“That Wasn’t the Math I Wanted to do!”—Students’ Beliefs During the Transition from School to University Mathematics

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.

Beliefs about school mathematics vs. university mathematics and beliefs about teaching and learning in different contexts of students’ achievement

“…As we pointed out int the introduction, the different nature between school mathematics and university mathematics may affect PSTs' beliefs about mathematics. Unlike school mathematics which emphasizes schematic calculations in solving mathematical tasks, university mathematics mostly emphasizes proofs (Tall, 2008) which the schematic calculations cannot be used to do the proofs (Geisler & Rolka, 2021).…”

“…Mathematics is shown in "finished form" (p. 128), the form which we see often in university mathematics textbooks and journals. Geisler and Rolka (2021) argue that presenting the front face of mathematics could be related to the phenomenon why university students see university mathematics in a static view (associated with the instrumentalist view).…”

“…Whereas, other studies (for example : Beswick, 2012) have revealed that teachers may hold different beliefs about school mathematics and pure mathematics (pure mathematics is usually learned at universities, and therefore, in this paper pure mathematics is also subsumed under the term university mathematics). Geisler and Rolka (2021) highlight the possibility that university students differ school mathematics from university mathematics because of the different nature of school mathematics and university mathematics. Therefore, in this study, we will also explore whether PSTs have different beliefs of both types of mathematics.…”

The transition from school to university in mathematics education research: new trends and ideas from a systematic literature review

“…The studies in this category consider a wide range of cognitive, social, and affective factors and are mostly quantitative, involving large samples. Their explicit goal is to highlight significant correlations between academic success and other factors, such as students' attitudes (Geisler, 2021), standardised test results (Culpepper et al, 2010), attended secondary school (Adamuti-Trache et al, 2013), prior knowledge (Rach & Ufer, 2020), students' learning prerequisites (Rach & Heinze, 2017), interest (Kosiol et al, 2019), and students' beliefs (Geisler & Rolka, 2021). (4) Failure in STT.…”

“…Many difficulties the learners experience in the passage from school mathematics to university mathematics appear to be related to a sudden change in their mathematics identity (Hernandez-Martinez et al, 2011). Many successful students develop a different view of mathematics in their passage to university, often perceiving that their ability in mathematics is suddenly reduced and, consequently, developing very strong negative emotions in their university experience (Geisler & Rolka, 2021). This affective phenomenon is however related to an epistemological aspect: the meaning of being a successful student in mathematics.…”