Digital Commons Network^™

Some Contributions To Free Probability And Random Matrices., Sukrit Chakraborty Dr.

Doctoral Theses

No abstract provided.

Supporting Teaching And Learning Reform In College Mathematics: Finding Value In Communities Of Practice, Kelly Gomez Johnson, Paula M. Jakopovic, Christine Von Renesse

Teacher Education Faculty Publications

Improving college STEM (science, technology, engineering, mathematics) student learning outcomes is an ongoing area of focus in Institutions of Higher Education (IHE). This reform includes challenging, changing, and adapting both teaching practices and the learning environment. Communities of practice (CoPs) can support faculty in making these shifts; however, creating large-scale instructional changes in STEM education requires a more careful look at the existing systems and structures in place. In this paper, we investigate a network of regional CoPs composed mainly of mathematics faculty from IHE focused on teaching with inquiry methods. Understanding what faculty need and value to support their …

Building Number Sense With Subitizing, Lindsey Herlehy

Publications & Research

Dice, fingers, tallies, and ten frames! Proficient mathematicians are problem solvers who work with quantities in flexible ways. Subitizing is a practice that builds number sense and is key to becoming a fluent mathematician at any grade level. Quick and easy games and activities will be shared.

Improving Teaching Mathematics Using Communicative Competence In Primary Education, Jasur Amirddinovich Mardonkulov Researcher

Central Asian Journal of Education

Human society is unthinkable outside of communication. Communication is a necessary condition for the existence of people, without which it is impossible to fully form not only individual mental functions, processes and properties of a person, but also the personality as a whole. The reality and necessity of communication is determined by joint activity: in order to live, people are forced to interact. Always an active person communicates, whose activities intersect with the activities of other people. Communication allows you to organize social activities and enrich it with new connections and relationships between people.

Mathematics Teaching Assistants’ Community-Building Activities During Remote Instruction, T. Royce Olarte, Damaris Hernandez, Hannali Pajela, Sarah A. Roberts

NERA Conference Proceedings 2021

The need to build community in mathematics learning spaces was exacerbated by the COVID-19 pandemic. This study examined the community-building efforts of mathematics TAs during a dynamically uncertain period and how they engaged in pandemic-sensemaking to make sense of and adapt their community-building efforts for remote instruction. We found that TAs engaged in various community-building activities through the synchronous and asynchronous interactions afforded by the design of the course (e.g., during sections, in office hours), and pandemic-sensemaking enabled them to better understand students’ challenges and adapt their efforts to attend to the challenges with building community.

Developing Mathematical Thinking In High Schoolers Through “Curricular Thinking Tasks”, Michaela Weispfennig

School of Education and Leadership Student Capstone Projects

A review of the literature and reflection on personal experience show a need to rethink the way we teach and learn mathematics. A traditional math class relies on direct instruction and emphasizes decontextualized procedures and algorithms. This type of instruction does not work well for the majority of students, nor does it prescribe to the goals of math education in our modern world. We don’t need “human computers'' like we did before the internet. Instead, the primary goal for most high school math students is to develop the mathematical thinking skills needed to tackle new problems. Inspired by Peter Liljedahl’s …

Developing A Deep Understanding Of Multiplication And A Growth Mindset In 5th Grade Students From Marginalized Groups, Rachael Johnson

School of Education and Leadership Student Capstone Projects

Traditionally mathematics has been taught with a focus of rote memorization of basic facts and procedures. Research has found that this often leaves students without the conceptual understanding behind procedures. This can prevent students from making the connections necessary to transfer their knowledge to other situations. It has also become clear that students from marginalized groups often score much lower on high stakes tests than their white counterparts. This project involved creating a multiplication unit that uses number talks, strategies from cognitively guided instruction as well as ideas on culturally relevant teaching. The goal of this project was for students …

Personalized Geometry Instruction: A Mixed Methods Action Research Study Implementing An Adaptive Web-Based Learning Environment To Support High School Students’ Geometry Problemsolving Skills, Catherine D. Jordan

Theses and Dissertations

The purpose of this action research study was to evaluate the implementation of an adaptive web-based learning environment to personalize geometry instruction and practice for high school students at a private school in North Carolina. This study was guided by the following three research questions: (1) How and to what extent does implementing personalized geometry instruction and practice through an adaptive web-based learning environment affect high school students’ knowledge of geometry? (2) How does using personalized geometry instruction and practice through an adaptive web-based learning environment affect students’ motivation to learn geometry as well as their mathematics self-efficacy, anxiety, and …

The Importance Of Math Fact Automaticity, Jessica Olson

School of Education and Leadership Student Capstone Projects

The retention of math facts is a critical step when it comes to solving mathematical equations. The website I designed for my project addresses this topic. It focuses on giving students, teachers and parents the research, tips and resources they need to be successful. Research shows that automaticity with math facts can lessen the academic load of students and also be a predictor of future math success. Using strategies such as interleaving, engaging with manipulatives and learning mnemonic devices has been shown to positively affect one’s recall of basic facts. However, drilling and mindless repetition has a much more negative …

Some Topics In Leavitt Path Algebras And Their Generalizations., Mohan R. Dr.

Doctoral Theses

The purpose of this section is to motivate the historical development of Leavitt algebras, Leavitt path algebras and their various generalizations and thus provide a context for this thesis. There are two historical threads which resulted in the definition of Leavitt path algebras. The first one is about the realization problem for von Neumann regular rings and the second one is about studying algebraic analogs of graph C ∗ -algebras. In what follows we briefly survey these threads and also introduce important concepts and terminology which will recur throughout.

Scaling Limits Of Some Random Interface Models., Biltu Dan Dr.

Doctoral Theses

In this thesis, we study some probabilistic models of random interfaces. Interfaces between different phases have been topic of considerable interest in statistical physics. These interfaces are described by a family of random variables, indexed by the ddimensional integer lattice, which are considered as a height configuration, namely they indicate the height of the interface above a reference hyperplane. The models are defined in terms of an energy function (Hamiltonian), which defines a Gibbs measure on the set of height configurations. More formally, letÏ• = {Ï•x}x∈Z dbe a collection of real numbers indexed by the d-dimensional integer lattice Z d. …

On The Inertia Conjecture And Its Generalizations., Soumyadip Das Dr.

Doctoral Theses

This thesis concerns problems related to the ramification behaviour of the branched Galois covers of smooth projective connected curves defined over an algebraically closed field of positive characteristic. Our first main problem is the Inertia Conjecture proposed by Abhyankar in 2001. We will show several new evidence for this conjecture. We also formulate a certain generalization of it which is our second problem, and we provide evidence for it. We give a brief overview of these problems in this introduction and reserve the details for Chapter 4.Let k be an algebraically closed field, and U be a smooth connected affine …

Expansion Of The Department Of Mathematics At Princeton University And The Founding Of The School Of Mathematics At The Institute For Advanced Study: 1900-1950, Andrew Beman-Cavallaro

Graduate Review

From 1900 to 1950 Princeton, New Jersey, hosted two of the most prestigious institutions and provided a location for the expansive mathematical investigations taking place just before, during, and immediately after the Second World War. Princeton University and the Institute for Advanced Study housed, fed, and provided workspaces for an array of Mathematicians uncovering new research methodologies (resulting in the defeat of both the Nazi Party and the Empire of Nippon), the foundation for modern experimental Mathematics, and expansions of Theoretical and Applied Physics.

Validation Of The Mathematics Motivation Questionnaire (Mmq) For Secondary School Students, Logan Fiorella, So Yoon Yoon, Kinnari Atit, Jason R. Power, Grace Panther, Sheryl Sorby, David H. Uttal, Norma Veurink

Michigan Tech Publications

Background: Motivation is critical for supporting persistence and achievement in science, technology, engineering, and mathematics (STEM) disciplines. In this study, we focus on the assessment of mathematics motivation among secondary school students. We provide validity and reliability evidence for the Mathematics Motivation Questionnaire (MMQ)—adapted from the Science Motivation Questionnaire designed for college students—using data from 2551 secondary students from seven states across the United States. Results: Exploratory and confirmatory factor analyses confirmed five latent factors of the MMQ indicated by 19 items: intrinsic value, self-regulation, self-efficacy, utility value, and test anxiety. The nonlinear SEM reliability coefficients of the five constructs …

Validation Of The Mathematics Motivation Questionnaire (Mmq) For Secondary School Students, Logan Fiorella, So Yoon Yoon, Kinnari Atit, Jason R. Power, Grace Panther, Sheryl Sorby, David H. Uttal, Norma Veurink

Department of Civil and Environmental Engineering: Faculty Publications

Background: Motivation is critical for supporting persistence and achievement in science, technology, engineering, and mathematics (STEM) disciplines. In this study, we focus on the assessment of mathematics motivation among secondary school students. We provide validity and reliability evidence for the Mathematics Motivation Questionnaire (MMQ)—adapted from the Science Motivation Questionnaire designed for college students—using data from 2551 secondary students from seven states across the United States. Results: Exploratory and confirmatory factor analyses confirmed five latent factors of the MMQ indicated by 19 items: intrinsic value, self-regulation, self-efficacy, utility value, and test anxiety. The nonlinear SEM reliability coefficients of the five constructs …

Commuting Isometries And Invariant Subspaces In Several Variables., Sankar T. R. Dr.

Doctoral Theses

A very general and fundamental problem in the theory of bounded linear operators on Hilbert spaces is to find invariants and representations of commuting families of isometries.In the case of single isometries this question has a complete and explicit answer: If V is an isometry on a Hilbert space â„‹, then there exists a Hilbert space Hu and a unitary operator U on â„‹u such that V on â„‹u and[ S ⊗ IW 0 0 U] ∈ B((l 2 (ℤ+) ⊗ W) ⊕ â„‹u),are unitarily equivalent, whereW = ker V∗ ,is the wandering subspace for V and S is the …

Maker Education In Mathematics, Jade Roy, Frank Oliveira, Celina Murray

Undergraduate Student Research Internships Conference

Over the past 4 months, undergraduate students participated in a variety of research-based activities under the supervision of several researchers. Activities included a literature review, professional development, thematic analysis, and so much more. All of these research-based activities were in the area of Education, particularly Maker Education in Mathematics.

Categorical Aspects Of Graphs, Jacob D. Ender

Undergraduate Student Research Internships Conference

In this article, we introduce a categorical characterization of directed and undirected graphs, and explore subcategories of reflexive and simple graphs. We show that there are a number of adjunctions between such subcategories, exploring varying combinations of graph types.

Spectral Graph Theory And Research, Nathan H. Kershaw, Lewis Glabush

Undergraduate Student Research Internships Conference

Our topic of study was Spectral Graph Theory. We studied the algebraic methods used to study the properties of graphs (networks) and became familiar with the applications of network analysis. We spent a significant amount of time studying the way virus’s spread on networks, with particular applications to Covid-19. We also investigated the relationship between graph spectra and structural properties.

Fostering Healthy Student-Teacher Relationships Through Mathematics: A Student's Perspective, Emily Catherine Beaulieu

Undergraduate Student Research Internships Conference

No abstract provided.

College Algebra Through Problem Solving (2021 Edition), Danielle Cifone, Karan Puri, Debra Maslanko, Ewa Stelmach

Open Educational Resources

This is a self-contained, open educational resource (OER) textbook for college algebra. Students can use the book to learn concepts and work in the book themselves. Instructors can adapt the book for use in any college algebra course to facilitate active learning through problem solving. Additional resources such as classroom assessments and online/printable homework is available from the authors.

Humanizing My Teaching, Ricela Feliciano-Semidei

Faculty Books & Book Chapters

Chapter 5 of the book entitled "Practices and Policies: Advocating for Students of Color in Mathematics".

For The Love Of Mathematical Research: A Conversation With Undergraduate Research Students, Mike Janssen

Faculty Work Comprehensive List

"One of my passions as a professor is creating opportunities for students to ask questions about mathematics."

Posting about students' perspectives on mathematics research from In All Things - an online journal for critical reflection on faith, culture, art, and every ordinary-yet-graced square inch of God’s creation.

https://inallthings.org/for-the-love-of-mathematical-research-a-conversation-with-undergraduate-research-students/

Game Based Intervention To Develop Early Childhood Mathematical Understanding And Decrease Gaps Related To Socioeconomic Status, Lydia Flynn

Boise State University Theses and Dissertations

Early mathematical understanding is important for later success in mathematics. Game based interventions can be a successful means by which to help young students to improve their mathematical understandings. The purpose of this study is to examine whether a math game that was to be played at home improved the mathematical understanding of kindergarten students. Kindergarten students, from rural Idaho, were assigned to a group that played math games (n = 15) or a control group that did not (n = 13). The intervention group was given a simple math game and instructed to play 20 times in a …

Pre-Service High School Mathematics Teachers’ Perceptions About Mathematics And Mathematics Teachers: A Metaphorical Approach, Yasemin Katranci, Busra Kiral, Diler Kedikli

University of South Florida (USF) M3 Publishing

This study aimed to examine the perceptions of pre-service high school mathematics teachers about the concepts of mathematics and mathematics teachers. Metaphors were used to reveal these perceptions. The study is descriptive. The study group was determined according to the convenient sampling method. In this scope, 46 pre-service high school mathematics teachers participated in the study. The data were obtained through the completion of the “Mathematics is like ..... because .....” and “Mathematics teacher is like ..... because .....” statements by the participants. In the analysis and interpretation of the data; i) naming, ii) elimination, iii) category, and iv) validity-reliability …

Examining The Use Of Culturally Relevant Pedagogy In Undergraduate Mathematics Learning Modules With Students Of Color, Thomas A. Mgonja

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In mathematics, Students of Color have persistently performed lower than their White counterparts, thus creating a need to explore instructional methods that could reduce performance disparities. This study investigated culturally relevant pedagogy (CRP) to understand how it might support students’ mathematics learning in undergraduate mathematics learning modules. The overarching research question focused on how CRP in undergraduate mathematics Learning Modules supported students’ mathematics learning. There were also two main questions that focused on participants’ evaluations of the CRP modules and how those evaluations were reported based on subgroups (Students of Color and White). The researcher employed a sequential explanatory mixed-methods …

Partial Representations For Ternary Matroids, Ebony Perez

Electronic Theses, Projects, and Dissertations

In combinatorics, a matroid is a discrete object that generalizes various notions of dependence that arise throughout mathematics. All of the information about some matroids can be encoded (or represented) by a matrix whose entries come from a particular field, while other matroids cannot be represented in this way. However, for any matroid, there exists a matrix, called a partial representation of the matroid, that encodes some of the information about the matroid. In fact, a given matroid usually has many different partial representations, each providing different pieces of information about the matroid. In this thesis, we investigate when a …

Efficient Estimation Of Integrated Volatility Functionals Under General Volatility Dynamics, Jia Li, Yunxiao Liu

Research Collection School Of Economics

We provide an asymptotic theory for the estimation of a general class of smooth nonlinear integrated volatility functionals. Such functionals are broadly useful for measuring financial risk and estimating economic models using high-frequency transaction data. The theory is valid under general volatility dynamics, which accommodates both Itô semimartingales (e.g., jump-diffusions) and long-memory processes (e.g., fractional Brownian motions). We establish the semiparametric efficiency bound under a nonstandard nonergodic setting with infill asymptotics, and show that the proposed estimator attains this efficiency bound. These results on efficient estimation are further extended to a setting with irregularly sampled data.

Contributions To The Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya

Department of Mathematics Facuty Scholarship and Creative Works

This issue showcases a compilation of papers on fluid mechanics (FM) education, covering different sub topics of the subject. The success of the first volume [1] prompted us to consider another follow-up special issue on the topic, which has also been very successful in garnering an impressive variety of submissions. As a classical branch of science, the beauty and complexity of fluid dynamics cannot be overemphasized. This is an extremely well-studied subject which has now become a significant component of several major scientific disciplines ranging from aerospace engineering, astrophysics, atmospheric science (including climate modeling), biological and biomedical science …

The Role Of Self-Efficacy And Academic Mindset On Middle School Math Achievement For At Promise Youth: An Explanatory Study, Michael Lockwood Mansfield

Dissertations

California’s accountability system has blended its focus on noncognitive factors of achievement as well as evidence of academic growth. School districts are becoming increasingly interested in developing noncognitive factors in their students to help increase student achievement. With the wide variety of mandates and responsibilities schools are shouldering, it will be important to continue developing methods to increase all school accountability metrics in relation with each other. This research aims to explore the relationship between noncognitive factors and mathematics achievement as measured by the Northwest Evaluation Association’s Measure of Academic Progress assessment (MAP). This study surveyed 8th graders throughout a …