This article describes an inquiry-oriented real analysis classroom in which students were guided to discover mathematics for themselves. To support student inquiry, the framework of "five practices" from K-12 education was used. To illustrate this framework, two case examples are given from actual discussions that took place in this…

Research reported in this article has been conducted from the theoretical perspective of the Anthropological Theory of the Didactic developed by Y. Chevallard and his collaborators, and from the institutional perspective of university mathematics education in France. It focuses on the teaching and learning of algebraic structures. The article…

We describe some classic experiments on the Möbius strip, the projective plane band, and the Klein bottle band. We present our experience with freshmen college students, college teachers, high school students, and Mathematics Education graduate students. These experiments are designed to encourage readers to learn more about the properties of the…

Increasing the success of Underrepresented Students of Color (USC) in science, technology, engineering, and mathematics (STEM) is a central concern to many researchers, policymakers, and educators. To help understand STEM college student success, many studies have utilized Holland's (1966, 1973, 1985, 1997) person-environment fit framework…

Understanding perceptions of graduate admissions from multiple stakeholders can cultivate an improved understanding about the process of graduate induction, the role that admissions plays in restricting diversity in physics, and contribute to more informed practices for all involved. Prior studies in graduate admissions have reported on how…

The research on methods used in graduate mathematics education courses is limited, however existing groundwork suggests that curriculum should provide students with experiences that align with the practices of mathematics education researchers. At the same time, calls to connect mathematics education research and classroom practice have been…

The trends of teaching mathematical thinking and the existence of two thinking skills (critical dan creative thinking) the required by 21st century skills have created needs for teachers to know their students' thinking processes. This study is intended to portray how mathematics teachers expect their students showing their thinking processes in…

The study investigated the effects of using the problem of the week in teaching (POWT) on teachers' learning and changes in knowledge and teaching skills, in algebraic thinking and algebra tasks, in the setting of a university mathematics education graduate program. The graduate students participated in learning POWT weekly in a mathematics…

The science of biology has been transforming dramatically and so the need for a stronger mathematical background for biology students has increased. Biological students reaching the senior or post-graduate level often come to realize that their mathematical background is insufficient. Similarly, students in a mathematics programme, interested in…

Background: New emerging online technologies have made dynamic changes in the structure of the online environment possible to address varying needs of diverse learners. Purpose: The purpose of this study was to identify the changes that occurred in online instructional design and strategies in mathematics education courses taught over a course of…

This hands-on project uses a paper helicopter to teach students how to distinguish between common and special causes of variability when developing and using statistical process control charts. It allows the student to experience a process that is out-of-control due to imprecise or incomplete product design specifications and to discover how the…

In this article, we outline the findings of a Canadian survey study (N = 302) that focused on the extent of computer algebra systems (CAS)-based technology use in postsecondary mathematics instruction. Results suggest that a considerable number of Canadian mathematicians use CAS in research and teaching. CAS use in research was found to be the…

We have applied the "practical paradigm" in teaching problem solving to secondary school students. The key feature of the practical paradigm is the use of a practical worksheet to guide the students' processes in problem solving. In this paper, we report the diffusion of the practical paradigm to university level courses for prospective…

The "Price Is Right" ("TPIR") provides a wealth of material for studying statistics at various levels of mathematical sophistication. The authors have used elements of this show to motivate students from undergraduate probability and statistics courses to graduate level executive management courses. The material consistently generates a high…

In this paper, canonical transformations generated by constants of motion in the case of the Kepler problem are discussed. It is shown that canonical transformations generated by angular momentum are rotations of the trajectory. Particular attention is paid to canonical transformations generated by the Runge-Lenz vector. It is shown that these…