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Undergraduate Mathematics Teaching in First Year Lectures: Can it be Responsive to Student Learning Needs? Georgia Petropoulou 1 & Barbara Jaworski 2 & Despina Potari 1 & Theodossios Zachariades 1

# Springer Nature Switzerland AG 2020

Abstract This paper investigates mathematics teaching to first year students of two mathematics departments in the context of large-group lectures. It goes beyond what may be seen as implicit in this context by focussing on the links between two lecturers’ thinking about students’ learning of advanced mathematics and their practice. Data includes lecture observations and reflective discussions with the lecturers. Three layers of data analysis are drawn on Activity Theory, the Teaching Triad, and, grounded analytical approaches. Findings suggest that the formation of teaching goals is motivated by aspects of sensitivity to student’s participation and that the complementarities among these aspects are important qualitative characteristics of teaching in this context. Keywords Teachers’ thinking . Teaching goals . Student learning needs . Teaching Triad

Introduction Undergraduate mathematics teaching is a foreground research object (Winsløw et al. 2018) as it ‘matters’ for students’ mathematical learning (Hiebert and Grouws 2007). In the case of teaching to large groups of exclusively mathematics students, what is at stake is generations of students’ enculturation into advanced mathematical practices * Georgia Petropoulou [email protected] Barbara Jaworski [email protected] Theodossios Zachariades [email protected]

1

National and Kapodistrian University of Athens, Athens, Greece

2

Loughborough University, Loughborough, UK

International Journal of Research in Undergraduate Mathematics Education

(Artigue et al. 2007). During their university studies, these students - some of whom will go on to become mathematics teachers themselves - are enculturated into both the practice of doing mathematics and also of teaching it. For Winsløw and Grønbæk (2014), university institutions must particularly take into account the needs of these students. Arguably, it is important to explore how this enculturation can be achieved. The predominant mode of large-group teaching is the lecture, which is also the most common form of teaching internationally (Paoletti et al. 2018). Although teaching in a lecture form has received particular criticism (e.g. Biggs 2003), research has shown that lecturing is not a unified teaching paradigm and it therefore needs - and is currently receiving - further exploration (e.g. Weber 2004; Speer et al. 2010; Weinberg et al. 2016). What differs in the enactment of teaching in lectures has been discussed and attributed to cultural differences among countries, to differences in teaching experience or to individual variations among teachers, such as different individual views of making mistakes (Artemeva and Fox 2011; Pinto 2013). Although research on lecture teaching and on the factors that frame it is developing and some studies highlight students’ alienation