This paper presents methodology aimed at developing a rich understanding of the interplay of mathematical progress in the different social settings in which learning in inquiry-oriented classrooms occurs: individually; in small groups; and as a whole class. For this purpose, we enhance a theoretical-methodological approach of coordinating…

Computational thinking and activity are vital aspects of what it means to conduct scientific and mathematical work. In light of this, some propose that students' mathematical education should include an integration of computing into their mathematical experiences, giving students opportunities to engage with computational tools as they reason…

The transition from school to tertiary mathematics courses, which involve advanced mathematics, is a challenge for many students. Prior research has established the central role of prior mathematical knowledge for successfully dealing with challenges in learning processes during the study entrance phase. However, beyond knowing that more prior…

College algebra has been noted as a critical course in post-secondary institutions because it serves as a gateway for major selection and college completion. Combinatorial topics like repeatable permutations are often overlooked in K-12 and undergraduate curricula. Likewise, students' achievement and motivation are affected by the type of…

In the United States (US) and elsewhere across the world, undergraduate mathematics instructors are increasingly aware of the value of inquiry-based instruction. In this research commentary, we describe the intellectual origins and development of two major strands of inquiry in US higher education, offer an explanation for apparent differences in…

This paper presents the development and validation of the 17-item mathematics Graduate Student Instructor Observation Protocol (GSIOP) at two universities. The development of this instrument attended to some unique needs of novice undergraduate mathematics instructors while building on an existing instrument that focused on classroom interactions…

Mathematics education research has been aware that calculus students can draw on single definite integrals as a model to compute areas (SImA), without minding whether the function changes its sign in the assigned interval. In this study, I take conceptual and empirical steps to understand this phenomenon in more depth. Building on Fischbein's…

In mathematics education, the research on proof by contradiction (PBC) often claims that this activity is more difficult for students than direct proof, or simply difficult in general. Many hypotheses have been offered to support or explain this belief, yet they span a disorientingly wide swath of journal articles, conference papers,…

Fractals describe many natural phenomena; their strong visual-figurative nature found its mathematical conceptualization in the concept of self-similarity. In the current study, we investigate how students construct (fully or partially) the self-similarity concept while recursively constructing the Sierpinski triangle, working in small group and…

A central problem in undergraduate mathematics education for future engineers consists in the perceived and actual relevance of the mathematical content. One strategy to strengthen both is to let students experience how that content appears in posing and solving authentic problems from the field of engineering which the students have signed up to…

In this paper, we provide an in-depth account of traditional IBL instruction. Understanding the nature and effects of this form of instruction is of growing importance due to the strength and breadth of the IBL movement and its connections to other forms of inquiry in undergraduate mathematics. In this case study of one real analysis course taught…

Over the last forty years of mathematics education research, a coherent body of knowledge has accumulated regarding the teaching of limits. On this basis, it remains a challenge to identify goals and design tasks compatible with ordinary teaching conditions. This paper reports on a teaching experiment carried out in France with year 12 students,…

The study reported here investigates the role, experiences and aspirations of a community of mathematics postgraduates as they learn to tutor in a mathematics support centre in a research-intensive university. This is achieved through in-depth interviews with nine postgraduate tutors all of whom had experience working in the centre. The data is…

We engaged five mathematicians who conduct research in the domain of complex analysis or use significant tools from complex analysis in their research in interviews about basic concepts of differentiation and integration of complex functions. We placed a variety of constructivist, social-constructivist, and embodied theories in mathematics…

Action-Process-Object-Schema (APOS) theory and tools resulting from dialogue with the Anthropological Theory of the Didactic (ATD) were used to analyse data from semi-structured interviews and teaching materials to study students' understanding of the relationship between tangent planes and the total differential. Results of the study show…