Digital Commons Network^™

Study On Algebras With Retractions And Planes Over A Dvr., Prosenjit Das Dr.

Doctoral Theses

Aim:The main aim of this thesis is to study the following problems:1. For a Noetherian ring R, to find a set of minimal sufficient fibre conditions for an R-algebra with a retraction to R to be an A1-fibration over R.2. To investigate sufficient conditions for a factorial A1-form, with a retraction to the base ring, to be A1.3. To investigate whether planes of the form b(X, Y)Zn – a(X, Y) are co- ordinate planes in the polynomial ring in three variables X, Y and Z over a discrete valuation ring.The 1st problem will be discussed in Chapter 3 entitled Codimension- …

Managing Cognitive Load In The Mathematics Classroom, Mohan Chinnappan, Paul Chandler

Paul Chandler

The results of research about cognitive load that is associated with mental processes and the management of such load so that students can be better supported in the construction of connected mathematical information is discussed. Ways in which worked examples can be effective in promoting useful and powerful mathematics schemes are highlighted.

A Sequel To “A Space Topologized By Functions From Omega To Omega”, Tetsuya Ishiu, Akira Iwasa

Faculty Publications

We consider a topological space ⟨𝑋, 𝜏 (ℱ)⟩, where 𝑋 = {𝑝 ∗} ∪ [𝜔 Å~ 𝜔] and ℱ ⊆ 𝜔𝜔. Each point in 𝜔 Å~ 𝜔 is isolated and a neighborhood of 𝑝∗ has the form {𝑝∗}∪{⟨𝑖, 𝑗⟩ : 𝑖 ≥ 𝑛, 𝑗 ≥ 𝑓(𝑖)} for some 𝑛 ∈ 𝜔 and 𝑓 ∈ ℱ. We show that there are subsets ℱ and 𝒢 of 𝜔𝜔 such that ℱ is not bounded, 𝒢 is bounded, yet ⟨𝑋, 𝜏 (ℱ)⟩ and ⟨𝑋, 𝜏 (𝒢)⟩ are homeomorphic. This answers a question of the second author posed in A space topologized by functions …

Information-Preserving Structures: A General Framework For Quantum Zero-Error Information, Robin Blume-Kohout, Hui Khoon Ng, David Poulin, Lorenza Viola

Dartmouth Scholarship

Quantum systems carry information. Quantum theory supports at least two distinct kinds of information (classical and quantum), and a variety of different ways to encode and preserve information in physical systems. A system’s ability to carry information is constrained and defined by the noise in its dynamics. This paper introduces an operational framework, using information-preserving structures, to classify all the kinds of information that can be perfectly (i.e., with zero error) preserved by quantum dynamics. We prove that every perfectly preserved code has the same structure as a matrix algebra, and that preserved information can always be corrected. We …

Gsu Students Teach Math To Educators, Office Of Public Affairs

Press Releases

Governors State University graduate and undergraduate students had the opportunity to teach educators recently when they presented at the 61st Annual Meeting of the Illinois Council of Teacher of Mathematics in Springfield, Illinois.

The students, all studying to be math teachers, presented math activities they designed based on the massive sculptures in the Nathan Manilow Sculpture Park. The students found that the 26 sculptures, which are located on the grounds of the university, can be used to illustrate various mathematical formulas and principles.

The Impact Of Secondary Mathematics Methods Courses On Preservice Secondary Teachers’ Beliefs About The Learning And Teaching Of Mathematics, Ronald Gene Smith Ii

Doctoral Dissertations

The Comprehensive Framework for Teacher Knowledge provides a model that describes an approach to the secondary mathematics methods course, as described by Robert Ronau and P. Mark Taylor. The model includes the orientation of preservice teachers toward mathematics and the teaching of mathematics, which includes the beliefs of the preservice teachers. The first questions deal with identifying the methods used in the methods course to address beliefs. The second set of questions deal with the effects of the methods course on the beliefs that preservice teachers hold on the learning and teaching of mathematics.

