Digital Commons Network^™

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.

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 …

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 …

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 …

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, …

The Local Isometric Embedding Problem For 3-Dimensional Riemannian Manifolds With Cleanly Vanishing Curvature, Thomas Edward Poole

Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions)

We prove the following result: Let $(M,g)$ be a 3-dimensional $C^\infty$ Riemannian manifold for which there exists a $p\in M$ and a $v\in T_pM$ such that$$ \mathbf{Riem}(p) = 0 \ \ \ \ \ \text{and} \ \ \ \ \ \nabla_v\mathbf{Riem}(p) \neq 0. $$ Then there exists a $C^\infty$ local isometric embedding from a neighbourhood of $p$ into $\mathbb{R}^6$.

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 …

Anxiety In The Math Classroom, Jean Benner

Mathematics Graduate Theses

Math anxiety is a learned response that inhibits cognitive performance in the math classroom. It is widespread among students from elementary age through college. Students suffering from math anxiety have difficulty performing calculations and maintaining a positive outlook on mathematics. Math anxiety is the result of a cycle of math avoidance that begins with negative experiences regarding mathematics. Facts pertaining to math anxiety are discussed and strategies are suggested to assist teachers in helping students to overcome math anxiety or avoid the phenomenon altogether.

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 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.

Reorganizing School Mathematics For Quantitative Literacy, Rick Gillman

Numeracy

This paper offers an alternative curriculum for high school mathematics. It proposes replacing the Algebra-Geometry-Algebra rush to calculus model with one which focuses on improving student problem-solving skills and general quantitative literacy skills while reinforcing basic manipulative skills. Most of these goals are gained by expanding the current single-year algebra-one course into two years. The model proposes moving “learning to write proofs” from the traditional geometry course into a separate discrete mathematics course. It requires statistics for every student, and requires a senior-level modeling course for every college-going student. In addition, the proposed model creates opportunities for students to move …

Quantitative Reasoning In The Contemporary World, 2: Focus Questions For The Numeracy Community, Bernard L. Madison, Shannon W. Dingman

Numeracy

Numerous questions about student learning of quantitative reasoning arose as we developed, taught and assessed the Quantitative Reasoning in the Contemporary World course described in the companion paper in this issue of Numeracy. In this paper, we present some of those questions and describe the context in which they arose. They fall into eight general problem areas: learning that is context-bound and does not easily transfer (i.e., situated learning); the need for a productive disposition regarding mathematics; the connection between QL and mathematical proficiency; the persistence of students, despite our efforts, for using the wrong base for percents; the inconsistent …

Quantitative Reasoning In The Contemporary World, 1: The Course And Its Challenges:, Shannon W. Dingman, Bernard L. Madison

Numeracy

The authors describe successes and challenges in developing a QL-friendly course at the University of Arkansas. This work is part of a three-year NSF project Quantitative Reasoning in the Contemporary World (QRCW) that supported the expansion of the course. The course, MATH 2183, began experimentally in Fall 2004 as a section of finite mathematics known informally as “News Math” for 26 students from arts and humanities disciplines. Over the past six years, the course has evolved and now MATH 2183 is approved to satisfy the College of Arts and Sciences mathematics requirement for the Bachelor of Arts degree. In 2009-2010, …

Advancing Assessment Of Quantitative And Scientific Reasoning, Donna L. Sundre, Amy D. Thelk

Numeracy

Advancing Assessment of Quantitative and Scientific Reasoning is a four-year NSF Project (DUE-0618599) in part designed to evaluate the generalizability of quantitative (QR) and scientific reasoning (SR) assessment instruments created at James Madison University to four other four-year institutions with very distinct missions and student demographics. This article describes the methods, results, and findings we obtained in our studies. More specifically, we describe how to conduct content-alignment exercises in which faculty members map each item from a prospective test to the student learning objectives taught at the institution. Our results indicated that 92-100% of the QR and SR items were …

Interview With Chad Topaz, Professor Of Mathematics, Chad Topaz

Math, Stats, and Computer Science Department Oral Histories

No abstract provided.

