Mathematics Commons^™

The Process And A Pitfall In Developing Biology And Chemistry Problems For Mathematics Courses, Mary Beisiegel, Lori Kayes, Devon Quick, Richard Nafshun, Michael Lopez, Steve Dobrioglo, Michael Dickens

Journal of Mathematics and Science: Collaborative Explorations

In this paper, we describe our process for developing applied problems from biology and chemistry for use in a differential calculus course. We describe our conversations and curricular analyses that led us to change from our initial focus on college algebra to calculus. We provide results that allowed us to see the overlaps between biology and mathematics and chemistry and mathematics and led to a specific focus on problems related to rates of change. Finally, we investigate the problems that were developed by the partner disciplines for use on recitation activities in calculus and how those problems were modified by …

Student Perceptions Of Learning Introductory Mathematics In An Online Environment In Higher Education, Jamie Lynn Brooks

Doctoral Dissertations and Projects

The purpose of this transcendental phenomenological study was to describe the essence of student perception of learning introductory mathematics courses in an online environment at the college level. The central research question was, “What are the lived experiences of students who have completed introductory college mathematics courses in the online learning environment?” The phenomenon described was that of the beliefs and attitudes of the students who participated in introductory mathematics courses on the college level. The ideas explored were if students believe they learn effectively in this environment and how they believe they can best learn. Student beliefs and attitudes …

The Grass Grows Green In Virginia: A Grassroots Effort Leading To Comprehensive Change In Removing Mathematics Barriers For Students., Patricia Parker

Inquiry: The Journal of the Virginia Community Colleges

The Virginia Community College System (VCCS) embarked on a comprehensive mathematics pathways project in October 2015 with a move from design to implementation in spring 2017. The VCCS Mathematics Pathways Project (VMPP) aimed not only to develop strategies to improve retention and completion, but also to address foundational barriers to students’ success. This grassroots effort involved collaboration among all 23 community colleges, over 200 mathematics faculty, and staff from career and technical support departments. Collaboration extended to the K–12 and university sectors, professional organizations, publishers, and foundations. VMPP goals focused on creating structured mathematics pathway courses for all program levels, …

Are We At A Watershed Moment For The Quantitative Literacy Movement?: Review Of Shifting Context, Stable Core: Advancing Quantitative Literacy In Higher Education, By Luke Tunstall, Gizem Karaali, And Victor Piercey, Eds., Maura Mast

Numeracy

Luke Tunstall, Gizem Karaali, and Victor Piercey, eds. 2019. Shifting Concepts, Stable Core: Advancing Quantitative Literacy in Higher Education. Math Notes 88. (Mathematics Association of America, MAA Press). Print ISBN 978-0-88385-198-2. Electronic ISBN 978-1-61444-324-7.

The thematic approach of the edited MAA Notes volume Shifting Contexts, Stable Core: Advancing Quantitative Literacy in Higher Education is that the “construct” of quantitative literacy is now fairly stable, but the contexts in which quantitative literacy is taught (and practiced) continue to change. Several chapters give the reader much to consider regarding what constitutes the foundation of this stable core and, relatedly, how quantitative …

Quantitative Literacy And The Mathematical Association Of America In The 2000’S: Ql Subcommittee Of Cupm , Sigmaa Ql, And Maa Notes #70, Rick Gillman

Numeracy

This Roots and Seeds article is a partial history of the quantitative literacy movement in the Mathematical Association of America in the first decade of the 21st century. It focuses on the inclusion of QL in the MAA Committee on the Undergraduate Program in Mathematics’ CUPM Curriculum Guidelines (2004), the creation of the special interest group for MAA members (SIGMAA QL, 2004), and the work of that body in subsequent years, in particular, the MAA Notes #70, Current Practices in Quantitative Literacy (2006). I discuss some issues that were problematic in the QL movement in the MAA in those years …

The Ultimatum Game: An Introduction To Quantitative Literacy In A Social Justice Context, Robert G. Root

Numeracy

The Ultimatum Game is a two-person, multiple-strategy game widely used in the experimental social sciences to demonstrate the human propensity for costly punishment in response to inequitable treatment. The game serves to provide quantitative evidence for a diversity of fairness norms across cultures. The play of the game and its interpretation offer nuanced views of the nature and importance of quantitative literacy. Its use in a writing seminar connecting quantitative literacy and social justice is described.

