This article gives an elementary proof of the famous identity [image omitted]. Using nothing more than freshman calculus, the present proof is far simpler than many existing ones. This result also leads directly to Euler's and Neville's identities, as well as the identity [image omitted].

One goal of an undergraduate education in mathematics is to help students develop a productive disposition towards mathematics. A way of conceiving of this is as helping mathematical novices transition to more expert-like perceptions of mathematics. This conceptualization creates a need for a way to characterize students' perceptions of…

This investigation utilized the qualitative case study method. Seventy-one College Algebra students were given a mathematical processing instrument. This testing device measured a student's preference for visual thinking. Two students were purposefully selected using the instrument. The visual mathematical learner (VL) was discussed in this…

We consider the effect on estimation of simultaneous variable centering and interaction effects in linear regression. We technically define, review, and amplify many of the statistical issues for interaction models with centering in order to create a useful and compact reference for teachers, students, and applied researchers. In addition, we…

In this paper, we explore the development of two grounded theories. One theory is mathematical and grounded in the work of university calculus students' collaborative development of mathematical methods for finding the volume of a solid of revolution, in response to mathematical necessity in problem solving, without prior instruction on solution…

Much research and many papers on mathematics pedagogy have discussed assessment and, in particular, the need to provide a varied diet of methods by which students are assessed for the award of their degree. In this article, we explore the mix of assessment methods provided across a range of UK university mathematics departments. We examine the…

We wish to divide a cake among some collection of people (who may have very different notions of the comparative value of pieces of cake) in a way that is both "fair" and "efficient." We explore the meaning of these terms, introduce two geometric tools to aid our analysis, and present a proof (due to Dietrich Weller) that establishes the existence…

In this article, ambiguous street and park signs are analysed and deciphered using symbolic logic. These examples showcase the ways in which instructors of undergraduate mathematics courses can blend their students' everyday exposure to logical reasoning with classroom experiences. (Contains 4 tables and 6 figures.)

Fractions are important in young students' understanding of rational numbers and proportional reasoning. The teacher is fundamental in developing student understanding and competency in working with fractions. The present study spanned five years and investigated prospective teachers' competency and confidence with fraction operations as they…

To promote student learning in a relearning situation in university-level mathematics, we developed the learning method TAU ("Think Ask Understand"). TAU provides support (i.e. a role script) for students' interaction during a collaborative problem-solving phase at the beginning of the learning process, while content-related instruction is delayed…

The classroom is a micro-culture where socio and socio-mathematical norms of interactions are fostered by an instructor who represents the mathematics community. Informed by the "emergent approach" developed by Cobb and Yackel (1996) that explains how mathematical growth takes place in the social context of classrooms, I explored the…

This submission contains the Proceedings of the 2017 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at McGill University in Montreal, Quebec June 2-6. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…

The Peer-to-Peer Learning Environment (P2PLE) is a proposed approach to helping learners co-construct their learning environment using recommendations about people, content, and tools. The work draws on current research on PLEs, and participant observation at the Peer-to-Peer University (P2PU). We are particularly interested in ways of eliciting…

A new 12 item research questionnaire was developed specifically to assess collegiate mathematics students' concept image of domain and zeros of rational functions. The study was designed to validate Tall and Vinner's (1981) cognitive model. Support was found for the hypothesis that students' mathematical experience influences their growth, with…

The Catseye Marble company tests the strength of its marbles by dropping them from various levels of their office tower, to find the highest floor from which a marble will not break. We find the smallest number of drops required and from which floor each drop should be made. We also find out how these answers change if a restriction is placed on…