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“What Line Can’T Be Measured With A Ruler?” Riddles And Concept-Formation In Mathematics And Aesthetics, William H. Brenner, Samuel J. Wheeler

Philosophy Faculty Publications

We analyze two problems in mathematics – the first (stated in our title) is extracted from Wittgenstein’s “Philosophy for Mathematicians”; the second (“What set of numbers is non-denumerable?”) is taken from Cantor. We then consider, by way of comparison, a problem in musical aesthetics concerning a Brahms variation on a theme by Haydn. Our aim is twofold: first, to bring out and elucidate the essentially riddle-like character of these problems; second, to show that the comparison with riddles does not reduce their solution to an exercise in bare subjectivity

Elementary Educators’ Beliefs And Practices Regarding Explicit Math Vocabulary And Language Instruction, Katherine Lee Berlin

School of Education and Leadership Student Capstone Theses and Dissertations

For the last couple decades, math achievement scores in the United States have remained stagnant or declined. Teachers are searching for ways to improve these scores. Much work has been done on number sense and math talks. But, are these the only tools to consider? What if the very language used to express mathematical knowledge is a key factor in how students gain their learning and ultimately express their thinking? Research has emerged that draws a relationship between explicit math vocabulary instruction and math achievement. While this is well documented, the practice is not commonly seen. Thus, I asked, “What …

The Influence Of The Student-Teacher Relationship On The Mathematics Confidence Of Students, Mary Tracey Plante

School of Education and Leadership Student Capstone Theses and Dissertations

The student-teacher relationship impacts student confidence and achievement. Many factors such as race, gender, language learning, and special education were researched as they influence this relationship. This research focused on using a correlational case study to determine how the student-teacher relationship influences the mathematics confidence of students when social-emotional supports and learning are implemented. Data collection methods involved using a Likert scale and interviews with the teacher. For the students, data collection was a Likert scale, number sense assessment, interviews, and anecdotal notes. The participants were a kindergarten teacher and 18 of her students from a diverse, midwestern suburban school …

Spiral Review In A Middle School Mathematics Classroom, Haley Birks

Master's Theses & Capstone Projects

The purpose of this action research project was to determine the relationship between daily spiral review bell ringers and students' assessment scores. The research was driven by the problem of students reaching the end-of-year assessments and being unable to remember material they had learned throughout the year. A quantitative study was used to determine the effectiveness of a ten-week spiral review intervention. The researcher is a seventh and eighth grade math teacher in her fifth year of teaching. Data was collected from a pre-test and post-test created by the researcher consisting of material from the Common Core State Standards and …

Math Educators, Positive Student Mindsets, And Math Centers, Riki Baker

School of Education and Leadership Student Capstone Projects

It is a math educator’s job to help each student develop academic, emotional, behavioral, and social skills in a supportive and rigorous instructional environment. Reinforcing a growth mindset is the pinnacle of successful teaching and learning. However, there are always experiences that deter students from feeling like they can become successful in an area or multiple areas. Instructional time can become feared and mindsets can become fixed. It could even potentially become a lifelong source of trauma. Math is perhaps one of the most notorious content areas that induce feelings of fear, failure, and perpetual condemnation. Teaching strategies play an …

Social-Emotional Learning Skills Embedded Within Math And Reading During The Primary Years, Cassandra Sutherland

School of Education and Leadership Student Capstone Projects

The research question asked in this capstone project was: How can social-emotional learning skills be taught within academic lessons to promote academic progress in primary years? Just like it is necessary to teach reading and math concepts; students need to be explicitly taught social-emotional learning skills. Students should feel a sense of belonging, feel successful and treat others with respect. All of these skills should lead to encountering academic success. This capstone project explores research about the importance of teaching social skills during primary years. The project portion of this capstone is a supplemental curricular resource that includes math and …

Reliable Identification Of Binary Supermassive Black Holes From Rubin Observatory Time-Domain Monitoring, Megan C. Davis, Kaylee E. Grace, Jonathan R. Trump, Jessie C. Runnoe, Amelia Henkel, Laura Blecha, W N. Brandt, J Andrew Casey-Clyde, Maria Charisi, Caitlin A. Witt

