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Journal of Humanistic Mathematics
Number of Followers: 1  

  This is an Open Access Journal Open Access journal
ISSN (Print) 2159-8118
Published by Claremont Colleges Homepage  [8 journals]
  • Mathematical Constants Beyond the Half-Circle: An Open Call for Poetry

    • Authors: Mark Huber et al.
      Abstract: The Journal of Humanistic Mathematics invites submissions of mathematical poetry for an upcoming poetry folder tentatively titled Mathematical Constants Beyond the Half-Circle. Please send your submissions via email to the editors by November 1, 2022. Publication decisions will be made by December 31, 2022. The folder is expected to appear in January 2023.
      PubDate: Sun, 31 Jul 2022 20:31:46 PDT
  • Squate

    • Authors: Tom Blackford
      Abstract: This is the story of a middle school student who befriends an irrational number, the square root of eight.
      PubDate: Sun, 31 Jul 2022 20:31:45 PDT
  • Perturbation - For Nature Computes On A Straight Line (In Seven Balancing

    • Authors: Vijay Fafat
      Abstract: What if all of our Reality is a simulation' What, perhaps, are the unintended artifacts if we are an "approximate" simulation because God could not muster sufficient computational power for the Equations capturing the ultimate Theory of Everything' Are life and Sentience something She intended, a problem with the simulation's code, or an irreducible, teleological inevitability in Creation'
      PubDate: Sun, 31 Jul 2022 20:31:44 PDT
  • A Topologist’s Broken Heart

    • Authors: Josh Hiller
      Abstract: A poem about a topologist's broken heart.
      PubDate: Sun, 31 Jul 2022 20:31:43 PDT
  • Spurious Correlation Sestina

    • Authors: Jules Nyquist
      Abstract: This is a sestina poem about Spurious Correlations with a magical realism angle for beginning students learning statistics for the first time during the COVID pandemic.
      PubDate: Sun, 31 Jul 2022 20:31:43 PDT
  • Doughnut at the End of Space

    • Authors: Deborah Coy
      PubDate: Sun, 31 Jul 2022 20:31:42 PDT
  • Scientists Confirm Euler's Identity is Math's Most Beautiful

    • Authors: John F. Donoghue
      Abstract: The poem is an exploration of the natures of mathematical and artistic beauty.
      PubDate: Sun, 31 Jul 2022 20:31:41 PDT
  • Ode to delta

    • Authors: Evandro il Cinico
      PubDate: Sun, 31 Jul 2022 20:31:40 PDT
  • Circular Meditations

    • Authors: Kevin Farey
      Abstract: Circular Meditations is a sequence of seventeen interconnected poems pertaining to mathematics, science, history, politics, religion, and spirituality.
      PubDate: Sun, 31 Jul 2022 20:31:40 PDT
  • Mathematics Education as Dystopia: A Future Beyond

    • Authors: Peter Appelbaum et al.
      Abstract: We argue that scholars and practitioners of mathematics education need to find new directions through recognition of its dystopic characteristics, and embrace these characteristics as both the source of challenges and method of response. This contrasts with the generally utopic approach of most scholarship in the field. We offer critical ethnomathematics education as a model, since it has its own origins in lingering dystopic legacies. A perpetual hopelessness and disempowerment is one implicit curriculum of contemporary mathematics education, where the mathematics one learns might help to describe things, yet hardly assists in transforming the reification of power and agency in society. Embracing dystopia rather than trying to circumvent it generates new questions and pathways.
      PubDate: Sun, 31 Jul 2022 20:31:39 PDT
  • Ramanujan Cab Numbers: A Recreational Mathematics Activity

    • Authors: Soumya Banerjee
      Abstract: In this paper, I introduce teaching activities about Ramanujan’s cab numbers and related software that can inspire people and help them enjoy these beautiful mathematical creations.
      PubDate: Sun, 31 Jul 2022 20:31:38 PDT
  • Mining the Soma Cube for Gems: Isomorphic Subgraphs Reveal Equivalence

    • Authors: Edward Vogel et al.
      Abstract: Soma cubes are an example of a dissection puzzle, where an object is broken down into pieces, which must then be reassembled to form either the original shape or some new design. In this paper, we present some interesting discoveries regarding the Soma Cube. Equivalence classes form aesthetically pleasing shapes in the solution set of the puzzle. These gems are identified by subgraph isomorphisms using SNAP!/Edgy, a simple block-based computer programming language. Our preliminary findings offer several opportunities for researchers from middle school to undergraduate to utilize graphs, group theory, topology, and computer science to discover connections between computation and geometric patterns.
      PubDate: Sun, 31 Jul 2022 20:31:37 PDT
  • Academic Hats and Ice Cream: Two Optimization Problems

