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Word Problem Wednesday, Elizabeth Ackerson

School of Education and Leadership Student Capstone Projects

My research question for my capstone project is: How does incorporating real-world word problems into weekly math curriculum in middle school affect students' learning, engagement, and understanding? I have created a math word problem curriculum, “Word Problem Wednesday”, to be used in my own math classroom to create real-world learning opportunities through problem-solving. I teach 5th-grade math, and I have noticed a lack of understanding of word problems related to problem-solving in the classroom. The curriculum I have developed is based on the need for a curriculum where word problems are purposefully incorporated weekly with meaning while creating understanding. Every …

Cognitively Guided Instruction Strategies For Strengthening Fifth-Grade Students Understanding Of Fraction Concepts, Hao Li

School of Education and Leadership Student Capstone Projects

An area in mathematics critical for building mathematical knowledge and reasoning is developing children's foundational knowledge of fractions. Understanding fractions is also a building block for developing students' algebraic reasoning and sense-making (NMAP, 2008;) It is very common to see in fifth-grade math classroom there are students who think fraction concepts and procedures seem to have no link to one another and for whom meaning-making in fractions is a challenge (Pitsolantis & Osana, 2013). Therefore, how to design math activities that will increase fifth-grade students' understanding of fraction concepts emerged as research question for this capstone project. History of learning …

Developing Motivation Of Adolescent Mathematics Students Through Instructional Choice, Todd K. Hunter

Capstone Projects and Master's Theses

Maintaining student motivation in mathematics increases the likelihood of long-term academic success. A key component to building motivation is having perceived control over a task. Students who maintain perceived control exhibit greater task engagement, motivation, and exhibit lower levels of stress and anxiety in that task (Bandura, 1989; Schunk, 2012; Skinner, 1990). This six-week study investigated the relationship between student choice and motivation in mathematics instruction, by affording students an individual choice of their instructor in their mathematics course. A quasi-experimental pretest-posttest two group design was implemented using a sample of Integrated Mathematics II high school students. Student motivation to …

Quantum Symmetries In Noncommutative Geometry., Suvrajit Bhattacharjee Dr.

Doctoral Theses

No abstract provided.

Quantum Markov Maps: Structureand Asymptotics., Vijaya Kumar U. Dr.

Doctoral Theses

No abstract provided.

Essays In Social Choice Theory., Dipjyoti Majumdar Dr.

Doctoral Theses

The purpose of this thesis is to explore some issues in social choice theory and decision theory. Social choice theory provides the theoretical foundations for the field of public choice and welfare economics. It tries to bring together normative aspects like perspective value judgements and positive aspects, like strategic con- siderations. The second feature which is our focus, is closely related to the problem of providing appropriate incentives to agents, an issue of prime importance in eco- nomics.Consider for example, a set of agents who must elect one among a set of can- didates. These candidates may be physical agents …

Examining Teachers' Use Of Adaptive Diagnostic Assessment To Improve Mathematics Teaching And Learning, Dalal H. Alfageh

Graduate Research Theses & Dissertations

This qualitative case study examined teachers’ perceptions and use of adaptive diagnostic assessment for improving teaching and learning of elementary level mathematics. Specifically, this case study was conducted at some of the leading primary schools in a Midwestern school district. TPACK theory was used as the theoretical framework for this case study to provide an understanding of how the teaching and learning of mathematics occurs in the classroom and the changes that occur due to the implementation of adaptive diagnostic assessments. A survey, individual interviews, a focus group, and journal reflections were used for data collection. The findings of this …

Zn Orbifolds Of Vertex Operator Algebras, Daniel Graybill

Electronic Theses and Dissertations

Given a vertex algebra V and a group of automorphisms of V, the invariant subalgebra V^G is called an orbifold of V. This construction appeared first in physics and was also fundamental to the construction of the Moonshine module in the work of Borcherds. It is expected that nice properties of V such as C2-cofiniteness and rationality will be inherited by V^G if G is a finite group. It is also expected that under reasonable hypotheses, if V is strongly finitely generated and G is reductive, V^G will also be strongly finitely generated. This is an analogue …

Understanding The Latinx Student Experience In A First-Year, Non-Remedial, Terminal College Math Course: A Convergent Mixed Methods Study, Ross Morgan

Electronic Theses and Dissertations

Working with Latinx students, a semester long study was conducted in the Spring of 2021 to better understand student’s perception of Culturally Responsive Teaching Practices (CRTP) at Mountain State University (MSU). The course sections selected are a part of a larger first year, non-remedial, terminal mathematics courses designed to provide students with smaller teacher to student ratios as well as opportunities to earn credit towards graduation. Instructors in two of the sections received special training around CRTP, while instructors in the other two sections did not receive this training. Findings demonstrate that simple adjustments to instructional practices had a statistically …