Faculty Publications

Periodic signatures in time-domain observations of quasars have been used to search for binary supermassive black holes (SMBHs). These searches, across existing time-domain surveys, have produced several hundred candidates. The general stochastic variability of quasars, however, can masquerade as a false-positive periodic signal, especially when monitoring cadence and duration are limited. In this work, we predict the detectability of binary SMBHs in the upcoming Rubin Observatory Legacy Survey of Space and Time (LSST). We apply computationally inexpensive sinusoidal curve fits to millions of simulated LSST Deep Drilling Field light curves of both single, isolated quasars and binary quasars. The period …

Doubly Almost Bipartite Leonard Pairs, Shuichi Masuda

Dissertations and Theses

In Linear algebra, the concept of Leonard pair (LP) was motivated by the theory of Q-polynomial distance-regular graphs. In this dissertation, we will first give a brief introduction to LPs and to two closely-related classes of objects: (i) bipartite Leonard pairs (BLPs) and (ii) almost bipartite Leonard pairs (ABLPs). Taking these as departure points, we will introduce a new class of object - doubly almost bipartite Leonard pairs (DABLPs). The primary aim of our work is to fully classify (up to isomorphism) this new family. In addition, since there is known to be a natural correspondence between Leonard pairs …

Changing The Culture Of Secondary School Mathematics: What Are The Effects Of Interventions On Student Attitudes, Beliefs, And Motivation?, Meagan Coronado

Student Theses and Dissertations

In this study, 80 ninth-grade students enrolled in Algebra I from a high school in south Texas completed the Implicit Theories of Intelligence Scale for Children (ITIS) Survey and the Attitudes Toward Mathematics Inventory (ATMI) Survey, before and after a set of interventions. The students were divided into one of four groups, three with applied intervention and one control group: intelligence theory, utility value theory, both intelligence theory and utility value theory, and no interventions (control group). Analyses were conducted to determine the impact of the interventions on the overall scores on the ITIS and ATMI surveys. The results showed …

Mathematically Modeling How Trapping Regimes That Target Specific Crayfish Life Stages Impact Removal Efficacy, Rini Pattison

Seaver College Research And Scholarly Achievement Symposium

The red swamp crayfish, Procambarus clarkii, is an invasive species introduced into several streams within the Santa Monica Mountains (SMM) in Southern California. Crayfish predation decimates native aquatic species. Thus, the Mountains Restoration Trust (MRT) and Environmental Restoration Group have worked to remove crayfish through regular trapping in Malibu Creek.

To aid conservation efforts, former SURB students William Milligan and Dev Patel developed mathematical models of crayfish removal efficacy. Milligan created a differential equation model of how crayfish removal affects local newt populations. Patel expanded Milligan’s crayfish model by creating a discrete model of the crayfish life cycle that newly …

The Myth Of Tightening Credit Rating Standards In The Market For Corporate Debt, Karolina Krystyniak, Viktoriya Staneva

Faculty Publications

This study revisits the existing evidence of a downward trend in credit rating standards indicating that CRAs have become more conservative over time. We find that the time-series variation in the proxy for rating standards is mostly driven by the market-based variables in the model, specifically market capitalization and idiosyncratic volatility. We examine an alternative specification of the model, incorporating risk characteristics of rated firms relative to those of the average firm in the economy, and find it to have a higher explanatory power. Most importantly, we find little evidence of increased conservatism over time, in contrast to prior studies.

The Myth Of Tightening Credit Rating Standards In The Market For Corporate Debt, Karolina Krystyniak, Viktoriya Staneva

Faculty Publications

This study revisits the existing evidence of a downward trend in credit rating standards indicating that CRAs have become more conservative over time. We find that the time-series variation in the proxy for rating standards is mostly driven by the market-based variables in the model, specifically market capitalization and idiosyncratic volatility. We examine an alternative specification of the model, incorporating risk characteristics of rated firms relative to those of the average firm in the economy, and find it to have a higher explanatory power. Most importantly, we find little evidence of increased conservatism over time, in contrast to prior studies.

