Introduction
By University Mathematics Education (UME), we shall refer to the teaching and learning of mathematics in higher education institutions. This field of practice is of significant importance in society as mathematics is taught to students in a great variety of fields, from business to physics and, of course, pure mathematics. This chapter outlines main questions, methods, and results from research on UME (here, abbreviated: RUME). University mathematics teachers (including famous researchers, such as Klein 1908) have certainly produced rich texts on their personal experience and views of UME. However, the systematic pursuit of RUME, based on explicit theoretical and empirical frameworks, dates back at most four decades. In the first section, we outline the most common frameworks, as well as the recent history of the field. The last three sections focus on specific themes in RUME: courses and curricula; students’, teachers’, and institutional perspectives on UME; and finally in...
References
Adiredja AP, Andrews-Larson C (2017) Taking the sociopolitical turn in postsecondary mathematics education research. Int J Res Undergrad Math Educ 3(3):444–465
Artemeva N, Fox J (2011) The writing’s on the board: the global and the local in teaching undergraduate mathematics through chalk talk. Writ Commun 28(4):345–379
Artigue M (1994) Didactical engineering for the conception of teaching products. In: Biehler R, Scholz RW, Stralier R, Winkelmann B (eds) Didactics of mathematics as a scientific discipline. Kluwer, Dordrecht, pp 27–39
Artigue M (2016) Mathematics education research at university level: achievements and challenges. In: Nardi E, Winsløw C (eds) Proceedings of the first conference of INDRUM. INDRUM and Université de Montpellier, Montpellier, pp 11–27
Artigue M, Blomhøj M (2013) Conceptualizing inquiry-based education in mathematics. ZDM 45(6):797–810
Artigue M, Batanero C, Kent P (2007) Mathematics thinking and learning at post-secondary level. In: Lester F (ed) Second handbook of research on mathematics teaching and learning. Information Age, Charlotte, pp 1011–1050
Barquero B, Bosch M, Gascón J (2013) The ecological dimension in the teaching of mathematical modelling at university. Rech didactique Math 33(3):307–338
Biza I, Geraldo V, Hochmuth R, Khakbaz A, Rasmussen C (2017) Research on teaching and learning mathematics at the tertiary level: state-of-the-art and looking ahead. ICME-13 topical surveys book series. Springer, Berlin
Dubinsky E (1991) Reflective abstraction in advanced mathematical thinking. In: Tall D (ed) Advanced mathematical thinking. Kluwer, Dordrecht, pp 95–123
Engelbrecht J, Harding A (2015) Interventions to improve teaching and learning in first year mathematics courses. Int J Math Educ Sci Technol 46:1046–1060
Freeman S, Eddy SL, McDonough M, Smith MK, Okoroafor N, Jordt H, Wenderoth MP (2014) Active learning increases student performance in science, engineering, and mathematics. Proc Natl Acad Sci 111(23):8410–8415
Grønbæk N, Winsløw C (2008) Developing and assessing specific competencies in a first course on real analysis. In: Hitt F, Harel G, Selden A (eds) Research in collegiate mathematics education VI. American Mathematical Society, Providence, pp 99–138
Gueudet G (2008) Investigating the secondary-tertiary transition. Educ Stud Math 67(3):237–254
Gueudet G, Buteau C, Mesa V, Misfeldt M (2014) Instrumental and documentational approaches: from technology use to documentation systems in university mathematics education. Res Math Educ 16(2):139–155
Holton D (ed) (2001) The teaching and learning of mathematics at university level. New ICMI study series, vol 7. Kluwer, New York
Jones SR (2013) Understanding the integral: students’ symbolic forms. J Math Behav 32:122–141
Klein F (1908) Elementarmathematik vom höheren Standpunkte aus. BG Teubner, Leipzig
Larsen S, Marrongelle K, Bressoud D, Graham K (2017) Understanding the concepts of calculus: frameworks and roadmaps emerging from educational research. In: Cai J (ed) Compendium for research in mathematics education. National Council of Teachers of Mathematics, Reston, pp 526–550
Lockwood E, Swinyard CA, Caughman JS (2015) Patterns, sets of outcomes, and combinatorial justification: two students’ reinvention of counting formulas. Int J Res Undergrad Math Educ 1(1):27–62
Nardi E, Biza I, Gonzáles-Martin A, Gueudet G, Winsløw C (eds) (2014) Institutional, sociocultural and discursive approaches to research in university mathematics education. Res Math Educ 16(2):91 (special issue)
Rasmussen C, Wawro M (2017) Post-calculus research in undergraduate mathematics education. In: Cai J (ed) Compendium for research in mathematics education. National Council of Teachers of Mathematics, Reston, pp 551–581
Reinholz DL, Apkarian N (2018) Four frames for systemic change in STEM departments. Int J STEM Educ 5(1):1–10
Seymour E, Hewitt NM (1997) Talking about leaving: why undergraduates leave the sciences. Westview Press, Boulder
Sonnert G, Sadler P (2015) The impact of instructor and institutional factors on students’ attitudes. In: Bressoud D, Mesa V, Rasmussen C (eds) Insights and recommendations from the MAA national study of college calculus. The Mathematical Association of America, Washington, DC, pp 17–29
Speer NM, Wagner JF (2009) Knowledge needed by a teacher to provide analytic scaffolding during undergraduate mathematics classroom discussions. J Res Math Educ 40(5):530–562
Tall D (1991) Advanced mathematical thinking. Kluwer, Dordrecht
Tucker A (2013) The history of the undergraduate program in mathematics in the United States. Am Math Mon 120(8):689–705
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. J Math Behav 23(2):115–113
Winsløw C, Gueudet G, Hochmut R, Nardi E (2018) Research on university mathematics education. In: Dreyfus T, Artigue M, Potari D, Prediger S, Ruthven K (eds) Developing research in mathematics education – twenty years of communication, cooperation and collaboration in Europe. New perspectives on research in mathematics education series, vol 1. Routledge, Oxon, pp 60–74
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Winsløw, C., Rasmussen, C. (2018). University Mathematics Education. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-77487-9_100020-1
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