Mathematics Commons^™

Table Of Contents (2011), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2011

Eighteenth Conference of the Association of Christians in the Mathematical Sciences

Schedule (2011), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2011

Eighteenth Conference of the Association of Christians in the Mathematical Sciences

Acms 18th Biennial Conference Proceedings, Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2011

Association of Christians in the Mathematical Sciences 18th Biennial Conference Proceedings, June 1-4, 2011, Westmont College, Santa Barbara, CA.

Connecting Mathematics Students To Philosophy And Faith, Nathan Moyer

ACMS Journal 2010-2011

This paper describes an upper-division class project that helps students wrestle with the deep philosophical questions of mathematics in a relevant way. Through article readings and group discussions, various historical views of mathematical philosophy are examined and critiqued. An emphasis is placed upon students making meaningful connections between their own views of mathematics and their personal Christian faith or worldview.

Perspectives On Deepening Teachers’ Mathematics Content Knowledge: The Case Of The Oregon Mathematics Leadership Institute, Libby Knott, Martha Vancleave

Faculty Publications

The Oregon Mathematics Leadership Institute (OMLI) project served 180 Oregon teachers, and 90 administrators, across the K-12 grades from ten partner districts. OMLI offered a residential, three-week summer institute. Over the course of three consecutive summers, teachers were immersed in a total of six mathematics content classes– Algebra, Data & Chance, Discrete Mathematics, Geometry, Measurement & Change, and Number & Operations—along with an annual collegial leadership course. Each content class was designed and taught by a team of expert faculty from universities, community colleges, and K-12 districts. Each team chose a few “big ideas” on which to focus the course. …

Middle School Mathematics Students' Perspectives On The Study Of Mathematics, Christy H. Vaughn

Walden Dissertations and Doctoral Studies

This qualitative study addressed the perceptions toward the study of mathematics by middle school students who had formerly been in a remedial mathematics program. The purpose of the study was to explore the past experiences of nine students in order to determine what is needed for them to feel successful in mathematics. The conceptual framework of the study was grounded in philosophies of motivation, including achievement goal theory, self-worth theory, self-efficacy theory, expectancy-value theory, and attribution theory. The study used a phenomenological research design to answer the key research question, which focused upon the experiences of students and the meaning …

Problem Solving Based Instruction In The High School Mathematics Classroom, Lawrence Vettleson, Jr.

Mathematics Graduate Theses

This paper is a review of research pertaining to the use of problem solving in classroom instruction. It covers the stages of problems solving as listed by George Polya and how they can be used to enhance mathematics instruction. This research paper will identify that problem solving is a need based on Minnesota state mathematics standards and National mathematics standards. Covered in this paper is the research on the effects of mathematics instruction using problem solving. The research covers some of the benefits to student education if students learn mathematics using a problem solving based approach to classroom instruction.

A Vision For Acms, James Bradley

ACMS Journal 2010-2011

This paper presents a vision for the mission of the ACMS. It considers some plausible connections between mathematics and theology as well as some big questions that Christian mathematicians might fruitfully explore. It examines the current cultural norms of the mathematics guild, why these are problematic for Christians, and some possible ways the ACMS might respond.

Investigating Mathematical Literacy Through Teacher Language, Alyson Lischka

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Communication about mathematical concepts using appropriate terminology is a standard established by the National Council of Teachers of Mathematics. However, international test results show that United States’ students are lagging in mathematical literacy. This case study analyzes the ways in which instructors use language to help students move toward conceptual understanding of mathematical vocabulary. Three mathematics education professors at a mid-size four year institution were observed teaching math classes to students enrolled in elementary or secondary certification programs. Collected data included: audio-recorded observations and field notes, lesson artifacts such as quizzes and handouts, and audio-recorded interviews with each participant. Findings …

The Influence Of Inclusion On Langauge Arts Literacy And Math Achievement On Non-Disabled Middle School Students, Faye Brady

Seton Hall University Dissertations and Theses (ETDs)

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Proceedings Of The Fourth Annual Meeting Of The Georgia Association Of Mathematics Teacher Educators Introductory Texts

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Contents of 1st Annual GAMTE Proceedings Front Matter:

• Proceedings Committee
• Officers of GAMTE
• Purposes and Goals of GAMTE
• Table of Contents

Collaborating To Meet The Standards: Implications For Professional Development, Erik D. Jacobson, Laura M. Singletary

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Researchers from the University of Georgia interviewed 27 Mathematics 1 teachers about their experiences during the first year of the high school implementation of the Georgia Performance Standards (GPS). We report our findings about teachers’ experiences with Mathematics 1 professional development and describe features of professional development that teachers identified as most beneficial. Some teachers offered suggestions for professional development that differed from the professional development they had experienced. In addition, we found that many teachers used collaborative strategies to meet the demands of the new curriculum and the perceived inadequacies of resources and training. We discuss the various models …

