Primus

provides nice problems suitable for a typical math major. We give examples of problems that have worked well in our senior seminar course and some nice results that senior math majors can obtain. We conclude with a brief overview of how we implement our seminar.

In this article I attempt to overcome extant obstacles in deriving fundamental, objective and logically deduced definitions of personhood and their rights, by introducing an a priori paradigm of beings and morality. I do so by drawing a distinction between entities that are sought as ends and entities that are sought as means to said ends. The former entities, I offer, are the essence of personhood and are considered precious by observers possessing a logical system of valuation. The latter entities - those sought only as a means to an end - I term 'materials.' Materials are sought for their conditional value: Important for achieving sought ends, they are not considered precious in and of themselves. A normative system for how this dichotomy of entities should interact is consequently derived and introduced. This paradigm has applicability for modern humanism and beyond. Assuming societal technological progression whereby human bodies and their surrounding infrastructures continue to evolve and integrate, the distinction between beings and their supporting materials, and a moral code for their interactions, will become ever more relevant.

Responding to a call for national reform of mathematical education, as well as a college-wide revision of general education (GE) requirements, we describe a new entry-level, GE course focused on the humanitarian utility of mathematics. This includes a detailed overview of how we taught the course using a Humanitarian MATLAB Lab Manual developed collaboratively with undergraduate students within an applied math program. A PRIMUS edition of this manual with complete MATLAB materials for a GE course is included as an Appendix for interested readers. A variety of social justice issues including peace-building after modern civil wars, continued cancer risk after Chernobyl, gang reduction, various dimensions of human trafficking, the use of a tractor and herbicide in subsistence farming, equitable resource distribution during the Syrian refugee crisis, and access to HIV vaccines are included in this special edition of the manual.

With the help of the National Science Foundation, the Department of Mathematics at the University of Puerto Rico in Mayaguez has developed a set of manipulatives to help students of science and engineering visualize concepts relating to points, surfaces, curves, contours, and vectors in three dimensions. This article will present the manipulatives that have been developed, describe how they have been used in multivariable calculus classes, and provide the results of initial studies on their effectiveness.

We present a question bank consisting of over 250 multiple-choice and true-false questions covering a broad range of material typically taught in an introductory undergraduate course in numerical analysis or scientific computing. The questions are ideal for polling students during lectures by means of a student response system that uses clicker remotes or smartphones running a suitable app. We describe our experiences implementing these clicker questions in a recent class and provide evidence of their effectiveness in terms of testing students' prior knowledge, gauging understanding of new material, increasing participation, and especially improving student satisfaction. Our conclusions are supported by a mid-semester student survey as well as anecdotal observations. The question bank has been released as an open-access educational resource under a Creative Commons license (BY-NC-SA) for free use by the mathematics community.

I propose that an irreducible property of physical space, consistency, is the origin of logic. I propose that an inconsistent space is inconceivable and that this inconceivability can be recognized as the force behind logical propositions. The implications of this argument are briefly explored and then applied to address two paradoxes: Zeno of Elea's paradox regarding the race between Achilles and the Tortoise, and Lewis Carroll's paradox regarding the Tortoise's conversation with Achilles after the race. I conclude that Achilles would have won on both accounts, in the race and the argument, by invoking the consistency of space as the foundation of both movement across space and logical argument.

Textbooks play an important role in undergraduate mathematics courses and have the potential to impact student learning. However, there have been few studies that describe students' textbook use in detail. In this study, 1156 undergraduate students in introductory mathematics classes were surveyed, and asked to describe how they used their textbook. The results indicate that students tend to use examples, instead of the expository text, to build their mathematical understanding, which instructors may view as problematic. This way of using the textbook may be the result of the textbook structure itself, as well as students' beliefs about reading and the nature of mathematics. Although many instructors may not clearly convey how they want their students to use the textbook, students do report using it more productively when they believe they are asked to do so. This suggests that instructors should carefully choose text materials to promote mathematical reasoning, and actively encourage their students to read the text in a way that supports the development of this reasoning.

