Digital Commons Network^™

Counting Conjugates Of Colored Compositions, Jesus Omar Sistos Barron

Honors College Theses

The properties of n-color compositions have been studied parallel to those of regular compositions. The conjugate of a composition as defined by MacMahon, however, does not translate well to n-color compositions, and there is currently no established analogous concept. We propose a conjugation rule for cyclic n-color compositions. We also count the number of self-conjugates under these rules and establish a couple of connections between these and regular compositions.

Exploring The Role Of The Teacher In Motivating Students To Learn Mathematics At Alternative High Schools, Anne-Marie Johanne Mohammed

Theses and Dissertations

The purpose of this applied dissertation was to provide an in-depth understanding of the teacher’s role in motivating students to learn mathematics at alternative high schools because motivation impacts academic achievement in mathematics. Students in South Florida must pass an end-of-course exam in algebra as a requirement to receive a high school diploma. Therefore, it is essential that students are motivated to learn the mathematics concepts that are necessary to pass the end-of-course exam. This research study was guided by the following research questions:

1. How and in what ways do mathematics teachers adjust and integrate instructional strategies to support …

Proof Of The Kresch-Tamvakis Conjecture, John Caughman, Taiyo S. Terada

Mathematics and Statistics Faculty Publications and Presentations

In this paper we resolve a conjecture of Kresch and Tamvakis.

Culturally Sustaining Math Word Problem Instruction With Hip-Hop Story Schemas, Michelle J. Cook, Jonte C. Taylor, Elizabeth M. Hughes, Thomas D. Deau

Journal of the Arts and Special Education

On August 11, 2023, Hip-Hop celebrated its 50^th anniversary. In honor of this milestone, we share an activity that is designed to harness the power and art of Hip-Hop to support learning in mathematics for students with and without exceptionalities. Using a vignette, we examine why culturally sustaining practices are pivotal to learning and how teachers can collaborate with middle-school students to strengthen an evidence-based practice such as schema-based instruction by honoring the funds of knowledge that students possess. The activity includes (a) the creation of culturally relevant word problems in mathematics, (b) schema-based instruction for solving additive-type word …

Indianapolis Gems Club: Engagement In Informal Mathematics And Science Learning, Maria Eloisa Nuguid

Purdue Journal of Service-Learning and International Engagement

There continues to be a need for the representation of women in science, technology, engineering, and mathematics (STEM) fields. To address this need, the Girls Excelling in Mathematics and Science (GEMS) research team at Purdue started a GEMS club at Lew Wallace School in Indianapolis, referred to as Indy GEMS Club. GEMS research assistants Maria Eloisa Nuguid, Yi Zhu, and Grace Gochnauer worked with Professor Elizabeth Suazo-Flores. This article is a description of the first Indy GEMS Club experience that consisted of hands-on activities created by GEMS founder Laura Reasoner Jones. The activities were hidden Legos, cup stacking, building a …

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

Masters Theses (Archived)

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 …

A Review Of “Making Black Girls Count In Math Education: Black Feminist Vision For Transformative Teaching, Michelle Craddock Guinn

Feminist Pedagogy

No abstract provided.

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 …

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 …

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.

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 …

Transforming Mathematics Education With Creativity, Natalie M. Zielinski

Masters 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, …

The Negative Stigma Surrounding Mathematics, Marissa A. Greisen

PSU McNair Scholars Online Journal

There is a negative stigma that surrounds mathematics in our education system. It is important to bring notice to this for the benefit of future students. There is a lot of research claiming that math is looked down on, but they do not answer why, or what we can do to fix it. Why is there a greater negative stigma around math and not other subjects? What roles to teachers, parents, and peers play in this stigma? In this article, I created a survey for people to answer questions regarding their opinion on math, who they believe typically does well …

Creating Mandalas For World Peace While Incorporating Mathematics, Art, Literature, Writing, And Technology, Joseph M. Furner

Transformations

Across the USA there are more and more students whose parents are from around the world. It is important teachers can effectively teach mathematics to reach all students, particularly those with limited English proficiency, while establishing interdisciplinary and cultural connections and even working toward world peace. The purpose of this paper is to share how a class of students from an elementary school in South Florida with their teacher created mandalas to teach mathematics, art, writing, and even world peace to their students. Math teachers should strive to bridge the cultural gap among all students by incorporating innovative ideas as …

