Learning in lectures: multiple representations

Abstract

Lectures remain the lynchpin of mathematics teaching at university even with advances in information technology and access to the internet. This paper examines the requirements for learning mathematics and shows how important it is for lecturers to be aware of the different modes of presentation they are using. Ways to assist students to make the connections between different representations are considered, with particular reference to students whose first language is not English.

A Facilitated Community of Practice: Enabling Student Success in the Blended Learning Environment

“…Yet, despite the range of possible alternatives afforded by new technologies and debate about their pedagogical merit (Gosper et al 2010), lectures remain a common teaching approach in Higher Education and research suggests that many students find lectures to be important and challenging modes of learning (Wood et al 2007). However, there is little problematising of how effectively students actually process online lectures (Chaudhury 2011).…”

Facilitating Student Engagement in Undergraduate Mathematics Lectures: A Multimodal Investigation

“…As mentioned, some research suggests that undergraduate mathematics lectures do not engage students and encourage passive, transmission-style learning (e.g., Yoon et al, 2011); however, there is an equally substantial body of literature which describes mathematics lecture learning contexts (discussed in-depth in Chapter 4 of this dissertation) as highly engaging and interactive sites of rich learning (e.g., Black, 2005;Rodd, 2003;Speer, 2008). Other authors (e. g., Wood, Joyce, Petocz, & Rodd, 2007) note variance between individual lectures, where "good lectures can inspire and motivate…”

“…As mentioned, the usefulness and effectiveness of traditional lectures have been questioned, in part, because they seem to be lacking active-learning strategies (e.g., Bligh, 1972;Lew, Fukawa-Connelly, Mejia-Ramos, & Weber, 2016;Yoon et al, 2010), and calls for active-learning strategies to be incorporated into university mathematics teaching abound (Auerbach et al, 2018). However, despite advances in teaching technologies, the prevalence of online learning forums, and access to materials online, lectures remain fundamental to the teaching of university mathematics (Speer, Smith, & Horvath, 2010;Wood et al, 2007).…”

“…Additionally, empirical research has shown that undergraduate students not only attend university mathematics lectures Cretchley, 2005;Hubbard, 2007), but also value lectures for their usefulness and sense of community and interaction, and view them as a highly important resource for learning Cretchley, 2005;Hubbard, 2007;Pritchard, 2010;Rodd, 2003;Wood et al, 2007). Nonetheless, the debate continues (Pritchard, 2015), perhaps fueled by a continued lack of empirical research on university mathematics lecturing (Iannone & Miller, 2019;Viirman, 2015) despite numerous explicit calls for research of this kind (e.g., Speer, Smith, & Horvath, 2010).…”

“…As mentioned, mathematics has been identified as a distinct discourse (e.g., O'Halloran, 2005;Sfard, 2014;Wood et al, 2007). Sfard (2008), who developed the commognitive approach which views mathematics as discursive activity, describes "university mathematical discourse" (Sfard, 2014, p. 200) which, as she explains, is fundamentally new to the first-year student transitioning from high school into university.…”