Roots And Seeds: Finding Our Place In The Social Practice Nexus That Is Quantitative Literacy, H. L. Vacher, Nathan D. Grawe

Numeracy

The purpose of our new Roots and Seeds feature is to provide an open-access space to archive first-hand accounts of QL activities that have preceded our journal (2008). The first two contributions in the collection appeared last issue: Linda Sons on the making of what has come to be known as the 1994 Sons Report (Mathematics Association of America), and Dorothy Wallace on her path to the Quantitative Literacy Design Team for Mathematics and Democracy (2001), and the questions that bedeviled them then – and us now. In this issue, we get Rick Gillman’s account of how the committee that …

Closing Banquet Eulogies, Russell Howell, C. Ray Rosentrater

ACMS Conference Proceedings 2019

A tribute to David Lay; A tribute to John Roe

Developing Mathematicians: The Benefits Of Weaving Spiritual And Disciplinary Discipleship, Patrick Eggleton

ACMS Conference Proceedings 2019

Part of the goal of discipleship at the Christian university is for faith development to seep into the hearts of the students. Similarly, the goal of the development of future mathematicians is for the mathematical proficiencies, the practices like problem solving and analytical reasoning that permeate each of the courses, to seep into the hearts of our majors. This presentation shares how the weaving of our spiritual and disciplinary discipleship efforts benefits the faith development of our students while also helping them to think like a mathematician.

From Perfect Shuffles To Landau's Function, Brian D. Beasley

ACMS Conference Proceedings 2019

If we view a given shuffle of a deck of cards as a permutation, then repeatedly applying this same shuffle will eventually return the deck to its original order. In general, how many steps will that take? What happens in the case of so-called perfect shuffles? What type of shuffle will require the greatest number of applications before restoring the original deck? This talk will address those questions and provide a brief history of the work of Edmund Landau on the maximal order of a permutation in the symmetric group on n objects. It will also note some recent progress …

Replacing Remedial Mathematics With Corequisites In General Education Mathematics Courses, Alana Unfried

ACMS Conference Proceedings 2019

Many colleges and universities offer courses, such as Remedial Mathematics or Elementary Algebra, that underprepared students must complete before they can take a college-level mathematics course. However, nationally there is a push to replace remedial mathematics courses with corequisite courses instead. This design allows students to enter directly into their general education mathematics course instead of first overcoming the barrier of a remedial course. Corequisite mathematics courses were implemented across the 23-campus California State University system during the 2018-19 academic year. I will discuss the design and implementation of a corequisite structure at California State University, Monterey Bay, in particular …

Charles Babbage And Mathematical Aspects Of The Miraculous, Courtney K. Taylor

ACMS Conference Proceedings 2019

Charles Babbage is widely known as the father of the computer, but he is lesser known for his contributions to natural theology and apologetics. In 1837 Babbage wrote the Ninth Bridgewater Treatise in response to a series of writings concerning faith and science that had been commissioned by the Royal Society. Among the remarkable features of the Ninth Bridgewater are mathematical analogies concerning the miraculous. We will explore these ideas, which range from the difference engine to a family of fourth degree curves, illustrating that for Babbage, miracles are not exceptions to natural law, but rather instances of a larger …

The Applicability Of Mathematics And The Naturalist Die, Ricardo J. Cordero-Soto

ACMS Conference Proceedings 2019

Philosopher and Christian apologist William Lane Craig has proposed a valid deductive argument for God’s existence that is rooted in the applicability of mathematics to the physical universe. This argument was presented by Craig during a debate with philosopher and atheist Alex Rosenberg. During the debate, Rosenberg presented a rebuttal to the soundness of this argument by appealing to chance as an explanation to the applicability of mathematics to the physical universe. In this talk, the presenter will discuss how the naturalist die is unable to produce “chance application” of mathematics while defending the soundness of the argument in light …

Faith, Mathematics, And Science: The Priority Of Scripture In The Pursuit And Acquisition Of Truth, Bob Mallison

