Education Commons^™

Teaching Time Savers: The Exam Practically Wrote Itself!, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

When I first started teaching, creating an exam for my upper division courses was a genuinely exciting process. The material felt fresh and relatively unexplored (at least by me), and I remember often feeling pleasantly overwhelmed with what seemed like a vast supply of intriguing and engrossing exam-ready problems. Crafting the perfect exam, one that was noticeably inviting, exceedingly fair, and unavoidably illuminating, was a real joy.

Problem Solving And Proving Via Generalisation, Michael De Villiers, Mary Garner

Faculty and Research Publications

No abstract provided.

Promoting Mathematical Communication And Community Via Blackboard, Kris H. Green, Erica L. Johnson

Mathematical and Computing Sciences Faculty/Staff Publications

Major changes in mathematics pedagogy include writing as pedagogy and the role of community in learning. The classroom community is naturally extended by the use of online discussion boards. In this paper several models for student use of online discussion boards that have been successfully used to promote mathematical discourse are presented. Structured and unstructured examples that are easily adaptable and transportable to a variety of mathematics classroom settings are offered. These assignments facilitate student engagement and interaction outside of the classroom. Assessment, utility, and transferability are offered. Although the authors use the discussion boards provided by Blackboard, this particular …

A New Framework For Grading, Kris H. Green, W. Allen Emerson

Mathematical and Computing Sciences Faculty/Staff Publications

Grading is one of the least liked, least understood and least considered aspects of teaching. After years of work, we have developed a grading system that is quite different from traditional and reformed approaches to grading and which meaningfully incorporates and integrates the collection of evidence, the evaluation of evidence, and the reporting of judgments about that evidence. This system satisfies the requirements of good grading system and answers many of the problems faced by more traditional methods by substantially changing the way in which grade information is aggregated, resulting in a final course grade that aligns qualitative evaluation with …

On The Simplification Of Certain Q-Multisums, Andrew Sills

Department of Mathematical Sciences Faculty Publications

Some examples of naturally arising multisum q-series which turn out to have representations as fermionic single sums are presented. The resulting identities are proved using transformation formulas from the theory of basic hypergeometric series.

Trigonometry Without Sines And Geometry Without Angles, Phillip Lestmann

ACMS Conference Proceedings 2007

In his book, Divine Proportions, N. J. Wildberger advocates for a "rational" trigonometry by substituting the squares of the common trigonometric ratios for those ratios themselves. This presentation examines and critiques the claims of the book by evaluating its presented methods.

Six Ways, Yea Seven, That Scripture Is Integral To Our Science And Math Classes, Sean Bird

ACMS Conference Proceedings 2007

This paper looks at the ways the Bible informs mathematics and its role in guiding our stewardship of God’s creation.

Counting Tulips: Three Combinatorial Proofs, Eric Gossett

ACMS Conference Proceedings 2007

A gardener has r ≥ 1 red tulips and b ≥ 1 blue tulips, each in its own pot. She plans to plant them in a line along the edge of her driveway. In how many visually distinguishable ways can she arrange them?

Rules And Insights: Connecting The Mathematical And Linguistic Abilities Of C.S. Lewis, Kim Jongerius

ACMS Conference Proceedings 2007

While most biographical works on C.S. Lewis give passing reference to Lewis' problems with elementary mathematics, few have made an attempt at diagnosing the difficulty or exploring its impact on his writing. A careful study of family correspondence, however, makes it clear that his learning difficulties were not with mathematics alone and suggests connections between attitudes toward and abilities in both mathematics and language. This paper will make these connections clear and will illustrate their ties to Lewis' effective mathematical references.

The Beautiful And Sublime In Mathematics, Paul Zwier

ACMS Conference Proceedings 2007

A précis of Paul Zwier's talk presented at the meetings of the ACMS Conference at Messiah College on June 1, 2007.

Connection-Oriented Computer Science Education, Kim Kihlstrom

ACMS Conference Proceedings 2007

Computers play an important role in every area of our society and are integral in every academic discipline. Today's computer science students need a background that will prepare them for the expanding range of computing opportunities. The opportunities for computer professionals are varied and increasing in diversity. However, undergraduate computer science programs tend to be narrowly focused on programming and related technical skills. Female students in particular tend to be highly interested in exploring connections between computer science and other fields.

