Mathematics for engineering students in the 'Dual System': Assistance in study start-up and conduct

Abstract

One major characteristic of the transition from secondary to tertiary education is the high heterogeneity of students’ knowledge. In STEM-programmes, knowledge gaps in basic mathematics are considered one risk factor regarding graduation. One approach to this problem is the provision of preparatory courses in mathematics. The purpose of this mixed methods evaluation study was to identify factors supporting “at risk” students’ successful pre-course participation and transition to university. This issue was addressed using quantitative and qualitative evaluations carried out with six cohorts of engineering students at Baden-Wuerttemberg Cooperative State University Mannheim.

Using the theory of self-regulated learning as a theoretical framework this thesis analysed the interplay between students’ preconditions, their learning behaviour, and the learning environment. The quantitative analyses revealed a dominant influence of cognitive variables, results in a diagnostic test being the strongest determinant of first year mathematics achievement. Pre-course learning gains had a moderating effect on this relation and an increase in gain score (pre-post-test difference) could be related to an increase in students’ first year mathematics exam.

The analyses of learning behaviour suggested that for the evaluation of successful learning processes of “at risk” students other variables are relevant than for the rest of the student body. Attitude towards mathematics or students’ use of time management and organisational strategies, for example, did not affect learning gains of this group and were identified as covariates of prior domain knowledge. Only one variable significantly contributed to explaining why “at risk” students obtained higher pre-course gain scores. The number of self-tests a student had submitted correlated with learning gains and even showed a significant impact on first year performance in mathematics.

The study also showed that this group of learners highly benefits from external structuring and guidance. A comparison of additional support programmes revealed much more learning activities and higher learning gains for participants in an e-tutored course than for participants in a less structured face-to-face version. Avoiding self-monitoring activities could be identified as an additional risk factor for students with poor domain knowledge.

Deviations from the quantitative model suggested that high learner engagement not necessarily results in increased first year performance. A set of interviews with first year students helped to understand counterintuitive results and clarify why even students with “ideal” data profiles sometimes struggle in their first year at university. It was shown that “at risk” students are less able to seek help and to benefit from peer learning.

Based on the analyses carried out in this thesis a set of recommendations for the design of preparatory courses in mathematics are made that are considered highly relevant for practitioners in the field of study preparation, e-learning and learning analytics.