Digital Commons Network^™

Social Justice Mathematics: Classroom Practices That Give Students Rigor While Building Agency, Emily Marquise

Masters Theses

The purpose of this study is to examine the impact of a social justice approach to mathematics instruction. While many students have math aversion, students in low socioeconomic communities exhibit this to a higher degree putting them at a disadvantage as they progress through their educational career. More than 3.4 million K-12 students in the United States come from families that earn less than the median income yet achieve scores in the top percentile (Wyner et al., 2007). This raises the question of why so many students in low-socioeconomic settings are not given rigorous content that will keep them competitive …

Rhythm And Meter As Text Expression: Jake Runestad's "Come To The Woods", Samantha Brewer

Master's Theses

Core to Western music education curriculum is the teaching and history of “word painting,” or text expression particularly as it pertains to the sixteenth-century madrigal. This approach to text expression is explored primarily through the lens of melodic and harmonic movement through a vocal line and the manner in which the line allows for better portrayal of the text or poem. The purpose of this thesis is to take a new approach to text expression in contemporary choral literature through the viewpoint of rhythm and meter. In this thesis, various analytical techniques from decades past and present are applied to …

Student Thinking Driving Collaboration And Teacher Knowledge, Rachel Cheney

Theses and Dissertations

The study in this paper examined how teachers engaged in their structured Professional Learning Community (PLC) time in a manner that focused their work on student mathematical thinking. The participants included two third-grade teachers and two fourth-grade teachers engaged in an alternative PLC process during their collaboration time. Interviews were conducted and focused on how the teachers thought about student thinking as the driving force of their collaboration. The teachers found their PLC time was more focused, student thinking led the discussions and lessons, they were more responsive to student needs, and their own mathematical understanding increased. The teachers also …

Transforming Mathematics Education With Creativity, Natalie M. Zielinski

Culminating Experience Projects

Mathematics achievement in elementary and middle school students has decreased across the United States since 2019. Research has shown that moving away from traditional lecture-style teaching and implementing creative and application based learning can result in higher academic achievement and engagement. By utilizing challenging curricular tasks, Project Based Learning, and arts integration, students can be presented with more authentic and engaging academic content to deepen mathematical understanding and success. This project explores the benefits and effects of integrating creative teaching strategies into the mathematics classroom as an equitable teaching approach. Through the use of non-scripted curricular tasks, Project Based Learning, …

An Evaluation Using Universal Design For Learning, Lilah Nye

Honors Projects

This research was conducted to evaluate the prevalence of an Educational framework known as the Universal Design for Learning (UDL) in a set of lesson plans published by a nationally recognized organization. The intention of this focus was to push major professional organizations in mathematics education to produce inclusive resources for all students. UDL is an opportunity to increase accessibility of curriculum for students by reducing barriers to learning that play a role in educational inequity, and generally the goal of UDL is that lessons are made accessible preemptively to benefit all students rather than for individual students as the …

Perceptions Of Educators On Motivational Strategies Influencing Middle School Students In Mathematics Courses, Amy Rigsby

Electronic Theses and Dissertations

This qualitative study examined educators' perceptions of motivational strategies influencing and motivating middle school students to comprehend and perform in mathematics courses. This study used interview data from 15 participants with 2 to 30 years of teaching experience. Educators may utilize this information in multiple settings within the classroom to influence and motivate students in mathematics courses.

Data collection strategies included one-on-one semi-structured middle school educator interviews. Analysis of data occurred in three phases: (a) categorization of data under the five organizational factors, (b) building the explanation in narrative form, and (c) re-examination of the data. The analysis of the …

A Survey Of Code-Based Cryptography, Antsa Rakotondrafara

All Theses

One of the biggest concerns of the digital era is to keep data secure. With the rise of quantum computers, some of the problems that were considered hard will be solved in polynomial time. Therefore, efforts are taken to design practical cryptosystems that will resist attacks from both classical computers and quantum computers. In this thesis, we analyze three quantum-resistant code-based cryptosystems. We propose a new type of attack based on mixed-integer non-convex programming for the NIST submission FuLeeca.