    • Authors: Valery F. Ochkov et al.
      Abstract: This article describes the use of computer software to optimize the design of an academic hat and an ice cream cone!
      PubDate: Sun, 31 Jul 2022 20:31:36 PDT
  • Creative Writing that Combines Mathematics and Literature

    • Authors: Hsueh-Chen Lee
      Abstract: In early 2015, the Mathematics-Literature Creativity Award was offered through competition for technological and vocational college students in Taiwan. This paper focuses on the two winning works, the poem Parabola and the flash-fiction, Love Letters of a Science Student, by analyzing the mathematical notions involved and their uses to enhance literary expression. The introduction surveys briefly the various ways of combining mathematics and literature in a piece of creative writing that enriches and supports communication in both disciplines.
      PubDate: Sun, 31 Jul 2022 20:31:35 PDT
  • Calculus III: Under the Influence of Peer Instruction

    • Authors: Alan Von Herrmann et al.
      Abstract: In peer Instruction, students engage with core course concepts and then explain those concepts to one another in small groups. Unlike in lecture format, peer instruction involves every student in the class. In Spring 2019, the first authot began using a modified version of peer instruction in Calculus III classes. He started each class by discussing important Calculus III concepts from three standpoints (the formula, the geometry behind the formula, and the physics behind the formula). During the last 20 minutes of each 50-minute class session, he polled the students using questions in the “Goldilocks Zone” – not too hard and not too easy, but just right for Calculus III students. These questions ignited student-to-student discussions. Students’ attendance and achievement have improved. The paper also describes how peer instruction has influenced the first author's own instructional practices.
      PubDate: Sun, 31 Jul 2022 20:31:35 PDT
  • The Fractal Geometry of Mathematics Classrooms: Navigating Classroom
           Environments in Factory-Model Schools

    • Authors: Cacey L. Wells
      Abstract: Mathematics education has a diverse and complex history. After decades of national reform, mathematics classrooms today are still in desperate need of change. This article examines the current state of factory-model schooling through the lens of Mandelbrot's The Fractal Geometry of Nature in order to rethink pedagogic practices.
      PubDate: Sun, 31 Jul 2022 20:31:34 PDT
  • In Mathematics, As In Art

    • Authors: Andrew Granville
      Abstract: The artist’s vision helps decide what should be created; the mathematician’s insight what can be created. Yet most people view art as merely decoration, or a reflection of existing reality, while they think of mathematics as just a tool for accurate scientific description. Can more people learn to value and enjoy both art and mathematics' And spend a lifetime exploring them and appreciating them for their own sakes'
      PubDate: Sun, 31 Jul 2022 20:31:33 PDT
  • Irruption of the New: Truth, Events, History, Parallels, Fidelity

    • Authors: David L. Neel
      Abstract: A historical meditation on non-Euclidean geometry, three Jesuits, a radical egalitarian mathematical philosopher, and the atom bomb, structured by word-count with attention to divisors of 441 and the Fano plane.
      PubDate: Sun, 31 Jul 2022 20:31:32 PDT
  • The Aleph of Borges and the Paradise of Cantor

    • Authors: Raffaella Mulas
      Abstract: The mathematician Georg Cantor, the writer Jorge Luis Borges, and the protagonist of Borges' short story The Aleph, Carlos Argentino Daneri, are seen here as three pieces of a single puzzle. We put these pieces together and we look at the surprising figure that we obtain.
      PubDate: Sun, 31 Jul 2022 20:31:32 PDT
  • Mathematical Counterpoint: A Short Essay on the Point

    • Authors: Ruža Jeličić
      Abstract: The dot is the simplest graphic symbol, and in the most diverse areas of human thought it signifies the original principle. At the point as a symbol lies the basis of antinomy in the corresponding areas; as the beginning of everything, the point is and is not. The dot represents emptiness, but also fullness. It is imagined on the border of being and non-being, either as a place of transition from what we consider reality in everyday life -- to its negation, or, on the contrary, as a transition from otherworldly reality to nothingness here. In any case, the point connects two worlds: the world of the real and the world of the imagined; it is a place of transcendence.
      PubDate: Sun, 31 Jul 2022 20:31:31 PDT
  • Conic Diagrams

