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Proceedings Of The First Annual Meeting Of The Georgia Association Of Mathematics Teacher Educators Front Matter

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
• Abstracts of Papers

Preservice Teachers’ Mapping Structures Acting On Representational Quantities, Gunhan Caglayan

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

In this article, I write about my research on five preservice secondary teachers’ (PST) understanding and sense making of representational quantities associated with magnetic color cubes and tiles. Data came from individual interviews during which I asked PST problems guided by five main tasks: prime and composite numbers, summation of counting numbers, odd numbers, even numbers, and polynomial expressions in x and y. My work drew upon an analysis framework (Behr et. al, 1994) supported by a unit coordination construct (Steffe, 1988) associated with linear and areal quantities inherent in the nature of figures produced by these PST. Linear quantities …

The Mathematical Preparation Of Secondary School Teachers, Kelly W. Edenfield

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

In the summer of 2007, a group of doctoral students at the University of Georgia gathered to discuss the mathematical preparation of secondary teachers. The group used Mathematics for High School Teachers: An Advanced Perspective by Usiskin, Peressini, Marchisotto, and Stanley (2003) as the catalyst for the discussion. Participants agreed that future teachers need opportunities to examine high school and college mathematics differently from the way they had as students, with specific emphasis on connections, representations, and history. Features of this text that were highlighted in the discussions were the attention topics with commonly held misconceptions, the historical rationales and …

Using Technology To Design Teaching Modules In Mathematics And Science, Ollie I. Manley

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

Technology is changing the way in which mathematics and science are taught, and this radical transformation in teaching is causing teachers to take a closer look at how lessons are designed. In an effort to demonstrate how to design instructional modules using technology, this paper will include the following: 1)A review of the National Educational Technology Standards for teachers to establish a framework for the development of the teaching modules; 2)instructional designs and techniques with special emphasis on multiple intelligence and critical thinking skills; 3) strategies and techniques for infusing technology into a standard based curriculum; and 4) an analysis …

Assessing Understanding Of Multiplication Through Words, Pictures, And Numbers, Stephanie Z. Smith

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

The objective of this session is to engage mathematics teacher educators in a discussion of how to assess an understanding of the concept of multiplication as an operation and its relationships to other operations. The session will begin with a presentation of a previously published study assessing children’s understanding of multiplication as grouping and the relationship between multiplication and addition. The assessment asked a series of problems involving words, pictures, and numbers. The results of the study indicate that the types of problems asked were successful in providing evidence of children’s understanding of multiplication. The study also found that a …

Change And Relationships In Elementary Preservice Teachers’ Mathematics Pedagogical Beliefs, Teaching Efficacy Beliefs, And Content Knowledge, Susan L. Swars, Lynn C. Hart , Ed., Stephanie Z. Smith, Marvin E. Smith

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

This study investigated the mathematics beliefs and content knowledge of 103 elementary preservice teachers in a developmental teacher preparation program that included a two course mathematics methods sequence. Preservice teachers’ pedagogical beliefs became more cognitively-oriented during the teacher preparation program with these changes occurring during the two methods courses. Pedagogical beliefs remained stable during student teaching. The preservice teachers also significantly increased their personal efficacy for teaching mathematics throughout the program with these shifts occurring across both methods courses and into student teaching. Pedagogical beliefs and teaching efficacy beliefs were not related at the beginning of the program, but, in …

The Kennesaw State University Mathematics Methods Model, Angela L. Teachey

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

Kennesaw State University’s comprehensive, nine-credit-hour, methods course integrates general and mathematics-specific pedagogical training with a structured four-week field experience prior to student teaching. This course blends essential units on conceptual understanding of mathematics, lesson planning, assessment, classroom management, and diversity with mathematics-specific methods. All topics are aligned with National Council of Teachers of Mathematics standards and Georgia Performance Standards. Throughout the course, students complete a variety of assignments that require them to practice the skills highlighted in class readings and discussions, and they adapt and generalize those skills during their field experiences. Students have numerous opportunities in class and in …

Istart 2: Improvements For Efficiency And Effectiveness, Irwin B. Levinstein, Chutima Boonthum, Srinivasa P. Pillarisetti, Courtney Bell, Danielle S. Mcnamara