Creating First Grade Math Learning Materials In The Chinese Immersion Learning Environment, Huishu Jia

School of Education and Leadership Student Capstone Projects

Math is everywhere in people’s daily lives. It is also a universal subject taught everywhere. Research has demonstrated that math education includes many different components, the most essential mathematical skill for younger learners is to establish their number sense. Students’ math fluency will increase and will develop their math automaticity once they have strong number sense. According to studies, the Mandarin Chinese language helps students effectively master basic mathematical skills due to the uniqueness of the language, such as the pronunciation of each Chinese character, the “base ten” number system, etc. The project involved creating a pacing chart that aligns …

Using L1 Student Narratives And Peer Teaching To Increase Secondary Education Mathematical Understanding, Marco Antonio Martinez Leandro

Teacher Education, Educational Leadership & Policy ETDs

This phenomenological study research presents an option to use both discourse in the native language and technology as an alternative to improve the understanding of mathematics in secondary education. 13 students whose native language is Spanish attended a high school in a large urban school district in the Southwest of the United States, participated in this study.

The study's main objective was to observe the effects of using students' discourse in their language and the support of technology to increase their academic literacy in mathematics. Solution-based pedagogy was central to helping students achieve the Development of Academic Literacy in Mathematics …

Investigation Of Student Understanding Of Representations Of Probability Concepts In Quantum Mechanics, William D. Riihiluoma

Electronic Theses and Dissertations

The ability to relate physical concepts and phenomena to multiple mathematical representations—and to move fluidly between these representations—is a critical outcome expected of physics instruction. In upper-division quantum mechanics, students must work with multiple symbolic notations, including some that they have not previously encountered. Thus, developing the ability to generate and translate expressions in these notations is of great importance, and the extent to which students can relate these expressions to physical quantities and phenomena is crucial to understand.

To investigate student understanding of the expressions used in these notations and the ways they relate, clinical think-aloud interviews were conducted …

Parents' Perceptions Of The Importance Of Teaching Mathematics: A Q-Study, Ashlynn M. Holley

Theses and Dissertations

Mathematics education has gone through multiple reform efforts over the last century and continues to be the target of improvement efforts. Past changes in curriculum and goals have sometimes led to heated debates between various stakeholders. Knowing the views of different stakeholders can help determine what common ground there is between these different groups and where areas of disagreement might arise. Parents are especially important to understand because they have been influential in past reform efforts. Despite the importance of parents' opinions, little research has been conducted concerning their perspectives on the importance of mathematics teaching. Using Q-methodology, I was …

Examining The Effectiveness Of Using Point-Of-View Video Modeling On Mathematics Improvement In Students With Learning Disabilities In Saudi Arabia, Tirad Alsaluli

Electronic Theses and Dissertations

Video Modeling (VM) is one of the most widely used approaches by researchers to improve many skills, such as academic skills in students with Learning Disabilities (LD; Boon et al., 2020). As the incidence rate of individuals with LD in Saudi Arabia increase (Almedlij & Rubinstein-Ávila, 2018), the need for evidence-based math interventions focused on the math development of individuals with LD also increases. Although VM is recognized as an Evidence-based Practice (EBPs), a limited number of studies have implemented VM as an intervention to improve mathematic skills. Implementing VM as a math intervention strategy would explore its effects on …

Evidence-Based Practices For Tiered Math Interventions For Elementary Students, James Schyma

Culminating Projects in Special Education

Abstract is not required for a Starred Paper.

Math And Employment, Elisabeth Mumford

Culminating Projects in Special Education

Children in the United States have not made adequate gains on national assessments in mathematics (Strickland & Maccini, 2012). Based on the National Assessment of Education Progress (NAEP), 65% of 8th graders and 76% of 12th graders scored below proficiency level, along with over 90% of secondary students (Strickland & Maccini, 2012). This is especially troubling since math is used outside of the classroom setting so commonly in the workplace, especially vocational (trade) jobs. Students with disabilities tend to have a hard time with basic math facts and this can become problematic later on when trying to obtain employment (Leach, …

Analyzing The Influence Of Mathematics Intervention Teacher Actions On Students' Mathematics Identities: An Examination Of Bipoc Student Perceptions And Past Learning Experiences., Sydni P. Morris

Electronic Theses and Dissertations

This dissertation examines mathematics education's past and present state in the United States, emphasizing mathematics intervention instruction. This dissertation includes a complex and critical analysis of intervention practices and historical and structural inequities based on race present in these interventions and mathematics education. In combination, it examines the construct of mathematics identities, their role in student success with mathematics, and trends surrounding mathematics education and its impact on populations of students of color. Using Critical Race Theory as an underlying framework and Critical Counter-Narrative as a methodology, it argues a need for marginalized student voices to be present in the …

