Digital Commons Network^™

The Assessment Of Mathematics And Science Teacher Quality, Patricia S. Moyer-Packenham, Johnna J. Bolyard, Anastasia Kitsantas, Hana Oh

Teacher Education and Leadership Faculty Publications

The purpose of this study was to examine the types of instruments being used to document mathematics and science teacher quality characteristics in 48 nationally funded mathematics and science education awards. Each of the 48 projects operationalized teacher quality and determined how to assess it. The main research questions examined the instruments awardees used to gather data on mathematics and science teacher quality, and the main characteristics of teachers examined by awardees. Results showed that awardees most frequently used surveys or questionnaires to assess characteristics of mathematics and science teacher quality. The most common teacher characteristics examined by awardees' included …

Virtual Manipulatives Used By K-8 Teachers For Mathematics Instruction: Considering Mathematical, Cognitive, And Pedagogical Fidelity, Patricia S. Moyer-Packenham, Gwenanne Salkind, Johnna J. Bolyard

Teacher Education and Leadership Faculty Publications

This study examined teachers’ uses of virtual manipulatives across grades K-8 after participating in a professional development institute in which manipulatives and technology were the major resources used throughout all of the activities. Researchers analyzed 95 lesson summaries in which classroom teachers described their uses of virtual manipulatives during school mathematics instruction. The findings indicated that the content in a majority of the lessons focused on two National Council of Teachers of Mathematics (2000a) standards: Number & Operations and Geometry. Virtual geoboards, pattern blocks, base-10 blocks, and tangrams were the applets used most often by teachers. The ways teachers used …

The Asteroid Puzzle And Games, Jeremiah Farrell, Karen Farrell

Scholarship and Professional Work - LAS

Each of our two-person games is a word version variation from the tic-tac-toe or noughts and crosses family. It is well known that classic tic-tac-toe is a draw when expertly played. It is also clear that not all of its plays are equal- a strong move for the first player is to initially take the powerul center square. ASTEROID and ASTEROID II, on the other hand, are both completely symmetric (in the sense that all letters are used equally) and each have rather suble forced wins for either the first or second player.

Mr. Bell, You Are Destroying Our Children!, David Rock

Perspectives In Learning

Is technology the wave of the future? Society says "YES" when it is convenient and educators respond with a multitude of answers. The use of technology in today's classroom has become a controversial curricular topic for those inside and outside the classroom. Why? I am sure that many of the same arguments used today against the use of technology in P-12 education are similar to those used during the past 100 years. Imagine the thousands of educators a hundred years ago that said, "The use of this new invention will destroy the writing ability of our children. There will be …

Unitarily Invariant Norms And Tensor Products Of Maximal Injective Von Neumann Subalgebras, Junsheng Fang

Doctoral Dissertations

This dissertation consists of four contributions to the study of von Neumann algebras. In the first part, we set up a representation theorem for unitarily invariant norms on finite factor von Neumann algebras. In the second part, we set up a representation theorem for unitarily invariant norms related to infinite factor von Neumann algebras. In the third part, we introduce a notion of completely singular von Neumann subalgebras and characterize the class of completely singular von Neumann subalgebras. In the fourth part, we study a longstanding open question on the tensor product of maximal injective von Neumann subalgebras.

The first …

Planar Algebra Of Families Of Subfactors, Paramita Das

Doctoral Dissertations

The standard invariant is an object that classifies a fairly general class of subfactors and was reformulated by Vaughan Jones as 'planar algebras'. We compute the planar algebra of two families of subfactors arising out of actions of finitely generated groups on a II 1 factor in an attempt to see whether this class can be enlarged. This is a joint work with Dietmar Bisch and Shamindra Ghosh.

Free Entropy Dimensions And Approximate Liftings, Weihua Li

Doctoral Dissertations

In the first chapter of the dissertation, we give a very elementary proof of a more detailed version of one of D. Voiculescu's results, which was a key ingredient in Voiculescu's proof that his free entropy is additive when the variables are free.

In the second chapter of the dissertation, based on the notion of upper free orbit-dimension introduced by D. Hadwin and J. Shen, we introduce a new invariant on finite von Neumann algebras that do not necessarily act on separable Hilbert space. We show that this invariant is independent of the generating set, and we obtain a number …

The Art Of Teaching Mathematics, Garikai Campbell, Jon T. Jacobsen, Aimee S A Johnson, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

On June 10–12, 2007, Harvey Mudd College hosted A Conference on the Art of Teaching Mathematics. The conference brought together approximately thirty mathematicians from the Claremont Colleges, Denison, DePauw, Furman, Middlebury, Penn State, Swarthmore, and Vassar to explore the topic of teaching as an art. Assuming there is an element of artistic creativity in teaching mathematics, in what ways does it surface and what should we be doing to develop this creativity?

