Digital Commons Network^™

Joint Equidistribution Of Maximal Flat Cylinders And Holonomies For Anosov Homogeneous Spaces, Elijah Fromm

Yale Graduate School of Arts and Sciences Dissertations

Let G be a connected semisimple real algebraic group and P < G be a minimal parabolic subgroup with Langlands decomposition P = MAN. Let Γ < G be a Zariski dense Anosov subgroup with respect to P. Since Γ is Anosov, the set of conjugacy classes of primitive elements of Γ is in one-to-one correspondence with the set of (positively oriented) maximal flat cylinders in Γ\G/M. We describe the joint equidistribution of maximal flat cylinders and their holonomies as their circumferences tend to infinity. This result can be viewed as the Anosov analogue of the joint equidistribution result in rank one by Margulis-Mohammadi-Oh.

Scattering For Schrödinger Operators In The Presence Of Anisotropic Potentials, Tal Malinovitch

Yale Graduate School of Arts and Sciences Dissertations

One of the classical questions in the scattering theory of quantum particles is asymptotic completeness for short-range potentials. Short-range potentials are potentials that decay fast enough in all directions, and asymptotic completeness means, in this context, that we can decompose any state into two functions: an asymptotically free one (that behaves as though there was no potential present) and one that lays in the closure of the $L^2$-eigenfunctions of our Hamiltonian.In this thesis, based on two papers, we study the scattering properties of Schrödinger operators with potentials that have short-range decay in some, but not all, directions. For these operators, …

Limits Of Asymptotically Fuchsian Surfaces In A Closed Hyperbolic 3-Manifold, Fernando Al Assal

Yale Graduate School of Arts and Sciences Dissertations

Let $M$ be a closed hyperbolic 3-manifold. Let $\nu_{\Gr M}$ denote the probability volume (Haar) measure of the 2-plane Grassmann bundle $\Gr M$ of $M$ and let $\nu_T$ denote the area measure on $\Gr M$ of an immersed closed totally geodesic surface $T\se M$. We say a sequence of $\pi_1$-injective maps $f_i:S_i\to M$ of surfaces $S_i$ is \emph{asymptotically Fuchsian} if $f_i$ is $K_i$-quasifuchsian with $K_i\to 1$ as $i\to \infty$. We show that the set of weak-* limits of the probability area measures induced on $\Gr M$ by asymptotically Fuchsian minimal or pleated maps $f_i:S_i\to M$ of closed connected surfaces $S_i$ …

Perspective Differentiation With Diffusion Geometry, Benjamin Ekeroth

Yale Graduate School of Arts and Sciences Dissertations

Extracting the common information amongst a collection of datasets has become a majortopic of research called Sensor Fusion. Instead, we explore a collection of methods for extracting the information which differentiates between collections of datasets. We focus on methods for differentating the perspectives of datasets using diffusion operators. We formulate a minimax problem for optimizing the relative smoothness of functions between collections of graphs, and prove a minimax theorem for generalized eigenvalues to compute the solution. We further investigate methods for extracting control variables from multidimensional time-series, motivated by a differentiation problem in stroke detection.

Using Visual Imagery To Develop Multiplication Fact Strategies, Gina Kling

Dissertations

The learning of basic facts, or the sums and products of numbers 0–10 and their related differences and quotients, has always been a high priority for elementary school teachers. While memorization of basic facts has been a hallmark of elementary school, current recommendations focus on a more nuanced development of fluency with these facts. Fluency is characterized by the ability to demonstrate flexibility, accuracy, efficiency, and appropriate strategy use. Despite recommendations to focus on strategy use, there is insufficient information on instructional approaches that are effective for developing strategies, particularly for multiplication facts. Using visual imagery with dot patterns has …

The Modern High School Learning Environment: A Study Of Differentiated Learning And Flexible Grouping Strategies, Aaron Wilken

Master's Theses & Capstone Projects

This research project explores the effects of differentiated learning and flexible grouping on students’ learning in high school mathematics. Specifically, the research demonstrates the effects of flexible grouping in a team-taught environment on students’ engagement and achievement. In this research study, students from two sections of team-taught Algebra 1 were used to determine changes in levels of engagement and achievement. First, students were grouped into a remediation group or an independent learning group based on their level of proficiency on an initial formative assessment. Students received instruction, practiced the necessary skills, and were assessed to conclude the study. Additionally, the …

Implementing A Multi-Tiered System Of Support For Mathematics Instruction In Preschool Classrooms, Jennifer Petty

Master's Theses & Capstone Projects

Early intervention in preschool mathematics instruction is key. Studies have shown that the development of early math skills may be the single most important factor for determining future school success. This school improvement plan lays out the necessary steps that the Sioux City Community School District (SCCSD) can follow to implement a Multi-tiered System of Support (MTSS) for the Preschool Initiative classrooms that are a part of the Iowa Statewide Voluntary Preschool Program for Four-Year-Olds. This plan includes providing teachers who are a part of the Sioux City Community School District’s early childhood special education classrooms and the community partner …

