The Transition from School to University in Mathematics: Which Influence Do School-Related Variables Have?

Abstract

Particularly in mathematics, the transition from school to university often appears to be a substantial hurdle in the individual learning biography. Differences between the characters of school mathematics and scientific university mathematics as well as different demands related to the learning cultures in both institutions are discussed as possible reasons for this phenomenon. If these assumptions hold, the transition from school to university could not be considered as a continuous mathematical learning path because it would require a realignment of students' learning strategies. In particular, students could no longer rely on the effective use of school-related individual resources like knowledge, interest, or self-concept. Accordingly, students would face strong challenges in mathematical learning processes at the beginning of their mathematics study at university. In this contribution, we examine these assumptions by investigating the role of individual mathematical learning prerequisites of 182 firstsemester university students majoring in mathematics. In line with the assumptions, our results indicate only a marginal influence of school-related mathematical resources on the study success of the first semester. In contrast, specific precursory knowledge related to scientific mathematics and students' abilities to develop adequate learning strategies turn out as main factors for a successful transition phase. Implications for the educational practice will be discussed.

Mathematical Prerequisites for STEM Programs: What do University Instructors Expect from New STEM Undergraduates?

“…The Transition Problem: Differences between School and University Mathematics A large body of research indicates fundamental differences between the mathematics education at school and at university (e.g., Engelbrecht 2010; Gueudet and Pepin 2018;De Guzmán et al 1998;Luk 2005;Rach and Heinze 2017;Selden 2005), which are regarded as problematic when transitioning from high school to university (Gueudet 2008;Engelbrecht 2010). For example, mathematical activities such as problemsolving, reasoning and proof, or mathematical modelling are employed in both school mathematics (e.g., CCSSI 2010; KMK 2012) and university STEM programs (e.g., Gueudet 2008).…”

“…The transition from secondary to tertiary education is of crucial importance for student retention and success in higher education (Gueudet 2008;Rach and Heinze 2017). Students' transitions come with difficulties, in particular for students taking mathematics courses in their first semester at university (Gueudet 2008;Thomas et al 2015;Engelbrecht 2010).…”

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

“…While many previous quantitative studies focused on students' achievement (e.g. Crawford et al, 1994;Rach & Heinze, 2017), we took into account students' dropout intention as well. We found a strong negative relation between students' dynamic beliefs and dropout intention.…”

“…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).…”

Abschreiben von Übungsaufgaben in traditionellen und innovativen Mathematikvorlesungen

“…In der Literatur finden sich zwei Untersuchungen von Studierenden aus der Veranstaltung Analysis 1 an der Universität Kiel, die zur Semestermitte durchgeführt wurden [6,7]. Studierende sollten dabei einschätzen, ob sie -ihre Aufgabenlösungen einfach abschreiben, ohne die Lösungen nachzuvollziehen, -versuchen Lösungen anderer nachzuvollziehen, aber nur selten eigene Erklärungen oder Verbesserungen geben, -oft nicht selbst auf die Lösung kommen, aber diese verbessern und/oder sich und Kommilitonen erklären, -ihre Aufgaben selbst lösen.…”