Science and Mathematics Education Commons^™

Reorganizing Freshman Business Mathematics Ii: Authentic Assessment In Mathematics Through Professional Memos, Kris H. Green, W. Allen Emerson

Mathematical and Computing Sciences Faculty/Staff Publications

Part I of this paper described the development of a new Freshman Business Mathematics (FBM) course at our college. In this second part of the paper, we discuss our assessment tool, the business memo, as a venue for students to apply mathematical skills, via mathematical modeling, to realistic business problems. These memos have proven a crucial step in turning our FBM course around from a dreaded course with little connection to students’ intended careers into a course where students experience the power of mathematics for solving problems and informing decisions. Comments from students in the course throughout its six-year history …

Dynamic Web Tools For Trigonometry, Steven J. Wilson

Innovations in Math Technology

In the last 20 years, computer technology having mathematical capability has been developed, improved, and become widely available, but textbook presentations are still largely free of any discussion that might require technology. Technology could be used in mathematical instruction for student drill and practice, for instructor demonstrations that promote conceptual understanding, or for the exploration of mathematical ideas, but software is often designed to be pedagogically generic, leaving its use to the creativity of the instructor. Technological solutions for local machines can be quite extensive, but cost and time constraints then limit availability for student use. The internet has the …

Mathematicians Playing A Role In Math Education: What We Learned At The Ime/Mime Workshop, Anna Bargagliotti, Rama Chidambaram, Gizem Karaali

Pomona Faculty Publications and Research

In Hollywood, some actors are regularly cast as mean, others as sweet and endearing, and some typically play innocent big-eyed youths who inevitably succeed after awakening to the particular facts of life that their producer wants them to awaken to. It is unusual and difficult for actors to cross the bridge between different types on a regular basis. However, there are always exceptions to the rule.

In the seemingly unrelated world of academics, mathematics faculty may find themselves playing different roles. People with different skills and interests strive to balance their careers in ways that will be uniquely fulfilling to …

Selecting U.S. Senators By The Original Method: Intersecting Mathematics And Social Studies, Bonnie H. Litwiller, David R. Duncan

Faculty Work

Mathematics teachers are concerned with incorporating connections with other academic areas in their mathematics curriculum. Social science provides a rich source of data which can be collected, organized, and interpreted by mathematics students. These data become of particular interest to many students if they involve political questions and processes.

Utilization Of Revoicing Based On Learners‘ Thinking In An Inquiry-Oriented Differential Equations Class, Oh Kwon Nam, Mi Kyung Ju, Chris Rasmussen, Karen A. Marrongelle, Jae Hee Park, Kyoung Hee Cho, Jung Sook Park, Jee Hyun Park

Mathematics and Statistics Faculty Publications and Presentations

Researchers of mathematics education are increasingly interested in a teacher's discursive moves, which refer to deliberate actions taken by a teacher to participate in or influence debate and discussion in the mathematics classroom. This study explored one teacher's discursive moves in an undergraduate inquiry-oriented mathematics class. The data for this study come from four class sessions in which students investigated initial value problems as represented by the phase portrait of a system of differential equations. Through the analysis and a review of the literature, we identified four categories of a teacher's discursive moves: revoicing, questioning/requesting, telling, and managing. This report …

What Allows Teachers To Extend Student Thinking During Whole-Group Discussions, Nesrin Cengiz

Dissertations

Research indicates that extending students' mathematical thinking during whole-group discussions is challenging, even for the most experienced teachers. That is, it is challenging for teachers to help students move beyond their initial mathematical observations and solutions during whole-group discussions. To better understand this phenomena, the teaching of six experienced elementary school teachers, who had been teaching aStandards-based curriculum for several years and had participated in a multi-year professional development project focused on that curriculum, is explored in this study. In particular, two issues are addressed: what it looks like to extend student thinking during whole-group discussions and how …

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

Faculty Articles

No abstract provided.

How Geometer’S Sketchpad Improves Student Learning, William George Awe

Mathematics Graduate Theses

This study investigated whether dynamic software improves learning and reviews different types of dynamic software. The study then narrows its focus to one type of dynamic software, Geometer’s Sketchpad and studies how Geometer’s Sketchpad, in itself, improves student learning. The researcher identified what dynamic software is, the importance of dynamic software and different types of dynamic software. The researcher also identifies how dynamic software is utilized in schools and researches how to improve the use of dynamic software in schools. Dynamic software, and Geometer’s Sketchpad, In particular, was found to improve learning across grade levels and with different levels of …

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 …

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 …

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.

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.

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.

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.

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.

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 …

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.

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?

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 …

Mathematical Knowledge And Leibniz' Epstemology, Jonathan Zderad

ACMS Conference Proceedings 2007

No abstract provided.

Integrating Ethics Into The Database Course With A Focus On Data Modeling And Normalization, James F. Glasgow, Ph.D

ACMS Conference Proceedings 2007

No abstract provided.

Optimize Your Matth Services Through Networking, Patrice Conrath

ACMS Conference Proceedings 2007

No abstract provided.

Modeling Growth In Christian Evangelism, Marvin Bittinger

ACMS Conference Proceedings 2007

No abstract provided.

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.

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.

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.

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 …

Exploring Loci In Geometry, Owen Byer, Deirdre Smeltzer

ACMS Conference Proceedings 2007

No abstract provided.