Mathematics Behind Machine Learning, Rim Hammoud

Electronic Theses, Projects, and Dissertations

Artificial intelligence (AI) is a broad field of study that involves developing intelligent
machines that can perform tasks that typically require human intelligence. Machine
learning (ML) is often used as a tool to help create AI systems. The goal of ML is
to create models that can learn and improve to make predictions or decisions based on given data. The goal of this thesis is to build a clear and rigorous exposition of the mathematical underpinnings of support vector machines (SVM), a popular platform used in ML. As we will explore later on in the thesis, SVM can be implemented …

How Equitable Teaching Practices Impact The Mathematical Identity Of English Language Learners From Teachers’ Perspectives, Xiaomei Segelstrom

School of Education and Leadership Student Capstone Theses and Dissertations

This mixed method research study examined the teacher’s perspectives on how equitable teaching practices impact the math identity of English language learners. A quantitative research survey instrument including five major themes that was generated from the frameworks in the literature review was used, and then followed by semi-structured interviews to address the research question. The data collected from the survey indicated that participants do believe that equitable teaching practices would impact the math identity of ELLs via: conveying high expectations, language support, modifying lessons, mathematical tasks and mathematical tools. Building on the survey results, interviewees furthermore informed that all these …

Using Cooperative Groups To Enhance Student Learning In A High School Math Class, Caitlin Mccain

School of Education and Leadership Student Capstone Projects

There are many ways that teachers can use cooperative learning in their classroom. The literature review found in this capstone dives into the research surrounding cooperative learning, starting with the four theoretical perspectives on cooperative learning identified by Slavin (1995, as cited by Slavin, 2011) and how they work together to enhance learning. Also discussed is a 2003 study by Kramarski and Mevarech which demonstrates the need to expose students to metacognitive training. Liljedahl et al.’s (2021) research on how to group students can also be found in this capstone. The research from this literature review, along with the author’s …

How To Design And Implement A Maker Space In The K-3 Classroom, Elizabeth Nelson

School of Education and Leadership Student Capstone Projects

A maker space is an area designated to be used by participants to make a product through a hands-on experience. While the term maker space is relatively new to education, ‘making’ is embedded into human history. The research on these spaces relies on the importance of the maker space for a student's social-emotional well-being. Creative hands-on work specifically for children from low-income backgrounds supports the student in their primary years. At the same time, there needs to be more evidence in the research that proves how effective these spaces are in supporting students' academics. The topics explored in the literature …

The Academic Outcomes Of Dual Language Programs In Mathematics And English Language Arts, Dana Lisbet Aguirre

M.Ed. Literature Reviews

This paper focuses on Dual Language students in both elementary and secondary schools and their academic outcomes in the content areas of mathematics and English language arts. Positive benefits of Dual Language Programs are highlighted in both content areas acorss various grade levels, locations, and states.

Imperfect Immunity And The Stability Of A Modified Kermack-Mckendrick Model, Kaylee Sims

Honors Theses

The classic Kermack-McKendrick model of mathematical epidemiology suggests that a population is only in equilibrium when there is no disease present. In the modern era, we have several cyclic infectious diseases that show no signs of eradication, despite global health measures. In this thesis, we introduce a coefficient of waning immunity in order to produce a modified Kermack-McKendrick model and analyze whether the model yields system stability with a certain amount of infection present. Ultimately, the model is incongruent with real-world case data, with its most glaring failure being exponential dampening of the height of each disease case peak due …

An Application Of The Pagerank Algorithm To Ncaa Football Team Rankings, Morgan Majors

Honors Theses

We investigate the use of Google’s PageRank algorithm to rank sports teams. The PageRank algorithm is used in web searches to return a list of the websites that are of most interest to the user. The structure of the NCAA FBS football schedule is used to construct a network with a similar structure to the world wide web. Parallels are drawn between pages that are linked in the world wide web with the results of a contest between two sports teams. The teams under consideration here are the members of the 2021 Football Bowl Subdivision. We achieve a total ordering …

What Is A Number?, Nicholas Radley

HON499 projects

This essay is, in essence, an attempt to make a case for mathematical platonism. That is to say, that we argue for the existence of mathematical objects independent of our perception of them. The essay includes a somewhat informal construction of number systems ranging from the natural numbers to the complex numbers.

