Digital Commons Network^™

On Integrals Of Matrix Coefficients Associated To Spherical Models, Elad Daniel Zelingher

Yale Graduate School of Arts and Sciences Dissertations

We define a local ingredient of the Ichino-Ikeda conjecture for isometry groups, for representations arising as local components of irreducible automorphic cuspidal representations lying in generic packets, without assuming temperedness everywhere. The representations in consideration are parabolically induced from characters and a tempered representation.

Vertex Identification In Graphs, Yuya Kono

Dissertations

In recent decades, there has been increased interest in studying ways touniquely identify the vertices of a given graph. Two of best-known vertex identification methods are referred to as the metric dimension introduced by Slater and by Harary, and Melter in the1970s, and the partition dimension introduced by Chartrand in 2000. The first method deals with locating an ordered set of vertices in a connected graph G and uniquely identifying each vertex of G by means of the distance between this vertex and the vertices in the ordered set. The second method deals with partitioning the vertex set of a …

Open-Ended Problems: How Much Time Is Enough Time?, Kaitlyn Solymosi

Honors Projects

The purpose of this action research is to observe and analyze students’ responses to open-ended questions, examine student engagement in assessment, and to gauge a reasonable timetable of how long students are predicted to work through them. A great amount of research has been conducted regarding the benefits and impact of open-ended problems in K-12 classrooms, but very little research has focused on the proper amount of time that should be allotted for them. This action research aims to establish a general rule for determining the proper amount of time allotted for open-ended problems. Implications for mathematics teachers will be …

A New Metaphor: How Artificial Intelligence Links Legal Reasoning And Mathematical Thinking, Melissa E. Love Koenig, Colleen Mandell

Marquette Law Review

Artificial intelligence’s (AI’s) impact on the legal community expands exponentially each year. As AI advances, lawyers have more powerful tools to enhance their ability to research and analyze the law, as well as to draft contracts and other legal documents. Lawyers are already using tools powered by AI and are learning to shift their methodologies to take advantage of these enhancements. To continue to grow into their shifting role, lawyers should understand the relationship between AI, mathematics, and legal reasoning.

Parental Involvement - Investigating The Roles, Barriers, And Strategies Of Effective Parent-Teacher Relationships In Middle School Math, Praise-El K. Pelemo

Doctor of Education (Ed.D)

The purpose of this single-instrument qualitative case study was to investigate the roles, barriers, and strategies for effective parent-teacher relationships in middle school mathematics. The focus of this study was the accounts of three parents of middle school mathematics students in independent schools and three middle school math teachers in independent schools on their perception of roles, barriers, and strategies that increase or reduce building effective partnerships. Audio recorded semi-structured interviews were conducted to gather details about participants' lived experiences. The goal of the research was to gain knowledge on current parent, teacher, and school practices on parental involvement and …

Effects Of Actively Involving Students With Ieps In The Progress Monitoring Process, Kelly Adams

Master's Theses & Capstone Projects

Special education teachers are trying many ways to help students with IEPs achieve their goals. This action research study looks at one way educators might do that with the involvement of students with IEPs in the progress monitoring process, specifically students with math goals. Instead of having the progress monitoring process as something done to them, students with disabilities were encouraged to take an active role by goal setting, getting feedback, reflecting, and graphing their scores. The five fifth-grade students that this study followed showed signs of growth over the six weeks of this intervention. The findings of this action …

Motivation In Online Course Design: Action Research Using A Self-Determination Theory-Based Mathematics Unit To Improve Students’ Autonomy, Competence, And Relatedness, Emily Rose Shank

Theses and Dissertations

Strong mathematics achievement is lacking in the United States, with motivation waning especially among mathematics and online students. Online mathematics students, in particular, struggle with self-regulation and self-efficacy (Kim, 2012; Sun & Rueda, 2012). Ryan and Deci (2017), in their well-established and empirical self-determination theory, contended that satisfying the psychological needs of autonomy (involving self-regulation), competence (involving self-efficacy), and relatedness (involving a sense of belonging) creates a suitable environment for integrated extrinsic and intrinsic motivation to thrive. The purpose of this action research was to create and implement a self-determination theory-based online unit on factoring polynomials for mathematics students at …

