Digital Commons Network^™

Geometric Shapes That Sing And Move: An Interdisciplinary Lesson With Pre-Service Teachers, Gladys Krause, Gustavo Velandia

Journal of Humanistic Mathematics

Our work shares a practical example of an interdisciplinary lesson in which two teacher educators collaborated to integrate mathematics and music in an elementary mathematics methods course. This paper describes the process of collaboration in designing the lesson and shares original instructional resources to be used in the classroom. We also discuss what the pre-service teachers participating in the lesson shared about their learning experience, and what we, the teacher educators, learned from this experience. In presenting this work we aim to promote the opening of spaces in teacher preparation programs that allow pre-service teachers to develop their own instructional …

Fibonacci-Inspired Spiral Quilts, Kathleen Offenholley, Sk Collins, David Radcliffe

Journal of Humanistic Mathematics

This article provides insight into the mathematics and designs of quilts inspired by Fibonacci and logarithmic spirals. We introduce the history and development of the Fibonacci number sequence and how to hand-draw a Fibonacci spiral. Further, we explain the relationship between the Fibonacci spiral and logarithmic spirals, the advantages of using logarithmic spirals to create designs, and how to produce digital spiral designs using Desmos, a free web-based graphing calculator. Finally, we discuss methods for designing spiral quilts or other triangle and spiral designs (such as collage or other media) and derive a formula for calculating the apex angles of …

States Of Matter, Todd Sformo

Journal of Humanistic Mathematics

This is a non-fiction essay overtly about three methods used in overwintering physiology, set in the context of my first learning them, along with associated thoughts and ideas as I began working on my PhD. The mathematics shows up mainly in the final section of the essay whose subtitle plays on a poem by Wallace Stevens called “Anecdote of the Jar”. This section is fable-like in its explanation of protein purification and begins with an impossible statement that is slowly adjusted to make sense by words and math.

Badass Women, Richard Delaware

Journal of Humanistic Mathematics

In this true story, one mathematics major supports another in an unexpected way.

Intuitive Explanations In Mathematical Education, Jerzy Pogonowski

Journal of Humanistic Mathematics

I discuss the role of intuitive explanations in the learning, teaching, and popularization of mathematics. Several examples of such explanations are presented, related to linguistic explanations, perception, empirical models, and internal explanations inside mathematics itself. I emphasize the fact that intuitive explanations in a sense transgress mere mathematical arguments. I also discuss in brief the role of paradox resolution in mathematical education.

Bootstraps And Scaffolds: What A Cognitive-Historical Analysis Of The Complex Number System Reveals About Numerical Cognition, Charles R. Card, Gary G. Miller

Journal of Humanistic Mathematics

The following investigation is a cognitive-historical analysis of the conceptual development of complex numbers. The history of this development spans nearly two millennia, from the earliest appearance of the square root of a negative quantity in the calculations of Heron of Alexandra (1st Century CE) to the full flowering of complex numbers in the first half of the 19th Century. The approach used for this analysis is Nersessian's, including her formulations of model-based reasoning and mental models. Additional aspects of the analysis feature the prominent roles played by process representations, including object-process complementarities, and by core numerical systems. Our analysis …

Building Communities Of Care For Equity, Justice, And Culturally Responsive Practice In Mathematics Education, Nicole Fletcher, B Waid

Journal of Humanistic Mathematics

Teaching is widely considered one of the “caring professions,” but conceptualizations of care and how care is put into practice in education are not universal. In this article, we draw from a range of perspectives on care that integrate supportive interpersonal relationships, high expectations, and culturally relevant theories of critical care, as well as Queer Theory and Disability Justice, to explore the application of these ideas in mathematics education. We identify key elements for building communities of care in mathematics education contexts: co-constructing community agreements, redefining participation, shifting traditional power structures, collaborative problem solving, and building networks of care beyond …

Mathematical Models And Pedagogy Of Marxist Political Economy, Christopher Perez

Journal of Humanistic Mathematics

How can we teach people about the economics of labor and exploitation in mathematics courses? We define a mathematical model for describing the relationships embodied by commodities and labor. We then use this model to illustrate the exploitative nature of profit and the tendency for catastrophic chain-reactions that lead to market crashes. Lastly, we discuss applications to pedagogy in mathematics courses using a simplified version of the model.

The Braids On Your Blanket, Michelle Cheng, Robert Uwe Laugwitz

Journal of Humanistic Mathematics

In this expository essay, we introduce some elements of the study of groups by analysing the braid pattern on a knitted blanket. We determine that the blanket features pure braids with a minimal number of crossings. Moreover, we determine polynomial invariants associated to the links obtained by closing the braid patterns of the blanket.