Play Based Learning A School Improvement Plan, Kalee Chamberlin

Master's Theses & Capstone Projects

Play-based learning is a topic that is often discussed at the early childhood level. Research has shown that play-based learning can lead to success within the classroom in the areas of social-emotional skills, literacy, and mathematics. Research conducted within the Muscatine Community School District suggests that children could benefit from additional time in play-based learning opportunities. This school improvement plan describes in detail the process needed to implement a plan to increase the amount of time spent in play-based learning opportunities within the preschool classroom.

Impacts Of Technology-Enhanced Dual Enrollment Mathematics Course On Rural High School Students’ Intentions Of Going To College, Nicolae Bordieanu

Theses and Dissertations

The purpose of this concurrent mixed methods action research study was to investigate the impact of new technology-enhanced Dual Enrollment (DE) math courses on students’ perception of college courses, the influence the technology-enhanced DE had on students’ intention of going to college, and the students' perception of the technology-enhanced DE math course. Examining student experiences in a technology-enhanced DE course informed all stakeholders as to what degree DE influenced students’ perception of college. The DE experience influenced students' postsecondary plans. The innovation of this action research study was the technology-enhanced DE math course. Software used to practice computational skills, conduct …

The Effects Of Problem-Based Learning On Mathematics Motivation In A Flipped Classroom Instructional Environment, Joshua David Harrison

Theses and Dissertations

In response to decreasing motivation in high school math classrooms, teachers are transforming classrooms with various instructional techniques. Traditional math instruction relies on direct instruction and memorization of content, processes, and skills. Teachers are transitioning to more constructivist student-led approaches. Utilizing multiple instructional designs provides teachers more opportunities to access the major components of the ARCS Model: attention, relevance, confidence, and satisfaction.

Therefore, the purpose of this action research was examining problem-based learning in a flipped classroom instructional environment and measuring its effect on students’ motivation and achievement in Algebra 2. The study addressed the following research questions: 1) What …

Examining The Impact Of Teachers’ Attitudes On College Students’ Attitudes In A Mathematics Classroom, Isiaka Busari, Adeola F. Oladeji, Tolulope O. Sulaimon

Science, Technology, Engineering, and Mathematics (STEM) Education Faculty Publications

This paper discusses the relationship between teachers' attitudes and students' attitudes toward mathematics in the classroom. Through a review of more than twenty relevant pieces of literature, the paper analyzes the impact of teachers' attitudes on students' achievement, performance, confidence, and motivation in mathematics. The study concludes that positive attitudes displayed by teachers can enhance students' positive feelings toward mathematics and increase their engagement in the subject. On the other hand, negative attitudes displayed by teachers can hinder students' motivation and engagement in mathematics. The paper suggests that teacher training programs should prioritize the development of positive attitudes toward mathematics …

Using Augmented Reality For Geometry Learning: Indonesian Elementary School Teachers' Experiences, Asep Nuryadin, Karlimah Karlimah, Dindin Abdul Muiz Lidinillah, Ika Fitri Apriani, Ikairn Rachmawati Putri, Lilis Susilawati, Ginna Islamiati, Dede Nurhidayah

Jurnal Pendidikan Sains

This study aims to discover Indonesian elementary school teachers' experiences (n = 257) of using Augmented Reality (AR) for learning, especially related to one of the topics in mathematics learning, namely, geometry. AR is considered to be an alternative instructional media that can be utilized for teaching geometry, including the topic of three-dimensional shapes. A questionnaire consisting of both close-ended and open-ended questions was used to collect data in this study. This study has successfully revealed teachers' use of digital instructional media during the COVID-19 pandemic, their familiarity with AR, frequency of AR use for geometry learning, and challenges in …

Euler's Anticipations, Christopher Goff, Erik Tou

Euleriana

Welcome to Volume 3 of Euleriana. This issue highlights occasions where Euler's work anticipated future results from other others, sometimes by decades or even centuries!

Ops Bus Scheduling: A Heuristic Approach To A Three-Tier Multi-Depot Vehicle Routing Problem With Inter-Depot Routes, Jordan Sahs, Brad Tuttle

Mathematics Theses, Dissertations, Research and Student Creative Activity

Omaha Public Schools (OPS) currently uses a Two-Tier Bus Transportation System and is investigating whether switching to a Three-Tier Bus Transportation System would be cost effective by reducing the number of buses and bus drivers OPS uses. This project aims to develop an algorithm that would allow OPS to test whether a Three-Tier system is more cost effective. The “Bus Scheduling Project” is composed of two different software components: a geographical analyzer and a heuristic bus route generator.

