## 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 first-semester 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.

This is a preview of subscription content, access via your institution.

## References

Bergsten, C. (2007). Investigating quality of undergraduate mathematics lectures.

*Mathematics Education Research Journal, 19*(3), 48–72.Bressoud, D., Mesa, V. & Rasmussen, C. (Eds.). (2015).

*Insights and Recommendations from the MAA National Study of College Calculus*. Washington, DC: MAA Press.Chen, S.-K., Yeh, Y.-C., Hwang, F.-M. & Lin, S. S. J. (2013). The relationship between academic self-concept and achievement: A multicohort–multioccasion study.

*Learning and Individual Differences, 23*, 172–178.Chi, M. T. H., de Leeuw, N., Chiu, M.-H. & Lavancher, C. (1994). Eliciting self-explanations improves understanding.

*Cognitive Science, 18*(3), 439–477.Clark, M. & Lovric, M. (2009). Understanding secondary-tertiary transition in mathematics.

*International Journal of Mathematical Education in Science and Technology, 40*(6), 755–776.Dieter, M. (2012).

*Studienabbruch und Studienfachwechsel in der Mathematik: Quantitative Bezifferung und empirische Untersuchung von Bedingungsfaktoren*[Drop-out and change of study in mathematics: Quantification and empirical analysis of factors] (Doctoral dissertation). Retrieved from http://duepublico.uni-duisburg-essen.de/servlets/DerivateServlet/Derivate-30759/Dieter_Miriam.pdf.Eley, M. G. & Meyer, J. H. F. (2004). Modelling the influences on learning outcomes of study processes in university mathematics.

*Higher Education, 47*, 437–454.Engelbrecht, J. (2010). Adding structure to the transition process to advanced mathematical activity.

*International Journal of Mathematical Education in Science and Technology, 41*(2), 143–154.Fenollar, P., Román, S. & Cuestas, P. J. (2007). University students’ academic performance: An integrative conceptual framework and empirical analysis.

*British Journal of Educational Psychology, 77*(4), 873–891.Frenzel, A. C., Goetz, T., Pekrun, R. & Watt, H. M. G. (2010). Development of mathematics interest in adolescence: Influences of gender, family, and school context.

*Journal of Research on Adolescence, 20*(2), 507–537.Gueudet, G. (2008). Investigating the secondary-tertiary transition.

*Educational Studies in Mathematics, 67*(3), 237–254.Hailikari, T., Nevgi, A. & Komulainen, E. (2008). Academic self‐beliefs and prior knowledge as predictors of student achievement in Mathematics: A structural model.

*Educational Psychology: An International Journal of Experimental Educational Psychology, 28*(1), 59–71.Halverscheid, S. & Pustelnik, K. (2013). Studying math at the university: Is dropout predictable? In A. M. Lindmeier & A. Heinze (Eds.),

*Proceedings of the 37th conference of the international group for the psychology of mathematics education*(Vol. 2, pp. 417–424). Kiel, Germany: PME.Hanna, G. (2000). Proof, explanation and exploration: An overview.

*Educational Studies in Mathematics, 44*(1–2), 5–23.Hannula, M. S., Maijala, H. & Pehkonen, E. (2004). Development of understanding and self-confidence in mathematics; grades 5–8. In M. Johnsen Høines & A. B. Fuglestadt (Eds.),

*Proceedings of the 28th conference of the international group for the psychology of mathematics education*(Vol. 3, pp. 17–24). Bergen, Norway: Univ. College.Hattermann & A. Peter-Koop (Eds.),

*Transformation - A Fundamental Idea of Mathematics Education*(pp.29-50). New York: Springer.Hoyles, C., Newman, K. & Noss, R. (2001). Changing patterns of transition from school to university mathematics.

*International Journal of Mathematical Education in Science and Technology, 32*(6), 829–845.Köller, O., Baumert, J. & Schnabel, K. (2001). Does interest matter? The relationship between academic interest and achievement in mathematics.

