Digital Commons Network^™

Math 665-102: Statistical Inference, A. Wang

Mathematical Sciences Syllabi

No abstract provided.

Math 664-102: Methods For Stat Consult, J. Loh

Mathematical Sciences Syllabi

No abstract provided.

Math 678-102: Stat Methods In Data Science, Z. Shang

Mathematical Sciences Syllabi

No abstract provided.

Math 699-102: Des & Analy Experiments, S. Dhar

Mathematical Sciences Syllabi

No abstract provided.

Math 689-002: Adv Applied Math Ii, A. Oza

Mathematical Sciences Syllabi

No abstract provided.

Math 791-002: Graduate Seminar, R. Goodman

Mathematical Sciences Syllabi

No abstract provided.

Combining The Concrete Representational Abstract Framework And Video Modeling To Increase Basic Addition Skills Among First Grade Students, Sara Ebner

Theses and Dissertations--Educational, School, and Counseling Psychology

Proficiency in mathematics is fundamental for academic success and is linked to numerous skills that are essential for success in the real-world. Despite its importance, many students struggle with math, leading to nationwide declines in math proficiency. This decline highlights the need for effective interventions that are accessible, able to be individualized, and feasible for implementation across settings. In the present study, a single case multiple probe across participants design was used to assess the efficacy of a concrete-representational-abstract (CRA) framework with video modeling intervention on the basic addition problem-solving accuracy of three first-grade students. Results show that participants’ accuracy …

Inexact Fixed-Point Proximity Algorithm For The ℓ₀ Sparse Regularization Problem, Ronglong Fang, Yuesheng Xu, Mingsong Yan

Mathematics & Statistics Faculty Publications

We study inexact fixed-point proximity algorithms for solving a class of sparse regularization problems involving the ℓ₀ norm. Specifically, the ℓ₀ model has an objective function that is the sum of a convex fidelity term and a Moreau envelope of the ℓ₀ norm regularization term. Such an ℓ₀ model is non-convex. Existing exact algorithms for solving the problems require the availability of closed-form formulas for the proximity operator of convex functions involved in the objective function. When such formulas are not available, numerical computation of the proximity operator becomes inevitable. This leads to inexact iteration algorithms. We investigate in this …

Exploring The Integration Of Neuroeducation Principles In Teaching Mathematics In Selected Secondary Schools In Iringa Municipality, Tanzania., Emmanuel Jonathan Kahise

Master of Education

This research explored the integration of neuroeducation principles in the mathematics curriculum of secondary educational institutions in Iringa Municipality, Tanzania, driven by the goal of enhancing learning outcomes and refining instructional strategies. Employing a qualitative case study methodology, the study examined teachers' perspectives, the actual implementation of neuroeducation concepts in classrooms, and the challenges encountered during integration. Through observations of form one and form three classes and interviews with three mathematics teachers, inconsistencies between claimed understanding and actual practices were identified. To address issues such as a lack of instructional resources, restricted technology access, and limited professional growth opportunities, specific …

The Impact Of Mental Health On Academic Performance In Ohio In 2022, Lily Chen, Samantha Gilbert

Scholarship in Medicine - All Papers

Background: Previous research has shown a significant link between mental health issues and low academic performance. Our study explores the delicate connection between mental health issues and academic performance in Ohio school children, in particular, how the dynamic may differ between rural and non-rural communities. Methods: We utilized County Health Rankings data from the years 2016 and 2022 from all 88 counties in Ohio, which we further substratified as 44 rural and 44 non-rural counties. From CHR, we chose data categories to represent measures of academic performance, internalizing mental health problems, and access to mental health services, and utilized SPSS …