Extending K-8 Mathematics Concepts In Alternate Bases, Dianna J. Spence

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

When learning to represent mathematics with manipulatives, many pre-service K-8 teachers rely on memorized rote procedures to perform the associated mathematical tasks; then they arrange the manipulatives to match their result, often with minimal understanding of underlying mathematical connections. In a Number and Operations course for K-8 pre-service teachers, a portion of the class was conducted in alternate bases: Base 6 and Base 8 Blocks were used to model operations with integers to facilitate deeper understanding of the number systems and arithmetic processes being represented. Fractions and decimals were later covered only in Base 10. On midterm and final exams, …

Basic Skills Testing In Math 2008, Susie M. Lanier, Sharon Taylor, Donna B. Saye

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Math 2008 is an Area F course for early childhood majors in the University System of Georgia. The course covers basic skills that pre-service teachers will most likely be teaching in their career. At Georgia Southern University, many students in the course do not possess or have forgotten these basic skills. In Fall 2009, a basic skills test was implemented for Math 2008. Students must earn a score of 90 or higher on the test in order to pass the course. The test not only serves to let students know their areas of weakness, but also informs the instructor’s teaching. …

Embracing The Vision: Our Work With Teachers Implementing Gps, Sarah Ledford, Wendy B. Sanchez

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Abstract: In 2005, three Kennesaw State University mathematics education faculty members began a series of workshops titled “Implementing the Georgia Performance Standards [GPS]: Embracing the Vision.” This workshop series has been underwritten by Georgia’s Teacher Quality Higher Education Program. The first series of workshops began with 6th grade teachers the first year the GPS was implemented and the project has been funded each subsequent year since its inception. Currently, we are working with Math III teachers as they implement the course for the first time. The initial focus for the project was on conceptual understanding versus procedural understanding, writing tasks …

The Effect Of Learning Styles Strategies On Benchmark Eighth Grade Middle School Mathematics Achievement, Jean Ferrara

Walden Dissertations and Doctoral Studies

Low standardized mathematics scores resulted in a suburban middle school not reaching adequate yearly progress (AYP) for the 2 previous years. There were many possible factors contributing to this problem, among them the design of instruction. The purpose of this study was to identify learning styles of students and implement differentiated instructional strategies that address the learners' needs. The study was based on the Silver and Hanson's theory of learning style instruction and Gardner's multiple intelligences as a model for differentiating instruction. This sequential mixed methods quasi-experimental causal comparative design study investigated the effect of classroom intervention based on learning …

Manipulatives In Mathematics Instruction, Jessica Strom

Mathematics Graduate Theses

This paper is a review of research pertaining to the use of manipulatives in middle and secondary school mathematics instruction. It covers the research on the rationale for using manipulatives, the psychology behind learning with manipulatives, the common mistakes when teaching with manipulatives, and the suggested process to follow when using manipulatives in the classroom. There is a large amount of research and information on manipulatives in the classroom. One of the most prevalent topics addresses that the concrete characteristics of manipulatives allow students to progress through a natural learning process on their way to an abstract understanding of mathematical …

Discussing Vocation As A Part Of A Senior Capstone Class, Maria Zack

ACMS Conference Proceedings 2009

Many of us in Christian higher education are seeking ways to help our students discern their own sense of call. At the 2007 ACMS meeting Greg Crow and I participated in a panel on vocation and published a related paper in the Journal of the ACMS. This current paper discusses what has been learned from incorporating some of our ideas into our department's senior capstone course. This has been very meaningful for both the students and the faculty involved.

Fire! Lessons Learned And Applied To Computer Systems, Kim P. Kihlstrom

ACMS Conference Proceedings 2009

A wildfire swept through Santa Barbara on November 13, 2008, burning 1940 acres and destroying 230 homes. Nine structures on the Westmont College campus were destroyed as well as fifteen faculty homes near campus. What insights can be drawn from this experience? We will examine some of the lessons that can be applied to the design of intrusion-tolerant computer systems.

Are Mathematical Entities Real?, Phillip E. Lestmann

ACMS Conference Proceedings 2009

This talk will introduce ontological questions related to mathematics. After surveying the views of Plato and Artistotle, other possible philosophical perspectives will be considered including realism, nominalism, conceptualism, and empiricism with their relative strengths and weaknesses. The discussion will conclude with a possible biblical foundation for mathematical ontology.

A Career Preparation Course For Students In Mathematics And Computer Science, Donna Pierce, Peter A. Tucker

ACMS Conference Proceedings 2009

As professors, we all want our students to succeed, and to be motivated to study. We all get questions from students that can be boiled down to, "What can I do with X degree?" Certainly, a quick answer is to point students to career websites, or to send them to the career services department on campus. However, we want to do better than that. We want students to learn how to investigate these future directions, and to have them think about their future more holistically--not just an effort to find a job. To that end, we have developed a course …

History Of Mathematics In The Service Of School Mathematics Education, Calvin Jongsma

ACMS Conference Proceedings 2009

This slide presentation outlines the author's use of history of mathematics in teaching a mathematics-content course to prospective middle school mathematics teachers. A pedagogical rationale for using history of mathematics is given, along with a case study illustrating its use for teaching the topic of ratio and proportion drawing upon the numerical and geometrical theories of such found in Euclid's Elements.