    • Authors: David Pierce
      Abstract: Textbooks may say that the so-called conic sections can be obtained from cones, but this is rarely proved. However, diagrams of the proof require no intuition for solids and can be read as flat. We construct the diagrams with ruler and compass and derive from them basic properties of conic sections as established by Apollonius of Perga, though again in a way that does not require a third dimension. The construction inevitably involves choices that give play to one’s aesthetic sense.
      PubDate: Sun, 31 Jul 2022 20:31:30 PDT
  • Higher Meanings: A Speaker Series Connecting Mathematics and Religion

    • Authors: Lawrence M. Lesser et al.
      Abstract: An innovative grant-funded general adult audiences international speaker series on connections between mathematics and religion yielded six 2021 (now archived) presentations. We share reflections and lessons learned, informed by two sets of surveys.
      PubDate: Sun, 31 Jul 2022 20:31:29 PDT
  • Navigating Mathematics Teacher Preparation During A Time of Crisis

    • Authors: Zareen G. Rahman et al.
      Abstract: In this paper we highlight the experience of a mathematics teacher educator (MTE) and their prospective teachers (PTs) in a middle school mathematics methods course during the 2020 shift to online instruction due to the COVID-19 pandemic. We believe it is valuable to report how the MTE reflected on their instructional decision-making in response to this massive transition to remote instruction. We also report that PTs needed support and guidance to employ new teaching practices they had learned in the methods course instead of reverting to familiar teaching methods.
      PubDate: Sun, 31 Jul 2022 20:31:28 PDT
  • What in the World Just Happened' Students’ Self-Regulation in
           Asynchronous PreCalculus During the COVID-19 Pandemic

    • Authors: Whitney George et al.
      Abstract: We describe students’ learning practices in an online asynchronous PreCalculus course during Fall 2020, the first complete semester of distance learning induced by the COVID-19 pandemic. Results were compiled using a thematic analysis of a questionnaire administered to 43 students enrolled in PreCalculus at a university in the Midwest (United States). Students were given opportunities for active learning and various synchronous Q&A sessions, yet they primarily learned through watching videos and reading worked examples, minimizing interactions with the instructor and available tutors. The questionnaire results show that students knew active learning was helpful, but they were unable to curtail unproductive learning practices. The questionnaire also showed that students struggled to stay motivated and keep to a schedule. We conclude that by developing their study techniques and self-regulatory habits, students will be able to take more control over their learning, particularly in asynchronous classes.
      PubDate: Sun, 31 Jul 2022 20:31:27 PDT
  • Social Justice and Exponential Functions: Using Pandemic Data to Increase
           Student Understanding

    • Authors: Jane Friedman
      Abstract: This paper describes a class activity based on real data about COVID-19 death rates in California. The activity helps students learn about exponential functions while providing an opportunity to integrate social justice concerns into the mathematics classroom.
      PubDate: Sun, 31 Jul 2022 20:31:26 PDT
  • Beyond Ethics: Considerations for Centering Equity-Minded Data Science

    • Authors: Nathan Alexander et al.
      Abstract: In this paper, we utilize duoethnography - a research method in which practitioners discursively interrogate the relationships between culture, context, and the mechanisms which shape individual autobiographical experiences - to explore what may be beyond ethics in the context of data science. Although ethical frameworks have the ability to reflect cultural priorities, a singular view of ethics, as we explore, often fails to speak to the multiple and diverse priorities held both within and across institutional spaces. To that end, this paper explores multiple perspectives, epistemologies, and worldviews that can collectively push researchers towards considerations of a data science education that is equity-minded both in concept and practice. Through a set of dialogues which examine our positionalities, journeys, ethics, local cultures, and accountabilities, this paper explores the contextual realities rooted in the authors’ educational settings. These conversations focus on the humanity of our students, the communities from which we come from and serve, as well as the unintentional harms and possibilities associated with the development of data science programs across institutional types. We take a set of five core questions to examine how we made, and continue to make, sense of our diverse cultural perspectives on data science education and equity with/in relation to others’ realities. Broadly, this paper seeks to offer reflections on the related but differing functions of ethics and equity in data science education.
      PubDate: Sun, 31 Jul 2022 20:31:25 PDT
  • Stewardship of Mathematics: Essential Training for Contributors to, and
           Users of, the Practice of Mathematics

