As new technological developments continue to change the educational landscape, it is not an exception in the area of proof and proving. This classroom note introduces the use of one of the trending proofs assistants -- the Lean theorem prover. We first provide a technical account of Lean, then exemplify Lean proofs in propositional logic, number…

The study examines the levels of understanding logarithmic expressions within the frames of a mathematical card game. The game is based on the popular card game Saboteur. In this paper, we analyse the progress of a group of six undergraduate students participating in a remedial course using games for recalling some fundamental mathematical…

The Students' Approaches to Learning (SAL) tradition comprehends an approach to learning as a combination of students' aims for learning and the processes used to achieve them. The tradition values a deep approach to learning; this is the case also in the context of university mathematics, where a deep approach is seen as a requirement for…

Theories of self-efficacy and approaches to learning are well-established in the psychology of learning. However, studies on relationships between the primary constructs on which these theories are developed are rarely reported in mathematics education research. Thus, the purpose of the current study is to provide empirical evidence for a…

Tangent lines are often first introduced to students in geometry during the study of circles. The topic may be repeatedly reintroduced to students in different contexts throughout their schooling, and often each reintroduction is accompanied by a new, nonequivalent definition of tangent lines. In calculus, tangent lines are again reintroduced to…

Programming is becoming increasingly common in mathematics degrees as it is a desirable skill for new graduates. However, research shows that its use is mostly restricted to computational or modelling tasks. This paper reports a study on students' perceptions of and difficulties with Lean, an interactive theorem prover introduced as part of a…

This work presents an evaluation of a unified Calculus 1 course in a large Brazilian federal university. By course unification we mean having all the sections following the same weekly schedule, under the same syllabus and common assessment. We analyse two sets of data: pass rates relative to the 9 semesters prior to the unification and to the…

In undergraduate mathematics education, students' collaborations have gained a reputation as a 'good' learning practice. A more complex image emerges once collaborations are construed as an arena where cognitive, social, and affective matters intertwine in ways that can fuel and impede learning. In this study, I take a close look at a…

There is a growing interest in using comparative judgement as a peer assessment tool involving students choosing the 'better' of two pieces of work. However, it has not been shown whether peer assessment through comparative judgement is effective for students' learning. To gain a better understanding of the comparative judgement process, we…

A review of related research found the use of recorded lecture videos (RLVs) in undergraduate mathematics to be negatively correlated with academic performance. To investigate this correlation, an initial study found students' regular RLV use to be linked to surface approaches to learning. The present study continued this investigation and was…

This paper aims to examine the extent to which pre-service teachers' mathematical connection skills were promoted through the course designed within the scope of pedagogies of practice (Grossman et al. [2009]. Teaching practice: A cross-professional perspective. Teachers College Record, 111(9), 2055-2100.…

The instrumental approach is a useful theoretical lens for understanding students' learning processes with a main focus on the transformation of an artefact (a human design for a goal-directed activity) into a meaningful instrument (i.e. an artefact and schemes developed by the student). In this paper, we articulate the instrumental approach for…

Logical statements are prevalent in mathematics, science and everyday life. The most common logical statements are conditionals, 'If H … , then C … ', where 'H' is a hypothesis and 'C' is a conclusion. Reasoning about conditionals depends on four main conditional contexts (intuitive, abstract, symbolic or counterintuitive). This study tested a…

Educational success is mainly based on the formation of effective learners. Students' learning is affected by several variables, such as intelligence, motivation, teaching and learning approaches. Research showed that approaches to learning are among one of the most important variables that influence students' learning quality. They are related to…

This paper explores analysis of feedback data collected from student consultations at two mathematics support centres at universities in Australia and Ireland. Unstructured text data was collected over six years and includes qualitative data on student queries collected during the consultations from mathematics and statistics related subjects.…