### Abstract:

The aims of this study were to develop prediction models with which to predict the mathematics achievement of third-year students at the PU for CHE. To develop a prediction analysis for continuous data by means of which the mathematics achievement of third-year students can be predicted in terms of a pass-fail dichotomy by using the fundamentals of Boolean algebra. To determine, as a secondary aim, the difference influence of several independent variables on the mathematics achievement of male and female students in their third year. Of the set of independent variables in this study, five indicated previous achievement, 10 were aptitude variables (including an estimated IQ score) and 21 were measures of different interests, while a measure of the algebraic preparedness of prospective mathematics students on the PU for CHE was also included. The mathematics achievement of students at the end of the first semester of the first year was used in part of the investigation as an independent variable. Four criteria were defined to quantify the mathematics achievement of students at the PU for CHE. In three of these, unsuccessful attempts to obtain a pass in mathematics courses were taken into consideration. The aptitude variables in this study were measured with the Senior Aptitude tests (HSRC), the 19-Field Interest Questionnaire (HSRC) and the algebraic preparedness of students was measured by means of a 60-item multiple-choice test developed by this researcher and of which measures of validity and reliability were reported. The data of two groups of subjects considered as study populations, were used in the study. The group of first-year students following mathematics courses for the first time in 1982 was employed as an experimental group. Of the 154 first-year students in this group, 58 were able to advance to the third year and wrote the examination in at least one mathematics course in that year. The class of first-year students registered for mathematics courses for the first time in 1983 was used as a cross-validation group in order to validate the prediction models. This group consisted of 138 students, of which 54 advanced to the third year. Six hypotheses were examined in this study by means of several statistical techniques. By means of singular correlation it was shown that certain independent variables exerted a bigger influence on the mathematics performance of third-year students than others and that the correlations of some independent variables with mathematics achievement decreased from the first year to the third year. Regarding other variables, the opposite tendency was found. By means of factor, regression, discriminant and Boolean analysis, it was further found that the mathematics achievement of male and female students on the third year level was influenced differently by independent variables. The hypothesis that a higher percentage of the variance of mathematics performance in the case of females than that of males can be accounted for, could not be accepted for all criteria of mathematics achievement. The validity of prediction models could also not be accepted for all criteria of mathematics performance, even if the mathematics achievement of students at the end of the first semester in the first year was included as an independent variable in the regression analysis. Finally it was found that prediction models for the pass/fail dichotomy for mathematics achievement, developed by means of Boolean analysis, were on the average more successful in terms of validity than the discriminant functions developed by using discriminant analysis. This result indicated a promising future for the use of Boolean analysis in the prediction of academic achievement.