The study included 16 different universities …

Developing Mathematical Content Knowledge For Teaching Elementary School Mathematics, Eva Thanheiser, Christine A. Browning, Meg Moss, Tad Watanabe, Gina Garza-Kling

Faculty and Research Publications

In this paper the authors present three design principles they use to develop preservice teachers' mathematical content knowledge for teaching in their mathematics content and/or methods courses: (1) building on currently held conceptions, (2) modeling teaching for understanding, (3) focusing on connections between content knowledge and other types of knowledge. The authors share results of individual research projects and teaching approaches focusing on helping preservice elementary teachers develop such knowledge. Specific examples from different content areas (whole number, fractions, angle, and area) are discussed.

Implementing Reading And Writing In Secondary Mathematics, Mari E. Eisenhart

Regis University Student Publications (comprehensive collection)

Literacy in secondary mathematics continues to be difficult for many. Mathematics teachers and researchers continue to develop support documents for secondary math teachers. It is important to utilize the literacy strategies already established by other content areas. It is feasible to adjust these strategies to suit the needs of mathematics students. Literacy across the content areas is a relatively new idea in education, but literacy in mathematics is even more foreign. It is necessary to use the available literacy strategies to develop materials applicable in the secondary mathematics classroom.

The Impact Of Content Courses On Pre-Service Elementary Teachers’ Mathematical Content Knowledge, Michael Matthews, Janice Rech, Neal Grandgenett

Teacher Education Faculty Publications

In response to research documenting the mathematical deficiencies of pre-service elementary teachers, many teacher preparation programs are requiring mathematical content courses specifically focusing on the mathematics taught at the elementary level. This study considers what impact two such courses (one course focusing on Arithmetic, and the other course focusing on Geometry and Measurement) had on the mathematical content knowledge and attitude towards mathematics by comparing a group of pre-service elementary teachers who took these courses to a group of pre-service elementary teachers who took only a more general mathematics course (such as College Algebra). Results indicated that those teachers who …

The Impact Of Smart Board Technology On Growth In Mathematics Achievement Of Gifted Learners, Patricia Ann Riska

Doctoral Dissertations and Projects

This study examined whether SMART Board technology increased growth in mathematics performance of fourth grade gifted students. Gifted students in North Carolina were studied to determine if the use of SMART Board technology during mathematics instruction impacted their growth on standardized state tests. The sample consisted of 175 students from six elementary schools with similar populations. Three of the schools used SMART Boards during mathematics instruction, and three schools did not use SMART Board technology. All students were taught the mathematics curriculum according to the North Carolina Standard Course of Study. The instrument for evaluating growth was the state End-of-Grade …

Teacher Quality, Content Knowledge, And Self-Efficacy In One Mathematics Teach For America Cohort, Brian R. Evans

NERA Conference Proceedings 2010

The purpose of this study was to understand the relationships between mathematical content knowledge and perceptions of teaching self-efficacy in one cohort of Teach for America teachers. It was found that teachers had high levels of self-efficacy. It was also found that mathematics related majors had higher mathematical content knowledge than did business majors, but similar levels of self-efficacy. Liberal arts majors had similar content knowledge and levels of self-efficacy as did mathematics related majors.

Middle And High School Mathematics Teacher Differences In Mathematics Alternative Certification, Brian R. Evans

NERA Conference Proceedings 2010

his study examined the differences in content knowledge, attitudes toward mathematics, and concepts of teacher self-efficacy among several different types of teachers in the New York City Teaching Fellows program, and informs teacher education in mathematics alternative certification. Findings revealed that high school teachers had significantly higher content knowledge than middle school teachers. Mathematics Teaching Fellows had significantly higher content knowledge than Mathematics Immersion Teaching Fellows. Mathematics and science majors had significantly higher content knowledge than other majors. Teachers had the same high positive attitudes toward mathematics and same high concepts of self-efficacy regardless of content ability.