Algebraic And Combinatorial Properties Of Certain Toric Ideals In Theory And Applications, Sonja Petrovic

University of Kentucky Doctoral Dissertations

This work focuses on commutative algebra, its combinatorial and computational aspects, and its interactions with statistics. The main objects of interest are projective varieties in Pⁿ, algebraic properties of their coordinate rings, and the combinatorial invariants, such as Hilbert series and Gröbner fans, of their defining ideals. Specifically, the ideals in this work are all toric ideals, and they come in three flavors: they are defining ideals of a family of classical varieties called rational normal scrolls, cut ideals that can be associated to a graph, and phylogenetic ideals arising in a new and increasingly popular area of …

Proof Processes Of Novice Mathematics Proof Writers, Hillary Dee Vanspronsen

Graduate Student Theses, Dissertations, & Professional Papers

Previous studies have shown that a large portion of undergraduate mathematics students have difficulties constructing, understanding, and validating proofs (Martin and Harel, 1989; Coe and Ruthven, 1994; Moore, 1994; Baker, 1996; Mingus and Grassl, 1999; Knuth, 2002; Weber, 2001, 2003). However, proofs are the foundation of mathematics; it is therefore essential that every university mathematics student be able to step through the proof writing process. Research has sought to describe the strategies involved in the process of mathematical problem solving (Baker, 1996; Bell, 1979; Carlson and Bloom, 2005; McGivney and DeFranco, 1995; Pape and Wang, 2003; Polya, 1973; Pugalee, 2001; …

New Classes Of Codes For Cryptologists And Computer Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Historically a code refers to a cryptosystem that deals with linguistic units: words, phrases etc. We do not discuss such codes in this book. Here codes are message carriers or information storages or information transmitters which in time of need should not be decoded or read by an enemy or an intruder. When we use very abstract mathematics in using a specific code, it is difficult for non-mathematicians to make use of it. At the same time, one cannot compromise with the capacity of the codes. So the authors in this book have introduced several classes of codes which are …

Using Communication Techniques In The Low-Performing Mathematics Classroom: A Study Of Fractions,Decimals,Performance And Attitu, Pamela Guyton

Electronic Theses and Dissertations

Within a low-performing seventh grade mathematics classroom, communication techniques including discourse, collaborative groups, listening, reading, and writing were implemented during a six week period. This study shows how the use of these techniques led to the twenty four students' conceptual understanding of fraction and decimal concepts. This research study provides insight to the deep-seeded beliefs of low-performing students. It provides a record of how the teacher used communication techniques in the classroom and had a strong positive impact on the attitudes and performance of these struggling students.

Pemberton Hydroelectric Power Station: A Teacher Resource, Les Pereira, Phil Gregory, Helen Kuehs, Amanda Draper, Jenny Staker, Rosalie Tomlinson, Christa Pereira

Research outputs pre 2011

This publication provides a resource for teachers of students in years seven to ten. Teachers are able to address a range of outcomes pertinent to the Western Australian curriculum within the context of the Pemberton Hydroelectric Power Station. The resource contains plans for four units of work, one in each of the following Learning Areas: Science, Mathematics, English, and Society and Environment.

Developing Mathematical Practices In A Social Context:An Instructional Sequence To Support Prospective Elementary Teachers', Debra Wheeldon

Electronic Theses and Dissertations

This teaching experiment used design-based research (DBR) to document the norms and practices that were established with respect to fractions in a mathematics content course for prospective elementary teachers. The teaching experiment resulted in an instructional theory for teaching fractions to prospective elementary teachers. The focus was on the social perspective, using an emergent framework which coordinates social and individual perspectives of development. Social norms, sociomathematical norms, and classroom mathematical practices were considered. A hypothetical learning trajectory (HLT) including learning goals, instructional tasks, tools and imagery, and possible discourse, was conjectured and implemented in the mathematics class. Video tapes of …

Co-Teaching: Using Video To Identify Current Practices And Promote Teacher Discussion In Middle School Mathematics Classrooms, Kimberly Davis

