Mathematics Commons^™

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.

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.

Closure Under Transfinite Extensions, Edgar Enochs, Alina Iacob, Overtoun Jenda

Department of Mathematical Sciences Faculty Publications

The closure under extensions of a class of objects in an abelian category is often an important property of that class. Recently the closure of such classes under transfinite extensions (both direct and inverse) has begun to play an important role in several areas of mathematics, for example, in Quillen's theory of model categories and in the theory of cotorsion pairs. In this paper we prove that several important classes are closed under transfinite extensions.

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 …

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 …

Playing Games To Build Understanding, Michele Carnahan, Bridgette Stevens

Faculty Publications

I am fortunate. I teach from Investigations in Number, Data, and Space [TERC] (1996), a standards-based elementary mathematics curriculum. My evolution from teaching in a traditional teacher-centered approach to one that supports a student-centered community of learners has been a slow and gradual process during the past six years of teaching. Fortunately, through experience, professional development, and graduate level courses, I have come to appreciate the conceptual understanding students acquire from learning mathematics via a student-centered approach and how playing games is an effective instructional strategy for learning mathematics. As intended by the authors of Investigations and envisioned by the …

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 …

A Note On Relations For Reliability Measures In Zero-Adjusted Models, Broderick O. Oluyede, Mavis Pararai

Department of Mathematical Sciences Faculty Publications

In this note we examine and study relations in zero-adjusted models. Relations for reliability measures in the adjusted and unadjusted models are established and appropriate comparisons including the relative error are presented. The relative error is shown to be a decreasing function of the counts. Some inequalities and comparisons for weighted zero-adjusted models are established.

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 …

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

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 …

The Wright Message, 2007, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- Dear Department Alumni and Friends
-- 2007 - 2008 Tenure or Tenure-Track Faculty
-- New Faces in the Mathematics Department
-- Faculty Notes
-- Alumni Survey Conducted
-- Actuarial Program Thrives
-- Board of Regents Collaborative Mathematics and Science Initiative
-- TEAM News
-- DoDEA/UNI Project
-- Online Course Development
-- Math Day at UNI
-- First Millar Scholarship Awarded
-- In Memory of Paul Trafton
-- Major Gifts to the Department