The Effects Of Positive School Engagement On Math And Reading Achievement In Midwestern Suburban Middle School Students, Heather C. Phipps

Student Work

Ensuring high academic achievement in schools with increasingly diverse students is a challenge. Assessing student engagement can be a powerful tool in predicting potential success and identifying students who may need additional support. Positive youth development theory supports focusing on a young person’s strengths, and an asset-based approach to education can raise student achievement. During the 2007-2008 school year, seventh grade students were assessed for school engagement using the Developmental Assets Profile. Students were identified as either not engaged or engaged in school. For two years, achievement in reading and math as well as grade point average was collected and …

Project: Application Of Algebra Or Analysis, Eduardo C. Balreira

Information Literacy Resources for Curriculum Development

No abstract provided.

Cooperative Learning And The Gifted Student In Elementary Mathematics, Christine C. Hecox

Doctoral Dissertations and Projects

The research was a quantitative research project dealing with Florida Comprehensive Assessment Test (FCAT) Mathematics scores of fourth grade students, including gifted and high-achieving students, in 2008-2009 under the exposure of daily cooperative learning in mathematics. The problem statement was as follows: In Polk County, Florida, how does cooperative learning affect the FCAT Mathematics scores among fourth grade students, including gifted and high-achieving students? The purpose of the quasi-experimental study was to explore the relationship of cooperative learning versus traditional learning on their student achievement. The null hypothesis was that cooperative learning would have no effect on fourth grade gifted …

Mathematics Self-Efficacy Of Community College Students In Developmental Mathematics Courses, David Walker Clutts

Doctoral Dissertations and Projects

Mathematics self-efficacy was defined as an individual's beliefs about how he or she would perform a specific math task or in a specific mathematics or related course. Mathematics self-efficacy was differentiated from self-esteem. Previous literature found self-efficacy in general and mathematics self-efficacy in particular to be significantly related to enrollment, retention, and completion. This study used the Mathematics Self-Efficacy Survey to investigate whether age, gender, developmental mathematics course, or developmental mathematics grade were significantly predictive of mathematics self-efficacy among developmental mathematics students course at a Kentucky community college. Multiple linear regression found that none of these variables were statistically significant …

Teaching Calculus With Wolfram Alpha, Andrew Lang

College of Science and Engineering Faculty Research and Scholarship

This article describes the benefits and drawbacks of using Wolfram|Alpha as the platform for teaching calculus concepts in the lab setting. It is a result of our experiences designing and creating an entirely new set of labs using Wolfram|Alpha. We present the reasoning behind our transition from using a standard computer algebra system (CAS) to Wolfram|Alpha in our differential and integral calculus labs, together with the positive results from our experience. We also discuss the current limitations of Wolfram|Alpha, including a discussion on why we still use a CAS for our multivariate calculus labs.

Relationship Of Self-Efficacy Beliefs Of Urban Public School Students To Performance On A High-Stakes Mathematics Test, Kolajo Akinbiyi Afolabi

Open Access Dissertations

The purpose of this study was to examine the relationship of self-efficacy for Enlisting Social Resources, Self-Regulatory Efficacy, self-efficacy for Self-Regulated Learning, and self-efficacy for Academic Achievement (Bandura's Children's Self-Efficacy Scale, 2006) of urban public school students to performance on the high stakes Massachusetts Comprehensive Assessment System (MCAS) math test. A survey questionnaire was administered to eighty three participants and the data, analyzed using linear regression, conformed to the assumptions of Independence, Linearity, Normality, and Homoscedasticity. Self-Regulatory Efficacy, Academic Achievement, and Socio-economic Status were statistically significant bivariate predictors of performance on MCAS math test. Self-Regulatory Efficacy was the only consistent …

Schrödinger Dispersive Dstimates For A Dcaling-Critical Class Of Potentials, Marius Beceanu, Michael Goldberg

Mathematics and Statistics Faculty Scholarship

Consider the focussing cubic nonlinear Schr\"odinger equation in R 3 :

iψ t +Δψ=−|ψ| 2 ψ.

