Authors:Lawrence M. Lesser Abstract: The fourth VOICES (Virtual Ongoing Interdisciplinary Collaborations on Educating with Song) conference will be held September 26, 2021, with its Sunday date especially targeting those whose teaching schedule precludes attendance on a weekday. This online-only conference explores the use of song to teach STEM content at the college or secondary school level and will include reviewed interactive sessions, video-posters, and discussions of interest to both practitioners and researchers. PubDate: Thu, 29 Jul 2021 09:10:20 PDT

Authors:Bonnie Jacob et al. Abstract: The following is an interview, conducted in April 2021, with a graph product known as the corona graph. Disclaimer: The views expressed herein are not ours. Actually, this entire interview is fiction, other than the mathematics, of course. PubDate: Thu, 29 Jul 2021 09:10:19 PDT

Authors:Sarah Glaz et al. Abstract: The poem-collage pair presented here is a work of collaboration between the mathematician and poet, Sarah Glaz, and the collage and ceramic artist, Mark Sanders. The piece is part of their larger joint poem-collage project involving the history of mathematics. Created at the height of the pandemic, the poem-collage pair reflects the reality of living during a plague and embodies the solace offered by long-distance collaboration and by the arts. Included as background is a brief discussion on the history and mathematics involved, information about Sarah’s poem and Mark’s collage, and a reflection on how the pandemic influenced both the choice of poem and the imagery appearing in the collage.To see the poem-collage pair as originally envisioned by Sarah and Mark please place them side by side. PubDate: Thu, 29 Jul 2021 09:10:18 PDT

Authors:Jonah Howell Abstract: In a series of letters to a faraway lover, an unnamed narrator attempts to make sense of his own internal struggles by fixating on the strange death of Kurt Gödel. PubDate: Thu, 29 Jul 2021 09:10:17 PDT

Authors:Cacey L. Wells Abstract: Connecting scholars and students with the human side of mathematics is critical. This poem about Évariste Galois provides a synopsis of his controversial life, while also providing details into his life that some may not be familiar with. PubDate: Thu, 29 Jul 2021 09:10:17 PDT

Authors:Oscar Gonzalez Abstract: A love poem about breaching mathematical limits, inspired by the tragic beauty of calculus. PubDate: Thu, 29 Jul 2021 09:10:16 PDT

Authors:Bruce McGuffin Abstract: A discussion of the contents of the Data Packet Payload Format Field in an ANSI/VITA 49.2 compliant data packet in the form of a Sonnet. PubDate: Thu, 29 Jul 2021 09:10:15 PDT

Authors:Michael J. Leach Abstract: This is a free-verse poem about the estimation of population parameters in statistical models. The spacing of words is intended to reflect uncertainty. PubDate: Thu, 29 Jul 2021 09:10:14 PDT

Abstract: The COVID-19 pandemic has affected mathematicians and teachers in many ways. In our January 2021 issue, we invited our community to submit essays and reflections, as well as fiction and poetry, based on their experiences during this globally unsettling (and still ongoing) event. This folder presents a select collection of poems submitted in response to that call, by Christopher Caruvana, Marion Cohen, Lawrence M. Lesser, Dan May, Vanessa Sun, and Michele Willman, ordered alphabetically by poet last name. PubDate: Thu, 29 Jul 2021 09:10:13 PDT

Authors:Lowell Abrams Abstract: There is a certain feel that is unique to the rarefied context of rigorous mathematics. These poems constitute an exploration of my experience of mathematical rigor when I am in the midst of exercising my skills as a research mathematician. PubDate: Thu, 29 Jul 2021 09:10:13 PDT

Authors:Heidi Goodson et al. Abstract: Predictive policing has its roots in crime hotspot modeling. In this paper we give an example of what goes into mathematical crime hotspot modeling and show that the modeling assumptions perpetuate systemic racism in policing. The goal of this paper is to raise objections to this field of research, not on its mathematical merit, but on the scope of the problem formation. We do not make any suggestions about how to incorporate race into predictive policing models in order to make them less biased. PubDate: Thu, 29 Jul 2021 09:10:12 PDT