    • Authors: Rochelle E. Tractenberg
      Abstract: A steward of the discipline was originally defined as an individual to whom “we can entrust the vigor, quality, and integrity of the field”, and more specifically, as “someone who will creatively generate new knowledge, critically conserve valuable and useful ideas, and responsibly transform those understandings through writing, teaching, and application” [8]. Originally articulated for doctoral education, in 2019 the construct of stewardship was expanded so that it can also be applied to non-academic practitioners in any field, and can be initiated earlier than doctoral education [18]. In this paper, we apply this construct to the context of mathematics, and argue that even for those early in their training in mathematics, stewardly practice of mathematics can be introduced and practiced. Postsecondary and tertiary education in mathematics — for future mathematicians as well as those who will use math at work — can include curriculum-spanning training, and documented achievement in stewardship. Even before a formal ethical practice standard for mathematics is developed and deployed to help inculcate math students with a “tacit responsibility for the quality and integrity of their own work”, higher education can begin to shape student attitudes towards stewardly professional identities. Learning objectives to accomplish this are described, to assist math instructors in facilitating the recognition and acceptance of responsibility for the quality and integrity of their own work and that of colleagues in the practice of mathematics.
      PubDate: Sun, 31 Jul 2022 20:31:24 PDT
  • Live by the Research, Die by the Research

    • Authors: Szilárd Svitek
      Abstract: The situation of doctoral students is a complex ethical issue. They are not really students any more, but they are not yet full members of the Academy, so they are less than it. PhD students focus primarily on research, since if they do not publish in quality scientific journals, their future (both career and financial) is very much in question. As most of the doctoral student's capacity is taken up by research and publication during the training period, another important task is relegated to the background: learning to teach and to supervise research. Will the student have the ambition to become a good teacher and research supervisor as well as a researcher' What ethical factors can influence the personality development of a doctoral student' What experiences and perspectives will the newly graduated doctoral student bring to their academic career' Here I raise these questions both in general and in relation to graduate studies in mathematics.
      PubDate: Sun, 31 Jul 2022 20:31:23 PDT
  • A Mini-seminar: Teaching Ethics in Mathematics in an Hour a Week

    • Authors: Allison N. Miller
      Abstract: This article describes a one-credit class on ethics in mathematics, which met once a week for an hour and discussed topics in cryptography, algorithms and big data, and the role of mathematics in public life. I offer anecdotal evidence that even a course with relatively little time commitment for both students and faculty can have a significant impact on students' understanding of and interest in ethics in mathematics. I also collect recommendations and resources in the hopes of encouraging others to consider teaching such a course.
      PubDate: Sun, 31 Jul 2022 20:31:23 PDT
  • A Case for Ethics in the Mathematics Major Curriculum

    • Authors: Feryal Alayont
      Abstract: When our students enter the workforce, be it in academia or in business, industry, government, they will be forced to make decisions about various ethical dilemmas. Once in a while, the scandalous stories like that of Enron, the three German auto-makers’ diesel fuel pact, and the Equifax data breach make the headlines. However, employees at every workplace are faced with small to large-scale ethical situations almost daily. In our majors’ future careers, a manager can be using an inappropriate graphic to display data to make the numbers look better, or the data collection processes used in a large public policy project can be completely skewed to support one conclusion that the client desires vs. another more reasonable conclusion. How well are our students prepared for dealing with these dilemmas' Can they even recognize an ethical dilemma' Do we provide them with the tools to be more vigilant about these situations and to make the appropriate decisions when the difficult choices have to be made' In this paper, I would like to invite us all to think about possible ways we can incorporate ethical decision making frameworks and case studies into our classes, particularly if our university does not have an ethics requirement for all majors. Even if there is a general ethics requirement, it is especially important for our students to be exposed to scenarios that are more relevant to the use of mathematics in the workforce since a general ethics course will not necessarily prepare them well for identifying subtle abuses of data processing and mathematical modeling.
      PubDate: Sun, 31 Jul 2022 20:31:22 PDT
  • Towards Pedagogy Supporting Ethics in Modelling

    • Authors: Marie Oldfield
      Abstract: Education for concepts such as ethics and societal responsibility that are critical in building robust and applicable mathematical and statistical models do currently exist in isolation but have not been incorporated into the mainstream curricula at the school or university level. This is partially due to the split between fields (such as mathematics, statistics, and computer science) in an educational setting but also the speed with which education is able to keep up with industry and its requirements. I argue that principles and frameworks of socially responsible modelling should begin at school level and that this would mean that ethics and real-life modelling are introduced much earlier than is currently done. Integrating these concepts with philosophical principles of society and ethics would ensure suitable foundations for future modellers and users of technology to build upon.
      PubDate: Sun, 31 Jul 2022 20:31:21 PDT
  • Benny, Barbara, and the Ethics of EdTech