What Is An Imaginary Number? The Plane And Beyond, Andrew W. Powell

Journal of Humanistic Mathematics

In this article I argue that i is a quantity associated with the two-dimensional real number plane, whether as a vector, a bi-vector, a point or a transformation (rotation). This position provides a foundation for the complex numbers and accounts for complex numbers in some equations of applied mathematics and physics. I also argue that complex numbers are fundamentally geometrical and can be described by geometric algebra, and that moreover the meaning of complex numbers in physics varies with dimension and geometry of the manifold.

Millions, Billions, Or Trillions: How To Partition Large Numbers Into Friendly Figures, Eryn Michelle Maher, Ha Nguyen, Cynthia Sanchez Tapia

Journal of Humanistic Mathematics

Communicating and making sense of large numbers — millions, billions, and trillions — is a persistent struggle in our society. Using large numbers is a learning requirement for elementary school children, but even adults struggle with it. Hence supporting future teachers in developing their own understanding of the concepts is valuable. To construct, enact, and revise an educational experience for preservice teachers, we apply three frameworks of teaching mathematics for social justice tasks, high cognitive demand tasks, and productive mathematics discussion. The context uses United States educational and defense spending, the national budget, and the gross domestic product. Preservice teachers …

Language Analysis Via The Run And Flattened Statistics On Permutations, Jennifer Elder, Pamela E. Harris, Anthony Simpson

Journal of Humanistic Mathematics

A permutation π in Sn can be decomposed into its runs π = τ₁τ₂ . . . τ_k, where a run of π is a maximal contiguous subsequence whose elements are in increasing order. If the first values of each run are in increasing order, then π is said to be flattened. Motivated by the study of flattened permutations, we study the words in the Danish, German, English, Spanish, French, Italian, Dutch, and Norwegian languages. In each language considered, our work provides the following: a list of the longest flattened words, histograms for the proportion …

The Modern Geometrician: Euclidean Construction For Digital Paper, Deborah A. Kent, David J. Muraki

Journal of Humanistic Mathematics

The emphasis on traditional hand-drawn compass and straight-edge geometrical constructions has been reduced in the core narrative of most current curricula. In response to this trend, this paper presents a virtual toolkit for producing precision geometrical figures within the popular note-taking app, Notability. These graphical procedures employ the app's stylus-based input and shape tools (for lines, circles and squares) to offer a modern take on classical geometrical construction. These procedures are adaptations of familiar textbook methods, necessary because the app's circle-drawing tool behaves differently from a standard compass. Beyond the familiar canon of elementary Euclidean constructions, such as angle bisectors …

Sociomathematical Norms And Automated Proof Checking In Mathematical Education: Reflections And Experiences, Merlin Carl

Journal of Humanistic Mathematics

According to a widely held view, mathematical proofs are essentially (indications of) formal derivations, and thus in principle mechanically checkable (this view is defended, for example, by Azzouni [3]). This should in particular hold for the kind of simple proof exercises typically given to students of mathematics learning to write proofs. If that is so, then automated proof checking should be an attractive option for math education at the undergraduate level. An opposing view would be that mathematical proofs are social objects and that what constitutes a mathematical proof can thus not be separated from the social context in which …

My Own Private World Of Non-Ordinary Associative Arithmetics, Marion D. Cohen

Journal of Humanistic Mathematics

A binary operation # on Z+ is said to be an associative arithmetic if both # and its iteration — the binary operation ∗ defined recursively by: x∗1 = x and x∗y = [x ∗ (y − 1)]#x — are associative. E. Rosinger [6] showed that under reasonable conditions an associative arithmetic must be ordinary addition. However, in the general case, there are associative arithmetics that are not ordinary addition. This paper gives examples of these as well as results towards a structure theorem for associative arithmetics. The paper also describes the role that this particular math problem has played …

Mathematical Anxiety In The Turkish Context: Mathematical Experiences Of High School Students, Vahap Yorgun, Serdal Mert

Journal of Humanistic Mathematics

Although a handful of studies have investigated the prevalence of math anx- iety among Turkish school children and its relationship with several variables like attitudes toward math, gender, self-efficacy, parental style, there is as of now no study focusing on development psychological interventions to cope with math anxiety. Most of the extant studies use quantitative approaches, but in order to develop intervention programs, researchers need to know how math anxiety develops, what kinds of personal variables or factors take place in this process, and what kind of emotional and cognitive reactions hold by students about math. Thus in our research, …

Picturing Mathematics (Education) In New Ways, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Adult Coping As A Function Of Perceived Parental Support, Brenda Manning