Authors:James Propp Abstract: Who gets called a genius, and why' What effect does having a special category of people called "geniuses" have on an intellectual community and on individuals within it' Drawing on my own experience, and reflecting on writings by Moon Duchin, Elizabeth Gilbert, and others, I try to find some answers. PubDate: Thu, 29 Jul 2021 09:10:11 PDT

Authors:Milton Rosa et al. Abstract: On May 12th, Brazil and the world said goodbye to one of its biggest names in mathematics education, Ubiratan D’Ambrosio (December 8, 1932 – May 12, 2021). D’Ambrosio is recognized both throughout Brazil and internationally for having been the creator of ethnomathematics, a concept that acknowledges, values, and respects different mathematical ideas, procedures, and practices developed by the members of distinct cultural groups. D’Ambrosio analyzed the history of explanations of life and of natural evolution in different cultures. In the last years, his motivation had been the pursuit of peace, in all its four dimensions: individual, social, environmental, and military. In this paper we pay homage to Ubiratan D’Ambrosio, sharing our thoughts related to his personal, professional, and academic life. PubDate: Thu, 29 Jul 2021 09:10:10 PDT

Authors:Manmohan Kaur Abstract: In this paper I describe an activity based on a 1903 Sherlock Holmes murder mystery, in which a substitution cipher is used to encrypt secret messages. The story provides a fun and interesting way to talk about frequency analysis, and can be used as a segue into mathematical constructs such as modular arithmetic and computation. The activity is accessible to ages twelve and above, and has been successfully used in mathematics outreach and popularization efforts as well as in general education and mathematics courses. PubDate: Thu, 29 Jul 2021 09:10:09 PDT

Authors:Igor Podlubny Abstract: A "lost chapter" from Antoine de Saint-Exupéry's Le Petite Prince about the Little Prince visiting a mathematician, written in French in the style of the original work, is presented along with several translations. PubDate: Thu, 29 Jul 2021 09:10:09 PDT

Authors:Benjamin Elkins Abstract: In 1900, Felix Hausdorff published Ekstasen (Ecstasy) under the pseudonym Paul Mongré. The book is comprised of 30 poems, 70 Sonnets, 32 Rondels & 25 Mixed Poems. Den Ungeflügelten (To The Wingless Ones) is the first poem in this book and provides an interesting, perhaps self describing confident Hausdorff as he embraces his muse. Here I present an English translation of this poem without (much) commentary. PubDate: Thu, 29 Jul 2021 09:10:08 PDT

Authors:Marshall Gordon Abstract: In contrast to problem-solving procedures that are the “bricks and mortar” of demonstrations in mathematics textbooks, heuristics, defined by Polya as “the study of means and methods of problem solving”, are those mental actions that enable the practitioner to make progress when it is not clear how to solve problems directly. Yet, as essential as heuristic tools are, they tend not to be included in presentations in mathematics textbooks. The overarching problem can be understood in terms of students’ not developing productive means for engaging problems. A few mathematics problems are included to argue for the validity, if not the priority, of the need for the incorporation of heuristics along with problem-solving procedures as standard content in mathematics textbooks. PubDate: Thu, 29 Jul 2021 09:10:07 PDT

Authors:Wyatte C. Hooper Abstract: Good mathematics stands the test of time. As culture changes, we often ask different questions, bringing new perspectives, but modern mathematics stands on ancient discoveries. Isaac Newton’s discovery of calculus (along with Leibniz) may seem old but is predated by Archimedes’ findings. Current mathematics students should be familiar with parabolas and simple curves; in our introductory calculus courses, we teach them to compute the areas under such curves. Our modern approach derives its roots from Newton’s work; however, we have filled in many of the gaps in the pursuit of mathematical rigor. What many students may not know is that Archimedes solved the area problem for parabolas long before the use of algebraic expressions became mainstream. Archimedes used the geometry of the ancient Greeks, which gave him a vastly different perspective. In this paper we provide both Archimedes’ and Newton’s proofs involving the quadrature of the parabola, trying to remain true to their original texts as much as feasible. PubDate: Thu, 29 Jul 2021 09:10:06 PDT