*Journal for Research in Mathematics Education, 32*(5), 448–470.Köller, O., Trautwein, U., Lüdtke, O. & Baumert, J. (2006). Zum Zusammenspiel von schulischer Leistung, Selbstkonzept und Interesse in der gymnasialen Oberstufe [The interaction of school achievement, self-concept, and interest in the upper secondary school].

*Zeitschrift für Pädagogische Psychologie, 20*(1/2), 27–39.Kristof-Brown, A. L., Zimmerman, R. D. & Johnson, E. C. (2005). Consequences of individuals’ fit at work: A meta-analysis of person–job, person–organization, person–group, and person–supervisor fit.

*Personnel Psychology, 58*, 281–342.Lubinski, D. & Benbow, C. P. (2000). States of excellence.

*American Psychologist, 55*(1), 137–150.Luk, H. S. (2005). The gap between secondary school and university mathematics.

*International Journal of Mathematical Education in Science and Technology, 36*(2–3), 161–174.Malmivuori, M.-L. (2006). Affect and self-regulation.

*Educational Studies in Mathematics, 63*(2), 149–164.Marsh, H. W., Trautwein, U., Lüdtke, O., Baumert, J. & Köller, O. (2007). The big-fish-little-pond effect: Persistent negative effects of selective high schools on self-concept after graduation.

*American Educational Research Journal, 44*(3), 631–669.Marsh, H. W., Trautwein, U., Lüdtke, O., Köller, O. & Baumert, J. (2005). Academic self-concept, interest, grades, and standardized test scores: Reciprocal effects models of causal ordering.

*Child Development, 76*(2), 397–416.Moore, R. C. (1994). Making the transition to formal proof.

*Educational Studies in Mathematics, 27*(3), 249–266.Nagy, G. (2006).

*Berufliche Interessen, kognitive und fachgebundene Kompetenzen: Ihre Bedeutung für die Studienfachwahl und die Bewährung im Studium*[Vocational interests, cognitive and scholastic abilities: Their role in choice of major and success at university] (Doctoral dissertation). Retrieved from http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000002714.Pekrun, R., Goetz, T., Titz, W. & Perry, R. P. (2002). Positive emotions in education. In E. Frydenberg (Ed.),

*Beyond coping: Meeting goals, visions, and challenges*(pp. 149–173). Oxford, United Kingdom: Oxford University Press.Rach, S. & Heinze, A. (2011). Studying Mathematics at the University: The Influence of Learning Strategies. In B. Ubuz (Eds.),

*Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education*(Vol. 4), (pp. 9-16). Ankara, Turkey: PME.Rasmussen, C. & Ellis, J. (2013). Who is switching out of calculus and why. In A. M. Lindmeier & A. Heinze (Eds.),

*Proceedings of the 37th conference of the international group for the psychology of mathematics education (Vol. 4)*(pp. 73–80). Kiel, Germany: PME.Richardson, M., Abraham, C. & Bond, R. (2012). Psychological correlates of university students’ academic performance: A systematic review and meta-analysis.

*Psychological Bulletin, 138*(2), 353–387.Schiefele, U., Streblow, L. & Brinkmann, J. (2007). Aussteigen oder Durchhalten: Was unterscheidet Studienabbrecher von anderen Studierenden? [Dropping out or persevering: What distinguishes university dropouts from other students?].

*Zeitschrift für Entwicklungspsychologie und Pädagogische Psychologie, 39*(3), 127–140.Seaton, M., Parker, P., Marsh, H. W., Craven, R. G. & Yeung, A. S. (2014). The reciprocal relations between self-concept, motivation and achievement: Juxtaposing academic self-concept and achievement goal orientations for mathematics success.

*Educational Psychology, 34*(1), 49–72.Selden, A. (2005). New developments and trends in tertiary mathematics education: Or, more of the same?

*International Journal of Mathematical Education in Science and Technology, 36*(2–3), 131–147.Swanson, J. L. & Fouad, N. A. (1999). Applying theories of person-environment fit to the transition from school to work.