Galileo's Solution To Dante's Riddle, Andrew Simoson

ACMS Conference Proceedings 2009

In Dante’s Inferno, several riddles are posed regarding the relative sizes of ordinary men versus giants versus Lucifer—all of which Galileo solves in his first public lecture—which we review herein.

Sage: Math In Your Dorm Room, From Calculus To Research, Karl-Dieter Crisman

ACMS Conference Proceedings 2009

As computers have revolutionized math research in disciplines as disparate as number theory and bioinformatics, it is natural for us to introduce our students to technology in ways beyond mere homework-checking. However, most familiar programs are either not comprehensive enough to encompass all the math in our curriculum, or are very expensive and accessible only in a lab or with a student license. The open source software package Sage addresses all of these issues.

Sage is suitable for discovery and computation in introductory courses such as calculus or linear algebra, while also being ideal for use in upper-level courses or …

Can Critical Thinking Be Redeemed?, Jeremy Case

ACMS Conference Proceedings 2009

We often claim that mathematics develops critical thinking skills. Critical thinking has many different definitions, but problem solving, deduction, analyzing arguments, and identifying assumptions are all certainly a part of critical thinking. As the trend in higher education moves away from focusing exclusively on content towards assessment and learning outcomes, we can justify our endeavors since mathematics and critical thinking align themselves well.

However, when examining the ultimate purpose of critical thinking in higher education, we must take care. If there is no agreed upon content knowledge in our postmodern age, the focus of education falls elsewhere. How one thinks …

Exploring The Limits Of Computing Through Exhaustive Search, Jeffrey L. Lehman

ACMS Conference Proceedings 2009

Many computing problems can be solved by identifying all possible moves or combinations of events and then picking the best solution. Problems in this domain provide fertile ground for exploring problem representation, storage requirements, and computational complexity. The problems and solution approaches are easy to understand, yet quickly push the memory and storage limits of a personal computer. This paper describes insights from a preliminary investigating of two exhaustive search problems, the 15-puzzle and Rubik’s cube. The insights gained by looking at exhaustive search problems can be integrated into classroom discussions and projects.

Monoids For Math Majors, Brian D. Beasley

ACMS Conference Proceedings 2009

Inspired by an MAA PREP workshop on “The Art of Factorization in Multiplicative Structures”, this paper will treat the basics of congruence monoids and arithmetical congruence monoids with their potential for a Modern Algebra or capstone course.

Supplemental Vocabulary Acquisition In The Desymbol Logic Translator, Darren F. Provine, Nancy Lynn Tinkham

ACMS Conference Proceedings 2009

DeSymbol is a program that translates first-order predicate logic expressions into English. It is designed to help students practice when learning or reviewing symbolic logic: students begin by translating English sentences into symbolic logic notation, and then they can use DeSymbol to translate the logic back into English to check their work.

The newest version of DeSymbol adds the ability for the user to expand the system’s vocabulary, using a web interface. The user can enter new nouns, verbs, or adjectives, specifying each word’s part of speech, its singular and plural forms, and (for verbs) whether the verb takes an …

Professor Peacock's Symbolical Algebra: Glimpses Into The Life And Work Of A Mathematical Reformer, Richard Stout

ACMS Conference Proceedings 2009

In his 1859 obituary of George Peacock (Royal Society of London, 1859),the nineteenth century mathematician and Dean of Ely Cathedral, his friend and long-time colleague J. F. W. Herschel not only lists Peacock's accomplishments as an educator, a churchman, and a mathematician, but also describes a man who embodies warmth and wisdom, the kind of person you would enjoy knowing and having as a colleague. Writing about Peacock in the Memoirs of the Royal Astronomical Society, Augustus DeMorgan echoes these sentiments when he says that "Whenever a man of safe judgment was wanted, who united kindness and courtesy to a …

The Development Of Mathematical And Spiritual Maturity In The Undergraduate Mathematics Curriculum, Angela Hare

ACMS Conference Proceedings 2009

Colleges and universities that teach mathematics have a responsibility to develop in students an appreciation of the powerful tools they are studying in the mathematics curriculum. Beyond this fundamental responsibility, the Christian college or university has the richer task of equipping mathematics graduates to use their mathematical knowledge and skills to sharpen their spiritual insight, to serve others, and to promote justice and freedom in society. The growth in mathematical maturity that occurs during the undergraduate years is an asset that enables Christian students of mathematics to participate in the redemptive work of Jesus Christ through their discipline of study. …