Computer Science Faculty Publications

iSTART (interactive strategy training for active reading and thinking) is a Web-based reading strategy trainer that develops students' ability to self-explain difficult text as a means to improving reading comprehension. Its curriculum consists of modules presented interactively by pedagogical agents: an introduction to the basics of using reading strategies in the context of self-explanation, a demonstration of self-explanation, and a practice module in which the trainee generates self-explanations with feedback on the quality of reading strategies contained in the self-explanations. We discuss the objectives that guided the development of the second version of iSTART toward the goals of increased efficiency …

[Introduction To] Nonparametric Statistics With Applications To Science And Engineering, Paul Kvam, Brani Vidakovic

Bookshelf

This book presents a practical approach to nonparametric statistical analysis and provides comprehensive coverage of both established and newly developed methods. With the use of MATLAB, the authors present information on theorems and rank tests in an applied fashion, with an emphasis on modern methods in regression and curve fitting, bootstrap confidence intervals, splines, wavelets, empirical likelihood, and goodness-of-fit testing.

Nonparametric Statistics with Applications to Science and Engineering begins with succinct coverage of basic results for order statistics, methods of categorical data analysis, nonparametric regression, and curve fitting methods. The authors then focus on nonparametric procedures that are becoming more …

Crippling America, Health Care Fraud Incentives, Colby Goetsch

Honors Program Theses

Clearly an imbalance is occurring in the system as health care fraud claims reach new bounds. There are many types of health care fraud, but the most general analysis involves the submission of claims that never occurred for reimbursement. This thesis will analyze the incentives acting upon different groups affected by the specific act of health care fraud of submitting fraudulent claims, and also possible solutions to change these incentives into the public's best interest. An analysis of the incentives given to the key players in this game will hopefully show where legislators can focus to improve the current state …

Positive Solutions Of A Nonlinear Higher Order Boundary-Value Problem, John R. Graef, Johnny Henderson, Bo Yang

Faculty Articles

The authors consider the higher order boundary-value problem u (n)(t) = q(t)f(u(t)), 0 ≤ t ≤ 1, u(i-1)(0) = u (n-2)(p) = u(n-1)(1) = 0, 1 ≤ i ≤ n -2, where n ≥ 4 is an integer, and p ∈ (1/2, 1) is a constant. Sufficient conditions for the existence and nonexistence of positive solutions of this problem are obtained. The main results are illustrated with an example.

S-Extremal Additive F4 Codes, Evangeline P. Bautista, Philippe Gaborit, Jon-Lark Kim, Judy L. Walker

Department of Mathematics: Faculty Publications

Binary self-dual codes and additive self-dual codes over F₄ have in common interesting properties, for example, Type I, Type II, shadows, etc. Recently Bachoc and Gaborit introduced the notion of s-extremality for binary self-dual codes, generalizing Elkies' study on the highest possible minimum weight of the shadows of binary self-dual codes. In this paper, we introduce a concept of s-extremality for additive self-dual codes over F₄, give a bound on the length of these codes with even distance d, classify them up to minimum distance d = 4, give possible lengths and (shadow) weight …

A Comparison Of Techniques To Forecast Consumer Satisfaction For Vehicle Ride, Elizabeth A. Cudney, David Drain, Kenneth M. Ragsdell, Kioumars Paryani

Engineering Management and Systems Engineering Faculty Research & Creative Works

This paper presents a comparison of methods for the identification of a reduced set of useful variables using a multidimensional system. the Mahalanobis-Taguchi System and a standard statistical technique are used reduce the dimensionality of vehicle ride based on consumer satisfaction ratings. the Mahalanobis-Taguchi System and cluster analysis are applied to vehicle ride. the research considers 67 vehicle data sets for the 6 vehicle ride parameters. This paper applies the Mahalanobis-Taguchi System to forecast consumer satisfaction and provides a comparison of results with those obtained from a standard statistical approach to the problem. Copyright © 2007 SAE International.