*The Career Development Quarterly, 47*(4), 337–347.Tall, D. (1991). The psychology of advanced mathematical thinking. In D. Tall (Ed.),

*Advanced mathematical thinking*(pp. 3–21). Dordrecht, The Netherlands: Kluwer Academic Publishers.Tall, D. & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity.

*Educational Studies in Mathematics, 12*(7), 151–169.Thomas,M., Klymchuk, S., Hong, Y. Y., Kerr, S., McHardy, J., Murphy, P., Watson, P. (2010).

*The transition from secondary to tertiary mathematics education*. Wellington, New Zealand: Teaching and Learning Research Initiative. Retrieved from http://www.tlri.org.nz/sites/default/files/projects/9262SummaryReport.pdf.Tinto, V. (1975). Dropout from higher education: A theoretical synthesis of recent research.

*Review of Educational Research, 45*(1), 89–125.Trautwein, U., Lüdtke, O., Köller, O. & Baumert, J. (2006). Self-esteem, academic self-concept, and achievement: How the learning environment moderates the dynamics of self-concept.

*Journal of Personality and Social Psychology, 90*(2), 334–349.Trigwell, K., Ashwin, P. & Millan, E. S. (2013). Evoked prior learning experience and approach to learning as predictors of academic achievement.

*British Journal of Educational Psychology, 83*(3), 363–378.Valle, A., Cabanach, R. G., Núnez, J. C., González-Pienda, J., Rodríguez, S. & Pineiro, I. (2003). Cognitive, motivational, and volitional dimensions of learning: An empirical test of a hypothetical model.

*Research in Higher Education, 44*(5), 557–580.Vollstedt, M., Heinze, A., Gojdka, K. & Rach, S. (2014). Framework for Examining the Transformation of Mathematics and Mathematics Learning in the Transition from School to University. In S. Rezat, M.

Wagner, D. (2011). Mathematische Kompetenzanforderungen in Schule und Hochschule: Die Rolle des formal-abstrahierenden Denkens [Mathematical competence requirements in school and university: The role of formal-abstract thinking]. In R. Haug & L. Holzäpfel (Eds.),

*Beiträge zum Mathematikunterricht 2011*(pp. 879–882). Münster, Germany: WTM Verlag.Weber, K. (2004). Traditional instruction in advanced mathematics courses: A case study of one professor’s lectures and proofs in an introductory real analysis course.

*Journal of Mathematical Behavior, 23*, 115–133.Weber, K. (2008). The role of affect in learning real analysis: A case study.

*Research in Mathematics Education, 10*(1), 71–85.Weinstein, C. E. & Mayer, R. E. (1986). The teaching of learning strategies. In M. C. Wittrock (Ed.),

*Handbook of research on teaching. A project of the American educational research association*(3rd ed., pp. 315–327). New York, NY: Macmillan.Witzke, I. (2015). Different understandings of mathematics. An epistemological approach to bridge the gap between school and university mathematics. In E. Barbin, U. T. Jankvist & T. H. Kjeldsen (Eds.),

*ESU 7*(pp. 304–322). Copenhagen, Denmark: Danish School of Education.

## Acknowledgments

We like to thank the reviewers for their careful reading of the manuscript and their helpful suggestions.

## Author information

### Affiliations

### Corresponding author

## Electronic supplementary material

Below is the link to the electronic supplementary material.

### ESM 1

(DOCX 46 kb)

## Rights and permissions

## About this article

### Cite this article

Rach, S., Heinze, A. The Transition from School to University in Mathematics: Which Influence Do School-Related Variables Have?.
*Int J of Sci and Math Educ* **15, **1343–1363 (2017). https://doi.org/10.1007/s10763-016-9744-8

Received:

Accepted:

Published:

Issue Date:

### Keywords

- Individual learning processes
- Role of learning prerequisites
- Study success
- Transition school – university