A Pade-Eno Flux Reconstruction For High-Speed Flows, Blake Martin

Browse all Theses and Dissertations

The development of high order numerical schemes has been instrumental in advancing computational fluid dynamics (CFD), particularly for applications requiring high resolution of discontinuities and complex flow phenomena prevalent in high-speed flows. This thesis introduces the Pade-ENO scheme, a high-order method that integrates Essentially Non-Oscillatory (ENO) techniques with compact Pade stencils to achieve superior accuracy, up to 7th order, while maintaining stability in harsh environments. The scheme’s performance is evaluated through benchmark tests, including the advection equation, Burgers’ equation, and the Euler equations. For high Mach number flows, such as the sod shock tube the Pade-ENO method demonstrates its ability …

Investigating Prodigy Math Program To Improve Students' Success In Mathematics, Justin A. Bledsaw

Masters Theses

This study investigates whether Prodigy improves student achievement in mathematics; whether Prodigy improves, specifically, math achievement of special education students, students of different ethnicities, and students of different genders. Further, the study wanted to explore student perceptions of Prodigy. The study was conducted in two fifth grade classrooms with a total of 31 participants. Two mathematics units were utilized to compare; one on multiplying whole numbers and the other on dividing whole numbers. In addition, participants completed a survey and a focus group interview to find out participant perceptions of Prodigy. Results reveal that the whole group scored higher in …

College Algebra, Leslie Bain

ATU Faculty OER Book Reviews

Review of OER College Algebra textbook by Carl Stitz, available at https://open.umn.edu/opentextbooks/textbooks/college-algebra

Investigating The Effect Of Streaming Based On Gender On Mathematics Learning In Mixed Secondary School: A Case Study Of A Selected Secondary School In Sheema District, Uganda, Naome Katumwebaze

Master of Education

Gender-based streaming, the practice of separating students into single-sex classes according to gender, is commonly implemented in some mixed secondary schools in Uganda. However, limited research exists on its impact on students' mathematics learning. This research study investigated the effect of gender-based streaming on mathematics learning in secondary schools in Uganda. The research is grounded in the context of Uganda's education system, which has a historical background of segregating education based on gender. It explores the expansion of formal education and the emergence of streaming as a practice in Ugandan secondary schools. The study recognizes the persistent gender gap in …

Zeckendorf Representation Analysis On Third Order Fibonacci Sequences That Do Not Satisfy The Uniqueness Property, Samuel A. Aguilar

Honors College Theses

Zeckendorf's Theorem states that every natural number can be expressed uniquely as the sum of distinct non-consecutive terms of the shifted Fibonacci sequence (i.e. 1, 2, 3, 5, ...). This theorem has motivated the study of representation of integers by the sum of non-adjacent terms of Nth order Fibonacci sequences, including the characterization of the uniqueness of Zeckendorf representation based on the initial terms of the sequence. Moreover, when this uniqueness property is satisfied for third order Fibonacci sequences, the ratio of integers less than a given number X that have a Zeckendorf representation has been estimated by Dr. Sungkon …

Recreational Mathematics: Where Is The Error?, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This short note is a funny problem for the trigonometry students!.

Evidence Of A Thick Heliopause Boundary Layer Resulting From Active Magnetic Reconnection With The Interstellar Medium, Drew L. Turner, Adam Michael, Elena Provornikova, Marc Kornbleuth, Merav Opher, Stefan Eriksson, Benoit Lavraud, Parisa Mostafavi, Matthew E. Hill, Pontus Brandt, Ian J. Cohen, Joseph Westlake, John D. Richardson, Nathan A. Schwadron, David J. Mccomas

Faculty Publications

Voyager 1 and 2 data from the vicinity of the heliopause and very local interstellar medium are reexamined to better understand the confounding lack of rotation in the magnetic field (B-field) across the heliopause observed by both Voyagers, despite their very large spatial separations (>100 au). Using three estimates for the orientation of the B-field in the pristine interstellar medium and four models of the heliosphere, we calculate draped interstellar B-field orientations along the model heliopauses and compare those estimates to the Voyager observations. At both Voyagers, expected draped B-fields are inconsistent with the observed B-field orientations after the boundary …

Ermakov Equations Can Be Derived From Zel’Dovich Pancake, And They Are Cold And Nonlocal Through Using Neutrosophic Venn Diagram, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

As we argue in a previous article, the labyrinthine worlds of Jorge Luis Borges are more than captivating narratives; they are portals to a deeper understanding of existence. By weaving elements of science-fiction fantasy with philosophical and ethical inquiries, Borges's short stories bridge the seemingly disparate realms of physics and the humanities, offering fertile ground for contemporary physics research. The present-day universe consists of galaxies, galaxy clusters, one-dimensional filaments and two-dimensional sheets or pancakes, all of which combine to form the cosmic web. The so called ”Zeldovich pancakes”, are very difficult to observe, because their overdensity is only slightly greater …

Pitching The Use Of Squared And Interaction Terms In Regression Via Baseball Heat Maps, Lucas Chepelsky

Williams Honors College, Honors Research Projects

This project will examine the impact of using second-order terms in regression. For illustration, we use an example of regression where a baseball player's three by three heat map, including the height and distance from inside to outside of the pitch, are variables used to predict batting average. We find that second-order terms are crucial in discovering nonlinear relationships and interaction effects in regression models, and maintain that the common practice of using first-order additive models is insufficient.

Asynchronous Class For Algebra I Preparation, Hunter Garretson

Williams Honors College, Honors Research Projects

Algebra I is the first high school mathematics class students take making it an important building block in the student’s growing mathematical foundation. Mitigating any losses in knowledge over the summer by using educational review tools has been proven helpful in previous studies. Every student comes from a different background, socioeconomic class, ethnicity, culture, etc., allowing each student to have a different summer experience. A meta-analysis looking into the concern of Summer Learning Loss (SLL) found that while some of its sample size would make summer knowledge gains, more than half of the sample size was projected to suffer from …

Seven Properties Of Highly Effective Problems, Thomas Ales, Kevin Peterson, Constantine Roussos

Journal of Mathematics and Science: Collaborative Explorations

In an effort to provide more critical thinking opportunities in their courses, instructors are embracing the power of problem- and project-based learning (PBL). In this paper we address the importance of problem quality when utilizing PBL. We list seven important properties that a high-quality problem should have. We conclude with an example of a problem that possesses all seven properties.

A Spiral Workbook For Discrete Mathematics 2nd Edition, Harris Kwong

Milne Open Textbooks

This updated text covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is …

Prospective Teachers' Conceptions Of Area, Betsy Mcneal, Sayonita Ghosh Hajra, Michael Battista, Ayse Ozturk

Teaching & Learning Faculty Publications

This study explored 10 prospective teachers’ (PTs’) understanding of the area of a rectangular region using square and non-square rectangular area-units. In an hour-long interview, each PT was first asked to explain how they would find the area of a given rectangular region in terms of a non-square notecard. For several PTs, this task prompted discussion of a square unit defined by the edge of the notecard. In a second task, PTs were presented with a rectangular array of squares and were asked to explain to a fictional child why multiplying length times width does not count the top left …

Evidence Of A Thick Heliopause Boundary Layer Resulting From Active Magnetic Reconnection With The Interstellar Medium, Drew L. Turner, Adam Michael, Elena Provornikova, Marc Kornbleuth, Merav Opher, Stefan Eriksson, Benoit Lavraud, Parisa Mostafavi, Matthew E. Hill, Pontus Brandt, Ian J. Cohen, Joseph Westlake, John D. Richardson, Nathan A. Schwadron, David J. Mccomas

Faculty Publications

Voyager 1 and 2 data from the vicinity of the heliopause and very local interstellar medium are reexamined to better understand the confounding lack of rotation in the magnetic field (B-field) across the heliopause observed by both Voyagers, despite their very large spatial separations (>100 au). Using three estimates for the orientation of the B-field in the pristine interstellar medium and four models of the heliosphere, we calculate draped interstellar B-field orientations along the model heliopauses and compare those estimates to the Voyager observations. At both Voyagers, expected draped B-fields are inconsistent with the observed B-field orientations after the boundary …

Student Engagement In Model School Math: A Phenomenological Study Of Student Perspectives At A Model Continuation High School, James Robert Coles Iii

