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Figure-Ground Perception: A Poem Proof, Richard Delaware Feb 2023

Figure-Ground Perception: A Poem Proof, Richard Delaware

Journal of Humanistic Mathematics

This is a proof, in poetic form, of a bit of real analysis, more specifically involving the topology of accumulation points, that exploits the human optical phenomenon of figure-ground perception. Sometimes it is not a change in content, but a snap shift in point of view that yields a proof.

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Using Bloom's Taxonomy For Math Outreach Within And Outside The Classroom, Manmohan Kaur Feb 2023

Using Bloom's Taxonomy For Math Outreach Within And Outside The Classroom, Manmohan Kaur

Journal of Humanistic Mathematics

Not everyone is a great artist, but we don’t often hear, “I dislike art.” Most people are able to appreciate visual arts, music and sports, without necessarily excelling in it themselves. On the other hand, the phrase “I dislike math” is widely prevalent. This is especially ironic in our current society, where mathematics affects our day-to-day activities in essential ways such as e-commerce and e-mail. This paper describes the opportunity to popularize mathematics by focusing on its fun and creative aspects, and illustrates this opportunity through a brief discussion of interdisciplinary topics that expose the beauty, elegance and value of …

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The Mathematics Of The Harp: Modeling The Classical Instrument And Designing Futuristic Ones, Cristina Carr, Daniel Chioffi, Maya Glenn, Stefan O. Nita, Vlad N. Nita, Bogdan G. Nita Feb 2023

The Mathematics Of The Harp: Modeling The Classical Instrument And Designing Futuristic Ones, Cristina Carr, Daniel Chioffi, Maya Glenn, Stefan O. Nita, Vlad N. Nita, Bogdan G. Nita

Journal of Humanistic Mathematics

We analyze and model the neck of the classical harp based on the length of the strings, their tension and density. We then use the results to design new and innovative harp shapes by adjusting the parameters of the model.

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Lessons From Human Experience: Teaching A Humanities Course Made Me A Better Math Teacher, Erin Griesenauer Feb 2023

Lessons From Human Experience: Teaching A Humanities Course Made Me A Better Math Teacher, Erin Griesenauer

Journal of Humanistic Mathematics

As a professor at a Liberal Arts college, I recently taught a General Education course called Human Experience. Far from my normal experiences in the mathematics classroom, in Human Experience I was tasked with teaching topics from the humanities, including art, philosophy, history, and political science. Teaching this course was challenging, but it was also transformative. Teaching a course so far from my background gave me the opportunity to experiment with different pedagogical techniques and to reflect on how I set up my math classes. I learned many lessons that I have brought back to my math classes—lessons that have …

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The Nothing That Really Matters, Szilárd Svitek Feb 2023

The Nothing That Really Matters, Szilárd Svitek

Journal of Humanistic Mathematics

Zero has (a) special role(s) in mathematics. In the current century, we take negative numbers and zero for granted, but we should also be aware that their acceptance and their emergence in mathematics, and their ubiquity today, have not come to happen as rapidly as, for example, that of natural numbers. Students can quickly become confused by the question: is zero a natural number? The answer is simple: a matter of definition. The history of zero and that of negative numbers are closely linked. It was in the calculations of debts that the negative numbers first appeared, where the state …

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The Use And Development Of Mathematics Within Creative Literature, Toby S C Peres Feb 2023

The Use And Development Of Mathematics Within Creative Literature, Toby S C Peres

Journal of Humanistic Mathematics

This paper presents a study on the extent to which creative literature been used as a vessel to carry forward the development of mathematical thought. The role of mathematics as a driving force for literature is highlighted, and while many examples exist that clearly show an attempt to disperse mathematical ideas, with Lewis Carroll, OuLiPo and ancient poetry considered, the argument that the sole purpose of the writings was for the sake of mathematical development is not clear-cut.

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The Genesis Of A Theorem, Osvaldo Marrero Feb 2023

The Genesis Of A Theorem, Osvaldo Marrero

Journal of Humanistic Mathematics

We present the story of a theorem's conception and birth. The tale begins with the circumstances in which the idea sprouted; then is the question's origin; next comes the preliminary investigation, which led to the conjecture and the proof; finally, we state the theorem. Our discussion is accessible to anyone who knows mathematical induction. Therefore, this material can be used for instruction in a variety of courses. In particular, this story may be used in undergraduate courses as an example of how mathematicians do research. As a bonus, the proof by induction is not of the simplest kind, because it …

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Where Do Babies Come From?, Marcio Luis Ferreira Nascimento Feb 2023