ABSTRACT Abstract Conceptually, the role of visual thinking is so fundamental to the understanding of calculus that it is difficult to imagine a successful calculus course which does not emphasize the visual elements of the subject. [18] With the help of the National Science Foundation (NSF-DUE 0442365), the Department of Mathematics at the University of Puerto Rico in Mayaguez has developed a set of manipulatives to help students of science and engineering visualize concepts relating to points, surfaces, curves, contours, and vectors in three dimensions. This article will present the manipulatives that have been developed, will describe how they have been used in multivariable calculus classrooms and will provide the results of initial studies on their effectiveness. Abstract Conceptually, the role of visual thinking is so fundamental to the understanding of calculus that it is difficult to imagine a successful calculus course which does not emphasize the visual elements of the subject. [18] With the help of the National Science Foundation (NSF-DUE 0442365), the Department of Mathematics at the University of Puerto Rico in Mayaguez has developed a set of manipulatives to help students of science and engineering visualize concepts relating to points, surfaces, curves, contours, and vectors in three dimensions. This article will present the manipulatives that have been developed, will describe how they have been used in multivariable calculus classrooms and will provide the results of initial studies on their effectiveness.

Abstract Calculus students’ difficulties in understanding integration have been extensively studied. Research shows that the difficulty lies with students understanding of the definition of the definite integral as a limit of a Riemann sum and with the idea of accumulation inherent in integration. We have created a set of manipulatives and activities around them to teach the idea of accumulation using the topics of volumes and work.

When one looks around in everyday life, one sees mathematics everywhere: ie, when making the right decisions whether to rent or buy a bicycle depending on the circumstances. Mathematics can determine (in case of renting a bicycle) the maximum rental cost to ensure that you ...

Abstract. In this paper we describe a hands-on activity for a liberal arts mathematics course that focuses on the beauty and unity of mathematics. The purpose of the activity is to tie to-gether several topics in the context of a “real-world ” situation. These topics include: fractals, non-Euclidean geometry, symme-try, and Platonic solids. This activity would also be appropriate for a geometry course. 1.

ABSTRACT The purpose of this paper is to describe the use of a problem involving superfactorials (a specific product of factorials) that provides an in-depth and comprehensive mathematical experience, encompassing skills that mathematicians view as tantamount to exploration. The problem is easily accessible and fosters creativity and perseverance, thereby allowing participants to practice standard steps in developing a mathematical argument: from the problem, to simplifications, then conjecture, and finally proof. We present a brief solution to this problem and then discuss how the experience in trying to solve this problem may evolve during a professional development session for teachers. By providing teachers with extended time to investigate a single problem, we aim to provide professional development opportunities beyond the standard mathematical content or instructional practices. This problem also makes a welcome addition to any undergraduate mathematics curriculum and could be used in a mathematics for liberal arts course, capstone course, or any course with a focus on developing problem-solving skills and the process of doing mathematics.

Introduction to the Flipped Classroom Krista Maxson Ph.D.; Professor & Chair, Mathematical Sciences How does the flipped classroom work? Dr. Maxson examines resources and issues in undergraduate classes that are flipped. She includes particular issues departmental chairs face with flipped classrooms, and she answers common questions about how to flip a class as well as the benefits and drawbacks of flipping a classroom.

Abstract Common arguments for integrating the arts into mathematics courses include the arts fostering student creativity, improving academic achievement, and encouraging transfer between subjects. Research supporting these arguments is limited and carries layered complexities – such as what constitutes creativity and transfer, and whether they can be measured. As such, bolstering the case in favor of arts integration calls for additional perspectives. In this report, we present three such arguments we have identified through analyzing students’ video and written reflections, as well as individual interviews, regarding their experiences creating artistic pieces in an undergraduate geometry course. In particular, through creating mathematically inspired art pieces, students were able to: (i) blend mathematics with a broad range of life experiences; (ii) encounter situations that fostered mathematical inquiry; and (iii) change some of their attitudes towards art.

ABSTRACT In the context of a department of applied mathematics, a program assessment was conducted to assess the departmental goal of enabling undergraduate students to recognize, appreciate, and apply the power of computational tools in solving mathematical problems that cannot be solved by hand, or would require extensive and tedious hand computation. A test was designed and administered in order to discover whether students are adept at thinking computationally at various levels of mathematical maturity in the program. The results were explained by the mathematical maturation that goes hand-in-hand with the development of computational thinking.