Educational data mining is the process of applying data mining tools and techniques to analyze data at educational institutions. In this paper, educational data mining was used to predict enrollment of students in Science, Technology, Engineering and Mathematics (STEM) courses in higher educational institutions. The study examined the extent to which individual, socio-demographic and school-level contextual factors help in pre-identifying successful and unsuccessful students in enrollment in STEM disciplines in Higher Education Institutions in Kenya. The Cross Industry Standard Process for Data Mining framework was applied to a dataset drawn from the first, second and third year undergraduate female students enrolled in STEM disciplines in one University in Kenya to model student enrollment. Feature selection was used to rank the predictor variables by their importance for further analysis. Various predictive algorithms were evaluated in predicting enrollment of students in STEM courses. Empirical results showed the following: (i) the most important factors separating successful from unsuccessful students are: High School final grade, teacher inspiration, career flexibility, pre-university awareness and mathematics grade. (ii) among classification algorithms for prediction, decision tree (CART) was the most successful classifier with an overall percentage of correct classification of 85.2%. This paper showcases the importance of Prediction and Classification based data mining algorithms in the field of education and also presents some promising future lines.