PRIMUS: problems, resources, and issues in mathematics undergraduate studies (Primus)

Publisher: Rose-Hulman Institute of Technology, Taylor & Francis

Journal description

PRIMUS is a refereed journal devoted to dialogue and exchange of ideas among those interested in teaching undergraduate mathematics. This includes those who prepare students for college level mathematics, those who teach college level mathematics, and those who receive students who have been taught college level mathematics. Each issue contains relevant and worthwhile material for those interested in collegiate mathematics education. While the primary interest is in first person descriptive and narrative articles about implemented teaching strategies and interesting mathematics, there is also opportunity for writing broad survey articles, formal studies of new teaching approaches, assessments of planned and in place strategies, and general discussion writing on teaching undergraduate mathematics. The journal motto, "The lightning spark of the thought generated in the solitary mind awakens in another mind . . ." by the Scottish essayist Thomas Carlyle means that publishing in PRIMUS is a way of sharing ideas so that others can use and build upon the author's efforts. We welcome your ideas and experiences.

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Additional details

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Website Primus website
Other titles PRIMUS (Terre Haute, Ind.), PRIMUS, Problems, resources, and issues in mathematics undergraduate studies
ISSN 1051-1970
OCLC 21889576
Material type Periodical, Internet resource
Document type Journal / Magazine / Newspaper, Internet Resource

Publisher details

Taylor & Francis

  • Pre-print
    • Author can archive a pre-print version
  • Post-print
    • Author can archive a post-print version
  • Conditions
    • Some individual journals may have policies prohibiting pre-print archiving
    • On author's personal website or departmental website immediately
    • On institutional repository or subject-based repository after either 12 months embargo
    • Publisher's version/PDF cannot be used
    • On a non-profit server
    • Published source must be acknowledged
    • Must link to publisher version
    • Set statements to accompany deposits (see policy)
    • The publisher will deposit in on behalf of authors to a designated institutional repository including PubMed Central, where a deposit agreement exists with the repository
    • STM: Science, Technology and Medicine
    • Publisher last contacted on 25/03/2014
    • This policy is an exception to the default policies of 'Taylor & Francis'
  • Classification
    ​ green