Teaching Growth Mindset In A Secondary Mathematics Classroom, Katherine Sneider

School of Education and Leadership Student Capstone Projects

Carol Dweck’s research in fixed and growth mindsets has garnered attention in mathematics education, especially as the frustration of students of mathematics becomes more apparent with new or more difficult content. The literature review and subsequent project seeks to answer the question: How can teaching high school students about growth mindset affect their attitudes toward mathematics learning and academic achievement? Research demonstrates that students with a growth mindset perform better academically than students with a fixed mindset. While these mindsets may be more inherent in nature, students have the potential to develop a growth mindset through classroom learning and skill …

Supplementing Math Instruction In The Elementary Classroom With Cognitively Guided Instruction (Cgi), Wai Yang

School of Education and Leadership Student Capstone Projects

Education in the United States has long used the traditional written algorithm for math. In other countries around the world with high student achievement on international math assessments, different approaches to math instruction are taken. Cognitively guided instruction (CGI) in math is one of the alternative approaches to teaching math in American classrooms. Teachers may sometimes avoid implementing different math instruction approaches in their profession. This capstone sought to answer the research question, How can cognitively guided instruction (CGI) in math supplement current math in the elementary classroom? The result is a collection of nine lessons that address the research …

Mindset, Stereotype Threat, And The Fear Of Failure: Why Female Students Leave A Secondary High Honors Mathematics Pathway, Annabelle Merg

Theses and Dissertations

The disproportionate attrition of female students in STEM is well documented in higher education but less well understood at the secondary level. In a large, public high school in an affluent, highly educated city, the high honors mathematics pathway is the only math pathway that has not yet achieved gender parity, an implication for future educational and economic equity. Female students leave this pathway at significantly higher rates than male students, especially during and immediately after the first course. Through an explanatory, mixed methods approach, this study found that these female students are not less well prepared than their male …

Children Receiving A Nutrition And High-Quality Early Childhood Education Intervention Are Associated With Greater Math And Fluid Intelligence Scores: The Guatemala City Municipal Nurseries, Ana M. Palacios, Lisa A. Villanueva, Matthew B. Flynn, Erik Parker, Stephanie Dickinson, Helen W. Bland, Greg A. Reinhart

Health Policy & Community Health: Faculty Publications

Background: About 47% of children < 5 years of age are stunted in Guatemala. In this study, the investigators aimed to compare growth and cognitive outcomes between children in second grade that attended five Guatemala City Municipal Nurseries (GCMN) vs. same sex, grade, and age-matched children. Methods: A cross-sectional design nested in a retrospective cohort was implemented between 2015 and 2019. Children that attended the GCMN and matched controls completed a math test and validated receptive language and fluid intelligence tests. The primary caregivers completed a sociodemographic survey. General and generalized linear mixed effect models were used to compare children that attended the GCMN vs. controls. The models were adjusted by maternal education, sex, asset score, and other relevant covariates. Results: Children that attended the GCMN exhibited greater math and fluid intelligence scores relative to the controls in the adjusted models (ß = 6.48; 95% CI (2.35–10.61)) and (ß = 1.20; 95% CI (0.12–2.29)), respectively. Lower odds of stunting were significant for children who went to any early childcare institution (AOR = 0.28; 95% CI (0.09–0.89)). Conclusions: The importance of integrating nutrition and high-quality early childhood education interventions in cognitive and growth outcomes is highlighted in this study. The GCMN model may be a scalable model in similar low-resource settings.

Approximation Of Functions In Barron’S Space Using Sums Of Separable Functions., Indupama Herath

Student Research and Creative Activity Expo

We show that sums of separable functions achieve similar error bound as single layer neural networks for functions in Barron’s space.