How can we leverage these observations at a liberal arts college, where interdisciplinary connections are highly desirable, and where …

Bach (To The Calculus Of) Variations, Charles R. Hampton

ACMS Conference Proceedings 2007

While it is quite common for professionals (doctors, lawyers, academics, etc) to be talented in many ways, including musical talent, there is a special connection between music and mathematics. Musicians collectively are not more talented in mathematics than other professionals and other academics. This paper examines the connections between math and music, particularly calculus and the music of Johann Sebastian Bach.

Portrayls Of Mathematics In Culture, Jeremy Case

ACMS Conference Proceedings 2007

This paper looks at various portrays of mathematicians in culture, and how that can influence perceptions of mathematics.

Breathing Life Into The Liberal Arts Math Course: Ten Teaching Tips, Mark Colgan

ACMS Conference Proceedings 2007

Teaching the liberal arts math course for general education students presents unique challenges, but the course also offers exciting life applications and opportunities for integrating faith with a variety of creative topics. I try to make the course interesting by actively involving students and relating mathematical topics to their lives. In this paper I will discuss some things I have tried in the liberal arts math course I teach at Taylor University: using students' names, use of undergraduate teaching assistants (T As), group guessing games, handout booklets, hangman, group projects, memory verses, reflection papers, and life lessons.

Teach A Course In The Math Of Voting And Choice, Karl-Dieter Crisman

ACMS Conference Proceedings 2007

Many mathematics instructors at the college level are looking for a curricular option that has the potential to serve a number of different constituencies. It could be to encourage more students to take math courses, or to give worthwhile options to students who need to take math but who are not ready for calculus (or its sequence). On the other hand, one may wish to add a new course for majors outside of the typical offerings, or even to prepare students for undergraduate research. The mathematics of voting and choice is ideally suited to meet all these needs in the …

Integrating Moral And Spiritual Themes In Middle School And High School Mathematics Teaching Units, Dave Klanderman, Sean Bird

ACMS Conference Proceedings 2007

In 2006, the Kuyers Institute published a total of nine math lessons for the middle school and high school which incorporate a Christian perspective. This paper examines the impact of teaching all of these lessons at a the high school level as well as selected lessons at the college level with preservice elementary and secondary mathematics teachers.

Tanzania, Mathematics, And Me: Reflections From My Work With Tanzanian Teachers, Mandi Maxwell

ACMS Conference Proceedings 2007

In June 2006 I had the privilege of participating in a four-day teacher training workshop in Mumba, Tanzania. In this paper I will discuss the challenges and triumphs of working with Tanzanian Secondary Mathematics teachers. We will discuss the educational environment, teaching strategies, and curricular issues that affect mathematics teachers in rural areas of Tanzania and contrast that with the American educational experience. We will also discuss some of the goals of the Teacher Training workshop that my colleagues and I led and look at some of the specific mathematical ideas and applications that I shared with the Mathematics teachers …

Voltaire: A Study In Finding A Needle In A Haystack, Andrew Simoson

ACMS Conference Proceedings 2007

In Euler’s popular notes to a German Princess of 1837, he describes Voltaire as laughing about the idea of a hole going to Earth’s center. Did Voltaire actually write about this idea? Herein we describe the answers to be found upon searching through the huge opus of Voltaire’s written work. The result has links to Newton’s 1687 Principia discoveries and the French Academy’s early eighteenth century international scientific expeditions to Lapland and Peru establishing the veracity of those discoveries.

An Augustinian Perspective On The Philosophy Of Mathematics, James Bradley

ACMS Conference Proceedings 2007

Enlightenment thinkers saw the universe as mechanistic and mathematics as the language in which the universe is written. They viewed mathematics as eternal, as transcending human minds, and as comprehensible by human beings. Thus mathematics, from their perspective, is our best tool for understanding the secrets of nature. This outlook was nicely summarized by Morris Kline: (Kline, 1953) In brief the whole world is the totality of mathematically expressible motions of objects in space and time, and the entire universe is a great, harmonious, and mathematically designed machine. From a Christian perspective, however, the Enlightenment outlook is flawed. It privileges …

Chaos Theory And Metaphysical (In) Determinism, Tim Rogalsky

ACMS Conference Proceedings 2007

This paper will begin by introducing the issues that arise from chaos theory for the Christian mathematician and scientist: What is at stake in this debate? It will then briefly review chaos theory, by means of two examples. It will then introduce the metaphysical interpretations given to chaos theory by three different scientist-theologians. The paper will conclude with a brief introduction to open theists, and analyze their use of chaos theory to supper their theological claims.