Publications in this journal

  • [Show abstract] [Hide abstract]
    ABSTRACT: Metacognition as a dimension of learning ranks highest in the revised Bloom’s Taxonomy of cognitive tasks. In this paper we illustrate how it can be incorporated into a repeated exercise in the mathematics classroom, through a specific case study in the context of a liberal arts mathematics course. Through the semester, students were asked weekly to evaluate their own progress and review their development in light of their personal goals. We observed positive affective changes (including engagement levels) in the students through the course of the semester. We argue that the weekly metacognitive and self-reflective activities helped students keep their focus on learning deeply and allowed them to remain engaged and motivated through the semester. A brief theoretical discussion is included, and other possible contexts suitable for the activities described are suggested.
    PRIMUS: problems, resources, and issues in mathematics undergraduate studies 05/2015; 25(5):439-452. DOI:10.1080/10511970.2015.1027837
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    ABSTRACT: This article introduces the notion of the quartile-quartile line as an alternative to the regression line and the median-median line to produce a linear model based on a set of data. It is based on using the first and third quartiles of a set of (x, y) data. Dynamic spreadsheets are used as exploratory tools to compare the different approaches and to investigate the effects of sample size on the lines that are produced to fit random samples.
    PRIMUS: problems, resources, and issues in mathematics undergraduate studies 05/2015; 25(5):389-399. DOI:10.1080/10511970.2014.993053
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    ABSTRACT: Mathematical ideas from number theory, group theory, dynamical systems and computer science have often been used to explain card tricks. Conversely, playing cards have been often used to illustrate mathematical concepts of probability distributions and group theory. In this paper, we describe how the 21-card trick may be used to illustrate concepts such as discrete dynamical system, fixed point and stability of a fixed point. The 21-card trick is a way of dealing cards in order to predict a card that is selected by a volunteer, within three moves. The 21-card trick and its two generalizations are examples of piece-wise linear, non-homogeneous, discrete dynamical systems, all of which have a global stable fixed point.
    PRIMUS: problems, resources, and issues in mathematics undergraduate studies 05/2015; 25(5):473-483. DOI:10.1080/10511970.2015.1031308
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    ABSTRACT: This paper presents an extended project that offers, through American football, an application of concepts from enumerative combinatorics and an introduction to proofs course. The questions in this paper and subsequent details concerning equivalence relations and counting techniques can be used to reinforce these new topics to students in such a transition-to-proofs type course or to offer an application of known theoretical mathematics to students with more advanced understanding in the major.
    PRIMUS: problems, resources, and issues in mathematics undergraduate studies 05/2015; 25(5):421-438. DOI:10.1080/10511970.2015.1025162
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    ABSTRACT: This paper reports the results of a survey study of clicker use and mathematics anxiety among students enrolled in an undergraduate calculus course during the Fall 2013 semester. Students in two large lecture sections of calculus completed surveys at the beginning and end of the course. One class used clickers, while the other class was taught without clickers. The purpose of the study is to determine what relationship, if any, exists between clicker use and mathematics anxiety among students enrolled in an undergraduate calculus course.
    PRIMUS: problems, resources, and issues in mathematics undergraduate studies 05/2015; 25(5):453-472. DOI:10.1080/10511970.2015.1027976
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    ABSTRACT: Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and extension of the Spectral Theorem and is commonly used within a variety of fields, including statistics, neuroscience, and image compression. We present a synopsis of PCA and include a number of examples that can be used within upper-level mathematics courses to engage undergraduate students while introducing them to one of the most widely used applications of linear algebra.
    PRIMUS: problems, resources, and issues in mathematics undergraduate studies 05/2015; 25(5):400-420. DOI:10.1080/10511970.2014.993446
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    ABSTRACT: The use of modeling projects serves to integrate, reinforce, and extend student knowledge. Here we present two projects related to tumor growth appropriate for a first course in differential equations. They illustrate the use of problem-based learning to reinforce and extend course content via a writing or research experience. Here we discuss methods of preparing students for a research/writing experience, the critical thinking involved in completing the project, and the basic assessment of student work.
    PRIMUS: problems, resources, and issues in mathematics undergraduate studies 04/2015; 25(4). DOI:10.1080/10511970.2014.975881
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    ABSTRACT: We propose an introduction to the Laplace transform in which Riemann sums are used to approximate the expected net change in a function, assuming that it quantifies a process that can terminate at random. We assume only a basic understanding of probability.
    PRIMUS: problems, resources, and issues in mathematics undergraduate studies 04/2015; 25(4). DOI:10.1080/10511970.2014.977474
  • [Show abstract] [Hide abstract]
    ABSTRACT: Clickers and classroom voting are used across a number of disciplines in a variety of institutions. There are several papers that describe the use of clickers in mathematics classrooms such as precalculus, calculus, statistics, and even differential equations. This paper describes a method of incorporating clickers and classroom voting in a Transition to Advanced Mathematics course. The clicker questions were used to initiate small-group discussions in order to improve the mathematical communication skills of the students. Student and instructor reactions to the clickers and group discussions are given.
    PRIMUS: problems, resources, and issues in mathematics undergraduate studies 04/2015; 25(4). DOI:10.1080/10511970.2014.977473
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    ABSTRACT: In this paper I will share my experience with flipping a math content course for pre-service elementary teachers. The flipped class format involves students receiving instruction outside the classroom through readings and/or video lectures and working on “homework” inside the classroom. I will share strategies for creating lessons for my students to view outside of class, the structure of the in-class sessions, reflections on student learning, and comments from students.
    PRIMUS: problems, resources, and issues in mathematics undergraduate studies 04/2015; 25(4). DOI:10.1080/10511970.2014.981902