Interactive Tools For Teaching Mathematical Proof, Garett Cunningham

Student Research and Creative Activity Expo

We present a custom-designed website for teaching mathematical proof using either LaTeX markup or proof assistants.

Connecting The “Real-World” To The Math Classroom: Implementing Professional Development For Mathematical Modeling, Rejoice Akapame

Northwest Journal of Teacher Education

This qualitative research study focused on the changes in classroom pedagogy and content of rural mathematics teachers who engaged in a year-long professional development project focused on mathematical modeling. During a 2-week summer institute, teachers solved mathematical modeling problems as learners and then went through an iterative design process of creating, testing and refining lessons for classroom implementation. The lessons were implemented during the academic year. Results of this study indicate that teachers developed a willingness to move from traditional lecture and replication as the main form of pedagogy. Instead they incorporated more group tasks, alternate assessments, and created their …

Exploration Of Piccirillo's Trick On Low Crossing Number Knots, Gabriel Adams

Honors Program: Senior Projects (Public)

Piccirillo recently discovered a process that can be applied to an unknotting number one knot to convert it into a different knot called a Piccirillo dual. Piccirillo duals have been shown to have the same n-trace and the same sliceness. However, exploration and knowledge of this process is limited. We were able to generate the Piccirillo duals for several low-crossing number knots. We offer the foundation for and explain how to follow the Piccirillo process and generate Piccirillo duals. This talk assumes little knowledge of knot theory and concisely gives newcomers a clear introduction to get started working with Piccirillo …

The Relationship Of Instructional Time On High School Students' Mathematical Achievement In The State Of New Jersey, Natalie Diaz

Seton Hall University Dissertations and Theses (ETDs)

This non-experimental quantitative study sought to analyze the relationship between instructional time and high school students' mathematical achievement as measured by the 2019 New Jersey Student Learning Assessment (NJSLA) for Algebra 1. In addition to determining to which extent the district factor groups (DFGs) affect the relationship between instructional time on the performance of high school students on the 2019 New Jersey Student Learning Assessment (NJSLA) for Algebra 1 when controlling for staff, student, and school variables. The 2018–2019 NJDOE Performance Report provided the variables used in this study. The unit of analysis was public high schools in New Jersey …

Mathematics From Scratch: Learning With Coding, Kimberly Beck, Jessica F. Shumway, Jody Clarke-Midura

Publications

Implementing successful cross-curricular lessons is challenging but possible. Participants in this session will learn about a partnership between Utah State University, Cache County School District, and Stanford University that has designed and implemented successful integrated mathematics-computer science lessons. Attendees will hear from researchers and in-service teachers on their experience with designing and carrying out the curriculum and will have an opportunity to view and interact with the computer programs that students used.

Data Analytics And Visualization Dsp 562, Harrison Dekker

Collection Development Reports and Documents

No abstract provided.

Advanced Topics In Machine Learning Dsp 566, Harrison Dekker

Collection Development Reports and Documents

No abstract provided.

Introduction To Statistical Computing Dsp 565, Harrison Dekker

Collection Development Reports and Documents

No abstract provided.

Mathematical Foundations For Data Science Ams/Dsp 563, Harrison Dekker

Collection Development Reports and Documents

No abstract provided.

Advanced Database Concepts, Cloud Computing And Big Data Dsp 567, Harrison Dekker

Collection Development Reports and Documents

No abstract provided.

