Science and Mathematics Education Commons^™

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.

Personal Reflections / 5.31.19, José M. Torres

Personal Reflections

No abstract provided.

Implementation Of Literacy Strategies And The Impact On Word Problems, Lindsey R. Glick

Theses and Dissertations

The purpose of this study is to determine whether the implementation of literacy strategies in a fifth grade mathematics classroom would affect comprehension. The specific aim is to see what happens when students utilize literacy strategies when solving mathematical word problems. Three literacy topics were the focal point in this study: vocabulary, writing, and comprehension. Literacy strategies from each topic were introduced and applied during a mathematics class. Surveys, math journals, graphic organizers, classroom discussions, and interviews were analyzed. The limitations and implications for incorporating literacy instruction in a mathematics class are discussed.

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.

The Effectiveness Of Google Classroom In The Self-Contained Chemistry Classroom, Steven J. Gross

Theses and Dissertations

The purpose of this exploratory investigation was to ascertain the effectiveness of Google Classroom in the self-contained Chemistry classroom in terms of student turning in of assignments, student performance on summative assessment, student satisfaction with the use of Google Classroom, student contribution to class discussion in terms of frequency and quality, and the student acceptance of Google Classroom as a system of technology. Results suggest increased growth on summative assessments, turning in of assignments, and less regression in turning in of assignments with the implementation and use of Google Classroom. Results also suggest that the student population performs better through …

A Qualitative Analysis To Identify The Elements That Support Department Level Change In The Life Sciences: The Pulse Vision & Change Recognition Program, Mary Peteroy-Kelly, Loretta Brancaccio-Taras, Judy Awong-Taylor, Teresa Balser, Thomas Jack, Sara Lindsay, Kate Marley, Sandra Romano, J. Akif Uzman, Pamela Pape-Lindstrom

Publications and Research

The 2011 report, Vision and Change in Undergraduate Biology Education: A Call to Action, provided the impetus to mobilize the undergraduate life sciences education community to affect change in order to enhance the educational experiences of life sciences majors. The work of the appointed Partnership for Undergraduate Life Sciences Education (PULSE) Vision and Change (V&C) Leadership Fellows has focused on the development of programs and resources to support departmental change. In this report, we present a qualitative assessment of several documents generated from the PULSE V&C Leadership Fellow Recognition Team. The Recognition Team developed two initiatives to provide …

An Exploratory Investigation Of The Effect Of Reading Strategies On Science Assessment Scores, Suzanne K. Lynch

Theses and Dissertations

The purpose of this study was to determine if the use of literacy strategies in a content area improves a summative assessment score. All of the students in this research had Individual Education Plans. Most of the students have specific learning disabilities that include reading comprehension, reading fluency, basic reading skills, and inferencing skills. Both pre-reading and during reading strategies were used for the study. Students were exposed to the use of graphic organizers and close reading strategies on given topics. Data gathered from the experiment showed that the use of a graphic organizer in addition to notes and labs …

Table Of Contents (2019), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2019

No abstract provided.

Association Of Christians In The Mathematical Sciences Proceedings 2019, Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2019

The conference proceedings of the Association of Christians in the Mathematical Sciences biannual conference, May 29-June 1, 2019 at Indiana Wesleyan University.

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

ACMS Conference Proceedings 2019

No abstract provided.

Cooperative Grouping In The Inclusive Stem Classroom, Catherine M. Elsey

Theses and Dissertations

The purpose of this study was to determine if using cooperative group role assignments impacted on-task behavior in an inclusive STEM classroom. This study investigated if students were positively engaged, remained on-task, and completed STEM challenges with their group. There were two 5th grade classes, each with sixteen participants, involved in the study. In the experimental class, students had role assignments in their cooperative group of four members. The other class, was a control group, and students did not have role assignments in their group of four members. Data was collected through observation procedures of on-task and off-task behaviors for …

Movin’ Right Along: Developing Creative Methods Of Science Communication In A Modern World, Charity Southworth

Critical and Creative Thinking Capstones Collection

This synthesis proposes ways to use the Internet and artistic endeavors to communicate about science to a wider range of audiences than currently reached by science communicators, even those who already use social media. Science communicators, who control who gets information about science and how, need to be welcoming and inviting to people from all walks of life. My own contributions in this spirit include science-themed jewelry and clothing patterns.

The Effectiveness Of The Question Formulation Technique On Open-Ended, Written Response Questions In Mathematics, Jessica M. Mannion

Theses and Dissertations

The purpose of this study was to determine the effectiveness of the Question Formulation Technique (QFT) on students' open-ended, written response questions in mathematics in a 4th grade inclusion classroom. Four students, three male and one female, participated in the study. All students were classified with specific learning disabilities (SLD) or other health impaired (OHI). Experimental research design was used. A baseline was collected using students previous written response scores.

The QFT was implemented over the course of three math chapters. Students were assessed after each chapter with three open-ended, written response problems. The results show that each students average …