Where Do Babies Come From?, Marcio Luis Ferreira Nascimento

Journal of Humanistic Mathematics

According to European folklore, popularized by a fairy tale, storks are responsible for bringing babies to new parents. This probably came from observation in certain European countries, such as Norway, Netherlands or Germany, that storks nesting on the roofs of households were believed to bring good luck, as the possibility of new births. People love stories, but correlation simply means that there is a relationship between two factors that tells nothing about the direction of said relationship, if any. Another possibility is simple coincidence. Let us say that it’s possible that one factor causes another. It’s also possible that the …

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Teaching Mathematics After Covid: A Conversation Not A Discussion, Wendy Ann Forbes, Joyce Mgombelo Feb 2023

Teaching Mathematics After Covid: A Conversation Not A Discussion, Wendy Ann Forbes, Joyce Mgombelo

Journal of Humanistic Mathematics

Inspired by Brent Davis' conceptualization of listening and conversation in his book Teaching Mathematics: Toward a Sound Alternative, we propose how we as a mathematics education community may move forward by continuing in the conversation that emerged from COVID. We encourage all involved to listen rather than assume a discussion-oriented stance. Using an enactivist lens, we look at the pandemic learning space, give an overview of the education conversation that emerged in Ontario, and offer a way to rethink Mathematics Education within the frame of a conversation. We believe that if mathematics education is to engage learners in a meaningful …

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A Classification Of Musical Scales Using Binary Sequences, Thomas Hillen Feb 2023

A Classification Of Musical Scales Using Binary Sequences, Thomas Hillen

Journal of Humanistic Mathematics

Every beginning music student has gone through the four main musical scales: major, natural minor, harmonic minor, and melodic minor. And some might wonder, why those four and not five, or six, or just three? Here we show that a mathematical classification can be used to identify these scales as representatives of certain scale families. Moreover, the classification reveals another scale family, which is much less known: the harmonic major scale. We find that each scale family contains exactly seven scales, which include the modes (dorian, phrygian,...) and other scales such as the Romanian, …

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Human-Machine Collaboration In The Teaching Of Proof, Gila Hanna, Brendan P. Larvor, Xiaoheng (Kitty) Yan Feb 2023

Human-Machine Collaboration In The Teaching Of Proof, Gila Hanna, Brendan P. Larvor, Xiaoheng (Kitty) Yan

Journal of Humanistic Mathematics

This paper argues that interactive theorem provers (ITPs) could play an important role in fostering students’ appreciation and understanding of proof and of mathematics in general. It shows that the ITP Lean has three features that mitigate existing difficulties in teaching and learning mathematical proof. One is that it requires students to identify a proof strategy at the start. The second is that it gives students instant feedback while allowing them to explore with maximum autonomy. The third is that elementary formal logic finds a natural place in the activity of creating proofs. The challenge in using Lean is that …

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The Merchant And The Mathematician: Commerce And Accounting, Graziano Gentili, Luisa Simonutti, Daniele C. Struppa Feb 2023

The Merchant And The Mathematician: Commerce And Accounting, Graziano Gentili, Luisa Simonutti, Daniele C. Struppa

Journal of Humanistic Mathematics

In this article we describe the invention of double-entry bookkeeping (or partita doppiaas it was called in Italian), as a fertile intersection between mathematics and early commerce. We focus our attention on this seemingly simple technique that requires only minimal mathematical expertise, but whose discovery is clearly the result of a mathematical way of thinking, in order to make a conceptual point about the role of mathematics as the humus from which disciplines as different as operations research, computer science, and data science have evolved.

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Collapsing Spaces, Colliding Places: Leveraging Constructs From Humanistic Geography To Explore Mathematics Classes, Valentin A. B. Küchle, Shiv S. Karunakaran, Mariana Levin, John P. Smith Iii, Sarah Castle, Jihye Hwang, Yaomingxin Lu, Robert A. Elmore Feb 2023

Collapsing Spaces, Colliding Places: Leveraging Constructs From Humanistic Geography To Explore Mathematics Classes, Valentin A. B. Küchle, Shiv S. Karunakaran, Mariana Levin, John P. Smith Iii, Sarah Castle, Jihye Hwang, Yaomingxin Lu, Robert A. Elmore

Journal of Humanistic Mathematics

Humanistic geographers distinguish between space and place: “What begins as undifferentiated space becomes place as we get to know it better and endow it with value” (Tuan, 1977, page 6). In this essay, we seek to demonstrate how mathematics education researchers and mathematics instructors may find space and place illuminating for understanding important aspects of students’ learning experiences during the coronavirus pandemic—and possibly beyond. Specifically, after introducing the terms and relating them to the context of a university mathematics class, we exemplify how home and class places collided for three undergraduate mathematics students forced to deal with the abrupt …

