Not the Norm: The Potential of Tree Analysis of Performance Data from Students in a Foundation Mathematics Module

Abstract

Quantitative methods of data analysis usually involve inferential statistics, and are not well known for their ability to reflect the intricacies of a diverse student population. The South African tertiary education sector is characterised by extreme inequality and diversity. Foundation programmes address issues of inequality of access by providing an opportunity for disadvantaged students with academic potential to enter mainstream degree programmes. Seeking to understand which factors are most influential in enhancing student selection and their performance in a foundation mathematics module, Classification and Regression Tree (CART) analysis is presented as a non-parametric alternative to traditional quantitative research methods. CART, a data-mining technique, is illustrated with reference to two cohorts of students enrolled in the foundation module. The two cohorts had experienced different secondary school curricula. The regression tree to examine students' final mathematics marks illustrated that the primary performance indicators for both cohorts related to the alternative selection criteria, whereas school-level performance was of little consequence. The classification tree showed that passing the module depended on socio-economic, and not academic, indicators, irrespective of school history. The hierarchy of context-dependent influences revealed in the trees illustrated that no single variable can be the basis for a framework for practical and policy responsiveness in a context of such student diversity.

Keywords:

• Student diversity
• Foundation Mathematics module
• classification and regression (decision) tree analysis

Acknowledgement

This research was part of Nicola Kirby's doctoral study. This author is particularly indebted to Professor Colleen Downs of the School of Life Sciences, UKZN, for her mentorship, encouragement and award of funding for this research.

Disclosure Statement

No potential conflict of interest was reported by the authors.

Notes

1 Working within the postpositivist paradigm, the first author finds it more appropriate to refer to ‘explanatory variables' rather than ‘predictor variables' (see Kirby, 2013). The former term is used throughout this paper.