Authors:Clara Ziskin et al. Abstract: This article aims to introduce the reader to a book published in 2016 under the title “Amazing Tales from the Magic Wood and Famous Problems of Mathematics” by Elli Shor and Clara Ziskin. The book offers an original method of presenting mathematical facts and history through a fantasy narrative. The book’s two authors, Clara Ziskin and Alla Shmukler (Elli Shor), together with consultant psychologist Esther Williams, share here several excerpts taken from the first part of the book as well as related illustrations and mathematical riddles, so that the reader can form an informed impression of the book, its structure, and its nature. PubDate: Thu, 29 Jul 2021 09:10:06 PDT

Authors:Bruce H. Pourciau Abstract: Topics chosen from first-year calculus illustrate a number of “sayings” or “proverbs,” the first three, for example, being: be awed, like a child; meaning before truth; and act with intention. Many are proverbs for life as well as mathematics. PubDate: Thu, 29 Jul 2021 09:10:05 PDT

Authors:Nat Banting Abstract: This article describes how an innocuous question from a primary schooler taught me to pay attention to the dynamic meaning making activities of children—particularly, those of my young daughter. Through this lens, I examine how the verb-based world of children might compel us to think differently about the largely nominalized project of schooling and, more specifically, about the craft of teaching mathematics. PubDate: Thu, 29 Jul 2021 09:10:04 PDT

Authors:Lawrence M. Lesser Abstract: The COVID-19 pandemic inspired reflections on the importance and challenges of teaching exponential growth, such as doubling, to varied audiences. PubDate: Thu, 29 Jul 2021 09:10:03 PDT

Authors:Zoe H. Austin et al. Abstract: During COVID-19 isolation, Dr. Jennifer Austin and her seven-year-old daughter Zoe co-authored the short story Math Girl Solves the Pattern. Here we meet the superheroine Math Girl and her nemesis Minus Girl. Math Girl is observant, curious, and creative. Houses, balls, and sailboats are disappearing! The mystery must be solved. Persevering Math Girl saves the day. PubDate: Thu, 29 Jul 2021 09:10:02 PDT

Authors:Priscilla Bremser Abstract: The COVID-19 pandemic forced instructors to adapt their assessment practices. For this author, that adaptation led to a reconsideration of evaluation systems, given the ways in which such systems can interfere with learning and perpetuate inequities. The author describes resulting changes in her grading of student work and evaluation of faculty colleagues. PubDate: Thu, 29 Jul 2021 09:10:02 PDT

Authors:Beyza C. Aslan Abstract: As it is often said, something good often comes out of most bad situations. The time I spent during COVID-19, at home and isolated with my two children, brought out one secret passion in me: crocheting. Not only did it help me pass the time in a sane and productive way, but also it gave me a new goal in life. It connected my math side with my artistic side. It gave me a new perspective to look at math, and helped me help others see math in a positive way. PubDate: Thu, 29 Jul 2021 09:10:01 PDT

Authors:Rachel Epstein et al. Abstract: Four women mathematicians at various stages of their careers at public liberal arts institutions share their struggles and challenges in their professional and personal lives during the pandemic. PubDate: Thu, 29 Jul 2021 09:10:00 PDT

Authors:Matilde Lalín Abstract: I share some of my adventures in mathematical research and homeschooling in the time of COVID-19. PubDate: Thu, 29 Jul 2021 09:09:58 PDT

Authors:Larson Fairbairn et al. Abstract: For many of us, the pandemic has changed how we teach and how we support students. This manuscript highlights creativity as a way to support for student mathematical and emotional well-being. It describes the positive impact that creative assignments in a mathematics content course for preservice K-8 teachers had on students during the early days of the pandemic. The story is told by the instructor and two former students in the course. PubDate: Thu, 29 Jul 2021 09:09:58 PDT

Authors:Frode Sirnes Larsen Abstract: At the center of the School of Athens, Raphael painted Plato with a face similar to that of Leonardo da Vinci. In this article I argue that the likeness was intentional, and that Raphael’s fresco contains a set of references to the book De Divina Proportione, to which Leonardo contributed with drawings of polyhedrons. De Divina Proportione was written by Leonardo’s friend and teacher of mathematics, Luca Pacioli, and contains arguments for raising the status of the art of painting, similar to the arguments found in Leonardo’s Paragone. Pacioli and Leonardo thought painting should be regarded as a liberal art, due to the painters' use of mathematical principles. In the article, I show how Plato with the face of Leonardo is part of a set of allusions to these arguments found in The School of Athens. PubDate: Thu, 29 Jul 2021 09:09:57 PDT