Using Game Theory To Model Tripolar Deterrence And Escalation Dynamics, Grace Farson

Honors Program: Senior Projects (Public)

The study investigated how game theory can been utilized to model multipolar escalation dynamics between Russia, China, and the United States. In addition, the study focused on analyzing various parameters that affected potential conflict outcomes to further new deterrence thought in a tripolar environment.

A preliminary game theoretic model was created to model and analyze escalation dynamics. The model was built upon framework presented by Zagare and Kilgour in their work ‘Perfect Deterrence’. The model is based on assumptions and rules set prior to game play. The model was then analyzed based upon these assumptions using a form of mathematical …

Moving From Theory To Practice: Examining Teaching Mathematics For Social Justice In An Elementary School Classroom, Krystal Giles

Electronic Theses and Dissertations

Teaching mathematics for social justice is a distinctive approach to mathematics education that seeks to have students use mathematics to navigate their identities, understand their lived experiences, examine inequities, and become agents of change. Current research provides a rich explanation of what teaching mathematics for social justice entails. Still, there is a need for research that studies how to move from theory to practice. The purpose of this research study is to examine the experience of teaching mathematics for social justice within my fifth-grade mathematics classroom for myself and my students, analyze the extent to which students’ ethnic and academic …

Generations Of Reason: A Family’S Search For Meaning In Post-Newtonian England (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: Generations of Reason: A Family's Search for Meaning in Post-Newtonian England by Joan L. Richards. New Haven, CT: Yale University Press, 2021. 456 pp. ISBN: 9780300255492.

Approach To Problem Solving And Use Of Intuition By Engineering Technology Students, Meher R. Taleyarkhan, Anne M. Lucietto, Natalie L. F. Hobson, Therese M. Azevedo

Journal of Global Education and Research

Engineering technology students often forgo a methodical approach of solving or answering questions on assignments or exams in favor of an intuition-based approach, emphasizing educated guessing (Broberg et al., 2008). Faculty observations have noted these student solutions often provide explanations, usually sans calculations, to support answers the students believe to be reasonable when in reality deviated from the correct answer. An extensive study was developed to assess several distinctions between student intuition and use of cognition in problem solving, as related to a generalized student population. The study was comprised of a survey and interview. The survey utilized two instruments, …

Gömböc The Great, Indigo M. Strickert, Lori E. Bradford

The Transdisciplinary STEAM+ Journal

A sonnet written about the mathematics behind the self-righting shape of some tortoise shells.

Creative Learning With Music And Mathematics: Reflections On Interdisciplinary Collaborations, Graham Johnson, Alesia M. Moldavan

The Transdisciplinary STEAM+ Journal

Culturally responsive content, accessible and inclusive tools, and meaningful interdisciplinary tasks can aid in developing equitable and creative learning environments. Music and mathematics are ideal disciplines for interdisciplinary creative learning. In this article, we reflect on our experiences engaging in interdisciplinary music and mathematics tasks with preservice teachers. In particular, we highlight specific efforts taken to design and implement a creative music and mathematics workshop for use in a mathematics methods course. Guided by these experiences, we offer examples of tools and practices that have helped preservice teachers collaborate, engage in inquiry, improvise, develop empathy, and take intellectual and social …

Impacting African American Student Achievement In The Middle School Stem Classroom By Teaching Mathematics Through Arts Integration And Design Thinking, Robert Lippert, Tjuannia R. Seals

Dissertations

Middle school is a transitional period in which many students experience content-specific teachers, travel between classrooms, and explore extracurricular activity options for the first time. Historically, African American middle school students have not fared well in Science, Technology, Engineering, and Mathematics (STEM) on standardized assessments, performing significantly below their Caucasian counterparts in mathematics and science. From the beginning of their academic careers, a lack of access to quality teachers, excessive use of direct instruction strategies, and a lack of resources in their school communities, contribute to their overall apathy towards the subject matter and factor into their underperformance. As a …

The Policy And Practice Of Mathematics Mastery: The Effects Of Neoliberalism And Neoconservatism On Curriculum Reform., N Pratt, J Alderton

Plymouth Institute of Education

This paper explores how the twin processes of neoliberalism and neoconservatism work together on, and through, curricula and their associated pedagogies. It bridges the gap between policy and classroom practice, focusing on the particular example of the school subject of mathematics and the notion of mastery, operationalised in the English education system as Teaching for Mastery (TfM). From this context it develops a theoretical argument using Dean’s analytics of government as part of a broader Foucauldian frame, to analyse how TfM is constructed as a particular policy truth. It then shifts the analysis from a wide, social one to the …

A Collection Of Calculus Lesson Plans: Deriving The 'Why' Behind Derivatives, Kasey Brabec

Honors Program: Senior Projects (Public)

