# The Transition from School Mathematics to University Mathematics: An Integrated Study of a Cultural Gap

Research project funded by the Swedish Research Council (project ID 2009-5571, 3 133 000 SEK)

#### Short Description of the Project

A student entering university to study a program that contains mathematics wants to pass the courses. To do this it is necessary to recognize what defines success in the mathematics courses at that institution. The content and the demands in the courses might be quite different from what she or he encountered at school. There is an anecdote from a mathematics lecturer who met the new students and said: "The first thing is to forget everything you learned at school. Now we are doing mathematics!". Also the forms of teaching and examinations do not resemble school mathematics classrooms. Moreover, the new student has to cope with many additional organisational and social issues. The culture shock he or she might experience in this situation is part of the 'transition problem' from secondary to tertiary mathematics education. At many places special bridging courses have been introduced to try to overcome it. In this project, the transition problem will be studied in an integrated way that takes into account mathematical, didactical as well as social dimensions. The researchers will follow two groups of first year students who take mathematics courses at two different Swedish universities, observe lectures, interview students and teachers and analyse the materials used.The outcomes of national surveys and of international research studies point to a bundle of issues that describe discrepancies, problems and difficulties arising from the
transition from school to university mathematics learning. The universities' perceptions are not uniform and it is not clear what exactly is expected from the students. Discrepancies are not so much a problem of specific topics to be mastered, but of a change in the type of mathematics.
The goal of the project is to develop an integrated view of mathematical, didactical and more general social aspects of the transition problem, by investigating:

- What type of mathematics is institutionalised in the beginning undergraduate mathematics courses, in lectures and in exams? What are the similarities and differences to the type of mathematics in upper secondary school?
- How do students experience the continuities and ruptures between learning mathematics at school and in university courses? How are their perceptions related to social dimensions of the transition from school to university, to their career aspirations and to their success?

#### Contributing researchers

- Christer Bergsten, professor of mathematics education at Linköping University, Sweden
- Eva Jablonka, professor of mathematics education at Freie Universität Berlin, Germany
- Hoda Ashjari, PhD student of mathematics education at Linköping University, Sweden