    • Authors: Geillan Aly
      Abstract: Erlwanger (1973) shook the mathematics education world when he introduced Benny, a student who successfully worked through a behavioristic curriculum. Erlwanger showed how far removed Benny’s understanding of mathematics was from expectations. Erlwanger’s legacy is the basis for this comparative case study which explores students’ actions in the modern, in-class computer-centered emporium classroom. Many striking similarities are found between Pearson’s MyMathLabs (MML) and Benny’s Individually Prescribed Instruction curriculum. In this case study we meet Barbara, a student who succeeds in MML but shows little understanding of mathematical concepts and demonstrates that the legacy of Benny is his continued appearance in our current students. However, what differentiates Benny and Barbara is more than time; it’s the inequities resulting from imposing a pedagogy with well-known problematic characteristics to developmental mathematics students. Most of these developmental students are members of marginalized communities. As such, the social justice and ethical implications of using such a course structure are explored.
      PubDate: Sun, 31 Jul 2022 20:31:20 PDT
  • Violence in Mathematics Teaching. Reflections Inspired by Levinas’
           Totality and Infinity

    • Authors: Adriano Demattè
      Abstract: In mathematics class, violence is carried out in some usually not recognized situations. In this article, I share some reflections on the topic inspired by some passages of Totality and Infinity, work of the French-Lithuanian philosopher Emmanuel Levinas (1906-1995). I find violence by the teacher in not promoting students’ understanding of mathematics, in a distorted use of rhetoric, and in interrupting an ethical relation. This article analyses situations taken from class activities, focusing on the teacher’s presentation of mathematical content and students’ interventions. I also propose that the improvement of interventions in mathematics education is possible and suggest theoretical ideas for acting on situations of violence.
      PubDate: Sun, 31 Jul 2022 20:31:20 PDT
  • Foundational Mathematical Beliefs and Ethics in Mathematical Practice and

    • Authors: Richard Spindler
      Abstract: Foundational philosophical beliefs about mathematics in the mathematical community may have an unappreciated yet profound impact on ethics in mathematical practice and mathematics education, which also affects practice. A philosophical and historical basis of the dominant platonic and formalist views of mathematics are described and evaluated, after which an alternative evidence-based foundation for mathematical thought is outlined. The dualistic nature of the platonic view based on intuition is then compared to parallel historical developments of universalizing ethics in Western thought. These background ideas set the stage for a discussion of the impact of traditional mathematical beliefs on ethics in the practice and education of mathematics in the mathematical community. This is compared to the potential of a belief in evidence-based mathematical foundations on mathematical practice and education.
      PubDate: Sun, 31 Jul 2022 20:31:19 PDT
  • The Formal Presentation Language of Mathematics and Communication Ethics

    • Authors: Marshall Gordon
      Abstract: Mathematics employs a formal language where symbols, verbs, and nouns serve to express terms, concepts, and rules that concatenate to definitions, problem-solving procedures, and proofs. Taken together these constitute the expository language of mathematics found in journals, textbooks, and demonstrations. As a communication given to informing, there are epistemological and ethical considerations that deserve examination. For in keeping with the commitment to an aesthetic of concision promulgated by tradition, the formal presentation language and style of mathematics, while valuable in furthering the body of knowledge, provides only the conclusion of an inquiry, completely excluding the language of investigation that informed the many steps of decision making involved in the process, so that little if any insight into the creative process is made available. Here we explore this problem of communication in the context of mathematics presented to students early in their education as well as at university level. The argument is made that the language of investigation -- the heuristic actions instrumental for their formulation -- ought to accompany the language of formal demonstration so as to provide a communication that is in the best interests of all students and members of the mathematics profession.
      PubDate: Sun, 31 Jul 2022 20:31:18 PDT
  • Ethics and Mathematics – Some Observations Fifty Years Later

    • Authors: Gregor Nickel
      Abstract: Almost exactly fifty years ago, Friedrich Kambartel, in his classic essay “Ethics and Mathematics,” did pioneering work in an intellectual environment that almost self-evidently assumed a strict separation of the two fields. In our first section we summarize and discuss that classical paper. The following two sections are devoted to complement and contrast Kambartel’s picture. In particular, the second section is devoted to ethical aspects of the indirect and direct mathematization of modern societies. The final section gives a short categorization of various philosophical positions with respect to the rationality of ethics and the mutual relation between ethics and mathematics.
      PubDate: Sun, 31 Jul 2022 20:31:17 PDT
  • Special Issue -- Ethics in Mathematics: Foreword

    • Authors: Catherine Buell et al.
      PubDate: Sun, 31 Jul 2022 20:31:16 PDT
  • Doughnuts and Ice Cream Cones: Sweet Mathematics

    • Authors: Mark Huber et al.
      PubDate: Sun, 31 Jul 2022 20:31:16 PDT
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