Linear Nearest Neighbor Flocks With All Distinct Agents, Robert G. Lyons

Dissertations and Theses

This dissertation analyzes the global dynamics of 1-dimensional agent arrays with nearest neighbor linear couplings. The equations of motion are second order linear ODE's with constant coefficients. The novel part of this research is that the couplings are different for each agent. We allow the forces to depend on the relative position and relative velocity (damping terms) of the agents, and the coupling magnitudes differ for each agent. Further, we do not assume that the forces are "Newtonian'" (i.e., the force due to A on B equals minus the force of B on A) as this assumption does not apply …

A Non-Euclidean Story Or: How To Persist When Your Geometry Doesn’T, Rami Luisto

Journal of Humanistic Mathematics

Too little mathematics has been written in prose. Thus we prove here, via a fantasy novellette, that a locally L-bilipschitz mapping f : X → Y between uniformly Ahlfors q-regular, complete and locally compact path-metric spaces X and Y is an L-bilipschitz map when Y is simply connected. The motivation for such a result arises from studying the asymptotic values of BLD-mappings with an empty branch set.

As far as the author is aware, the result is new, even though it would not be hard for specialists in the field to prove. The proof is essentially a modest extension of …

Alice’S Adventures In Wonderland: Carroll’S Symbolic Attack On Mathematical Symbolism, Firdous Ahmad Mala

Journal of Humanistic Mathematics

In 2009, a literature scholar, Melanie Bayley, proposed that Lewis Carroll's famous books about Alice visiting the magical and illogical Wonderland were attempts to mock and critique the modern mathematics of the day. In this short paper, I aim to support Bayley's thesis and expound upon Carroll's artful use of symbolism to attack excessive use of symbolism in mathematics.

The Hamster Diaries, Pamela B. Pierce

Journal of Humanistic Mathematics

When the pandemic hits, the author acquires a hamster, who provides some humorous anecdotes and some much-needed inspiration.

Makers Do Math! Legitimizing Informal Mathematical Practices Within Making Contexts, Amber Simpson, Signe Kastberg

Journal of Humanistic Mathematics

In this paper, we argue that making activities within non-formal learning environments (e.g., museums, libraries) provide opportunities to engage youth in what we define as mathematical practices for making, everyday mathematical practices within the context of making activities. The mathematical practices identified from two non-formal school-based contexts highlighted three mathematical practices for making: informal measurement, spatial reasoning, and curiosity. These practices are identified in prior scholarship as being beneficial and foundational for the understanding of mathematical concepts. As educators and researchers turn to non-formal and informal contexts, with an eye toward understanding ways youth engage in the activity of making, …

University Mourns Mathematics Professor Emeritus Nick Pavel, Ohio University College Of Arts & Sciences

All Forum Articles

No abstract provided.

Evaluation Of The Availability And Utilization Status Of Texts In Core Subjects In Primary Schools’ Libraries, Valentine Joseph Owan, Daniel Clement Agurokpon, Abahcham V. Owan

Library Philosophy and Practice (e-journal)

The study evaluated primary texts' availability and utilisation status in core subjects (English Language, Mathematics, Social Studies and Basic Science) in primary schools’ libraries in Obubra Local Government Area of Cross River State. The researchers formulated six null hypotheses to guide the study. The study adopted the descriptive survey research design. The target population of this study comprised a total of 30,036 teachers and pupils, distributed across the 73 public primary schools. A proportionate stratified sampling technique was used to select 30% and 5% of the available teachers and pupils in each school, resulting in a sample of 270 respondents. …

A Systematic Review Of Research Syntheses For Students With Mathematics Learning Disabilities And Difficulties, Gena Nelson, Angela Crawford, Jessica Hunt

Early and Special Education Faculty Publications and Presentations

The purpose of this document is to provide readers with the coding protocol that authors used to code 36 research syntheses (including meta-analyses, evidence-based reviews, and quantitative systematic reviews) focused on mathematics interventions for students with learning disabilities (LD), mathematics learning disabilities (MLD), and mathematics difficulties (MD). The purpose of the systematic review of mathematics intervention syntheses was to identify patterns and gaps in content areas, instructional strategies, effect sizes, and definitions of LD, MLD, and MD. We searched the literature for research syntheses published between 2000 and 2020 and used rigorous inclusion criteria in our literature review process. We …