It admits special solutions of the form e itα ϕ , whereϕ is a Schwartz function and a positive (ϕ>0 ) solution of

−Δϕ+αϕ=ϕ 3 .

The space of all such solutions, together with those obtained from them by rescaling and applying phase and Galilean coordinate changes, called standing waves, is the eight-dimensional manifold that consists of functions of the form e i(v⋅+Γ) ϕ(⋅−y,α) . We prove that any solution starting sufficiently close to a standing wave in the Σ=W 1,2 (R 3 …

Review Of: Pearls Of Discrete Mathematics By Martin Erickson, Robert A. Beezer

All Faculty Scholarship

This article reviews the book "Pearls of Discrete Mathematics," by Martin Erickson.

An Explicit Super‐Time‐Stepping Scheme For Non‐Symmetric Parabolic Problems, Stephen O'Sullivan, Katharine Gurski

Conference papers

Explicit numerical methods for the solution of a system of differential equations may suffer from a time step size that approaches zero in order to satisfy stability conditions. When the differential equations are dominated by a skew-symmetric component, the problem is that the real eigenvalues are dominated by imaginary eigenvalues. We compare results for stable time step limits for the super-time-stepping method of Alexiades, Amiez, and Gremaud (super-time-stepping methods belong to the Runge-Kutta-Chebyshev class) and a new method modeled on a predictor-corrector scheme with multiplicative operator splitting. This new explicit method increases stability of the original super-time-stepping whenever the skew-symmetric …

Is Competition Making A Comeback? Discovering Methods To Keep Female Adolescents Engaged In Stem: A Phenomenological Approach, Kathryn B. Notter

College of Education and Human Sciences: Dissertations, Theses, and Student Research

The decreasing number of women who are graduating in the Science, Technology, Engineering and Mathematics (STEM) fields continues to be a major concern. Despite national support in the form of grants provided by National Science Foundation, National Center for Information and Technology and legislation passed such as the Deficit Reduction Act of 2005 that encourages women to enter the STEM fields, the number of women actually graduating in these fields is surprisingly low. This research study focuses on a robotics competition and its ability to engage female adolescents in STEM curricula. Data have been collected to help explain why young …

Virtual Manipulatives In The Classroom And Resulting Articles And Lesson Plans, Cheryl Juliana

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Upon coming across mathematical manipulatives generated and produced by Utah State University, as a math teacher, I conducted a classroom teaching experiment in three pre-algebra classes with students of various achievement levels. After teaching the entire year using no manipulatives in the classroom, I tested my students with a general, end-of-year, core criterion, or cumulative test. Their scores were noted. The students in the study group were then given opportunities to try several manipulatives offered on the "National Library of Virtual Manipulatives," both as a class, and alone, and then retested. The following paper gives the parameters of the study, …

Perpendicular Ion Heating By Low-Frequency Alfvén-Wave Turbulence In The Solar Wind, Benjamin D. G. Chandran, Bo Li, Barrett N. Rogers, Eliot Quataert, Kai Germaschewski

Dartmouth Scholarship

We consider ion heating by turbulent Alfvén waves (AWs) and kinetic Alfvén waves (KAWs) with wavelengths (measured perpendicular to the magnetic field) that are comparable to the ion gyroradius and frequencies ω smaller than the ion cyclotron frequency Ω. We focus on plasmas in which β < 1, where β is the ratio of plasma pressure to magnetic pressure. As in previous studies, we find that when the turbulence amplitude exceeds a certain threshold, an ion's orbit becomes chaotic. The ion then interacts stochastically with the time-varying electrostatic potential, and the ion's energy undergoes a random walk. Using phenomenological arguments, we derive an analytic expression for the rates at which different ion species are heated, which we test by simulating test particles interacting with a spectrum of randomly phased AWs and KAWs. We find that the stochastic heating rate depends sensitively on the quantity ε = δv _ρ/v _⊥, where v _⊥ (v _∥) is the component of the ion velocity perpendicular (parallel) to the background magnetic field B ₀, and δv _ρ (δB _ρ) is the rms amplitude of the velocity (magnetic-field) fluctuations at the gyroradius scale. In the case …

