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In this paper, we briefly introduce three theoretical frameworks for mathematical identity and why they matter to practitioners teaching undergraduate mathematics courses. These frameworks are narrative identities, communities of practice, and figured worlds. After briefly describing each theory, we provide examples of how each framework can be used to interpret or inform classroom discourses by applying the framework to a selected transcript from a student-centered mathematics project called the Catwalk problem. We summarize how an awareness of students' forming mathematical identities can be used positively in the undergraduate classroom to help educators support students to form productive mathematical identities. [ABSTRACT FROM AUTHOR]

In summer 2013, Manhattan College introduced an online summer "bridge to calculus" course for incoming first-year students in science, engineering, and mathematics education who marginally did not receive a calculus recommendation based on a mathematics placement test. In this paper, we describe the development of the bridge course and demonstrate statistically that this course continues to prepare its students for Calculus at a level comparable to those who took a full semester of Precalculus, yet at a significantly lower cost in terms of both time and money. [ABSTRACT FROM AUTHOR]

This editorial provides an introduction to the special issue, Infusing active learning into precalculus and calculus courses: Insights and lessons learned from mathematics departments in the process of change. We begin with providing the background for the special issue, including an overview of the current status of active learning in precalculus through calculus, what many of the papers in this issue mean by the term "active learning" (inquiry based mathematics education), and a brief overview of the literature on institutional change. We then offer an overview of each of the three issues, explaining how various papers relate to each other within each issue. We conclude the editorial with some reflections on the institutional changes efforts in light of the COVID-19 pandemic. [ABSTRACT FROM AUTHOR]

Mathematics education faculty working in mathematics departments are commonly involved in teaching undergraduate mathematics courses, teaching and supervising postgraduate students of mathematics education, and developing mathematics teachers (pre-service and/or in-service). This paper proposes a new elective course that can be taken by either undergraduate mathematics majors or by graduate teaching assistants pursuing degrees in mathematics and teaching undergraduates themselves. Twenty-eight topics are suggested, and the rationale for each is briefly described. Offering such a course provides different opportunities for students; for example, familiarizing them with effective ways to teach and learn mathematics, which has the potential to improve their effectiveness as tutors within the department. A similar course has been successfully taught to undergraduate students majoring in mathematics at an Iranian university for nearly two decades. [ABSTRACT FROM AUTHOR]

Preparing students placing into developmental mathematics for success in undergraduate mathematics and preparing future teachers for the increasing demands of K–12 school settings are both persistent, yet seemingly divergent, problems facing higher education. In this paper, we shed light on a model that attempts to address aspects of each problem and share preliminary evidence of success in a multi-year application of this model. The paper highlights the benefits of implementing the model, particularly to support collaboration between faculty in mathematics and teacher education. [ABSTRACT FROM AUTHOR]

Mastery-grading techniques such as mastery-based grading, specifications grading, and standards-based grading are assessment techniques professors are implementing in order to support a growth mindset of learning, decrease test anxiety, and help students develop a deeper understanding of course objectives. In this paper, we provide an analysis of research conducted in a variety of courses which used mastery-based testing (MBT). Some of the questions we explore include whether the students' attitudes about mathematics and learning changed throughout the course in addition to whether MBT impacted test anxiety and growth mindset. [ABSTRACT FROM AUTHOR]

This paper contains a description of my experiences flipping undergraduate mathematics and statistics courses for the first time with some advice for any fellow novice flippers. This paper discusses ways to start small and build up to a completely flipped class over the span of a few terms with advice on what technology to use including software and hardware. [ABSTRACT FROM PUBLISHER]

Inquiry-based pedagogies have a strong presence in proof-based undergraduate mathematics courses, but can be difficult to implement in courses that are large, procedural, or highly computational. An introductory course in statistics would thus seem an unlikely candidate for an inquiry-based approach, as these courses typically steer well clear of proof, have a list of required topics, and depend critically on computational software. On the other hand, the American Statistical Association (ASA) has long advocated the sort of active and exploratory class design that in many respects parallels traditional inquiry-based learning (IBL). This paper reports on the author’s recent attempt to implement an inquiry-based course in introductory statistics that fuses established IBL techniques with the specific pedagogical recommendations of the ASA. A signature feature of this course is that many of the inquiry-based activities are explicitly tied to computer work in the open source language R. [ABSTRACT FROM PUBLISHER]

This issue is the first of a specialPRIMUStwo-part issue collecting articles from experienced faculty mentors. We offer it as a valuable resource for faculty leading undergraduate research programs. It is inspired by the “Regional Faculty Workshop on REU Issues” in 2013 and the Joint Mathematics Meeting 2015 Mathematical Association of America’s “Themed Session on Perspectives and Experiences on Mentoring Undergraduate Students in Research.” This issue consists of seven papers focusing on the larger issues involved in creating, running, and sustaining an undergraduate research program in mathematics. [ABSTRACT FROM AUTHOR]

The basic rules of elementary algebra can often appear beyond the grasp of many students. Even though most subjects, including calculus, prove to be more difficult, it is the simple rules of algebra that continue to be the “thorn in the side” of many mathematics students. In this paper we present a result intended to help students achieve a greater understanding of a familiar algebraic error. [ABSTRACT FROM AUTHOR]

The purpose of this article is to describe a general procedure for implementing group poster projects in lower and upper division mathematics courses. The authors have found that students who complete projects gain a deeper understanding of the mathematics they study, refine their ability to communicate mathematically, and engage in an activity that requires initiative and persistence. The paper gives examples of successful projects and includes grading rubrics. [ABSTRACT FROM AUTHOR]

When students take their first upper division mathematics course after an introduction to proof course, they are often over- whelmed by the prospect of writing in a mathematics course. In mathematics, unlike other disciplines, students are very seldom asked to respond via writing to a reading assignment, to write an essay about a topic they have always used their intuition to explain, or to fully research a mathematics topic and report on it to their peers. This paper will highlight the ways in which writing, reading, and group work can be used to develop skills in geometry in one semester. [ABSTRACT FROM AUTHOR]