ACMS Conference Proceedings 2019

This research will examine some approaches for identifying truth as well as some issues involved in recognizing reliable sources of information. We will proceed from a decidedly Christian perspective including the conviction that God created an orderly universe (and that studying nature provides valuable information about Him) and that His Word, the Bible, even more clearly expresses in- formation about Him. We will discuss some of the essential tools used by mathematicians and scientists for the discovery of truth – namely, models. We will examine some valuable models from history, and briefly discuss that as additional scientific information became available, …

Teaching Mathematics At An African University -- My Experience, Kathleen Lewis

ACMS Conference Proceedings 2019

For eight years (2010-2018), I was the head of the math department at The University of The Gambia, a small, new (started in 1999) university in a very small, mostly Muslim, West African country that most Americans have never heard of. During that time, a number of other Americans and Europeans came to teach for shorter periods of time. I will talk about what this experience was like for us, both the good and the bad. I will describe the possibilities for others to spend either a sabbatical or an extended period of time at such a university and suggest …

Lagrange's Interpolation, Chinese Remainder, And Linear Equations, Jesús Jiménez

ACMS Conference Proceedings 2019

Consider a finite set of points {(x1, y1), (x2, y2), . . . , (xk , yk )} in R2. The Lagrange’s interpolation problem is to find a polynomial p(x) of degree k − 1 satisfying p(xi) = yi for 1 ≤ i ≤ k. We will recall the solution to Lagrange’s interpolation problems as an instance of the Chinese Remainder Theorem. Next, we will show that a similar approach can be used to construct solutions to a system of linear equations.

Addressing Challenges In Creating Math Presentations, David Schweitzer

ACMS Conference Proceedings 2019

When it comes to composing presentation slides with extensive mathematical content, each of the slide creation platforms has at least one significant drawback. Whether it is Beamer and its steep learning curve, PowerPoint and its relative inefficiency with math, Google Slides and its complete lack of math capabilities, or some other platform, no one tool single-handedly offers an ideal solution. Additionally, if users desire creative flexibility, such as the ability to easily change fonts or colors, the platforms’ respective limitations can become even more pronounced. In a project that has been well suited for undergraduate research, the presenter and his …

Overcoming Stereotypes Through A Liberal Arts Math Course, Jessica Hamm

ACMS Conference Proceedings 2019

"I'm just not a math person.” We’ve heard this comment countless times from our students. It is a mentality that both paralyzes and strangely comforts them. In this talk I will describe how I use my liberal arts Joy of Mathematics course to help students address and overcome stereotypes. In particular, I will discuss a specific assignment as well as share some student comments and perspectives on how this course helped change their viewpoint on more than just math.

Maximum Elements Of Ordered Sets And Anselm's Ontological Argument, Doug Ward

ACMS Conference Proceedings 2019

I will present a simple theorem concerning maximal elements of a set T endowed with an ordering “>” that is antisymmetric, i.e., if A and B are elements of T , we cannot have both A > B and B > A. A special case of this theorem is a simple version of the ontological argument, one of the classical proofs for the existence of God.

Numerical Range Of Toeplitz Matrices Over Finite Fields, Derek Thompson, Maddison Guillaume Baker, Amish Mishra

ACMS Conference Proceedings 2019

We characterize the kth numerical range of all n×n Toeplitz matrices with a constant main diagonal and another single, non-zero diagonal, where the matrices are over the field Zp[i], with p a prime congruent to 3 mod 4. We find that, for k ∈ Z∗, the kth numerical range is always equal to Zp[i] with the exception of the scaled identity. We also use similar techniques to discover a general connection between the 0th numerical range and the kth numerical range. Lastly, we conclude with a conjecture regarding the general numerical range of all triangular Toeplitz matrices.

Is Mathematical Truth Time Dependent? Comments From A Paper By Judith Grabiner, Richard Stout

ACMS Conference Proceedings 2019

Judith Grabiner, a renowned historian of mathematics, has written many papers related to signifi- cant changes in the content and nature of analysis, from the 17th through the 19th century. In her paper “Is Mathematical Truth Time Dependent?” Professor Grabiner gives several reasons for the changing nature and requirements in rigor that occurred over this period of two hundred years. In this talk I will briefly summarize her conclusions, particularly in light of how they might influence a Christian perspective on mathematics.