Effective Use Of Process Capability Indices For Supplier Management, Elizabeth A. Cudney, David Drain

Engineering Management and Systems Engineering Faculty Research & Creative Works

Process capability indices were originally invented to enable an organization to make economically sound decisions for process management. Process capability is a comparison of the voice of the process with the voice of the customer. Current practice is to use Cp and Cpk regardless of the validity of the underlying assumptions necessary for their use. Even if all necessary assumptions are satisfied, important problems can be missed if these indices are the sole process evaluation examined. Customer-supplier axioms are introduced to motivate more useful process evaluations and foster long-term harmonious relationships. This paper explores the alternative capability indices Cpm, Cpmk, …

Graded Sparse Graphs And Matroids, Audrey Lee, Ileana Streinu, Louis Theran

Computer Science: Faculty Publications

Sparse graphs and their associated matroids play an important role in rigidity theory, where they capture the combinatorics of some families of generic minimally rigid structures. We define a new family called graded sparse graphs, arising from generically pinned bar-and-joint frameworks, and prove that they also form matroids. We also address several algorithmic problems on graded sparse graphs: Decision, Spanning, Extraction, Components, Optimization, and Extension. We sketch variations on pebble game algorithms to solve them.

A New Lower Bound On Guard Placement For Wireless Localization, Mirela Damian, Robin Flatland, Joseph O'Rourke, Suneeta Ramswami

Computer Science: Faculty Publications

The problem of wireless localization asks to place and orient stations in the plane, each of which broadcasts a unique key within a fixed angular range, so that each point in the plane can determine whether it is inside or outside a given polygonal region. The primary goal is to minimize the number of stations. In this paper we establish a lower bound of ⌊2n/3⌋−1 stations for polygons in general position, for the case in which the placement of stations is restricted to polygon vertices, improving upon the existing ⌈n/2⌉ lower bound.

Neutrality And Many-Valued Logics, Florentin Smarandache, Andrew Schumann

Branch Mathematics and Statistics Faculty and Staff Publications

ThisbookwrittenbyA. Schumann &F. Smarandache isdevotedtoadvances of non-Archimedean multiple-validity idea and its applications to logical reasoning. Leibnitz was the first who proposed Archimedes’ axiom to be rejected. He postulated infinitesimals (infinitely small numbers) of the unit interval [0,1] which are larger than zero, but smaller than each positive real number. Robinson applied this idea into modern mathematics in [117] and developed so-called non-standard analysis. In the framework of non-standard analysis there were obtained many interesting results examined in [37], [38], [74], [117].

There exists also a different version of mathematical analysis in that Archimedes’ axiom is rejected, namely, p-adic analysis (e.g., …

Neutrosophy In Arabic Philosophy, Florentin Smarandache, Salah Osman

Branch Mathematics and Statistics Faculty and Staff Publications

Is there an absolute reality? Yes, “God” is the only absolute reality. The three main religions: Judaism, Christianity and Islam have all claimed that God is a supreme reality, and that all other creatures are finite beings. Since they relatively continue and also relatively change, so they can not be absolute. The world is full of paradoxes, there is no absolute persistence, and also there is no change at a stretch. There is no absolute truth and there is no continuous falsehood. What exist are many faces or aspects between the two terms. Those faces are reduced to a neutral …

Techno-Art Of Selariu Supermathematics Functions, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this album we include the so called Super-Mathematics functions (SMF), which constitute the base for, most often, generating, technical, neo-geometrical objects, therefore less artistic. These functions are the results of 38 years of research, which began at University of Stuttgart in 1969. Since then, 42 related works have been published, written by over 19 authors, as shown in the References. The name was given by the regretted mathematician Professor Emeritus Doctor Engineer Gheorghe Silas who, at the presentation of the very first work in this domain, during the First National Conference of Vibrations in Machine Constructions, Timişoara, Romania, 1978, …

Quantization In Astrophysics, Brownian Motion, And Supersymmetry, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

The present book discusses, among other things, various quantization phenomena found in Astrophysics and some related issues including Brownian Motion. With recent discoveries of exoplanets in our galaxy and beyond, this Astrophysics quantization issue has attracted numerous discussions in the past few years. Most chapters in this book come from published papers in various peer-reviewed journals, and they cover different methods to describe quantization, including Weyl geometry, Supersymmetry, generalized Schrödinger, and Cartan torsion method. In some chapters Navier-Stokes equations are also discussed, because it is likely that this theory will remain relevant in Astrophysics and Cosmology While much of the …

Elementary Fuzzy Matrix Theory And Fuzzy Models For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

This book aims to assist social scientists to analyze their problems using fuzzy models. The basic and essential fuzzy matrix theory is given. The book does not promise to give the complete properties of basic fuzzy theory or basic fuzzy matrices. Instead, the authors have only tried to give those essential basically needed to develop the fuzzy model. The authors do not present elaborate mathematical theories to work with fuzzy matrices; instead they have given only the needed properties by way of examples. The authors feel that the book should mainly help social scientists who are interested in finding out …