Traveling Wave Fronts Of Reaction Diffusion Differential Equations With Diffusive Delay In Biological And Chemical Models, William Barker

Theses and Dissertations

Functional differential equations (FDE) incorporate past states and or rates in the modeling of physical phenomena. Unlike ordinary and even some partial differential equations there is no method to find solutions of general FDE explicitly. Therefore, in order to study solutions of FDE, iterative techniques are often employed. Reaction diffusion equations are a specific type of partial differential equations that model diffusive spread, the rate of spread of due to a reaction term of some quantity. These equations arise naturally in fields such as biology, ecology and chemistry. In terms of studying dynamics of populations, previous states and even rates …

The Difficulties Faced By Teachers Of The Lower Basic Stage In Teaching Mathematics Under The Corona Pandemic "Ain Al-Basha Brigade As A Model", هيام صالحية

Jerash for Research and Studies Journal مجلة جرش للبحوث والدراسات

This study aims to identify the severity of the difficulties faced by teachers of the lower basic stage in teaching English in the shadow of the Corona pandemic in Ain Al-Basha District, according to the estimates of its teachers, over the period between 2021 and 2022, and also aimed to identify the extent of statistically significant differences in the level of The severity of the difficulties is attributed to the variables of gender (male, female) or age, according to the responses of mathematics teachers for the lower basic stage in Ain Al-Basha District.

The study followed the descriptive analytical method. …

Origami In The Mathematics, Education And Medical Fields, At-Ziry Torres

Young Scientists and Philosophers on the Border

No abstract provided.

On The Manifold Wisdom Of Origami: Reconsidering Origami As A Natural Philosophy, Joseph De Leon Flores

Young Scientists and Philosophers on the Border

No abstract provided.

Uniting Students With Literacy Connections In Mathematics, Bridget K. Coleman, Michelle Rasheed, Nancy B. Ruppert, Toni M. Williams

South Carolina Association for Middle Level Education Journal

Literature provides opportunities for students to connect to mathematics, as well as each other. Reflecting on personal identities, storytelling, and place-based connections are avenues to enhancing the relevancy of content across the curriculum. Literature can bridge the divide for students reluctant to see the beauty in mathematics. It can also be the impetus in helping unite students as they gain a better understanding of cultures and places beyond their own. Stories, along with interactive tasks, give context for collaborative experiences. This article shares resources and strategies for building understanding and collaboration among students using cross-curricular connections between mathematics and literacy.

X-Ray Polarization Of The Black Hole X-Ray Binary 4u 1630–47 Challenges The Standard Thin Accretion Disk Scenario, Ajay Ratheesh, Michal Dovčiak, Henric Krawczynski, Jakub Podgorný, Lorenzo Marra, Alexandra Veledina, Valery F. Suleimanov, Nicole Rodriguez Cavero, James F. Steiner, Jiří Svoboda, Andrea Marinucci, Stefano Bianchi, Michela Negro, Giorgio Matt, Francesco Tombesi, Juri Poutanen, Adam Ingram, Roberto Taverna, Andrew West, Vladimir Karas, Francesco Ursini, Paolo Soffitta, Fiamma Capitanio, Domenico Viscolo, Alberto Manfreda

Faculty Publications

A large energy-dependent X-ray polarization degree is detected by the Imaging X-ray Polarimetry Explorer (IXPE) in the high-soft emission state of the black hole X-ray binary 4U 1630–47. The highly significant detection (at ≈50σ confidence level) of an unexpectedly high polarization, rising from ∼6% at 2 keV to ∼10% at 8 keV, cannot be easily reconciled with standard models of thin accretion disks. In this work, we compare the predictions of different theoretical models with the IXPE data and conclude that the observed polarization properties are compatible with a scenario in which matter accretes onto the black hole through a …