Curriculum Connectivity In Montclair State University’S Undergraduate Mathematics Program, Ana G. Da Silva Jesus

Theses, Dissertations and Culminating Projects

According to Piaget’s cognitive development theory and the constructivism learning theory of education, real learning occurs when students establish long term connections between disciplines by either adapting or redefining previously acquired knowledge. These ideologies have important teaching and learning implications that directly influence curriculum development and the design of a course of study. This thesis explores the interconnectedness of the subjects required for the successful completion of an undergraduate math program at Montclair State University. More specifically, it models students’ unique connections through a learning network and investigates the correlation between the interconnectivity of subjects and students’ overall performance. Results …

Connecting Music To The Mathematics Classroom, Nicholas Parr

Honors Projects

This project investigates the importance of integrating music into mathematics classrooms K-12. By outlining the numerous connections between mathematics and music, and applying those to pedagogy, the project provides interdisciplinary overlaps that may be unknown to current teachers. Evidence supports the conclusion that mathematical abilities improve after musical infusion, yet the presence of this intervention is lacking in grades 7-12. Therefore, both mathematical and musical intelligence suffer as a result of the separation of electives and core classes. This project contains eight original mathematics content standards, which would coincide with the Ohio Learning Standards for Mathematics, as well as a …

Reflecting On Movement In The Math Classroom, Zoey Berger

Honors Projects

The purpose of this paper is to determine how reflection on movement effects the learning and connections made by students in the math classroom. Kinesthetic Movement is a learning style that is oftentimes forgotten about and left out of classroom instruction. It can help increase motivation, build deeper connections, and create a more positive disposition towards math for students. Research was conducted in four, eighth grade, pre-algebra classes, with some classes being given the opportunity to reflect more than others. Test scores, journal responses, and interest surveys done by the students are used to show inconclusive results that reflection on …

Using A Distributive Approach To Model Insurance Loss, Kayla Kippes

Student Research Submissions

Insurance loss is an unpredicted event that stands at the forefront of the insurance industry. Loss in insurance represents the costs or expenses incurred due to a claim. An insurance claim is a request for the insurance company to pay for damage caused to an individual’s property. Loss can be measured by how much money (the dollar amount) has been paid out by the insurance company to repair the damage or it can be measured by the number of claims (claim count) made to the insurance company. Insured events include property damage due to fire, theft, flood, a car accident, …

The Theatre Of Math: The Stage As A Tool For Abstract Math Education, Blaine Hudak

Honors Projects

So often in the education of Mathematics does instruction solely consist of the lecture. While this can be an effective method of communicating the ideas of math, it leaves much to be desired in gathering the interest and intrigue of those who have not dedicated their lives to the study of the subject. Theatre, by contrast, is a tool that has been used in the past as means of teaching complicated and difficult to understand moral and emotional subjects. While Theatre and Mathematics have been used in combination many times in the past, it is most often done in the …

Length Bias Estimation Of Small Businesses Lifetime, Simeng Li

Honors Theses

Small businesses, particularly restaurants, play a crucial role in the economy by generating employment opportunities, boosting tourism, and contributing to the local economy. However, accurately estimating their lifetimes can be challenging due to the presence of length bias, which occurs when the likelihood of sampling any particular restaurant's closure is influenced by its duration in operation. To address the issue, this study conducts goodness-of-fit tests on exponential/gamma family distributions and employs the Kaplan-Meier method to more accurately estimate the average lifetime of restaurants in Carytown. By providing insights into the challenges of estimating the lifetimes of small businesses, this study …

Investigating Correlations Among A Growth-Mindset Intervention, Students’ Math Anxiety, And Students’ Math Self-Efficacy, Anna Grace Chamberlain

Honors Projects

This paper details the methodology, data, and conclusions of a research study investigating the correlations among a growth-mindset intervention, math anxiety, and math self-efficacy. The study found that teaching students about mindset through an intervention approach did not make a significant difference in students’ math anxiety or math self-efficacy. Teacher-centered factors are discussed as having a greater impact on students’ math anxiety and math self-efficacy.