Definitions play an important role in mathematics by stipulating objects of interest to mathematicians in order to facilitate theory building. Nevertheless, limited research has examined how mathematicians approach writing definitions or the values of the mathematical community that are upheld through norms related to definition use and writing.…

In the HPM (History and Pedagogy of Mathematics) literature, the three mathematicians Henri Poincaré (1854-1912), Felix Klein (1849-1925), and Hans Freudenthal (1905-1990) are often mentioned in relation to having opinions about the role of the history of mathematics in the teaching and learning of mathematics. Such mentioning often appears…

This article describes the background of Fibonacci and his numeral system and how he made arithmetic easier. It includes ways students can learn about Fibonacci sequences and the Fibonacci spiral.

Isomorphism and homomorphism are topics central to abstract algebra, but research on mathematicians' views of these topics, especially with respect to sameness, remains limited. This study examines open response survey data from 197 mathematicians on how sameness could be helpful or harmful when studying isomorphism and homomorphism. Using…

Offering explanations is a central part of teaching mathematics, and understanding those explanations is a vital activity for learners. Given this, it is natural to ask what makes a good mathematical explanation. This question has received surprisingly little attention in the mathematics education literature, perhaps because the field has no…

A teacher of mathematics knows mathematics as a teacher and as a mathematician. Whilst the existing research on teacher knowledge contributes to our understanding of the ways of knowing mathematics as a teacher, little is known about ways of knowing mathematics as a mathematician. Guided by the conceptual framework of mathematical practices (MPs)…

Isomorphism and homomorphism are topics central to abstract algebra, but research on mathematicians' views of these topics, especially with respect to sameness, remains limited. This study examines 197 mathematicians' views of how sameness could be helpful or harmful when studying isomorphism and homomorphism. Instructors saw benefits to…

This study explores calculus students' opportunities to learn the concepts of integral by examining one mathematician's videotaped lessons and the textbook. Results show that both lessons and the textbook introduce important cognitive resources briefly and focus on other units of knowledge. Implications to these results are also discussed.

We offer a new angle to explain the comprehension of mathematical infinity. We use Action-Process-Object-Schema (APOS) theory to explore the construction of different aspects of the cognitive Object related to this notion. We focus our attention on different ways of interacting with infinity, and how to act on infinite entities. Our aim is to shed…

In this paper, we examine mathematicians' views on the value of advanced mathematics for secondary mathematics teachers. The data comprise semi-structured interviews with 24 mathematicians from 10 universities. The findings indicate that the value of advanced mathematics courses for prospective secondary mathematics teachers lies in their…

This is the third article in the "On the Shoulders of Giants" series that takes an outstanding mathematician, tells something of their life and work, and provides an item or two based on their achievements that can be used in a primary class. This article focuses on the work of Cheryl Praeger, with an activity based upon her work with…

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,…

In this paper the author looks at the letters of two renowned women mathematicians and scientists of the Victorian period, Mary Somerville and Ada Lovelace, while also considering the imperceptibility of Sophie Germain, an important French mathematician and philosopher in their epistolary exchanges and philosophical writings. Drawing on the…

This paper aims to investigate the reasons some female mathematicians give to justify their choice to not work in academia after finishing their doctoral studies. Nine female mathematicians who finished a PhD in Sweden answered a written questionnaire. Through collective narrative analysis, two main tracks were identified. One narrative described…

In this article the author looks at processes of becoming a woman philosopher and scientist in eighteenth-century Europe, by focusing on educational experiences, discourses and practices revolving around the Italian mathematician, scientist and philosopher Maria Gaetana Agnesi. The author uses the Arendtian notion of "agonism" as a lens…