Skip to main content
Log in

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

  • Published:
International Journal of Science and Mathematics Education Aims and scope Submit manuscript


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, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others


  • Bergsten, C. (2007). Investigating quality of undergraduate mathematics lectures. Mathematics Education Research Journal, 19(3), 48–72.

    Article  Google Scholar 

  • Bressoud, D., Mesa, V. & Rasmussen, C. (Eds.). (2015). Insights and Recommendations from the MAA National Study of College Calculus. Washington, DC: MAA Press.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Chi, M. T. H., de Leeuw, N., Chiu, M.-H. & Lavancher, C. (1994). Eliciting self-explanations improves understanding. Cognitive Science, 18(3), 439–477.

    Google Scholar 

  • Clark, M. & Lovric, M. (2009). Understanding secondary-tertiary transition in mathematics. International Journal of Mathematical Education in Science and Technology, 40(6), 755–776.

    Article  Google Scholar 

  • 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

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Gueudet, G. (2008). Investigating the secondary-tertiary transition. Educational Studies in Mathematics, 67(3), 237–254.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Lubinski, D. & Benbow, C. P. (2000). States of excellence. American Psychologist, 55(1), 137–150.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Malmivuori, M.-L. (2006). Affect and self-regulation. Educational Studies in Mathematics, 63(2), 149–164.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Moore, R. C. (1994). Making the transition to formal proof. Educational Studies in Mathematics, 27(3), 249–266.

    Article  Google Scholar 

  • 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

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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

  • Tinto, V. (1975). Dropout from higher education: A theoretical synthesis of recent research. Review of Educational Research, 45(1), 89–125.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Weber, K. (2008). The role of affect in learning real analysis: A case study. Research in Mathematics Education, 10(1), 71–85.

    Article  Google Scholar 

  • 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.

Download references


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

Author information

Authors and Affiliations


Corresponding author

Correspondence to Stefanie Rach.

Electronic supplementary material

Below is the link to the electronic supplementary material.


(DOCX 46 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: