Digital Commons Network^™

A Novel Approach To Detect Shapes Of Constant Width, Ian D. Monk

Theses and Dissertations

Bodies of constant width have been studied mathematically since Euler and have found various applications in engineering and other areas. In this paper, we seek to develop novel tools to gain deeper insights into these shapes and to better be able to analyze them. The idea which motivates the development in this paper is as follows: a body has constant width if and only if the chord connecting the intersections of the boundary of the body with each pair of parallel hyper planes which lie tangent to a body lies perpendicular to the hyper planes.This is a known fact and …

Reinventing Mathematics Learning: An Exploration Of Undergraduate Mathematics Learning Post-Pandemic, Morgan R. Balesano

Honors Scholar Theses

In response to the COVID-19 pandemic, beginning in March 2020 nearly all secondary and undergraduate mathematics students were forced to adapt to new methods of learning and testing. As a result, the current experience for these mathematics students has changed vastly, as have the opinions and preferences of these students in terms of their learning. This study aims to identify instruction and testing resources and methods that students prefer and those that students find less beneficial in their current, post-pandemic educational experience. The past few years have seen a focus on the direct impacts of online learning during the pandemic, …

Exploring Teacher Knowledge In Meeting The Expectations Of Integrated Content Language Development In Mathematics: A Descriptive Case Study, Carrissa Rozelaar-Miller

Doctoral Dissertations and Projects

The purpose of this descriptive case study was to discover how knowledge is applied to meet the expectations of integrated content and language development in mathematics for Title I elementary teachers at an urban school district in the central United States. Halliday’s theory on systemic functional linguistics guided the research as it relates to the function and purpose of language through meaning and social interaction in different genres. The central research question was: How do Title I elementary teachers apply specific integrated content and language development knowledge in mathematics? The participants consisted of 10 teachers with at least three years …

The Importance Of Motivation And Self-Concept For Predicting Performance In Service Mathematics Modules: Replicating And Extending Previous Findings, Catherine Palmer, Maryna Lishchynska, Declan O’Connor, Seán Lacey

Department of Mathematics Publications

Students’ difficulties and lower-than-desired mathematics performance in higher education have been the focus of educational research and practice for a period of time. In a recent study by Lishchynska et al. (2023), learners’ motivation, dispositions towards mathematics and learning strategies were examined as factors potentially affecting performance in service mathematics modules. The main objectives of this study were to replicate the findings of Lishchynska et al. (2023) with a new student cohort; determine if self-concept is a significant contributortomathematicsperformance;andexploreifmathematicalbackgroundremainsan important predictor of mathematics performance for students as they migrate from first year to final year of study. A survey of …

Improving Preschoolers' Number Sense Using Counting Collections And Ten Frames, Ashley Gellings

Master's Theses & Capstone Projects

Recently, literacy has received considerable attention in education, often overshadowing mathematics instruction. This inquiry-based research study investigates the impact of counting collections and ten frames on improving preschoolers' number sense to determine if it can serve as an effective Tier 1 instructional strategy for younger learners. After reviewing the literature, the researcher decided on a Tier 1 instructional change to support further growth in number sense. Research indicates that students who master counting and cardinality skills by the end of preschool are more likely to succeed in future mathematics. While there is no specific information to determine the correct type …

Numbas For Formative Assessment, Louise Lynch

Case studies: Digital Education

Numbas is an open-source e-assessment system aimed at mathematics and other numerate disciplines. It allows for the setup of individual assessments for students, increasing academic integrity. Numbas can autograde attempts, and the use of the Learning Tool Interoperability (LTI) within Brightspace allows instructors to view attempts, monitor progress, and alter marks where applicable. This adds a valuable element for both formative and summative assessments. In this module, Numbas was used to provide students with individual parameters for the same problems as part of their continuous assessment. These problems would consist of several steps and typically take over 30 minutes to …

Assessing Maths Modules Online, Blathnaid Sheridan

Case studies: Digital Education

With class sizes increasing and students anxious to know their CA results asap, I began looking at an alternative way of assessing students on their maths modules. Furthermore, in an attempt to ensure better engagement with the content and continuity across maths modules in Years 1 & 2, students are now assessed using online quizzes with immediate results.

Exploring The Use Of Artificial Intelligence As An Instructional Learning Tool In Middle School Mathematics Classrooms, Maurice Guest Jr

Student Theses and Dissertations

This quantitative causal-comparative study explored the effectiveness of AI instructional/learning tools, specifically the IXL platform, in middle school mathematics classrooms. In this study, AI tools, such as IXL, were investigated to determine if there was a significant influence on students’ academic growth and achievement in light of the continuing teacher shortage in Arkansas. The lack of highly qualified teachers has led to Arkansas high school students’ underperformance in mathematics. Framed by a Constructivist approach, the study viewed learning as an active, engaged experience in which students shaped their own learning, rather than passively receiving information in the classroom. Data from …

Improving Mathematical Achievement And Engagement Through Technology Integration, Jennifer Ham

Master's Theses & Capstone Projects

Engaging students effectively requires continuous effort from educators to improve their classroom learning experiences. Research has demonstrated the benefits of educational technology in enhancing student learning outcomes. Nonetheless, there is a lack of research in the United States on how the integration of technology affects students' engagement and comprehension of mathematical concepts in elementary education. This inquiry-based research aims to investigate the impact of technology integration on the understanding and engagement of fourth graders in mathematics. This study aims to address the following questions: How does integrating technology in fourth-grade mathematics impact students' understanding of math concepts? What impact does …

Integrating Elementary Computer Science And Mathematics Instruction: One Size Does Not Fit All, Umar Shehzad, Jody Clarke-Midura, Mimi Recker

Publications

This paper presents a model, the double integration model, for integrating Computer Science (CS) and mathematics in upper elementary instruction. Fifth-grade students (n=1,037) participated either in the double integrated model (Condition 1; integrated in both CS and Math instruction) or integrated lessons only in CS instruction (Condition 2). After each lesson, students rated their enjoyment, perceived ease, and perceptions of CS-math connections. Multilevel analyses revealed that Condition 1 students reported significantly more positive perceptions and stronger CS-math connections of the lessons than Condition 2 students. Girls in Condition 1 responded more positively than boys on enjoyment and connection items, and …

Navigating Geometry With Interactive Lessons: A Collection Of Resources In Geogebra That Address Frequently Held Misconceptions, Sara Vance

Honors Program: Senior Projects (Public)

Nearly every high school student in the United States is required to take a geometry class, and for many, it’s unlike any math class they’ve taken before. Additionally, there are certain topics with which past and present geometry students alike tend to struggle. This project was created to address these issues; my goal is that these materials will help students better understand these topics and clear up their frequently held misconceptions about geometry. This project was supported by interviews I conducted with veteran high school geometry teachers with over 75 years of teaching math between them.

This collection of interactive …

Galerkin Finite Element Methods Error Estimates Analysis For [1+2] Equations Of Integro-Differential On Linear Triangular, Ali Kamil Al-Abadi, Shurooq Kamel Abd

Baghdad Science Journal

In this research, the two-dimensional parabolic integral-differential equation was solved using one of the numerical methods, which is the finite element method (Galerkin) on triangular elements. This method was chosen to make extensive use of finite elements because it has many high-quality numerical properties. The main benefit of finite elements is their ability to solve a wide range of problems in different computational fields in different forms, especially complex ones that cannot be solved by other numerical methods. Given the semi-discrete error estimates for the normal space H¹, the polynomial linear boundary element space defined in triangles was …

Modules Whose St-Closed Submodules Are Fully Invariant, Maysaa Riadh Abbas, Muna Abbas Ahmed

Baghdad Science Journal

The duo module plays an important role in the module theory. Many researchers generalized this concept such as Ozcan AC, Hadi IMA and Ahmed MA. It is known that in a duo module, every submodule is fully invariant. This paper used the class of St-closed submodules to work out a module with the feature that all St-closed submodules are fully invariant. Such a module is called an Stc-duo module. This class of modules contains the duo module properly as well as the CL-duo module which was introduced by Ahmed MA. The behaviour of this new kind of module was considered …

Maximizing Reliability In The Age Of Complexity: A Novel Optimization Approach, Ahmed Hasan Alridha, Fouad Hamza Abd Alsharify, Zahir Al-Khafaji

Baghdad Science Journal

Calculating the reliability of complex systems is an urgent matter that deserves attention due to its wide applications, ranging from engineering and economic sciences to applications in medical fields Traditional methods often suffer from computational complexity when dealing with large systems when calculating their reliability. This paper presents a new method to calculate and improve the reliability of highly complex systems. Furthermore, the proposed methodology combines the principles of system reliability analysis and optimization techniques to determine the optimal means for a system that increases reliability. A mathematical optimization approach was employed to undertake the task of improving the reliability …

Topological And Hyper Topological Coindices Of Benzenoid Circumcoronene Series, Walid Yousef, Abdu Alameri, Mohammed Alsharafi, Noman Al-Naggar, Belal Al-Fuhaid

Baghdad Science Journal

Numerous applications in chemistry are enabled by chemical graph theory, which is a branch of graph theory. Numerical quantities derived from the chemical graphs of a molecule, known as topological indices and co-indices, are used to model the chemical and physical properties of molecules in quantitative Structure-Property relationships (QSPR) and quantitative structure-activity relationships (QSAR) research. Fortunately, chemical-based experiments have found a strong connection between Topological descriptors (topological indices and co-indices) of molecular structures and their Physicochemical Properties, such as boiling point, and toxicity of drugs. Although several research reports have contributed to the computation of topological indices of the benzenoid …

Development And Initial Validation Of The Increasing Mathematical Processes Opportunities For Vital Engagement Instrument, Joseph A. Ours

USF Tampa Graduate Theses and Dissertations

Many undergraduate students struggle to learn college level mathematics. This may be because they have not developed their mathematical processes. Mathematical processes are the habits of mind of successful mathematicians and are how one learns and subsequently applies mathematics content. Five categories of mathematical processes are problem solving, reasoning and proof, communication, connections, and representation.

Students need opportunities to develop their mathematical processes. This is the foundation of high quality mathematics instruction. Many instructors, however, lack practical knowledge on how to enact a pedagogy that provides students with opportunities to engage in mathematical processes.

The purpose of this study was …

Study Of The Toxicity And Cell Viability Of Zirconium Oxide Nanoparticles Prepared From An Extract Of The Vitex Agnus Castus Plant, Saba H. Mahdi, Lekaa K. Abdul Karem

Baghdad Science Journal

In the current study, ZrO₂ nanoparticles were synthesized using a plant extract derived from Vitex agnus castus, and an alkaline medium such as sodium hydroxide. A biosynthetic approach was utilized to prepare zirconium oxide nanoparticles for this research project. This method stands out from others due to its cost-effectiveness, simplicity, and lack of potential risks.The prepared samples were characterized using transmission electron microscopy TEM, scanning electron microscopy SEM, Fourier transform infrared spectroscopy FT-IR, ultraviolet-visible spectroscopy UV-VIS, X-ray diffraction, and energy-dispersive X-ray spectroscopy EDX. The size of the crystal was determined using X-ray diffraction in conjunction with the Debye-Scherer equation, …

The Origins Of Mathematics: Invented Or Discovered?, Andrew Watts

Osmosis Magazine

A divisive subject amongst students of all ages, Mathematics remains an integral part of each student’s educational journey. Why is that? you may wonder. The answer is that Mathematics lies at the center of the natural world.

The Nctm/Cec Position Statement On Teaching Mathematics To Students With Disabilities: What’S In It And What’S Not, Sarah R. Powell, Marcia A. Barnes, Jenny Root, Elizabeth M. Hughes, Leanne Ketterlin-Geller, Gena Nelson, Megan Rojo, David H. Allsopp, Bradley S. Witzel, Jonté A. Myers, Margaret M. Flores, Erica S. Lembke, Matthew K. Burns, Jessica Namkung, Brian Poncy, Robin Parks Ennis, Lisa L. Morin, Tessa L. Arsenault, Christian T. Doabler, Vanessa Hinton, Rajiv Satsangi, Jennifer E. Kong, Bree Jimenez, Kaitlin Bundock, Robin S. Codding, Sarah King, Scott A. Dueker, Genesis Arizmendi, Deidre Gilley, Tasia Brafford, Elizabeth A. Stevens, Ben Clarke, Paul J. Riccomini, Corey Peltier

Education Faculty Articles and Research

A joint position statement issued in December 2024 by the National Council of Teachers of Mathematics (NCTM) and the Council for Exceptional Children (CEC) on teaching mathematics to students with disabilities lacked substantive, actionable, research-validated recommendations to support the work of practitioners in the field. Herein, we provide a rationale for ways in which the eight recommendations for teachers included in the position statement fell short, provided misleading information, and ignored the large body of research on providing mathematics instruction for students with mathematics disability or difficulties. In response, we offer seven actionable, research-validated recommendations, including: (a) use systematic, explicit …

My Gai Study Partner For Odes, Milena C. Cuellar

Open Educational Resources

My GAI Study Partner for ODEs is a scaffolded sequence of learning activities designed to support students in an Ordinary Differential Equations (ODEs) course by integrating the use of Generative AI tools—specifically Copilot, a platform accessible to all CUNY students and faculty. The activities are rooted in experiential learning, flipped classroom strategies, and self-directed learning principles. The sequence begins with two preparatory activities that introduce students to the ethical use and foundational concepts of Generative AI, fostering digital literacy and critical reflection. These are followed by a series of main activities—initially structured (Activity 3) and later more flexible …

Outcome For The Case (11,10; 1), Waleed Khalid Jaber, Niran Sabah Jasim

Baghdad Science Journal

Through this work R is a commutative ring with 1, ℱ is a free R-module and 𝒟_𝒾 is the divided power algebra of degree 𝒾. A partition of length ℓ(λ) = n is a sequence ( λ ) = (λ₁, λ₂, …, λ_n) of non-negative integers in non-increasing order λ_1≥λ₂ ≥ … ≥ λn > 0. The weight of a partition λ is |λ| =λ ₁ + λ₂ + … + λ_n. A relative sequence is a pair ( λ,μ ) of sequences such that μ ≤ …

On (J - Δ) Semi Homogeneous Systems Of Differential Equations, Aya H. Hasan, Bassam Jabbar Al-Asadi

Baghdad Science Journal

The concept of homogeneity in differential equations can be generalized to systems of differential equations as shown in this work. The classification of three-dimensional differential equation systems is presented based on the definition of the Jacobean matrix and its determinant, where two systems of the homogeneous system are defined, called the J-semi-homogeneous system and the other δ-semi-homogeneous system, where the first definition is based on the Jacobian matrix, while the second is based on the determinant of the Jacobite matrix. Examples are given for both definitions, and the relationship between the two definitions will be studied. In addition to finding …

Analysis Of Prey, Predator And Top Predator Model Involving Various Functional Responses, Divya B., K. Kavitha

Baghdad Science Journal

This research proposes a mathematical model to investigate the dynamical behavior of the system of three species, namely prey, predator and top predator. The feeding behavior of each predator serves as a functional response. The interaction between the species is carried out by a functional response. Crowley Martin functional response is incorporated between prey and predator while Holling type III functional response occurs between predator and top predator. The existence of positivity and boundedness of the system have been examined. The equilibrium points of the system are determined. The system has been linearized by applying the Jacobian matrix. The main …

New Approximating Results By Weak Convergence Of Forked Sequences, Bareq Baqi Salman, Salwa Salman Abed

Baghdad Science Journal

The modular function spaces are natural generalization of spaces like Lebesgue space, Orlicz space, Lorentz p-space, Orlicz--Lorentz space, Musielak--Orlicz space, et al. The function modulars lack basic and flexible properties that norm functions have, as they are functional lacks homogeneity and subadditivity and, therefore, it might be surprising to use techniques involving asymptotic centers, normal structure and uniform convexity to obtain fixed point theorems. The purpose of this paper is to give a new accelerated iterative algorithm for multi valued\single valued mappings in modular function spaces and to prove some results about their convergence (strong or weak) to a fixed …

Hopf And Zero-Hopf Bifurcation Of The Four-Dimensional Lotka-Volterra Systems, Sirwan A. Mustafa, Niazy H. Hussen

