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.
As an alternative to questionnaires suitable for young students, pictures, texts and interviews are used as data sources for studying mathematical world views of fifth and sixth graders in a several-step design. The project was developed in three successive studies. In the first study, the approach of using pictures, texts and interviews for researching young students' mathematical world views was investigated. Object of the second study was the development of an interrater-method for determining mathematical world views which delivered a satisfactory degree of reliability. The empirical results in the second study indicated as well that quite often mathematics courses were dominated by a view on mathematics emphasizing numbers or calculations.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.