Theses and Dissertations

The purpose of this phenomenological study was to explore the perspectives on engagement of students who had passed Model School Math (Integrated Math 1 or Algebra 1) and graduated within the years 2015 to 2019 from a Model Continuation High School in California. This study sought to discover the strategies, policies, and procedures which best supported at-risk students and adequately prepared them for college and career after attending a continuation high school. The theoretical framework used for this study was flow theory. This phenomenological qualitative study was conducted in one school district with students who attended a single site. Each …

Preface, Mohamed Mahdi Tekitek, Manfred Krafczyk, Li-Shi Luo

Mathematics & Statistics Faculty Publications

[Introduction] Matter, conceptually classified into fluids and solids, can be completely described by the microscopic physics of its constituent atoms or molecules. However, for most engineering applications, a macroscopic or continuum description has usually been sufficient due to the large disparity between the spatial and temporal scales relevant to these applications and the scales of the underlying molecular dynamics. In this case, the microscopic physics merely determines material properties such as the viscosity of a fluid or the elastic constants of a solid. These material properties cannot be derived within the macroscopic framework, but the qualitative nature of the macroscopic …

Solvability Of Self Reference Functional Integro-Differential Equation With Nonlocal Initial Condition, A.A. Darwish, M.A. Seddeek, Reda Gamal Ahmed, Ahmed A. El-Deeb, Moataz Ashraf Mohamed, Hossam A. Ghany

Trends in advanced sciences and technology

We present in this paper a new type of self-reference functional integro-differential equation with a nonlocal initial condition. Also, we present a nonlocal problem of the functional integro-differential equation with the infinite point boundary condition for more generalization. An integral representation equivalent to the functional integro-differential equation is obtained to use the theorems needed for proving the existence, and uniqueness. Then we prove the continuous dependence of the solution on the nonlocal parameter and the initial data of the equation. To prove the existence of the solution of the equation we present the Schauder fixed point theorem for both finite …

On The Use Of The Local Reflection Coefficient To Assess The Diffuse Field Sound Absorption Coefficient Of A Porous Material, Franck Sgard, Noureddine Atalla, Olivier Robin

Études primaires

The diffuse field sound absorption coefficient (SAC) of a sound absorber can be obtained from an average over the incidence angles of the oblique incidence plane wave SAC. The plane wave SAC can be derived from the plane wave complex-valued reflection coefficient defined as the ratio of the reflected sound pressure at a given point on the material surface to the incident sound pressure at the same point. In practice, the material is excited by a monopole, and the reflection coefficient becomes a local quantity which is a function of the source height and the radial distance from the source. …

Perceptions Of Secondary School Mathematics Teachers Regarding Teaching Mathematics With Conceptual Understanding, Latisa Williams

Theses and Dissertations

This dissertation was designed to provide current knowledge on the mindset of secondary school mathematics teachers regarding the use of Conceptual Understanding (CU) as an approach to teaching the subject. It is well-documented that when students learn to engage in mathematical conceptual explanations in meaningful ways, they improve their learning. However, reports have shown that students in secondary schools lack effective skills in explaining and applying CU for successful problem-solving. As a result, teachers struggle with methods of instruction that can effectively improve the level of CU with their students in mathematics.

For this study, the researcher used a qualitative …

Defining Success For An Introductory Mathematics Non-Stem Pathway Course, Clark D. Metz

Graduate Theses, Dissertations, and Problem Reports (ETD)

The enduring debate surrounding college algebra, traditionally a gateway for STEM pathways, underscores the necessity for curricular evolution in response to the rising popularity of non-STEM majors. This dissertation explores the success of an applied college algebra course designed for non-STEM students. The study aimed to determine whether this alternative course could meet diverse student needs while promoting academic achievement and fostering positive attitudes towards mathematics. Findings revealed through a novel approach of a difference-in-differences analysis that students enrolled in the applied college algebra course exhibited higher pass rates due to the introduction of the new course. The lower failure …