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The Roles Of Mathematical Metaphors And Gestures In The Understanding Of Abstract Mathematical Concepts, Omid Khatin-Zadeh, Zahra Eskandari, Danyal Farsani Feb 2023

The Roles Of Mathematical Metaphors And Gestures In The Understanding Of Abstract Mathematical Concepts, Omid Khatin-Zadeh, Zahra Eskandari, Danyal Farsani

Journal of Humanistic Mathematics

When a new mathematical idea is presented to students in terms of abstract mathematical symbols, they may have difficulty to grasp it. This difficulty arises because abstract mathematical symbols do not directly refer to concretely perceivable objects. But, when the same content is presented in the form of a graph or a gesture that depicts that graph, it is often much easier to grasp. The process of solving a complex mathematical problem can also be facilitated with the use of a graphical representation. Transforming a mathematical problem or concept into a graphical representation is a common problem solving strategy, and …

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From A Doodle To A Theorem: A Case Study In Mathematical Discovery, Juan FernáNdez GonzáLez, Dirk Schlimm Feb 2023

From A Doodle To A Theorem: A Case Study In Mathematical Discovery, Juan FernáNdez GonzáLez, Dirk Schlimm

Journal of Humanistic Mathematics

We present some aspects of the genesis of a geometric construction, which can be carried out with compass and straightedge, from the original idea to the published version (Fernández González 2016). The Midpoint Path Construction makes it possible to multiply the length of a line segment by a rational number between 0 and 1 by constructing only midpoints and a straight line. In the form of an interview, we explore the context and narrative behind the discovery, with first-hand insights by its author. Finally, we discuss some general aspects of this case study in the context of philosophy of mathematical …

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Where Does Mathematics Come From? Really, Where?, Mark Huber, Gizem Karaali Feb 2023

Where Does Mathematics Come From? Really, Where?, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

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Front Matter Feb 2023

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

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The Effects Of Covid-19 On Clinical Coordination And The Education Of Physician Assistant Students, Halley Barke Feb 2023

The Effects Of Covid-19 On Clinical Coordination And The Education Of Physician Assistant Students, Halley Barke

SIU Journal of Medical Science Scholarly Works

COVID-19 left a damaged path since its arrival in December 2019. Clinical Coordination in a Physician Assistant (PA) program is an important aspect of PA education. It is important to examine the effects, good or bad, that COVID-19 and other factors have played in the clinical rotation scheduling and placement of PA students in their clinical rotation experiences. To evaluate those effects, it was determined to look at the encounter numbers from the past seven years in the Evalue online system of students in the Southern Illinois University (SIU) PA program as well as survey results obtained from other institutions …

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Speech Pathology Student Perspectives On Virtual Reality To Learn A Clinical Skill, Bridget Kelly, Joanne Walters, Rachael Unicomb Feb 2023

Speech Pathology Student Perspectives On Virtual Reality To Learn A Clinical Skill, Bridget Kelly, Joanne Walters, Rachael Unicomb

Teaching and Learning in Communication Sciences & Disorders

Evidence supports the use of simulation in educating speech pathology (SP) students, however most of the research has centered on low fidelity techniques as opposed to high fidelity and immersive technologies like virtual reality (VR). Whilst there has been research on the use of VR to teach clinical skills to students in other health disciplines (e.g., dentistry, nursing), use of VR in SP has focused mainly on its use in client intervention. There is an opportunity to use VR to teach clinical skills to SP students, particularly in response to barriers to clinical placement opportunities like the COVID 19 pandemic. …

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Teaching End-Of-Life Care In Speech-Language Pathology: A Tutorial, Amanda Stead, Sara Haynie, Monica Vinson Feb 2023

Teaching End-Of-Life Care In Speech-Language Pathology: A Tutorial, Amanda Stead, Sara Haynie, Monica Vinson

Teaching and Learning in Communication Sciences & Disorders

Speech-language pathologists often lack preparation for working with patients near the end of life (EoL). Few academic training programs offer dedicated or sufficient content in the area of end-of-life care (EoLC). Furthermore, traditional knowledge-focused outcomes are not the most effective pedagogical strategy in teaching EoL and palliative care to students. Instead, a focus on self-awareness and personal beliefs in relation to death and dying have been shown to have a positive effect on attitudes toward EoLC. The purposes of this paper are three-fold: First, to explore what is known about the teaching and training of EoL in the discipline of …

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Examining The Item-Level Psychometric Properties Of The Self-Efficacy Questionnaire (Seq) For Students In Communication Sciences And Disorders, Sabiha Parveen, Neila Donovan, Gina Morris, Kristi Dickey Feb 2023