#### Publications

- Jablonka, E., Ashjari, H., & Bergsten, C. (2016). "Much palaver about greater than zero": First year engineering students' recognition of university mathematics.
*International Journal of Research in Undergraduate Mathematics Education.*doi:10.1007/s40753-016-0037-y (link to article as pdf) - Bergsten, C. & Jablonka, E. (2016). Studying mathematics at university - Views of first year engineering students.
In R. Göller, R. Biehler, R. Hochmuth, & H-G. Rück
*Didactics of Mathematics in Higher Education as a Scientific Discipline, Proceedings*(pp. 458-465). khdm-Report 16-05, Universität Kassel. - Bergsten, C., Jablonka, E., & Ashjari, H.(2016). The transition from secondary to tertiary mathematics education: A Swedish study. Paper presented at TSG2 at
*The Thirteenth International Congress on Mathematical Education*, Hamburg (Germany), 24-31 July 2016. - Bergsten, C., Jablonka, E., & Ashjari, H. (2015). Övergången från skolans till högskolans matematik: En integrerad studie av en kulturkrock. I
*Resultatdialog 2015*(ss. 29-41). Stockholm: Vetenskapsrådet. (link to pdf) - Bergsten, C., & Jablonka, E. (2015). The construction of the 'transition problem' by a group of mathematics lecturers. In K. Krainer & N. Vondrova (Eds.),
*CERME 9 - Ninth Congress of the European Society for Research in Mathematics Education (CERME9, 4-8 February 2015)*(pp. 2053-2059). Prague, Czech Republic: Charles University in Prague, Faculty of Education and ERME. (available as pdf) - Jablonka, E., & Bergsten, C. (2014). Engineering students' recognition of university mathematics and their conceptualization of the role of mathematics for their future career. In
*Mathematics in undergraduate study programs: Challenges for research and for the dialogue between mathematics and didactics of mathematics*(pp. 52-53). Mathematische Forschungsinstitut Oberwolfach, Report No. 56/2014. - Jablonka, E., Bergsten, C., & Ashjari, H. (2014). "Arbitrary numbers and much palaver" - Engineering students' recognition of university mathematics. Paper presented at BSRLM Day Conference, King's College London, 1 March 2014.
- Ashjari, H. (2013). Tendencies in engineering students' assertions about exam tasks. Paper presented at TAD4, IVth International Congress on the Anthropological Theory of Didactics, Toulouse, 21-26 April 2013. To appear in the Proceedings.
- Bergsten, C., & Jablonka, E. (2013). Mathematics as "Meta-Technology" and "Mind-Power": Views of engineering students. In B. Ubuz, C. Haser & M. A. Mariotti (Eds.),
*Proceedings of the Eighth Congress of the European Society for Research in Mathematics Education (CERME8)*(pp. 2286-2295). Antalya, Turkey: Middle East Technical University. - Ashjari, H., Jablonka, E., & Bergsten, C. (2012). Recognizing texts in undergraduate mathematics. In Proceedings of The 36
^{th }Conference of the International Group for the Psychology of Mathematics Education, Taipei-Taiwan, July 18-22, 2012. - Bergsten, C. (2012). A calculus lecture: What made it good? In G.H. Gunnarsdottir et al. (Eds.),
*Proceedings of NORMA 11, The Sixth Nordic Conference on Mathematics Education*(pp. 167-176). Reykjavik: University of Iceland Press. - Jablonka, E., Ashjari, H., & Bergsten, C. (2012). Recognising knowledge criteria in undergraduate mathematics education. In C. Bergsten, E. Jablonka & M. Raman (Eds.),
*Evaluation and comparison of mathematical achievement. Proceedings of MADIF8, Umeå, 24-25 January 2012*(pp. 101-110). Linköping: SMDF. - Jablonka, E., Ashjari, H., & Bergsten, C. (2012). Recognising texts in undergraduate mathematics education. Paper presented at ICME12 (Topic Study Group 2), Soeul, 8-15 July 2012.
- Bergsten, C. (2011). Why do students go to lectures? In E. Svobodova (Ed.),
*Proceedings of CERME7, The Seventh Congress of the European Society for Research in Mathematics Education*(pp. 1960-1970). Rzeszow, Poland.*Related publications* - Jablonka, E. & Bergsten, C. (2010). Theorising in mathematics education research: differences in modes and quality.
*Nordic Studies in Mathematics Education, 15*(1), 25-52. - Bergsten, C., Jablonka, E., & Klisinska, A. (2010). Reproduction and distribution of mathematical knowledge in higher education: constructing insiders and outsiders.
In U. Gellert, E. Jablonka, & C. Morgan (Eds.),
*Mathematics education and society. Proceedings of MES6, Berlin 20-25 March 2010*(pp. 130-140). Freie Universität, Berlin. - Bergsten, C., Jablonka, E., & Klisinska, A. (2010). A remark on didactic transposition theory. In C. Bergsten, E. Jablonka, & T. Wedege (Eds.),
*Mathematics and mathematics education: Cultural and social dimensions. Proceedings of MADIF7, Stockholm, January 26-27, 2010*(pp. 58-68). Linköping: SMDF. - Jablonka, E. & Bergsten, C. (2010). Commentary on Theories of mathematics education: Is plurality a problem? In B. Sriraman, B. & L. English (Eds.),
*Theories of Mathematics Education: Seeking New Frontiers (pp. 111-120).*New York: Springer. - Bergsten, C. & Jablonka, E. (2010). Interpreting students' reasoning through the lens of two different languages of description: integration or juxtaposition? In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.),
*Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education. January 28th - February 1st 2009, Lyon*(pp. 1555-1564). Lyon: Institut National de Recherche Pédagogique. - Bergsten, C. (2008). On the influence of theory on research in mathematics education: the case of teaching and learning limits of functions.
*ZDM - The International Journal of Mathematics Education*, 40, 189-199. - Bergsten, C. (2007). Investigating quality of undergraduate mathematics lectures.
*Mathematics Education Research Journal*, 19, 48-72. - Bergsten, C. (2006). Trying to reach the limit - The role of algebra in mathematical reasoning. Proceedings of PME 30 (Vol. 2, pp. 153-160), Prague, July 2006.
- Bergsten, C. (2004). Exploiting the gap between intuitive and formal knowledge in mathematics. Regular talk at ICME 10, Copenhagen (published in the ICME10 Proceedings).
- Bergsten, C. (2002). Critical factors and prognostic validity in mathematics assessment. In Proceedings of ICTM2 (CD-R).

Sidansvarig: christer.bergsten@liu.se

Senast uppdaterad: 2016-12-08