The traditional mathematics classroom is led with a focus on procedural understanding, with deep conceptual understanding considered to be unimportant or too difficult to teach within the allotted time. Both levels of understanding are important mathematical competencies, as it is rare for either of them to function well without accessibility to the other. The disparity between conceptual understanding and procedural understanding in the mathematics classroom is no larger than in courses like Calculus. This project is a collection of fifteen lesson plans constructed with an emphasis on conceptual understanding and the connectivity of Calculus. Each lesson plan’s overview contains the …

The Importance Of Early Number Concepts For Learning Mathematics In Deaf And Hard Of Hearing Children, Clifton Langdon, Christopher Kurz, Marie Coppola

Perspectives on Early Childhood Psychology and Education

This chapter discusses important background knowledge and research findings from a variety of disciplines that inform best practices for supporting optimal mathematical achievement in all children. First, discussion will begin with the importance of early numeracy for later academic outcomes, and why prioritization of instruction time and early intervention are needed to increase the likelihood of a strong foundation in numeracy. Second, a brief overview of numeracy development milestones will provide a basis for discussion of our central thesis: language experiences can impact numerical cognition, which then have a significant impact on academic outcomes. Third, given the importance of numeracy …

Mathematics Tracking: Policy Brief, Melissa P. Donham

Journal of Multicultural Affairs

Tracking is a long-standing practice in schools. Students are often placed in tracks beginning in upper elementary or middle school. The tracks in which students are placed in earlier grades set them up for the mathematics courses they are able to take in high school. The number of mathematics tracks for students can differ from school to school, but the policy of having mathematics tracks is common throughout schools in the United States. This policy brief will discuss the arguments for and against mathematics tracking policies, implications for educators and policymakers, and future directions.

Sources Of Mathematics Learning Disabilities For Middle School Classes From The Point Of View Of Supervisors And Teachers And Their Suggestions For Addressing Them, Eidah M. Alruwaili Phd

International Journal for Research in Education

The study aimed to identify the sources of mathematics learning Disabilities for middle school classes from the point of view of supervisors and teachers and their suggestions to address them. The study sample consisted of 38 male and female supervisors and 151 teachers for the mathematics course who were chosen by the available random method during the first semester of the academic year 2021 / 2022. To achieve the objectives of the study, a tool was prepared that consisted of four subscales (36 items), namely the student, the teacher, the textbook, and the classroom environment. The results showed that the …

The Difference In Geometry Achievement Between Students Who Utilize Lfm Strategies And Those Who Do Not: A Nonequivalent Control-Group Pretest/Posttest Study, Amanda Nicol

Doctoral Dissertations and Projects

The purpose of this quantitative, quasi-experimental nonequivalent control-group pretest/posttest study was to identify whether there is a difference in Geometry achievement between students who utilize Learning for Mastery (LFM) strategies compared to those who do not at the high school level. This study provided insight into instructional and assessment strategies that may increase student achievement, understanding, and retention. Seventy-three high school mathematics students enrolled in Geometry courses, grades nine through twelve, from a suburban high school in Northwestern New Jersey were assessed in this study. Students were given a pretest, participated in daily classwork and instructional strategies for ten weeks, …

The Mathematics Of The Harp: Modeling The Classical Instrument And Designing Futuristic Ones, Cristina Carr, Daniel Chioffi, Maya Glenn, Stefan O. Nita, Vlad N. Nita, Bogdan G. Nita

Journal of Humanistic Mathematics

We analyze and model the neck of the classical harp based on the length of the strings, their tension and density. We then use the results to design new and innovative harp shapes by adjusting the parameters of the model.

Cache Code Math: Mathematics Lesson Plans: Fractions, Kimberly Beck, Jessica F. Shumway, Aubrey Rogowski, Umar Shehzad, Jody Clarke-Midura, Mimi Recker

Instructional resources

This document entails three 5^th grade mathematics lesson plans. The lessons are intended to be implemented in conjunction with the computer lab activities found in "Cache Code Math: Fractions, Functions, & For-Loops." The mathematics focus of these lessons is multiplying fractions, which is paired with the computer coding concepts of functions and for-loops.

3-D Packing In Container Using Teaching Learning Based Optimization Algorithm, Linda Fitriyani, Larissa Alva Zerinda, Asri Bekti Pratiwi, Edi Winarko

Baghdad Science Journal

The paper aims to propose Teaching Learning based Optimization (TLBO) algorithm to solve 3-D packing problem in containers. The objective which can be presented in a mathematical model is optimizing the space usage in a container. Besides the interaction effect between students and teacher, this algorithm also observes the learning process between students in the classroom which does not need any control parameters. Thus, TLBO provides the teachers phase and students phase as its main updating process to find the best solution. More precisely, to validate the algorithm effectiveness, it was implemented in three sample cases. There was small data …