Examining The Item-Level Psychometric Properties Of The Self-Efficacy Questionnaire (Seq) For Students In Communication Sciences And Disorders, Sabiha Parveen, Neila Donovan, Gina Morris, Kristi Dickey

Teaching and Learning in Communication Sciences & Disorders

The purpose of this study was to examine the psychometric properties of the Self-Efficacy Questionnaire (SEQ), a self-reported questionnaire using Rasch analysis, a one-parameter logistic probability model based on scientific measurement principles. Rasch analysis was completed using the rating scale model. The various analyses allow researchers to examine the item-level psychometric properties of the SEQ, which result in measures that provide evidence for validity, reliability, and sensitivity of the instrument. Rasch analysis demonstrated that the latent trait established by the SEQ, Perceived Self-efficacy (called self-efficacy from here on), was a unidimensional construct that could be measured on a linear scale. …

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Falconnier Lincoln Statue Feb 2023

Falconnier Lincoln Statue

Statuettes and Figurines

The object depicts a standing Abraham Lincoln. A man kneels in front of Lincoln. A chain and whip lay at the feet of Lincoln.

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The Boy Lincoln, Bryant Baker, Roman Bronze Works, Inc. Feb 2023

The Boy Lincoln, Bryant Baker, Roman Bronze Works, Inc.

Statuettes and Figurines

The bronze sculpture is after a life-sized statue located in Buffalo, New York entitled Young Lincoln. It depicts Abraham Lincoln seated on a log with a book on his proper right knee. Beneath the sculpture at its base, two threaded holes appear.

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Lincoln, The Friendly Neighbor, D. Lee Snarr, Avard T. Fairbanks Feb 2023

Lincoln, The Friendly Neighbor, D. Lee Snarr, Avard T. Fairbanks

Statuettes and Figurines

The sculpture depicts a full-length Abraham Lincoln dressed in a suit. He stands with two children - male and female - and a dog. This particular sculpture is number one in a limited release of thirty.

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Mccormick Abe Lincoln Bourbon Whiskey Decanter, Mccormick Distilling Company, American Porcelain Feb 2023

Mccormick Abe Lincoln Bourbon Whiskey Decanter, Mccormick Distilling Company, American Porcelain

Statuettes and Figurines

The porcelain decanter was produced for McCormick Straight Bourbon Whiskey. It has been shaped in the form of a young Abraham Lincoln, who stands in front of a table holding a law book. His hat and coat rest on the table, and a dog sits at his feet. A piece of U.S. Internal Revenue tape runs down the decanter's back, and a gold informational label is located at its base.

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Last Full Measure, John Mcclarey Feb 2023

Last Full Measure, John Mcclarey

Statuettes and Figurines

The plaster sculpture depicts two Union soldiers, one of which is wounded. The wounded soldier stands erect with the help of the second soldier, who uses his proper right arm as support. The sculpture has been painted in a dark brown hue and is mounted on a wooden base. A small placard with title and artist information is mounted to the base.

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A. Lincoln 1809-1865 Seated Statuette, F. Cook Feb 2023

A. Lincoln 1809-1865 Seated Statuette, F. Cook

Statuettes and Figurines

In the painted plaster statuette, a seated Abraham Lincoln is depicted. He sits in a small chair that is low to the ground. Books, coins, his top hat, and the Great Seal of the United States rest at his feet. In his proper left hand, he holds a document from the Executive Mansion.

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Standing Abraham Lincoln Statuette Feb 2023

Standing Abraham Lincoln Statuette

Statuettes and Figurines

The statuette features a standing Abraham Lincoln. He stands next to a short pillar that has a document draped over its top. His proper right hand rests on the document. The statuette stands on a small rectangular base and is painted in a light gray finish.

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Abraham Lincoln Bust, P.P. Caproni And Brother, Martin Milmore Feb 2023

Abraham Lincoln Bust, P.P. Caproni And Brother, Martin Milmore

Statuettes and Figurines

The plaster bust depicts the likeness of Abraham Lincoln, who is forward-facing. The bust is situated on a round pedestal and has been painted a dark brown hue. Under the pedestal's base, a metal artist marker may be found.

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Abraham Lincoln Age 47 "A Grand Rally" For Fremont In Sterling, Il On July 18, 1856, John Mcclarey, Don Morris, David Seagraves Feb 2023

Abraham Lincoln Age 47 "A Grand Rally" For Fremont In Sterling, Il On July 18, 1856, John Mcclarey, Don Morris, David Seagraves

Statuettes and Figurines

The statuette features a standing Abraham Lincoln in a bronze finish. Lincoln stands with his proper right hand outstretched and a book in his proper left. He is beardless and wearing a coat jacket, vest, shirt, tie, and trousers. The statuette is a limited edition release and is number seven out of seven.

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