We review the history of snarks and give a selected survey of recent research. The article and snarks themselves are much more interesting than this summary makes them sound.

Mathematics experts often choose appropriate procedures to produce an efficient or elegant solution to a mathematical task. This "flexible procedural knowledge" distinguishes novice and expert procedural performances. This article reports on an intervention intended to aid the development of undergraduate calculus students' flexible use…

Although the mathematics community has long accepted the concept of limit as the foundation of modern Calculus, the concept of limit itself has been marginalized in undergraduate Calculus education. In this paper, I analyze the strategy of conceptual conflict to teach the concept of limit with the aid of an online tool--Desmos graphing calculator.…

On any finite graph, the number of closed walks of length k is equal to the sum of the kth powers of the eigenvalues of any adjacency matrix. This simple observation is the basis for the combinatorial trace method, wherein we attempt to count (or bound) the number of closed walks of a given length so as to obtain information about the graph's…

The aim of this paper is to examine students' understanding of the limiting behavior of a function from [set of real numbers][superscript 2] to [set of real numbers] at a point "P." This understanding depends on which definition is used for a limit. Several definitions are considered; two of these concern the notion of a neighborhood of "P", while…

This paper analyzes 16 preservice secondary mathematics education majors' mathematical autobiographies. Participants wrote about their previous experiences with mathematics. All participants discussed why they wanted to become mathematics teachers with the key factors being past experience with mathematics teachers, previous success in mathematics…

We explore mathematics written both by and for women in eighteenth-century Europe, and some of the interesting personalities involved: Maria Agnesi, Emilie du Chatelet, Laura Bassi, Princess Charlotte Ludovica Luisa, John Colson, Francesco Algarotti, and Leonhard Euler himself.

Existing research on limits documents many difficulties students encounter when learning about the concept. There is also some research on teaching of limits but it is not yet as extensive as the research on student learning about limits. This study explores the discourse on limits in a beginning-level undergraduate calculus classroom by focusing…

In recent years, changes in the Brazilian economic and social scenario have generated a growing demand for higher education in the country. In response to this new context, the federal government launched in 2007 a programme aiming at expansion of the enrolment to public higher education. In such environment of changes, several proposals have…

When Martin Gardner first presented the Two-Children problem, he made a mistake in its solution. Later he corrected the error, but unfortunately the incorrect solution is more widely known than his correction. In fact, a Tuesday-Child variation of this problem went viral in 2010, and the same flaw keeps reappearing in proposed solutions of that…

Martin Gardner's "The Annotated Alice," and Robin Wilson's "Lewis Carroll in Numberland" led the authors to put this article in a fantasy setting. Alice, the March Hare, the Hatter, and the Dormouse describe a straightforward, elementary algorithm for counting the number of ways to fit "n" identical objects into "k" cups arranged in a circle. The…

In this paper we outline the main tenets of the commognitive approach and we exemplify its application in studies that investigate the learning and teaching of mathematics at university level. Following an overview of such applications, we focus on three studies that explore fundamental discursive shifts often occurring in the early stages of…

This paper outlines a method for teaching topics in undergraduate mathematics or computer science via historical curricular modules. The contents of one module, "Networks and Spanning Trees," are discussed from the original work of Arthur Cayley, Heinz Prüfer, and Otakar Boruvka that motivates the enumeration and application of trees in…

This study aims to investigate the nature of different mathematics teaching modes (prescriptions) that guide prospective teachers during their instruction. The participants were 24 junior prospective middle school mathematics teachers (19 females and 5 males) who were attending a mathematics methods course at a private university in central…

Most students thinking mathematics is a difficult subject. This study aims to enhance students' motivation and efficiency in learning mathematics. This study developed 3D animation on the binomial theorem with historical stories of mathematics as the plot. It also examined the effect of animation on students' learning willingness and…