X-Ray Polarization Of The Black Hole X-Ray Binary 4u 1630–47 Challenges The Standard Thin Accretion Disk Scenario, Ajay Ratheesh, Michal Dovčiak, Henric Krawczynski, Jakub Podgorný, Lorenzo Marra, Alexandra Veledina, Valery F. Suleimanov, Nicole Rodriguez Cavero, James F. Steiner, Jiří Svoboda, Andrea Marinucci, Stefano Bianchi, Michela Negro, Giorgio Matt, Francesco Tombesi, Juri Poutanen, Adam Ingram, Roberto Taverna, Andrew West, Vladimir Karas, Francesco Ursini, Paolo Soffitta, Fiamma Capitanio, Domenico Viscolo, Alberto Manfreda, Fabio Muleri, Maxime Parra, Banafsheh Beheshtipour, Sohee Chun, Nicolò Cibrario, Niccolò Di Lalla, Sergio Fabiani, Kun Hu, Philip Kaaret, Vladislav Loktev, Romana Mikušincová, Tsunefumi Mizuno, Nicola Omodei, Pierre-Olivier Petrucci, Simonetta Puccetti, John Rankin, Silvia Zane, Sixuan Zhang, Iván Agudo, Lucio A. Antonelli, Matteo Bachetti, Luca Baldini, Wayne H. Baumgartner, Ronaldo Bellazzini, Stephen D. Bongiorno, Raffaella Bonino, Alessandro Brez, Niccolò Bucciantini, Simone Castellano, Elisabetta Cavazzuti, Chien-Ting Chen, Stefano Ciprini, Enrico Costa, Alessandra De Rosa, Ettore Del Monte, Laura Di Gesu, Alessandro Di Marco, Immacolata Donnarumma, Victor Doroshenko, Steven R. Ehlert, Teruaki Enoto, Yuri Evangelista, Riccardo Ferrazzoli, Javier A. Garcia, Shuichi Gunji, Kiyoshi Hayashida, Jeremy Heyl, Wataru Iwakiri, Svetlana G. Jorstad, Fabian Kislat, Takao Kitaguchi, Jeffery J. Kolodziejczak, Fabio La Monaca, Luca Latronico, Ioannis Liodakis, Simone Maldera, Frédéric Marin, Alan P. Marscher, Herman L. Marshall, Francesco Massaro, Ikuyuki Mitsuishi, Stephen C.-Y. Ng, Stephen L. O'Dell, Chiara Oppedisano, Alessandro Papitto, George G. Pavlov, Abel L. Peirson, Matteo Perri, Melissa Pesce-Rollins, Maura Pilia, Andrea Possenti, Brian D. Ramsey, Oliver J. Roberts, Roger W. Romani, Carmelo Sgrò, Patrick Slane, Gloria Spandre, Douglas A. Swartz, Toru Tamagawa, Fabrizio Tavecchio, Yuzuru Tawara, Allyn F. Tennant, Nicholas E. Thomas, Alessio Trois, Sergey S. Tsygankov, Roberto Turolla, Jacco Vink, Martin C. Weisskopf, Kinwah Wu, Fei Xie

Faculty Publications

A large energy-dependent X-ray polarization degree is detected by the Imaging X-ray Polarimetry Explorer (IXPE) in the high-soft emission state of the black hole X-ray binary 4U 1630–47. The highly significant detection (at ≈50σ confidence level) of an unexpectedly high polarization, rising from ∼6% at 2 keV to ∼10% at 8 keV, cannot be easily reconciled with standard models of thin accretion disks. In this work, we compare the predictions of different theoretical models with the IXPE data and conclude that the observed polarization properties are compatible with a scenario in which matter accretes onto the black hole through a …

Structuralism In Differential Equations, Colin Mclarty

Faculty Scholarship

Structuralism in philosophy of mathematics has largely focused on arithmetic, algebra, and basic analysis. Some have doubted whether distinctively structural working methods have any impact in other fields such as differential equations. We show narrowly construed structuralism as offered by Benacerraf has no practical role in differential equations. But Dedekind’s approach to the continuum already did not fit that narrow sense, and little of mathematics today does. We draw on one calculus textbook, one celebrated analysis textbook, and a monograph on the Navier–Stokes equation to show structural methods like Dedekind’s have long been central to differential equations, and have philosophically …