Exploring The Use Of Concrete Materials In Teaching And Learning Of Fractions In Grade Three: A Case Study Of A Public Primary School In Homa-Bay County, Kenya, Ouma Patrick Okoth

Theses & Dissertations

Learners who struggle with mathematics may have difficulties in comprehending the core ideas in mathematics. The concrete-representational-abstract (CRA) instructional sequence of teaching allows teachers to assist pupils in making sense of numbers and the mathematical concepts they represent. The use of concrete materials is critical in the teaching of mathematics to young children; they are the major instruments that early childhood teachers use to train young learners in their mathematics classes today. To encourage the use of concrete materials in mathematics instruction, this research investigates how mathematics teachers use concrete materials in the teaching and learning of mathematics, as well …

Exponential Random Graphs And A Generalization Of Parking Functions, Ryan Demuse

Electronic Theses and Dissertations

Random graphs are a powerful tool in the analysis of modern networks. Exponential random graph models provide a framework that allows one to encode desirable subgraph features directly into the probability measure. Using the theory of graph limits pioneered by Borgs et. al. as a foundation, we build upon the work of Chatterjee & Diaconis and Radin & Yin. We add complexity to the previously studied models by considering exponential random graph models with edge-weights coming from a generic distribution satisfying mild assumptions. In particular, we show that a large family of two-parameter, edge-weighted exponential random graphs display a phase …

Exploring How Teachers Deal With Students’ Errors In Mathematics: A Case Of A Secondary School In Siaya County, Kenya., John Robert Owala Ouko

Theses & Dissertations

Making errors in mathematics during learning by students is a common occurrence in our classrooms. Errors signal gaps in students’ understanding, competencies or knowledge that require to be addressed. Teachers employ a wide range of approaches to identify these gaps to provide interventions. The purpose of this study was to explore how teachers deal with students’ errors in mathematics during teaching and learning inside and outside the classroom in a secondary school in Siaya County, Kenya. Specifically, the study sought to understand how teachers identify, communicate and follow up on students’ errors and the challenges that teachers faced while following …

Mathematics Teachers’ Pedagogical Content Knowledge And Its Relation To Student Achievement, Michelle Emmalyn Peters-George

Walden Dissertations and Doctoral Studies

Students' performance in national assessments of mathematics at Grades 2, 4, and 6 has been a cause for concern in the Eastern Caribbean. Researchers have called for studies to focus on primary mathematics teachers' pedagogies rather than on laptops and curriculum; however, it is unclear how primary mathematics teachers' pedagogical knowledge influences these student’s achievement. The purpose of this quantitative study was to investigate the relationship between primary mathematics teachers' pedagogical content knowledge (mathematical knowledge for teaching, quality of instruction, and pedagogical qualifications) and student achievement, measured by national assessment scores in Grenada, controlling for teachers’ age, gender, and experience. …

District Scores And Demographics As Predictors Of State Mathematics Assessment Scores, Carlos Alexander Bocel

Walden Dissertations and Doctoral Studies

Prior research in mathematical assessments has indicated varying results of predictive variables and further research has been recommended to support students, parents, teachers, and school administration. The purpose of this research was to determine how well a student’s performance on a mathematics domain at the state level may be predicted based on student’s midyear and end of the year assessment scores, race, gender, and socioeconomic status. The constructivist theoretical foundation was reviewed because of the impact that this theory has on the assessments being researched. Archival records (n = 100) for eighth grade students were received from suburban South Florida …

The Effect Of Coding Classes On Mathematics Achievement Of Preschool Students, Ebru Hacer Erbilgin

Walden Dissertations and Doctoral Studies

The problem that inspired this study is that Turkish students’ mathematics rankings on global exams such as The Program for the International Students Assessment (PISA) and Trends in International Mathematics and Science Study (TIMMS) had been below the average for many years, a problem that may have rooted in children’s early experiences with mathematics. The purpose of this quantitative pretest posttest quasi-experimental control group study was to determine the effect of computer-programming classes with Code Studio on mathematics scores of preschool students. Siemens’s connectivism theory for the digital age formed the foundation for this research. A single research question regarding …

Teacher Understanding Of Instructional Strategies In Elementary Mathematics, Erica Boatwright Glover

Walden Dissertations and Doctoral Studies

Synergizing Elementary School (pseudonym) consistently experiences low state-required mathematics test scores in grades 3 and 4 below district and state proficiency rates in mathematics. The purpose of this qualitative case study was to investigate what instructional practices used by Grade 3 and Grade 4 teachers are, aligned or not aligned, with research-based planning, standards-based instruction, attention to conditions of learning, and professional responsibilities of teachers to support students’ achievement in mathematics. This study's conceptual framework was grounded in Robert Marzano's model of teaching effectiveness called the focus teacher evaluation model. Data for this case study were gathered from semi-structured interviews …

District Scores And Demographics As Predictors Of State Mathematics Assessment Scores, Carlos Alexander Bocel

Walden Dissertations and Doctoral Studies

Prior research in mathematical assessments has indicated varying results of predictive variables and further research has been recommended to support students, parents, teachers, and school administration. The purpose of this research was to determine how well a student’s performance on a mathematics domain at the state level may be predicted based on student’s midyear and end of the year assessment scores, race, gender, and socioeconomic status. The constructivist theoretical foundation was reviewed because of the impact that this theory has on the assessments being researched. Archival records (n = 100) for eighth grade students were received from suburban South Florida …

Characterizing Insecure Error Distributions For Various Rlwe Problems, Alec Lee Critten

UVM Patrick Leahy Honors College Senior Theses

This thesis studies how a chosen set of parameters for a Ring Learning With Errors (RLWE) cryptographic instance affects its ability to withstand a certain type of attack. We begin with some non-technical motivation on the specific qualities of RLWE that support its candidacy as a post-quantum cryptographic protocol, and why such protocols are necessary due to recent developments in computing. We then discuss some of the context for RLWE, providing some overview on important concepts in algebraic number theory that underpin the mathematical structure of RLWE. We define several variants of RLWE which researchers in this field have analyzed, …

An Exploratory Study Of Mathematics Anxiety In Caribbean Preservice Teachers, Franka Atwell-Chin Hong

Dissertations

The Problem

Correlational studies suggest that gender, attitudes to mathematics, mathematics performance, the number of college mathematics courses taken, and mathematics teacher efficacy beliefs may be related to mathematics anxiety among preservice teachers (Boyd et al., 2014; Gresham, 2018; Jaggernauth & Jameson-Charles, 2015). Exploratory studies of mathematics anxiety and teacher self-efficacy among elementary teachers exist in Trinidad and Tobago (Jaggernauth 2012; Jaggernauth & Jameson-Charles, 2015). However, the differences in samples, and weakness in methodology, may make it challenging to generalize the results to the preservice teacher population. In addition, no studies have found which variable or combination of variables is …

A Phenomenological Study Of The Lived Experiences Of African American Women In Undergraduate Stem Degree Programs, Vernon H. Smith

Theses and Dissertations

This applied dissertation was designed to provide a better understanding of the lived experiences of African American women in STEM undergraduate degree programs at a 4-year degree granting institution in the southernmost part of central Virginia. The central problem is that there is disparity between the number of African American women with STEM degrees and that of other races in the STEM job market. The existing literature has gaps in the research of African American women’s perception of undergraduate STEM programs. Further, the researcher posits there is a lack of consideration for diversity that is detrimental to the United States; …

Option Implied Volatility's Predictability On Monthly Stock Returns, Hung T. Dao

Senior Independent Study Theses

Since the trading of options is based on underlying stocks, it is reasonable to assume that information from the options market can be used to explain the returns in the stock market. Our independent study investigates the relationship between options implied volatility and stock returns. Previous studies have found significant results in using implied volatility in predicting stock returns. This paper provides a discussion of such studies, the theoretical framework for the research topic, and the Black-Scholes model, which is famous for its application in implied volatility calculation. Monthly returns of 20 large US firms are regressed against implied volatility …

Statistical And Machine Learning Approaches To Depressive Disorders Among Adults In The United States: From Factor Discovery To Prediction Evaluation, Minhwa Lee

Senior Independent Study Theses

According to the National Institutes of Mental Health (NIMH), depressive disorders (or major depression) are considered one of the most common and serious health risks in the United States. Our study focuses on extracting non-medical factors of depressive disorders diagnosis, such as overall health states, health risk behaviors, demography, and healthcare access, using the Behavioral Risk Factor Surveillance System (BRFSS) data set collected by the Centers for Disease Control and Prevention (CDC) in 2018.

We set the two objectives of our study about depressive disorders diagnosis in the United States as follows. First, we aim to utilize machine learning algorithms …

Remote Math Or Remotely Math? : A Qualitative Study Of The Challenges Of A Covid-19 Induced Transition To Ict-Based Teaching For High School Mathematics Teachers, David Hurst

Legacy Theses & Dissertations (2009 - 2024)

In the blink of an eye schools across the country closed their doors in March 2020 and teachers were forced to transition from face-to-face instruction within a brick-and-mortar setting to ICT-based remote teaching. Many high school mathematics teachers were accustomed to their students having devices as their schools had established 1:1 computing programs. Even so, not all teachers had fully embraced ICT enhanced instruction in their classrooms. Research has shown that the degree of ICT utilization in a classroom has a strong positive correlation with the comfort level of the teacher. The COVID-19 closures required teachers to incorporate ICT in …

Applying Cognitive Measures In Counterfactual Prediction, Lori A. Mahoney

Browse all Theses and Dissertations

Counterfactual reasoning can be used in task-switching scenarios, such as design and planning tasks, to learn from past behavior, predict future performance, and customize interventions leading to enhanced performance. Previous research has focused on external factors and personality traits; there is a lack of research exploring how the decision-making process relates to both task-switching and counterfactual predictions. The purpose of this dissertation is to describe and explain individual differences in task-switching strategy and cognitive processes using machine learning techniques and linear ballistic accumulator (LBA) models, respectively, and apply those results in counterfactual models to predict behavior. Applying machine learning techniques …

Computational Simulation And Analysis Of Neuroplasticity, Madison E. Yancey

Browse all Theses and Dissertations

Homeostatic synaptic plasticity is the process by which neurons alter their activity in response to changes in network activity. Neuroscientists attempting to understand homeostatic synaptic plasticity have developed three different mathematical methods to analyze collections of event recordings from neurons acting as a proxy for neuronal activity. These collections of events are from control data and treatment data, referring to the treatment of neuron cultures with pharmacological agents that augment or inhibit network activity. If the distribution of control events can be functionally mapped to the distribution of treatment events, a better understanding of the biological processes underlying homeostatic synaptic …

Applying Cognitive Measures In Counterfactual Prediction, Lori A. Mahoney

Browse all Theses and Dissertations

Counterfactual reasoning can be used in task-switching scenarios, such as design and planning tasks, to learn from past behavior, predict future performance, and customize interventions leading to enhanced performance. Previous research has focused on external factors and personality traits; there is a lack of research exploring how the decision-making process relates to both task-switching and counterfactual predictions. The purpose of this dissertation is to describe and explain individual differences in task-switching strategy and cognitive processes using machine learning techniques and linear ballistic accumulator (LBA) models, respectively, and apply those results in counterfactual models to predict behavior. Applying machine learning techniques …

Cross-Model Parameter Estimation In Epidemiology, Julia R. Fitzgibbons

Honors Theses and Capstones

No abstract provided.

Teacher Perceptions Of The Impact Of Vertical Non-Permanent Surfaces In Mathematics Classrooms, Michelle Mikes

Ed.D. Dissertations

The historical, traditional mathematics classroom of students sitting in rows receiving information from the teacher and working individually was still prevalent in the 21st century. Many teachers had resorted to student-centered activities to engage passive students, but the minimal progress of math achievement of United States students denoted a need for the reform of the traditional mathematics classroom. In this multi-site, multi-case qualitative study, I explored teacher perceptions of the use of vertical non-permanent surfaces on the impact of engagement, including the use of formative assessment and feedback with mathematics students, and the lesson structure of 360 Degree Math. The …

Bayesian Inspired Multi-Fidelity Optimization With Aerodynamic Design, Christopher Corey Fischer

Browse all Theses and Dissertations

In most engineering design problems, there exist multiple models of varying fidelities for use in predicting a single system response such as Computational Fluid Dynamics (CFD) models constructed using Potential Flow, Euler equations, or full physics Navier Stokes implementation. Engineering design is constantly pushing the forefront of the field through imposing stricter and more complex constraints on system performance, thus elevating the need for use of high-fidelity models in the design process. Increasing fidelity level often correlates to an increase in cost (financial, computational time, and computational resources). Traditional design processes rely upon low-fidelity models for expedience and resource savings. …

Accessibility Of Mathematics Examinations To Students With Hearing Impairment: A Case Study Of A School For The Deaf In Nyeri County-Kenya, Peter Mwangi Kabethi

Theses & Dissertations

The objective of this study was to establish the extent to which mathematics examinations are accessible to students with HI. The study adopted a qualitative approach via a case study design. The participants included the principal, Head of the mathematics department, teachers, and students from Clifftop school for the deaf. Purposive sampling was used to select the 5 students with HI and 3 mathematics teachers. Data was collected through focus group discussion (FGD) with students and teachers separately and classroom observation. In addition, the principal and the head of the mathematics department were interviewed to ascertain the general accessibility of …