Models, Values, And Disasters, Michael H. Veatch

ACMS Conference Proceedings 2019

Decision-support models have values embedded in them and are subjective to varying degrees. Philosophical and ethical perspectives on operations research models are used to describe this subjectivity. Approaches to model building are then suggested that take into account subjectivity and values. For the decisions to reflect the right values, the model must align with the decision-maker’s values. I argue that it is appropriate and important for Christians applying mathematical models to be keenly aware of decision-maker’s values and seek to reflect them in the model. Disaster response planning is presented as an example where incorporating values is challenging. The responding …

Factors That Motivate Students To Learn Mathematics, Dave Klanderman, Sarah Klanderman, Benjamin Gliesmann, Josh Wilkerson, Patrick Eggleton

ACMS Conference Proceedings 2019

What motivates some students to want to learn mathematics while others do not share similar motivation? Are these factors intrinsic, extrinsic, or a combination of both? To answer these questions, we adapted a survey originally developed by Tapia (1996) and later shortened by Lim and Chapman (2015). We administered the survey in multiple middle schools, a high school, and multiple colleges and universities. We obtained over 100 completed surveys for each of these educational levels. This presentation offers an analysis of these data, including descriptive statistics and confidence intervals for each educational level. For the college and university sample, we …

Thinking Beautifully About Mathematics: A View Of Mathematics As The Science Of Measurable Orders, James M. Turner

ACMS Conference Proceedings 2019

At Calvin College, First Year Students are required to take a section of our Discovering the Christian Mind course during our January term. For the past 3 years, I have taught a section of this course titled Thinking Beautiful ly about Mathematics. In it, I explored, with the students, various areas of mathematics, as well as how mathematicians have explored them, while addressing such questions as “Is mathematics invented or discovered?” and “Why is mathematics unreasonably effective?” Ultimately, we look to identify ways and characterizations for how beauty displays itself in mathematics and how and it what ways beauty is …

Marin Mersenne: Minim Monk And Messenger; Monotheism, Mathematics, And Music, Karl-Dieter Crisman

ACMS Conference Proceedings 2019

If you have taught a number theory course or even watched the mathematical news, you know that occasionally a new (and enormous) “Mersenne prime” is discovered. Those who have introduced students to the prehistory of calculus may know of a certain Marin Mersenne as the interlocutor who drew Fermat and Descartes (and others) out to discuss their methods of tangents (and more). But who was Mersenne, and what did he actually do? This presentation will give an overview of his times, his role in the history of science, and his own writings. We’ll especially look into why a monk from …

Analyzing The Impact Of Active Learning In General Education Mathematics Courses, Amanda Harsy, Marie Meyer, Michael Smith, Brittany Stephenson

ACMS Conference Proceedings 2019

This talk shares the preliminary results of a study that explores the general perceptions and attitudes of students in general education mathematics courses taught using primarily active learning- based methods (like group work, projects, and discovery learning), and compares them with those enrolled in a general education mathematics course taught in a more traditional and lecture-based method. We present an analysis of survey data collected throughout the semester, which explores the disposition and mindset of students, their mathematical confidence and anxiety, and perceptions of pedagogical methods used for the teaching of mathematics. We also explored how these perceptions and dispositions …

Computer Science: Creating In A Fallen World, Russell Tuck

ACMS Conference Proceedings 2019

When God created people in his image, he gave us the gift of sub-creation. One of the great joys of Computer Science is exercising that gift to create tools : software and computer systems that serve people and solve problems. Like all God’s gifts, he charges us to exercise the gift of sub-creation wisely and for good. While there are many obvious implications and challenges, being good stewardship of users’ time and reducing discrimination are particularly relevant and perhaps less obvious examples. Although computer scientists exercise the gift of sub-creation, we do so as fallen people in a fallen world. …

A Unifying Project For A Tex/Cas Course, Andrew Simoson

ACMS Conference Proceedings 2019

We describe a CAS and TEX usage course for mathematics majors. As a unifying project, each student selects two primes p and q with pq < 100, explores mathematical pq ideas, and generates associated graphs, figures, tables for a final TEX paper. We summarize several pq explorations: stu- dents render page pq from Schwartz’s picture book about primes, You Can Count on Monsters, via Mathematica and TEX’s picture environment; students generate fractal images of pq; and students discover the primes of the ring Z r√pql.

Introduction (2019), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2019

No abstract provided.

Paper Abstracts (2019), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2019

No abstract provided.