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    ABSTRACT: It is now increasingly recognized that mathematics is not a neutral value-free subject. Rather, mathematics can challenge students’ taken-for-granted realities and promote action. This article describes two issues, namely deforestation and income inequality. These were specifically chosen because they can be related to a range of calculus concepts including rates of change, optimization, Riemann sums, the Fundamental Theorem of Calculus, and partial derivatives. The aim is to give ideas about how an issue may be examined from different mathematical perspectives. The impact of discussing relevant issues in the calculus classroom is described through student reflections and course evaluation.
    PRIMUS: problems, resources, and issues in mathematics undergraduate studies 04/2015; 25(4). DOI:10.1080/10511970.2014.978983
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    ABSTRACT: This paper describes how one university mathematics department was able to improve student success in Calculus I by requiring a co-requisite lab for certain groups of students. The groups of students required to take the co-requisite lab were identified by analyzing student data, including Math ACT scores, ACT Compass Trigonometry scores, and grades in Pre-Calculus. Following the creation of the required lab, we collected the same data on the lab students as we had on similar students enrolled in Calculus I prior to the creation of the lab. The data were analyzed comparing the grades of students who had taken the co-requisite lab with the grades of similar students that had taken Calculus I prior to the creation of the lab. Our observations indicate that there is an improvement in the pass rate (grade of C or better) in Calculus I for a certain group of lab students.
    PRIMUS: problems, resources, and issues in mathematics undergraduate studies 04/2015; 25(4). DOI:10.1080/10511970.2014.992561
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    ABSTRACT: Inquiry-based learning is a topic of growing interest in the mathematical community. Much of the focus has been on using these methods in calculus and higher-level classes. This article describes the design and implementation of a set of inquiry-based learning activities in a Math for Liberal Arts course at a small, private, Catholic college. Activity design, student responses, class management, and student and instructor attitudes are discussed.
    PRIMUS: problems, resources, and issues in mathematics undergraduate studies 03/2015; 25(3). DOI:10.1080/10511970.2014.971474
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    ABSTRACT: This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context, identifying patterns, and venturing conjectures. A sequence of open-ended instructional tasks that aim to capitalize on students’ prior experiences with equation solving is provided along with notes and sample student responses for prospective instructors.
    PRIMUS: problems, resources, and issues in mathematics undergraduate studies 03/2015; 25(3). DOI:10.1080/10511970.2014.971475
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    ABSTRACT: Oulipo (Ouvroir de Littérature potentielle, or Workshop on potential literature), an over 50-year old movement that began in France, seeks to apply mathematical constraints to literature and the arts. In this article, I will give a brief survey of this movement and how I have built a learning module based on it for my mathematics for the liberal arts course. I will provide descriptions of student-created, mathematically constrained poetry, music compositions, and videos. These projects allow my students to apply mathematics (for example, modular arithmetic, combinatorics, and graph theory) to their interests in literature and the arts.
    PRIMUS: problems, resources, and issues in mathematics undergraduate studies 03/2015; 25(3). DOI:10.1080/10511970.2014.966935
  • [Show abstract] [Hide abstract]
    ABSTRACT: Inquiry-based learning (IBL) techniques can be used in mathematics courses for non-majors, such as courses required for liberal arts majors to fulfill graduation requirements. Unique challenges are discussed, followed by adaptations of IBL techniques to overcome those challenges.
    PRIMUS: problems, resources, and issues in mathematics undergraduate studies 03/2015; 25(3). DOI:10.1080/10511970.2014.967369
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    ABSTRACT: Mathematics for liberal arts courses are a staple of most mathematics departments and are often populated with students who have disengaged from mathematics. Inquiry-based learning is a student-centered pedagogical tool for re-engaging students in mathematics. In this paper, we introduce a Special Issue of PRIMUS on “Using Inquiry-Based Learning in Mathematics for Liberal Arts Courses.”
    PRIMUS: problems, resources, and issues in mathematics undergraduate studies 03/2015; 25(3). DOI:10.1080/10511970.2014.971476
  • [Show abstract] [Hide abstract]
    ABSTRACT: Our particular flavor of inquiry-based learning (IBL) uses mathematical discourse, conversations, and discussions to empower students to deepen their mathematical thinking, building on strengths of students in the humanities. We present an organized catalog of powerful questions, discussion prompts, and talk moves that can help faculty facilitate a classroom focused on mathematical discourse. The paper brings this discourse alive through classroom vignettes and explores various teacher moves and their impacts. The mathematical theme of the classroom investigations, Maypole dance patterns, stems from the learning guide “Discovering the Art of Mathematics: Dance.” Both authors are part of the NSF-funded project “Discovering the Art of Mathematics,” which provides IBL materials for mathematics for liberal arts courses, see www.artofmathematics.org.
    PRIMUS: problems, resources, and issues in mathematics undergraduate studies 03/2015; 25(3). DOI:10.1080/10511970.2014.921799
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    ABSTRACT: A college mathematics placement test with 25 basic algebra items and 15 calculus readiness items was administered to 1572 high school seniors, and first college mathematics course grades were obtained for 319 of these students. Test results indicated that more than two thirds of the high school graduates were not college ready, and the test results were reasonably consistent with the ACT Math benchmark score of 22 for college readiness. Analysis of ACT Math scores, basic algebra scores, calculus readiness scores, and course grades indicated that basic algebra scores are reasonable predictors of grades in College Algebra, whether traditional or modeling-based.
    PRIMUS: problems, resources, and issues in mathematics undergraduate studies 02/2015; 25(2). DOI:10.1080/10511970.2014.921653
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    ABSTRACT: Students sometimes struggle with visualizing the three-dimensional solids encountered in certain integral problems in a calculus class. We present a project in which students create solids of revolution with clay on a pottery wheel and estimate the volumes of these objects using Riemann sums. In addition to giving students an opportunity for tactile learning, this project focuses students’ attention on concepts relating to (i) functions that have no algebraic formula; (ii) notation and construction of Riemann sums; and (iii) error estimation. We will describe our project design, implementation, and suggested adaptations.
    PRIMUS: problems, resources, and issues in mathematics undergraduate studies 02/2015; 25(2). DOI:10.1080/10511970.2014.922151