Observational Features Of Charge Distribution In Earth's Inner Magnetosphere, Lai Gao, Chao Shen, Yufei Zhou, Yong Ji, Zuyin Pu, George Parks, Christopher T. Russell, Gang Zeng, Lan Ma, Roy B. Torbert, Yanyan Yang, James L. Burch

Faculty Publications

Understanding the motion of charged particles in the electromagnetic field in the inner magnetosphere is essential for space science and space weather. Charge accumulation can occur due to the dipole magnetic and convective electric fields in this region. However, until the recent Magnetospheric Multiscale (MMS) mission, there were few means to detect charge distribution in situ. We report unambiguous in situ observation of the spatial distribution of the excess charge density in the inner magnetosphere by the MMS mission. We find that a positive (negative) charge accumulates in the dusk (dawn) side inner magnetospheres, which is contrary to the long …

Observational Features Of Charge Distribution In Earth's Inner Magnetosphere, Lai Gao, Chao Shen, Yufei Zhou, Yong Ji, Zuyin Pu, George Parks, Christopher T. Russell, Gang Zeng, Lan Ma, Roy B. Torbert, Yanyan Yang, James L. Burch

Faculty Publications

Understanding the motion of charged particles in the electromagnetic field in the inner magnetosphere is essential for space science and space weather. Charge accumulation can occur due to the dipole magnetic and convective electric fields in this region. However, until the recent Magnetospheric Multiscale (MMS) mission, there were few means to detect charge distribution in situ. We report unambiguous in situ observation of the spatial distribution of the excess charge density in the inner magnetosphere by the MMS mission. We find that a positive (negative) charge accumulates in the dusk (dawn) side inner magnetospheres, which is contrary to the long …

Stack For Computational Science, Mathematics And Engineering E-Learners, Idrissa S. Amour

Tanzania Journal of Engineering and Technology (TJET)

Petroleum economic evaluation involves estimating revenues from forecasted production profiles and field costs including capital expenditures (CAPEX), drilling expenses (DRILLEX), and operating expenses (OPEX). The existing cost-estimating tool requires several inputs making it time-intensive and difficult to use with few data during the early stages of projects. Majority of the previously developed time saving cost estimations proxy models rely on unrealistic assumptions that include uniform operational costs for different fields with a different number of wells, casings, and drilled depths. This work focused at developing proxy models that consider the variability of the development costs with different parameters. The developed …

What Diameter? What Height? Influence Of Measures Of Average Tree Size On Area-Based Allometric Volume Relationships, Yilin Wang, John A. Kershaw, Mark J. Ducey, Yuan Sun, James B. Mccarter

Faculty Publications

Volume is an important attribute used in many forest management decisions. Data from 83 fixed-area plots located in central New Brunswick, Canada, are used to examine how different measures of stand-level diameter and height influence volume prediction using a stand-level variant of Honer's (1967) volume equation. When density was included in the models (Volume=f(Diameter,Height,Density)) choice of diameter measure was more important than choice of height measure. When density was not included (Volume=f(Diameter,Height)), the opposite was true. For models with density included, moment-based estimators of stand diameter and height performed better than all other measures. For models without density, largest tree …

What Diameter? What Height? Influence Of Measures Of Average Tree Size On Area-Based Allometric Volume Relationships, Yilin Wang, John A. Kershaw, Mark J. Ducey, Yuan Sun, James B. Mccarter

Faculty Publications

Volume is an important attribute used in many forest management decisions. Data from 83 fixed-area plots located in central New Brunswick, Canada, are used to examine how different measures of stand-level diameter and height influence volume prediction using a stand-level variant of Honer's (1967) volume equation. When density was included in the models (Volume=f(Diameter,Height,Density)) choice of diameter measure was more important than choice of height measure. When density was not included (Volume=f(Diameter,Height)), the opposite was true. For models with density included, moment-based estimators of stand diameter and height performed better than all other measures. For models without density, largest tree …

Melding Mindsets: Isolated Content, Same Destination, Hidden Opportunity, Kenneth Holman M.Ed., Shalece Kohnke Ph.D.