Testing The Knowledge Of Early Childhood Educators, Dianne S. Mccarthy

Journal of Inquiry and Action in Education

Teacher certification exams are supposed to assess if a student is likely to succeed in teaching. What if an exam seems to be inappropriate? This article is an inquiry of the New York State Content Specialty Test for Early Childhood Candidates, particularly the math section. It raises the issue of whether we are asking the right questions and ascertaining the right data to decide if someone has the appropriate math knowledge and is ready to teach math to young children.

Using Technology To Teach/Learn Mathematics, How Are We As Teachers Fostering Mathematics Education Mobility?, Deolinda Maria L. Dias Rasteiro, Ascensión Hernandez Encinas, Araceli Queiruga-Dios, María Jesús Santos Sánchez, Agustin Martín, Luis Hernández-Álvarez, Miguel Ángel González De La Torre, Alicia Pose Díez De La Lastra

Workshops

No abstract provided.

Benford’S Law And Its Applications To Accounting, Lucy Wilson

Mathematics Student Projects

In this paper, we introduce the concept of Benford’s Law, which is the mathematical observation that in many naturally occurring numerical datasets, the leading digits are not evenly distributed. We actually find that smaller leading digits appear more often than larger ones. We will explore when and why this phenomenon occurs and how we can use statistical tests to determine how well a dataset conforms to Benford’s Law. We will also see how Benford’s Law can be used by auditors in the accounting field to catch potential fraud.

The Traveling Salesman Problem At Taylor University, Jonathan Jinoo Pawley

Mathematics Student Projects

What is the shortest route to walk to every residence hall on campus, beginning and ending with the same hall? This question can be considered by applying the Traveling Salesman Problem, an easy to understand yet hard to solve problem in the realm of discrete combinatorial optimization. The Traveling Salesman Problem is useful as an introduction to optimization problems, and it also has immensely practical applications. This paper will serve as an introduction to the computational difficulty of the Traveling Salesman Problem and will also explore various approximation algorithms. We will subsequently apply our new understanding of the theory to …

Random Matrix Perturbation: Entry-Wise Analysis, Abhinav Bhardwaj

Yale Graduate School of Arts and Sciences Dissertations

Consider a symmetric, additive perturbation $E$ of a symmetric, low rank matrix $A$. Given access to the perturbed data $\tilde{A}$, an important problem in statistics and numerical analysis is to draw conclusions about the matrix $A$. Of particular importance are the eigenvectors of $A$. Classical eigenvector perturbation theory gives conditions under which the eigenvectors and eigenspaces of $A$ and $\tilde{A}$ are close in the $\ell_2$ norm. In many real-world settings, $E$ is a random matrix. I will demonstrate that the classical perturbation theory falls short when $E$ is random. Furthermore, very little is known about the $\ell_{\infty}$ perturbation of the …

Assessing Controls On Ice Dynamics At Crane Glacier, Antarctic Peninsula, Using A Numerical Ice Flow Model, Rainey Aberle, Ellyn M. Enderlin, Hans-Peter Marshall, Michal Kopera, Tate G. Meehan

Geosciences Faculty Publications and Presentations

The Antarctic Peninsula's widespread glacier retreat and ice shelf collapse have been attributed to atmospheric and oceanic warming. Following the initial post-collapse period of retreat, several former tributary glaciers of the Larsen A and B ice shelves have been slowly re-advancing for more than a decade. Here, we use a flowline model of Crane Glacier to gauge the sensitivity of former tributary glaciers to future climate change following this period of long-term dynamic adjustment. The glacier's long-term geometry and speed changes are similar to those of other former Larsen A and B tributaries, suggesting that Crane Glacier is a reasonable …

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 …

The Effect Of Instructionally Embedded Cognitive Reframing On Students’ Self-Beliefs Of Their Mathematical Competence, Kelly Eyre Frazee