Special Fuzzy Matrices For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

This book is a continuation of the book, "Elementary fuzzy matrix and fuzzy models for socio-scientists" by the same authors. This book is a little advanced because we introduce a multi-expert fuzzy and neutrosophic models. It mainly tries to help social scientists to analyze any problem in which they need multi-expert systems with multi-models. To cater to this need, we have introduced new classes of fuzzy and neutrosophic special matrices. The first chapter is essentially spent on introducing the new notion of different types of special fuzzy and neutrosophic matrices, and the simple operations on them which are needed in …

A Unifying Field In Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability And Statistics - 6th Ed., Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

It was a surprise for me when in 1995 I received a manuscript from the mathematician, experimental writer and innovative painter Florentin Smarandache, especially because the treated subject was of philosophy - revealing paradoxes - and logics. He had generalized the fuzzy logic, and introduced two new concepts: a) “neutrosophy” – study of neutralities as an extension of dialectics; b) and its derivative “neutrosophic”, such as “neutrosophic logic”, “neutrosophic set”, “neutrosophic probability”, and “neutrosophic statistics” and thus opening new ways of research in four fields: philosophy, logics, set theory, and probability/statistics. It was known to me his setting up in …

Auxiliary Information And A Priori Values In Construction Of Improved Estimators, Florentin Smarandache, Rajesh Singh, Pankaj Chauhan, Nirmala Sawan

Branch Mathematics and Statistics Faculty and Staff Publications

This volume is a collection of six papers on the use of auxiliary information and a priori values in construction of improved estimators. The work included here will be of immense application for researchers and students who employ auxiliary information in any form. Below we discuss each paper: 1. Ratio estimators in simple random sampling using information on auxiliary attribute. Prior knowledge about population mean along with coefficient of variation of the population of an auxiliary variable is known to be very useful particularly when the ratio, product and regression estimators are used for estimation of population mean of a …

Collected Papers Vol. 1, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Towards The Computation Of The Convex Hull Of A Configuration From Its Corresponding Separating Matrix, Elie Feder, David Garber

Publications and Research

In this paper we cope with the following problem compute the size of the convex hull of a configuration C where the given data is the number of separating lines between any two points of the configuration (where the lines are generated by pairs of other points of the configuration)

We give an algorithm for the case that the convex hull is of size 3 and a partial algorithm and some directions for the case that the convex hull is of size bigger than 3.

A Functional Calculus In A Non Commutative Setting, Fabrizio Colombo, Graziano Gentili, Irene Sabadini, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we announce the development of a functional calculus for operators defined on quaternionic Banach spaces. The definition is based on a new notion of slice regularity, see [6], and the key tools are a new resolvent operator and a new eigenvalue problem. This approach allows us to deal both with bounded and unbounded operators.

Carathéodory Functions In The Banach Space Setting, Daniel Alpay, Olga Timoshenko, Dan Volok

Mathematics, Physics, and Computer Science Faculty Articles and Research

We prove representation theorems for Carathéodory functions in the setting of Banach spaces.

Portfolio Selection In Gaussian And Non-Gaussian Worlds, Jing Wang

Theses and Dissertations (Comprehensive)

In the case of minimizing risk with a given level of expected return, we discuss the portfolio selection problem with the asset returns are characterized by a Gaussian distribution and heavy tailed distribution.

More specifically, under the Gaussian assupmtion, we give the explicit solutions to the problems of minimizing risk variance, CaR and EaR respectively. When a compound Poisson process is assumed, we derive explicit solutions to the variance, CaR and EaR. Furthermore, we give the explicit soultion for the CaR when a Lévy distribution is considered.

For the more realistic process-normal inverse process, we are able to obtain the …

Partial Separability And Partial Additivity For Orderings Of Binary Alternatives, Md. Abul Bashar

Theses and Dissertations (Comprehensive)

In Multiple-Criteria Decision Analysis (MCDA), a good way to find the best alternative is to construct a value function that represents a Decision Maker’s (DM) preferences. For multidimensional alternatives, an additive value function is easiest to work with because it assesses the alternatives in a simple and transparent manner. A DM’s preferences over consequences on a subset of the set of criteria may or may not depend on consequences on the rest of the criteria. Preferences that are free from all such interdependence are said to be separable. The existence of an additive value function implies separability and, when consequences …