Physical Models In Community Detection With Applications To Identifying Structure In Complex Amorphous Systems, Peter Ronhovde

All Theses and Dissertations (ETDs)

We present an exceptionally accurate spin-glass-type Potts model for the graph theoretic problem of community detection. With a simple algorithm, we find that our approach is exceptionally accurate, robust to the effects of noise, and competitive with the best currently available algorithms in terms of speed and the size of solvable systems. Being a "local" measure of community structure, our Potts model is free from a "resolution limit" that hinders community solutions for some popular community detection models. It further remains a local measure on weighted and directed graphs. We apply our community detection method to accurately and quantitatively evaluate …

Noncommutative Topology And The World’S Simplest Index Theorem, Erik Van Erp

Dartmouth Scholarship

In this article we outline an approach to index theory on the basis of methods of noncommutative topology. We start with an explicit index theorem for second-order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-brow index formula is expressed in terms of winding numbers. We then proceed to show how it is derived as a special case of an index theorem for hypoelliptic operators on contact manifolds. Finally, we discuss the noncommutative topology that is employed in the proof of this theorem. The article is intended to illustrate that noncommutative topology can be a powerful tool …

Preservice Elementary Teachers‟ Pedagogical Content Knowledge Related To Area And Perimeter: A Teacher Development Experiment Investigating Anchored Instruction With Web-Based Microworlds, Matthew S. Kellogg

USF Tampa Graduate Theses and Dissertations

Practical concepts, such as area and perimeter, have an important part in today's school mathematics curricula. Research indicates that students and preservice teachers (PSTs) struggle with and harbor misconceptions regarding these topics. Researchers suggest that alternative instructional methods be investigated that enhance PSTs' conceptual understanding and encourage deeper student thinking. To address this need, this study examined and described what and how PSTs learn as they engage in anchored instruction involving web-based microworlds designed for exploring area and perimeter. Its focus was to examine the influences of a modified teacher development experiment (TDE) upon 12 elementary PSTs' content knowledge (CK) …

A Statistical Analysis Of Defined Benefit, Defined Contribution, And Hybrid Plans, Katie Heeder

Honors Projects in Mathematics

The purpose of this study is to compare three major types of employer sponsored retirement plans, Defined Benefit (DB), Defined Contribution (DC), and hybrid, and their impact on the employee. Employee careers are simulated to understand the employee’s advantages and disadvantages of each type of plan, especially in the state of an economic depression. The study uses actuarial assumptions and the simulation varies a number of quantities to better understand the impact of employee savings. The variables which are simulated at different levels are: service start age, retirement age, current compensation, salary increase rate, rate of return on market investments, …

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Ordinary Differential Equations, Taylor Mcadam

Interface Compendium of Student Work

This painting was the final project for Math 13 -- Introduction to Differential Equations. The aim of the final project was to display the knowledge we had gained throughout the course in a creative way. My painting displays plots of solutions to a variety of specific differential equations we studied in the course, as well as some more general tools we learned for solving ODEs (such as the Wronskian in the background). The piece is acrylic on canvas.

Rate Of Change, Elizabeth Schofield

Interface Compendium of Student Work

This piece was created for an introductory course in Differential Equations. The goal of the work is to visually represent the shared context and commonalities of applications of ordinary differential equations. The piece was created with colored pencil on paper. Applications displayed include flow rate of a fluid, a mass-spring system, and a pendulum.

The Life Of Evariste Galois And His Theory Of Field Extension, Felicia N. Adams

Senior Honors Theses

Evariste Galois made many important mathematical discoveries in his short lifetime, yet perhaps the most important are his studies in the realm of field extensions. Through his discoveries in field extensions, Galois determined the solvability of polynomials. Namely, given a polynomial P with coefficients is in the field F and such that the equation P(x) = 0 has no solution, one can extend F into a field L with α in L, such that P(α) = 0. Whereas Galois Theory has numerous practical applications, this thesis will conclude with the examination and proof of the fact that it is impossible …

Neutrosophic Physics: More Problems, More Solutions, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

When considering the laws of theoretical physics, one of the physicists says that these laws – the actual expressions of the laws of mathematics and logics being applied to physical phenomena – should be limited according to the physical meaning we attribute to the phenomena. In other word, there is an opinion that a theoretical physicist should put some limitations onto mathematics, in order to “reduce” it to the observed reality. No doubt, we can do it. However, if following this way, we would arrive at only mathematical models of already known physical phenomena. Of course, this might be useful …

Unbreakable Codes: Rsa Public Key Cryptosystem, Razia Amzad

Honors College Theses

The purpose of this paper is to comprehend the evolution of codes and ciphers; along with understanding how to encode and decode a message using RSA coding. In this paper "Unbreakable Codes" we will highlight the historical advances of communicating secure messages by illustrating the process of RSA coding with an example.