Theses and Dissertations

Many students lack the ability to maintain positive perceptions of their mathematical self-belief, resulting in undesirable social, emotional, and academic outcomes. The purpose of this study was to investigate the impact of a cognitive reframing strategy on third and fourth grade math intervention students’ perceptions of their mathematical competence. This study sought to understand the impact of this emotional regulation strategy on students’ ability to autonomously regulate their negative or irrational thoughts related to their mathematics abilities, as well as the impact on their self-beliefs. Data for this study were collected through semi-structured interviews with students, student reflections, and researcher …

Polybenzimidazole Membranes For Electrochemical Applications With Harsh Operating Conditions, Kris Likit-Anurak

Theses and Dissertations

Polybenzimidazole (PBI) membranes are high temperature proton exchange membranes (PEMs) which have advantages such as being able to operate in high temperatures, strong acid environments, and have no need for external humidity during operation. PBI membranes have been demonstrated to work effectively in multiple electrochemical devices, including fuel cells, hydrogen separation pumps, redox flow batteries, and a hybrid sulfur electrolyzer. In this work, para-PBI and densified para-PBI membrane have been used to improve electrochemical performance in harsh operating conditions that are both high temperature (≥120 ̊C) and high acid concentration (≥ 5M). First, we demonstrated the use of para-PBI membranes …

Mathvision Prototype Using Predictive Analytics, Yuzi Mahmud, Muhd Syahir Abdul Razak, Shuzlina Abdul-Rahman, Mastura Hanafiah, Amien Ashraf Suhaimi

Malaysian Journal of Computing (MJoC)

Malaysia is currently going towards Industrial Revolution (IR) 4.0 which makes Science, Technology, Engineering and Mathematics (STEM) subjects become more crucial. IR 4.0 covers a lot of aspects especially in digital transformation in manufacturing, and this certainly requires strong mathematical knowledge. To achieve this goal, students need to have a good foundation in Mathematics subject. However, due to the increased number of students nowadays, teachers are facing challenges to track students’ progress efficiently. In this study, a predictive model has been developed that aims to assist Mathematics teachers in monitoring their students. The prototype, called MathVision, can track students’ progress …

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 …

Near Peer Pedagogies For Culturally Sustaining Computer Science And Mathematics, Cliff Freeman, Eli Tucker-Raymond, Juan Gutierrez

Journal of Computer Science Integration

In this study, College STEM Literacy Workers act as co-teachers in 9th and 10th grade classrooms alongside mathematics teachers as they both learn to integrate a 30-hour integrated computer science/mathematics curriculum. As part of the curriculum for educator learning, we adapted the Algebra Project’s “Model of Excellence” for culturally relevant-sustaining pedagogies. We used the framework to explore how teachers understand College STEM Literacy Workers’ contributions in the model as well as College STEM Literacy Workers’ own experiences in the classroom. We found that while teachers and College STEM Literacy Workers did not individually instantiate the model of excellence, they were …

Bringing Learning Progressions Down To 2-Year-Olds In Reading And Mathematics, Prue Anderson

2021-2030 ACER Research Conferences

ACER’s learning progressions in reading and mathematics describe growth that is mainly focused on skills students demonstrate at and beyond school. These progressions have recently been extended down to describe earlier levels of growth so we now have seamless progressions from skills and understandings toddlers might demonstrate up to highly sophisticated skills and concepts. This presentation briefly outlines ACER’s work and identifies key implications for educators. The pathways that support early reading development were described in progressions for listening comprehension and sounds and letters. Along with an early mathematics progression, these were conceptualised as embedded in an oral language progression. …

Research Conference 2023: Becoming Lifelong Learners. Proceedings And Program, Kylie Burns (Ed.)

2021-2030 ACER Research Conferences

We know learning in the early years sets the foundations for people’s ongoing academic, cognitive and socio-emotional development. Education across those formative first 12 years is currently segmented, with children often starting fresh in new systems. How can each of us make learning in the early childhood and primary years more effective? Research Conference 2023 will examine research around how we can improve the continuity of learning from birth to 12 years. It will bring together leading international and Australian researchers to provide insights into the best ways to identify, conceptualise, develop and assess these new linkages for learning.

Math 111 Honors, Fall 2023: Calculus I - Honors, John Bechtold

Mathematical Sciences Syllabi

No abstract provided.