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1. Francastillo15 on October 4, 2022 at 10:41

   Some of the evidence is as follows:

   • The literature firmly contradicts some unflattering portrayals of lectures being excessively formal and mathematicians’ choice of lecture being due to ignorance or apathy lecture being due to ignorance or apathy (Melhuish et al., 20220).

   • However, we do not know what types of lecture-based pedagogy (if any) will significantly improve students’ understanding of advanced mathematics, influence how they engage with the material, or influence how they affectively feel about mathematics (Melhuish et al., 20220).

   • Regarding student-centered instruction, the situation is different. We have promising evidence that student-centered instruction can lead to positive outcomes, especially in terms of students’ affect and student engagement in authentic mathematical practice (e.g., Laursen et al., 2014), although we have limited knowledge on cognitive outcomes (Melhuish et al., 20220).

   Bibliography:

   • Melhuish, K., Fukawa-Connelly, T., Dawkins, P. C., Woods, C., & Weber, K. (2022). Collegiate mathematics teaching in proof-based courses: What we now know and what we have yet to learn. In The Journal of Mathematical Behavior (Vol. 67, p. 100986). Elsevier BV. https://doi.org/10.1016/j.jmathb.2022.100986

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2. thomaisk on October 5, 2022 at 13:57

   “the use of the lecture format has been the subject of heated debate among scholars of university education for many years. Although some mathematics education researchers (e.g. Alsina, 2001; Mason, 2002) have expressed scepticism about the value of the traditional lecture, the harshest criticism of the lecture as an effective mode of teaching has been voiced by general education scholars (e.g. Biggs & Tang, 2011; Bligh, 2000).  Bligh, drawing on various empirical studies, identifies four distinct kinds of objectives a lecture might have: The acquisition of information; the promotion of thought; changes in attitudes; and behavioural skills (Bligh, 2000, p. 4). He concludes that lectures are as effective as other methods for transmitting information, but less effective regarding the other objectives. On the other hand, some scholars, both of mathematics education (e.g. Pritchard, 2010; Rodd, 2003) and of general university education (e.g. Friesen, 2011; Jones, 2007) have argued the continued relevance of the lecture format. It has also been claimed, for instance by Neumann (2001), that much of the criticism of the lecture format fails to consider differences between academic disciplines. As remarked by Pritchard (2010), this tends to make this criticism less relevant to university mathematics education. However, the above debate is rarely informed by empirical research based on observations of actual lecturing.” (Viirman, 2021, p.  467)

   Viirman, O. (2021). University mathematics lecturing as modelling mathematical discourse. International Journal of Research in Undergraduate Mathematics Education, 7(3), 466-489

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3. bentin on October 7, 2022 at 11:45

   “To conclude, the research literature suggests that there exists diversity with respect to instructors’ pedagogical perspectives and overarching goals, and that this diversity could lead to substantial variability with respect to the informal content made available for students in lectures by different instructors.”

   Reference:

   Pinto, A. (2019). Variability in the formal and informal content instructors convey in lectures. In The Journal of Mathematical Behavior (Vol. 54, p. 100680). Elsevier BV. https://doi.org/10.1016/j.jmathb.2018.11.001

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