Electronic Theses and Dissertations

This study explored the co-teaching practices occurring within four middle school mathematics classrooms and the influence of video discussions on each co-teaching team. The study took place within three middle schools in central Florida. The study provides a clear picture of the current status of middle school co-taught mathematics classrooms. The research results were inconclusive in that the key components of co-teaching were not observed (co-planning, co-instructing and co-assessing) and the findings were similar to past co-teaching research indicating mixed results. Overall, concerns that emerged from the study were a lack of heterogeneous classrooms, clarity for the role of the …

Comparing Middle School General And Special Educators' Use Of Research-Based Instruction In Mathematics For Students With Learni, Shelby Robertson

Electronic Theses and Dissertations

The purpose of this study was to investigate the differences between general and special educators regarding the implementation of research-based strategies that target the needs of students with LD in mathematics, as well as general and special educators' perceptions of their preparedness to use instructional strategies in mathematics. A sample of general and special educators who taught mathematics to students with learning disabilities (LD) at the middle school level responded to an online survey. The survey examined teacher self-reported classroom use of instructional practices specifically aligned with NCTM standards, direct instruction, graduated instruction, grouping practices, and self-monitoring. Additionally, educators responded …

Effects Of Discussion And Writing On Student Understanding Of Mathematics Concepts, Joseph Roicki

Electronic Theses and Dissertations

For this action research project, I wanted to examine my practice of teaching mathematics. Specifically, I encouraged students to improve their communication skills during my math class through daily discussion and writing tasks. After establishing a class set of sociomathematical norms, the students solved problems provided by the Every Day Counts: Calendar Math program and used verbal and written formats to describe their problem solving methods and reasons. My study showed the effects of using discussion and writing to help students develop their conceptual understanding of mathematical ideas. Focus was placed on the quality of daily discussions and written tasks …

Is Mathematics Created By Humans Or Is It Discovered By Humans? A Catholic Intellectual Perspective, Jason J. Molitierno

Presidential Seminar on the Catholic Intellectual Tradition

In this essay, Dr. Molitierno intends to show that not only is it appropriate to discuss the Catholic Intellectual Tradition in light of mathematics, the CIT can actually be exemplified in mathematics!

Numerical And Adaptive Grid Methods For Ideal Magnetohydrodynamics, Burlen Loring

Master's Theses and Capstones

In this thesis numerical finite difference methods for ideal magnetohydrodynamics (MHD) are investigated. A review of the relevant physics, essential for interpreting the results of numerical solutions and constructing validation cases, is presented. This review includes a discusion of the propagation of small amplitude waves in the MHD system as well as a thorough discussion of MHD shocks, contacts and rarefactions and how they can be pieced together to obtain a solutions to the MHD Riemann problem. Numerical issues relevant to the MHD system such as: the loss of nonlinear numerical stability in the presence of discontinuous solutions, the introduction …

Mise Au Point Et Validation D’Un Outil De Calcul Du Temps De Service Des Cartouches Filtrantes Pour Vapeurs Organiques, Daniel Cossement, Iheb Bellasfar, Patrick-Daniel Dubois, Tapan K. Bose, Jaime Lara, Daniel Drolet, François Lemay, Zélie Fortin

Rapports de recherche scientifique

Le but de cette activité étalée sur une période de 12 mois, était de fournir un logiciel disponible sur le site Web de l’IRSST permettant de calculer le temps de service de six cartouches filtrantes pour les vapeurs organiques pour des solvants réglementés au Québec. La mise au point de ce logiciel est le fruit d’une coopération entre l’IRSST, avec son expertise dans la caractérisation de la durée de vie des cartouches chimiques, et l’Institut de recherche sur l’hydrogène (IRH) via son expertise sur les charbons activés.

Le modèle de base pour estimer la durée de vie des cartouches est …

Controlled Transitions Between Orbits In Nonlinear Systems, Erica G. Johnson

Master's Theses and Capstones

In recent years, several methods of controlling chaotic systems have been developed and implemented. The main idea in each method is to stabilize on an orbit around a chaotic attractor, which generally has a dense set of unstable periodic orbits. One such control scheme repeatedly applies a sequence of controls to a double scroll oscillator. Most control sequences result in the stabilization of an approximate unstable periodic orbit regardless of initial condition. These stabilized periodic orbits are called chaotic unstable periodic orbit-lets (cupolets). Due to the nature of cupolets, it is possible to switch between cupolets, and thus periodic orbits, …

The Effectiveness Of One Week Of Remediation For Geometry, Martha L. Hopkins

OTS Master's Level Projects & Papers

The purpose of this study was to explore how remediation affects SOL retake scores in geometry. The following hypothesis was developed to guide this study: Students who passed high school geometry, but failed the SOL test, will pass the SOL retest after completing the one-week Geometry SOL Remediation Recovery Program.

