The dominant image of mathematics as an abstract, universal, disinterested, and pure body of knowledge both misrepresents disciplinary practice and alienates many students. Undergraduate proof-based courses such as real analysis, which are supposed to introduce students to contemporary academic mathematics, often contribute to such idealized…

This paper explores student emotion and learning experiences fostered by lecturing-style instruction in Real-Analysis problem-centered lessons. We focus on two lessons that were taught by two reputable instructors and involved challenging, mathematically-related problems the students did not understand. Nonetheless, one lesson evoked negative…

This paper presents a research framework for investigating the role of language use in mathematics learning. The paper draws on the wider M[superscript 2]EID study, which explores whether differences in languages (English and Irish) and their use by bilingual mathematical students have a differential impact on their mathematics meta-level…

In this paper we develop knowledge of the discourse that takes place between teacher and students in two large undergraduate classes which use a flipped, active learning approach. In flipped classes students encounter the content through pre-class resources, freeing up class time for more active engagement with the material. This results in…

University lectures are by far the most common method of teaching at Spanish universities. More recently, however, this knowledge transmission has become increasingly interactive. Students' participation and verbal output becomes especially important in classes where the language of instruction is not the students' mother tongue but a second or…