There is a growing body of evidence suggesting that secondary mathematics teachers may not be drawing significant benefit from the tertiary mathematics courses they take in preparation programs or in-service for professional development. While there are some theory-driven attempts to re-design or complement such courses for teachers, empirical…

Calculus courses have been attracting the attention of mathematics education researchers over the last decades. Recent publications and special issues dedicated to calculus highlight the diverse roles of calculus courses in the pathways for STEM studies within and across educational levels, as well as issues related to the academic preparation of…

In this paper, we explore the role of mathematical proof summaries as a tool for capturing students' reading comprehension of a given proof. We present an interview study based on mathematicians' pairwise evaluations of student-produced summaries of a proof demonstrating the uncountability of the open unit interval. We present a thematic analysis,…

Online learning environments are being used for teaching and learning of mathematics at university level. Exploiting the potential of digital technology, these Internet-based environments administer computer-generated homework, assistance and feedback for students. This article presents a case-study of a small group of ?undergraduate engineering…

In response to a recent Canada-wide survey, where it was found that mathematicians use computer programming much less in their teaching than in their research, an exploratory study involving 14 Canadian mathematicians sought to gain a deeper understanding of the place of programming in both contexts. To capture the differences in the degree of…

We present a theoretical approach to the problem of the transition from Calculus to Analysis within the undergraduate mathematics curriculum. First, we formulate this problem using the anthropological theory of the didactic, in particular the notion of praxeology, along with a possible solution related to Klein's "Plan B": here,…

Concerns over the quality and diversity of the future workforce in science, technology, engineering and mathematics (STEM) in the United States have led to repeated calls to reform undergraduate education. This paper focuses on the efforts of one mathematics education reform movement in higher education to frame itself and its inquiry-based…

This article focuses on the didactic transposition of the homomorphism concept and on the elaboration and evaluation of an activity dedicated to the teaching of this fundamental concept in Abstract Algebra. It does not restrict to Group Theory but on the contrary raises the issue of the teaching and learning of algebraic structuralism, thus…

In this paper we investigate task design in an unusual professional development course for elementary school teachers, conceived and taught by research mathematicians. Prior analysis singled out "relevance for teaching" as a critical design issue for engaging teachers in effective learning. The aim of the current research is to uncover…

In this paper we give a general definition of structural reasoning, followed by a typology that instantiates the definition in mathematical practices. Five major categories of structural reasoning, some with subcategories, are offered: (a) pattern generalization, (b) reduction of an unfamiliar structure into a familiar one, (c) recognizing and…

In light of the recent growing interest in conceptual learning and teaching of calculus, and especially with the focus on using technological environments, our study was designed to explore the learning processes and the role played by multiple-linked representations and by interactive technological environment in objectifying the accumulation…

Adopting Schiralli and Sinclair's notions of conceptual mathematics (CM) and ideational mathematics (IM), we investigated mathematicians' reasoning about continuity of complex-valued functions. While CM centers on formal mathematics as a discipline, IM focuses on how an individual perceives formal mathematics. There were four IM notions that the…

Mathematics is the discipline that a significant majority of most incoming researchers in mathematics education have prior qualifications and experience in. Upon entry into the field of mathematics education research, these newcomers--often students on a postgraduate programme in mathematics education--need a broadened understanding on how to…