Inverse Spectral Results On Even Dimensional Tori, Carolyn Gordon, Pierre Guerini, Thomas Kappeler, David Webb

Dartmouth Scholarship

Given a Hermitian line bundle L over a flat torus M, a connection ∇ on L, and a function Q on M, one associates a Schrödinger operator acting on sections of L; its spectrum is denoted Spec(Q;L,∇). Motivated by work of V. Guillemin in dimension two, we consider line bundles over tori of arbitrary even dimension with “translation invariant” connections ∇, and we address the extent to which the spectrum Spec(Q;L,∇) determines the potential Q. With a genericity condition, we show that if the connection is invariant under the isometry of M defined by the map x→-x, then the spectrum …

Understanding Children's Mathematical Learning: The Relationship To Instruction In Preschool Classrooms, Renee B. Whelan

Seton Hall University Dissertations and Theses (ETDs)

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An Investigation Of The Effects Of Using Handhelds To Increasecomputational Speed By Enhancing Working Memory Forsecondary Stude, Marcey Kinney

Electronic Theses and Dissertations

Using a single subject research design, the effects of computer based brain training were examined to determine if computational fluency increased after completing the brain training activities. The study took place in a large public high school. Participants were students with learning disabilities who were also below level in mathematics. During the baseline phase, all participants completed a timed math probe daily for 1 week. Because the timed math probes were timed, the researcher was looking for an average gain for each student. During week two students completed the brain age activities daily, prior to completing the math probe. Average …

Effects On Student Performance Of Using Hands-On Activities To Teach Seventh Grade Students' Measurement Concepts, Darlene Hoke

Electronic Theses and Dissertations

Student performance on measurement concepts in mathematics was the basis for this action research study. This study summarizes research conducted in a seventh grade classroom at an urban middle school during fall of 2005. The study investigated the practice of using hands-on activities in addition to the standard mathematics curriculum to improve student performance in measurement tasks. Students were asked to respond to questions posed by both teacher and other students in the classroom. Data were collected using measurement survey, focus group discussions, math journals, and teacher observations. Results of this study showed that student performance on measurement tasks increased …

The Relationship Among Working Memory, Mathematics Anxiety, And Mathematics Achievement In Developmental Mathematics Courses In Community College, Janet Marie Spybrook

Doctoral Dissertations

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Multimedia Mathematics Intervention For Math-Delayed Middle School Students, Lisa L. Stokes

LSU Doctoral Dissertations

The purpose of this study is to determine if the Sharpening Math Skills Lab technology-mediated mathematics instructional practices for math-delayed middle school students have positive effects on their mathematics achievement and spatial visualization ability and to gauge student engagement in learning, implementation of the principles of instructional design, and attitudes toward mathematics instruction. The results of a recent meta-analysis report a range of significantly positive to significantly negative effect sizes which establish a need for further evaluation of academic achievement utilizing technology-mediated mathematics programs at the middle school level (Slavin, Lake, & Groff, 2007). The literature (Moreno & Mayer, 2000) …

Computerized Adaptive Testing In Mathematics For Primary Schools In Thailand, Chaowprapha Chuesathuchon

Theses: Doctorates and Masters

A new system-wide educational change has been introduced in Thailand requiring, amongst other things, that technologies for education be utilized in all levels of education. This study focuses on Mathematics Computerized Adaptive Testing (CAT) designed to provide Thai primary school teachers with an innovative method of assessment, one of the effective tools of new technology to be used in Thai primary schools. This study aims to: (1) construct multiple-choice test items for a Mathematics course on the topic of Equations for Year 6 (Prathom Suksa 6) students in Thailand; (2) calibrate the test items using a Rasch Measurement Model, investigate …

Solutions For 2-Dimensional Stabilized Kuramoto -Sivashinsky System, Maomao Cai

Graduate Theses, Dissertations, and Problem Reports (ETD)

We study a stabilized Kuramoto-Sivanshinsky system in two-dimensional space. A model consists of a mixed Kuramoto-Sivanshinsky-Korteweg-de Vires equation, linearly coupled to an extra linear dissipative equation. The model is proposed to describe the surface waves on multi-layered liquid films. In this work, we investigate the stability of the solution to this system by establishing a priori energy estimate for the linearized problem of this non-linear system. We use linear iteration to prove the local existence of the solution to this system. Based on a weak global priori energy estimate, we further prove the global existence and uniqueness of classical solution …