Journal of Counseling and Psychology

The present study examined the function of perceived parental support in childhood on adult coping strategies. A convenient sample taken from social media collected data from fifty-three participants aged 20-68 who completed the Parental Acceptance-Rejection Questionnaires (PARQ) and Screening Tool for Adult Children of Alcoholic Traits (STACAT). Participants indicated moderate levels of parental (maternal and paternal) rejection (M=130.61, SD=37.67). Additionally, participants reported moderate levels of adult children of alcoholic traits related to perceived parental rejection (M=99.86, SD=22.82). Results indicated a statistically significant positive relationship (r = .534; p =.001) between perceived parental acceptance-rejection and adult children of alcoholic traits, suggesting …

Exploring The Use Of Student-Professional Simulation-Based Interprofessional Education: A Preliminary Qualitative Study, Catherine M. Andrea, Summer San Lucas, Anne Boddy

Journal of Innovation in Health Sciences Education

Introduction: Simulation is commonly used to address interprofessional learning within healthcare programs to develop practice-ready clinicians. However, barriers such as scheduling, and discrepancy of learners’ knowledge and attitudes often pose challenges for educators to implement student-student (S-S) simulation-based interprofessional education (IPE). This study explored student perceptions about a novel simulation-based IPE mode in which students were paired with professionals from other disciplines.

Methods: The qualitative study explored 14 Doctor of Physical Therapy (DPT) students’ perceptions about a simulated-learning activity with professionals from other disciplines. One-on-one semi-structured interviews with students from two private universities were analyzed using a constant comparative method …

The Effect Of Blood Flow Restriction Training On Quadriceps Activity After Anterior Cruciate Ligament Reconstruction: A Preliminary Randomized Controlled Trial, Florian Forelli, Camille Nguyen, Jean Mazeas, Georgios Kakavas, Timothy E. Hewett, Andreas Bjerregaard, Vasileios Korakakis, Alexandre Jm Rambaud

Marshall Journal of Medicine

Background

After anterior cruciate ligament reconstruction, a crucial priority is restoring knee muscle strength, especially the quadriceps, to reach the pre-injury strength levels as fast as possible. A feasible alternative to heavy loading might be blood flow restriction training that may elicit quadriceps muscle strength adaptations using low external loads. This study assessed whether quadriceps strengthening using low load blood flow restriction (LL-BFR) would enhance electromyographic (EMG) activity of the vastus medialis (VMO), vastus lateralis (VLO), and rectus femoris (RF) similar to quadriceps strengthening using heavy loads resistance training (HLRT). The secondary objective was to assess intra-quadriceps regional EMG differences …

A Case Of Herpes Zoster In An Immunocompetent 19-Year-Old Female, Martin Nguyen, Jennifer Read, Emma Filary, Aaron Mcguffin

Marshall Journal of Medicine

This case report describes the unusual presentation of herpes zoster in a fully vaccinated teenage patient and highlights management considerations. The patient is a 19-year-old female who presented with pain in her left lower back, side, and upper thigh for approximately 3 days, which was then followed by the eruption of a vesicular rash along the L2 dermatome consistent with herpes zoster. Herpes zoster is predominantly observed only in elderly and immunocompromised individuals, primarily due to the widespread use of the varicella-zoster virus vaccine for children since 1995, when it became part of the routine immunization schedule. However, this case …

Management Of Multiple Infantile Hemangiomas In A Preterm Infant: A Clinical Case Report, Erin Reese, Wyatt Grimm, Aaron Mcguffin

Marshall Journal of Medicine

Infantile hemangiomas (IH), the most prevalent infantile tumor, are benign vascular tumors arising from proliferation and dysregulation of angiogenesis. Hemangiomas are present after birth and undergo 3 stages: proliferation, plateau, and involution. IH are further categorized into superficial, deep, and mixed based on skin and internal organ involvement. IH are clinically diagnosed, and treatment options include active observation, corticosteroids, beta-blockers, pingyangmycin, vincristine, or laser treatment. Complications of untreated IH include ulceration, airway obstruction, and visual obstruction at sites of enlarging lesions. While most cases are benign, there are associated complications prompting a thorough investigation and proper management. Understanding a hemangioma …

Enhancing Fuel Injection System Reliability Through Weibull Family Functions Analysis, Ali Nouri Qarahasanlou, Abbas Barabadi, Meisam Saleki, Ali Rahimazar, Parisa Rezakhania, Masoume Gholamia

Journal of Sustainable Mining

The efficient operation of heavy machinery is crucial to the success of mining and civil construction operations. To guarantee this performance, equipment performance is assessed using the Reliability Index, which analyzes failures to study the ability of a system to carry out its intended functions under predetermined conditions. On the other hand, the failure rate and operational environmental condition (such as management decisions, maintenance performance, etc., that are defined as “risk factors”) over the life cycle of industrial systems pose a significant challenge to reliability analysis. This paper proposes an approach to address these challenges by extending Weibull family functions …