Authors:Ilana Shapiro et al. Abstract: Random generation of music goes back at least to the 1700s with the introduction of Musical Dice Games. More recently, Markov chain models have been used as a way of extracting information from a piece of music and generating new music. We explain this approach and give Python code for using it to first draw out a model of the music and then create new music with that model. PubDate: Thu, 29 Jul 2021 09:09:56 PDT

Authors:Anthony DeLegge et al. Abstract: Learning communities can be an effective means of engaging university students across disciplines. Games have always been a source of both enjoyment and interesting mathematics. Based on our own interest in games, and the deep, strategic discussions we found ourselves having with students when we played games with them, we decided to design a learning community around the mathematics of games. We hoped in particular that such a community could be a great pathway to introducing mathematical thinking to students not majoring in mathematics, and that they would gain a greater appreciation for our field. In this paper, we describe our Math Games Seminar learning community, from its origins in 2016, to its organization and to its impact on our students through the years. PubDate: Thu, 29 Jul 2021 09:09:55 PDT

Authors:Uffe Thomas Jankvist et al. Abstract: In this paper we propose a thematic focus on aesthetics in the context of an interdisciplinary collaboration between mathematics and literature (Language Arts) as a way to further students’ reflections on and deeper understanding of what characterizes the two subjects. Furthermore, we argue that approaching aesthetics through the perspective of literacy can potentially strengthen students’ understanding of ways of thinking particular to specific (academic) disciplines; ways of thinking that are otherwise often hidden when teaching focuses on more pragmatic aspects. G. H. Hardy’s A Mathematician’s Apology from 1940 serves as the recurring illustrative example in our discussions of the pedagogical potentials of an interdisciplinary rendezvous between mathematics and literature. PubDate: Thu, 29 Jul 2021 09:09:54 PDT

Authors:Siddhi Desai et al. Abstract: The International Study Group on Ethnomathematics (ISGEm) supports incorporating cultural diversity of mathematical practices to promote the teaching and learning of school mathematics. Through The Mathematics Heritage Project, students at a middle school in the southeastern United States developed unique creations to connect with the mathematics connected to their identities and self-identified cultural group. Upon reflection, students reported an increased awareness of the relevance of mathematics in their lives and a sense of ownership that is both meaningful and modern. PubDate: Thu, 29 Jul 2021 09:09:53 PDT

Authors:Paolo Mancosu Abstract: This article makes available some early letters chronicling the relationship between the biologist Joseph H. Woodger and the logician Alfred Tarski. Using twenty-five unpublished letters from Tarski to Woodger preserved in the Woodger Papers at University College, London, I reconstruct their relationship for the period 1935-1950. The scientific aspects of the correspondence concern, among other things, Tarski’s reports on the work he is doing, his interests, and his --- sometimes critical but always well-meaning --- reactions to Woodger’s attempts at axiomatizing and formalizing biology using the system of Principia Mathematica. Perhaps the most interesting letter from a philosophical point of view is a very informative letter on nominalism dated November 21, 1948. But just as fascinating are the personal elements, the dramatic period leading to the second world war, their reaction to the war events, Tarski's anguish for his family stranded back in Poland, the financial worries, and his first reports on life in the East Coast and, as of 1942, at the University of California, Berkeley. PubDate: Thu, 29 Jul 2021 09:09:53 PDT

Authors:Veselin Jungic Abstract: This article demonstrates that “The Raven Legend”, a Haida myth transcribed by Franz Boas in 1888, is full of (ethno)mathematical concepts that Haida society used to make sense of the natural, real world. Calculus can be used to model several segments of the story since the narrative relied heavily on ideas that a mathematician would identify as the concepts of infinity and mathematical limits. PubDate: Thu, 29 Jul 2021 09:09:52 PDT