Baghdad Science Journal

In this work, the four-dimensional Lotka-Volterra model (4DLV) involving four species in a constant environment is considered. The objective of this investigation is to study the local bifurcations occurring in the system. This system has at most sixteen possible equilibrium points. One of the equilibrium points is considered in order to investigate the periodic solutions that bifurcate from the Hopf and the zero-Hopf equilibrium points, respectively. It has been proven that, five families of sufficient conditions exist on the parameters of the system in which the Jacobian matrix at equilibrium point has a pair of purely imaginary ± iω …

Sdg 4.1.1 Minimum Proficiency Levels: Definition And Blueprint For Assessment [Presentation], Colin Watson, Ursula Schwantner

Monitoring Learning

A critical element for aligning assessments to the UIS eligibility criteria is mapunderstanding minimum proficiency levels (MPLs) in reading and mathematics. The Global Education Monitoring (GEM) Centre, in collaboration with the UIS, has defined clear MPL benchmarks and developed a blueprint for assessment for the 3 educational stages under SDG 4.1.1. This presentation shared the definition and blueprint with key stakeholders at the 11th meeting of the Global Alliance to Monitor Learning in Paris from 25-26 February 2025, to ensure a shared understanding of the criteria needed for meaningful global reporting.

The Efficacy Of Utilizing Artificial Intelligence Techniques In Developing Critical Thinking In Mathematics Among Secondary School Students And Their Attitudes Toward It, Mohammad A. Tashtoush, Aida B. Qasimi, Nawal H. Shirawia, Lubna A. Hussein

Iraqi Journal for Computer Science and Mathematics

The aim of this study is to investigate the efficacy of Artificial Intelligence (AI) techniques and programs in developing Critical Thinking Skills (CTSs) in mathematics among secondary school students, as well as their attitudes towards it. This study employed an experimental methodology, which was applied to a sample of 91 students. A critical thinking test and a scale to measure students' Attitudes Towards Mathematics (ATM) were also utilized. This study revealed significant improvements in the mean scores of critical thinking skills among secondary students who were exposed to Artificial Intelligence Techniques (AITs), particularly in deduction, interpretation, inference, and evaluation. Additionally, …

The Effect Of Pdeode And Pq4r Strategies On The Development Of Reflective Thinking And Self-Efficacy In Mathematics Among Ninth-Grade Female Students In Palestine, Ayman Mahmoud Alashqar

International Journal for Research in Education

This study investigates the effect of PDEODE and PQ4R strategies on the development of reflective thinking and self-efficacy in mathematics among ninth grade female students in Palestine. PDEODE and PQ4R are two educational strategies based on constructivist theory, each consisting of six sequential steps; the steps of the PDEODE strategy are: Prediction, Discuss, Explain, Observe, Discuss, Explain, while the steps of the PQ4R strategy are: Preview, Question, Read, Reflect, Recite, Review. The experimental approach was used in a quasi-experimental design based on the application of pre-post measurement. The sample of the study consisted of (96) ninth grade students. It was …

Math Is _______: A Study On Prospective Teachers' Perceptions Of Math And Teaching Math, Kayla Mead, Katherine Baker

Journal of Humanistic Mathematics

In this project, we examined one cohort of twenty-eight college students and their perceptions of mathematics at the beginning and end of a semester-long mathematics content course for K-8 prospective teachers (PTs). More specifically, our study explored PTs’ perceptions of what mathematics is and what mathematics teaching is, and how and why those perceptions might change over the semester-long mathematics course. PTs’ perceptions were captured through open-ended surveys and follow-up interviews. Our intention was to better understand the reasonings for changes in perceptions during the course to support teacher educators in their work of preparing prospective teachers.

A New Algorithm For Finding The Roots Of Nonlinear Algebraic Equations, Ahmad Yousef Alrazzo, Nasr Al Din Ide, Mohammad Assaad

Baghdad Science Journal

In this paper, the algorithm (Stochastic Gradient Descent) SGD, which is one of the most famous optimization algorithms, was hybridized with genetic algorithms in finding the roots of non-linear equations, which is one of the most important mathematical problems due to its application in all sciences. Genetic algorithms are used here to find the optimal primary root of SGD algorithm and its application in reducing the studied objective function. Some famous algorithms need initial point to reach the solution in terms of stability. The proposed algorithm is tested on several standard functions and the results are compared with the famous …