Abstract
It is a well-known fact that many students struggle during the transition from school to university mathematics. The aim of our quantitative study was to clarify the role of students’ beliefs concerning the nature of mathematics for a successful transition. We distinguish between static beliefs (mathematics as a finished system of rules, facts and formula) and dynamic beliefs (mathematics as a dynamic discipline with applications in everyday life). In particular, we examined whether first year students’ beliefs are suitable to predict students’ exam achievement and their satisfaction (as criteria for a successful transition) and how students’ beliefs develop during the transition. Therefore, we used questionnaires at the beginning and in the middle of the first term at university. Our results indicate that dynamic beliefs decrease during transition, whereas static beliefs remain rather stable. This seems problematic since dynamic beliefs turned out to negatively predict students’ dropout intention, while static beliefs are a negative predictor of students’ achievement in real analysis. Furthermore, the beliefs assessed in the middle of the term had a stronger predictive power than those at the beginning of the term. Based on these results, we discuss implications for the teaching of mathematics during the transition.
Highlights
The transition from school to university is a challenging process for many students, likewise in mathematics
In contrast to previous studies that only examined the development of beliefs in a whole sample, our results enable a more differentiated perspective by comparing the development of successful and rather unsuccessful students: The decrease of dynamic beliefs is significantly smaller for students without dropout intention than for those who thought about quitting their studies
In line with theories of person-environment fit, we focused on objective criteria and subjective criteria of success in the transition to gain a more comprehensive picture of the role that students’ beliefs play in this phase
Summary
The transition from school to university is a challenging process for many students, likewise in mathematics. This is illustrated by high dropout and subject change rates. Many students fail their first exams or do not even attend them (Geisler & Rolka, 2018). These findings underline the necessity to understand students’ problems during the transition phase. In this contribution, we focus on the development and influence of students’ beliefs concerning the nature of mathematics during the transition. In order to better understand the role that students’ beliefs play in this transition process, we first give an overview about major differences between mathematics at school and university and second discuss theories of person-environment fit (Lubinski & Benbow, 2000; Nagy, 2006; Swanson & Fouad, 1999), which have already been used in the context of transition from school to university mathematics (e.g. Rach & Heinze, 2017)
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