Constellations: Online STEM Teacher Education Journal

The authors emphasize the underutilized opportunities that exist in overlapping and integrating these two disciplines, advocating for a cross-curricular approach to enhance student learning and understanding. The paper highlights the connections between mathematics and science standards, particularly focusing on the National Council of Teachers of Mathematics (NCTM) Process Standards and Next Generation Science Standards (NGSS) Science and Engineering Practices. These standards not only demonstrate the interconnection between the two subjects but also highlight their importance in shaping informed citizens.

Forecasting The Strength Of Graphene Nanoparticles-Reinforced Cementitious Composites Using Ensemble Learning Algorithms, Majid Khan, Roz-Ud-Din Nassar, Waqar Anwar, Mazhar Rasheed, Taoufik Najeh, Yaser Gamil, Furqan Farooq

Faculty Publications

Contemporary infrastructure requires structural elements with enhanced mechanical strength and durability. Integrating nanomaterials into concrete is a promising solution to improve concrete strength and durability. However, the intricacies of such nanoscale cementitious composites are highly complex. Traditional regression models encounter limitations in capturing these intricate compositions to provide accurate and reliable estimations. This study focuses on developing robust prediction models for the compressive strength (CS) of graphene nanoparticle-reinforced cementitious composites (GrNCC) through machine learning (ML) algorithms. Three ML models, bagging regressor (BR), decision tree (DT), and AdaBoost regressor (AR), were employed to predict CS based on a comprehensive dataset of …

Forecasting The Strength Of Graphene Nanoparticles-Reinforced Cementitious Composites Using Ensemble Learning Algorithms, Majid Khan, Roz-Ud-Din Nassar, Waqar Anwar, Mazhar Rasheed, Taoufik Najeh, Yaser Gamil, Furqan Farooq

Faculty Publications

Contemporary infrastructure requires structural elements with enhanced mechanical strength and durability. Integrating nanomaterials into concrete is a promising solution to improve concrete strength and durability. However, the intricacies of such nanoscale cementitious composites are highly complex. Traditional regression models encounter limitations in capturing these intricate compositions to provide accurate and reliable estimations. This study focuses on developing robust prediction models for the compressive strength (CS) of graphene nanoparticle-reinforced cementitious composites (GrNCC) through machine learning (ML) algorithms. Three ML models, bagging regressor (BR), decision tree (DT), and AdaBoost regressor (AR), were employed to predict CS based on a comprehensive dataset of …

New Calabi–Yau Manifolds From Genetic Algorithms, Per Berglund, Yang-Hui He, Elli Heyes, Edward Hirst, Vishnu Jejjala, Andre Lukas

Faculty Publications

Calabi–Yau manifolds can be obtained as hypersurfaces in toric varieties built from reflexive polytopes. We generate reflexive polytopes in various dimensions using a genetic algorithm. As a proof of principle, we demonstrate that our algorithm reproduces the full set of reflexive polytopes in two and three dimensions, and in four dimensions with a small number of vertices and points. Motivated by this result, we construct five-dimensional reflexive polytopes with the lowest number of vertices and points. By calculating the normal form of the polytopes, we establish that many of these are not in existing datasets and therefore give rise to …

Quik Church, Route 3.141592, Sarah Voss

Journal of Humanistic Mathematics

The following set of poems are from one of ten sections in a collection of poetry called Quik Church: Short Poems that Travel Far. Each section illustrates one of many “streets” which individuals often take on their spiritual journey through life, e.g., the Old Gods Path, Nature Trail, Memory Skyway, Mystic Avenue, Pastoral Lane, and so on. This one, Route 3.141592, is the route of mathematics and the science that depends on mathematics.