar wanneer dit toegevoeg word tot die keuringsbattery nie. Deur egter die oorspronklike Ghiselli prosedure aan te pas word gevind dat die toevoeging van die indeks tot die regressiemodel wel beduidend unieke variansie verklaar. Die vermoë van die indeks om variansie te verklaar wanneer dit tot die battery toegevoeg word, is beduidend wanneer die indeks gebaseer word op die werklike waardes van die residue, maar toon geen beduidendheid wanneer dit gebaseer word op die absolute waardes van die residue nie. Die resultate dui ook daarop dat die insluiting van die voorspellingsindeks in die model 'n betekenisvolle toename in die voorspellingsgeldigheid van die keuringsprosedure teweegbring, en dat die toename in voorspellingsgeldigheid vertaal na 'n substantiewe styging in nut. Gevolgtrekkings word uit die verkreë resultate afgelei, en aanbevelings vir toekomstige navorsing word gemaak.

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