Affective Socialization Processes In Mathematics Doctoral Study: Gaining Insight From Successful Students, Lauren L Wagener

Doctoral Dissertations

Mathematics has the highest attrition rate among all liberal arts disciplines (and among all disciplines, except for health professions) and the second highest attrition rate of all doctoral programs in the United State. In order to prevent the loss of so many students, mathematics departments must consider the root causes for attrition and determine what individual skills and knowledge and departmental systems and support will help more mathematics doctoral students to succeed. The purpose of this qualitative interview study was to explore the interactions mathematics doctoral candidates at one institution have had during graduate school and the value that the …

Learning And Serving: An Exploratory Action Research Case Study Of A Middle School Service Learning Curriculum Project, Georgina Levey

Electronic Theses and Dissertations

Service learning, a natural link between community service and standards-based education, encourages students to learn about themselves in the context of the world in which they live. In other words, service learning is a method of teaching that enriches learning by engaging students in meaningful service to their schools and communities, and integrating that service with established curricula or learning objectives (NYLC Service-Learning Glossary, 2005). Educational service activities can be done directly or indirectly and they can have a varying degree of “involvement” ranging from community service, community exploration, community action or advocacy and research. In this study, a service …

Design Of Computer-Based Assessment Secondary Education For Understanding Of Mathematics, Mark Damian Lewis

Boise State University Theses and Dissertations

The purpose of this study was to evaluate the effectiveness of a computer-based assessment to reveal mathematical understanding. Relevant literature suggested that developments in cognitive science and computer-based assessments could allow the outcomes of cognitively guided instruction to be made explicit. An assessment instrument designed to make mathematical thinking explicit was developed and administered, consisting of 15 animations showing the solutions of one and two digit multiplication problems. A consistent set of five questions followed each animation. The assessment was administered to four classes of fourth grade students in two elementary schools participating in cognitively guided instruction professional development programs. …

Mathematics In Motion: A Handbook Of Kinesthetic Teaching Strategies, Janie Brown Salazar

Regis University Student Publications (comprehensive collection)

Howard Gardner first proposed his theory of Multiple Intelligences and the bodily-kinesthetic intelligence in 1983. Unfortunately, almost three decades later, teacher programs still do not train teachers about Bodily-Kinesthetic intelligence in depth; nor do they train teachers how to integrate Bodily-Kinesthetic intelligence into daily learning procedures and classroom environment. Schools focus very little on other factors that contribute to how successful a person might be in life, throughout life. Incorporating bodily-kinesthetic strategies in teaching can positively influence children's learning experience. The following research project investigates the research on the bodily-kinesthetic intelligence, bodily-kinesthetic teaching strategies, teaching strategies linked to student achievement, …

Mathematics Vocabulary And English Learners: A Study Of Students' Mathematical Thinking, Hilary Hart

Theses and Dissertations

This study examined the mathematical thinking of English learners as they were taught mathematics vocabulary through research-based methods. Four English learners served as focus students. After administering a pre-performance assessment, I taught a 10-lesson unit on fractions. I taught mathematics vocabulary through the use of a mathematics word wall, think-pair-shares, graphic organizers, journal entries, and picture dictionaries. The four focus students were audio recorded to capture their spoken discourse. Student work was collected to capture written discourse. Over the course of the unit, the four focus students used the mathematics vocabulary words that were taught explicitly. The focus students gained …

Parts Of The Whole: Thinking About Variance: Standards, Targets, Tracking, And Other Thoughts, Dorothy Wallace

Numeracy

Variation is a natural result of any process, including education. Understanding how variation propagates and increases is necessary for designing educational interventions that work for the intended population. We show how common strategies such as setting standards and tracking can accidentally produce unintended and undesirable results due to the way variation moves through a system.