Fatal Fatigue: Thrombotic Thrombocytopenic Purpura, Rachel K. Kitzmann

SIU Journal of Medical Science Scholarly Works

A 75 year old female presented to the family medicine clinic with complaints of fatigue, intermittent epigastric pain, decreased appetite with associated weight loss, easy bruising, and bilateral hand tremors. Physical exam was positive for scattered bruising, but otherwise benign. Initial differential diagnoses included hypothyroidism, anemia, vitamin or mineral deficiency, sleep apnea, malignancy, and tick-borne illness. Preliminary labs were drawn in clinic. The patient presented to the Emergency Department within 2 hours of leaving the clinic due to stroke-like symptoms. Workup revealed markedly low platelets with schistocytes identified on peripheral blood smear. PLASMIC score was applied, which indicated a high …

The Composite Light Capturing Configuration That Contains 3 Categories Of Focal Lengths Which Is Utilized To Capture The Same Scene., Punarjeewa Abeysekera

Defensive Publications Series

This paper describes a composite light capturing configuration that contains 3 categories of focal lengths which is utilized to capture the same scene. The composite light capturing configuration will contain 2 main light capturing configurations, one main light capturing configuration per each eye. Each main light capturing configuration will contain 3 light capturing configurations where each light capturing configuration will have a unique focal length. The composite light capturing configuration, by utilizing the 6 light capturing configurations it contains, will have the capability to capture the scene in front of it where the 3 categories of focal lengths will enable …

Factors Influencing Online Repurchase Intention In Indonesia’S E-Commerce Market: A Structural Equation Modeling Approach, Egia Etha, Pijar Suciati, Ajenk N. Citra

Jurnal Sosial Humaniora Terapan

The rapid expansion of e-Commerce in Indonesia has revolutionized consumer behavior, shifting preferences from traditional retail to the dynamic world of online shopping. This paradigm shift necessitates a deep understanding of consumer online buying behavior, which unfolds in two critical stages: initial purchase intention and the all-important repurchase intention. The latter is a key determinant of e-Commerce success, reflecting customer loyalty and the overall health of an online business. This research delves into the significant factors driving Indonesian consumers' online repurchase intentions, employing a robust quantitative methodology. A comprehensive survey was conducted with 200 e-commerce shoppers, utilizing both email and …

“Trying To Remain Calm…But I Do Reach My Limit Sometimes”: An Exploration Of The Meaning Of Gentle Parenting, Anne E. Pezalla, Alice J. Davidson

Faculty Publications

Raising young children has always been hard, but evidence suggests that it may be getting harder. The isolation of the pandemic, the pressures to fulfill exacting parenting standards, and the explosion of “expert” parenting advice on social media have fueled the rise of “gentle parenting,” an approach that pivots away from older, discipline-heavy parenting typologies and which promises the development of happier, healthier children. Despite the popularity of gentle parenting, it has received no empirical scrutiny. The current study represents the first systematic investigation of what gentle parenting entails. Data were gathered from a sample (N = 100) of parents …

Exploring The Dark And Gothic: An Analysis Of Edgar Allan Poe And Nathaniel Hawthorne’S Gothic Elements In American Literature, Alejandra Serna

Theses and Dissertations

This paper examines the significant contributions of Edgar Allan Poe and Nathaniel Hawthorne to the development of American Gothic literature. Poe’s stories “The Tell-Tale Heart” and “The Black Cat” are renowned for their psychological elements and exploration of the human psyche, while Hawthorne’s “The Birthmark” questions the nature of evil as a universal human experience. By examining the ways in which these authors engage with themes of mental disorders, symbolism, and science versus nature, this thesis explores how such work by Poe and Hawthorne play in shaping the readers' understanding of the darker elements of American Gothic literature and its …

Parental Attitudes Toward Infant Sleep In The First Year Of Life: A Systems Framework, Shayna Sarah Zargari

ETD Collection

Previous research indicates that infant sleep is a complex topic for parents to navigate. Parents often face exhaustion and stress in putting their infants to sleep and may try different methods of encouraging them to sleep independently. Utilizing Uri Bronfebrenner’s Ecological Systems Theory (1979), this study examines parental background (e.g., occupation, race, religion, socioeconomic status) in relation to attitudes and interventions towards infant sleep. This research also considers where and how parents receive information regarding infant sleep and what supports parents rely on in navigating their infants’ sleep journeys. From a sample of mothers, this study finds that the macrosystem …