Introduction (2007), Angela Hare

ACMS Conference Proceedings 2007

Sixteenth Conference of the Association of Christians in the Mathematical Sciences

Schedule (2007), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2007

Sixteenth Conference of the Association of Christians in the Mathematical Sciences

Table Of Contents (2007), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2007

Sixteenth Conference of the Association of Christians in the Mathematical Sciences

Calculus Students’ Difficulties In Using Variables As Changing Quantities, Susan S. Gray, Barbara J. Loud, Carole Sokolowski

Mathematics Faculty Publications

The study of calculus requires an ability to understand algebraic variables as generalized numbers and as functionally-related quantities. These more advanced uses of variables are indicative of algebraic thinking as opposed to arithmetic thinking. This study reports on entering Calculus I students’ responses to a selection of test questions that required the use of variables in these advanced ways. On average, students’ success rates on these questions were less than 50%. An analysis of errors revealed students’ tendencies toward arithmetic thinking when they attempted to answer questions that required an ability to think of variables as changing quantities, a characteristic …

Bounds And Comparisons For Weighted Renewal-Type Integral Equations, Broderick O. Oluyede

Department of Mathematical Sciences Faculty Publications

In this note, inequalities and bounds for weighted renewal-type integral equations are presented. Some upper and lower bounds for the weighted renewal-type integral equations with monotone weight functions are derived. Some upper and lower bounds for the weighted renewal-type equations with monotone weight functions are derived. Bounds for the difference between two weighted renewal functions as well between the parent and weighted renewal functions are obtained in terms of the parent renewal reliability functions and their first and second moments. Relations for renewal-type integrals of the ruin probability are presented. Some inequalities, bounds and convergence results are also established.

Critical Mathematics Pedagogy: Transforming Teachers’ Practices, David W. Stinson, Carla R. Bidwell, Christopher C. Jett, Ginny C. Powell, Mary M. Thurman

Middle-Secondary Education and Instructional Technology Faculty Publications

This study reports the effects of a graduate-level mathematics education course that focused on critical theory and teaching for social justice on the pedagogical philosophies and practices of three mathematics teachers (middle, high school, and 2-year college). The study employed Freirian participatory research methodology; in fact, the participants were not only co-researchers, but also co-authors of the study. Data collection included reflective essays, journals, and “storytelling”; data analysis was a combination of textual analysis and autoethnography. The findings report that the teachers believed that the course provided not only a new language but also a legitimization to transform their pedagogical …

What Is Mathematics?: Teachers Exploring The Philosophy Of Mathematics, Kimberly White-Fredette, David W. Stinson

Middle-Secondary Education and Instructional Technology Faculty Publications

No abstract provided.

Teaching Time Savers: Is Homework Grading On Your Nerves?, Lisette G. De Pillis, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

You have probably heard it said that we learn mathematics best when we do mathematics, or that mathematics is not a spectator sport. For most of our students, this means that their mathematics courses will involve a fair amount of homework. This homework is often used to evaluate individual student progress, but it can also be used, for example, as a catalyst for discussion, to emphasize a point made in class, and to identify common misunderstandings throughout the class as a whole. There is, however, the matter of grading homework.

Promoting Undergraduate Research In Mathematics At The University Of Nebraska – Lincoln, Judy L. Walker, Glenn Ledder, Richard Rebarber, Gordon S. Woodward

Department of Mathematics: Faculty Publications

The Department of Mathematics at the University of Nebraska – Lincoln (UNL) has several programs which promote undergraduate research in a variety of ways. Two of these are summer programs which draw from a national applicant pool: The Nebraska REU in Applied Mathematics (Section 1) is a traditional NSF-funded REU site, and Nebraska IMMERSE (Section 2) offers a summer “bridge” program (with a research bent) for students about to start graduate school in mathematics. IMMERSE is a relatively new program, started in 2004 as part of the department’s Mentoring through Critical Transition Points (MCTP) grant from NSF. The MCTP grant …

On Energy And Expected Uncertainty Measures In Weighted Distributions, Broderick O. Oluyede, Mekki Terbeche

Department of Mathematical Sciences Faculty Publications

In this note, bounds and inequalities for the comparisons of weighted energy functions, entropy, and discrimination information measures and their unweighted counterparts are presented. Inequalities for weighted expected uncertainty, cross-entropy or discrimination information measures are also presented. A useful result on the convergence of the weighted kernel density informational energy estimates is given and some informational energy applications presented.