Physical Sciences and Mathematics Commons^™

What In The World Just Happened? Students’ Self-Regulation In Asynchronous Precalculus During The Covid-19 Pandemic, Whitney George, Keith Gallagher

Journal of Humanistic Mathematics

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 …

Social Justice And Exponential Functions: Using Pandemic Data To Increase Student Understanding, Jane Friedman

Journal of Humanistic Mathematics

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.

Beyond Ethics: Considerations For Centering Equity-Minded Data Science, Nathan Alexander, Carrie Diaz Eaton, Anelise H. Shrout, Belin Tsinnajinnie, Krystal Tsosie

Journal of Humanistic Mathematics

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 …

Stewardship Of Mathematics: Essential Training For Contributors To, And Users Of, The Practice Of Mathematics, Rochelle E. Tractenberg

Journal of Humanistic Mathematics

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 …

A Mini-Seminar: Teaching Ethics In Mathematics In An Hour A Week, Allison N. Miller

Journal of Humanistic Mathematics

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.

Towards Pedagogy Supporting Ethics In Modelling, Marie Oldfield

Journal of Humanistic Mathematics

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 …

A Case For Ethics In The Mathematics Major Curriculum, Feryal Alayont

Journal of Humanistic Mathematics

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 …

Benny, Barbara, And The Ethics Of Edtech, Geillan Aly

Journal of Humanistic Mathematics

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 …

Violence In Mathematics Teaching. Reflections Inspired By Levinas’ Totality And Infinity, Adriano Demattè

Journal of Humanistic Mathematics

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 …

Foundational Mathematical Beliefs And Ethics In Mathematical Practice And Education, Richard Spindler

Journal of Humanistic Mathematics

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 …

The Formal Presentation Language Of Mathematics And Communication Ethics, Marshall Gordon

Journal of Humanistic Mathematics

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 …

Ethics And Mathematics – Some Observations Fifty Years Later, Gregor Nickel

Journal of Humanistic Mathematics

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.

Special Issue -- Ethics In Mathematics: Foreword, Catherine Buell, Victor Piercey

Journal of Humanistic Mathematics

No abstract provided.

Doughnuts And Ice Cream Cones: Sweet Mathematics, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Maintaining Ecosystem And Economic Structure In A Three-Species Dynamical System In Chesapeake Bay, Maila Hallare, Iordanka Panayotova

CODEE Journal

We consider a three-species fish dynamical system in Chesapeake Bay consisting of the Atlantic menhaden as the prey and its two competing predators, the striped bass and the catfish. Building on our previous work in this system, we consider the issue of balancing economic harvesting goals (financial gain for fishermen) with ecological harvesting goals (non-extinction of species). In particular, we investigate the bionomic equilibria, maximum sustainable yield, and the maximum economic yield. Analytical computations and numerical simulations are employed to provide some mathematical guidance on fisheries management policies.

Calcium Bistriflimide-Mediated Sulfur (Vi)–Fluoride Exchange (Sufex): Mechanistic Insights Toward Instigating Catalysis, Nicholas Ball, Brian Han, Samuel R. Khasnavis, Matthew Nwerem, Michael Bertagna, O Maduka Ogba

Pomona Faculty Publications and Research

We report a mechanistic investigation of calcium bistriflimide-mediated sulfur(VI)–fluoride exchange (SuFEx) between sulfonyl fluorides and amines. We determine the likely pre-activation resting state─a calcium bistriflimide complex with ligated amines─thus allowing for corroborated calculation of the SuFEx activation barrier at ∼21 kcal/mol, compared to 21.5 ± 0.14 kcal/mol derived via kinetics experiments. Transition state analysis revealed: (1) a two-point calcium-substrate contact that activates the sulfur(VI) center and stabilizes the leaving fluoride and (2) a 1,4-diazabicyclo[2.2.2]octane additive that provides Brønsted-base activation of the nucleophilic amine. Stable Ca–F complexes upon sulfonamide formation are likely contributors to inhibited catalytic turnover, and a proof-of-principle redesign …

Sulfondiimidamides Unlocked As New S(Vi) Hubs For Synthesis And Drug Discovery, Nicholas Ball

Pomona Faculty Publications and Research

Despite their promise as drug targets, access to nitrogen-rich S(VI) compounds has been a significant synthetic challenge. In this issue of Chem, Zhang and Willis explore a new class of S(VI) compounds-sulfondiimidamides-providing robust strategies toward their synthesis, derivation, and promise as new sulfonamide bioisosteres.

Human Impact On Planetary Temperature And Glacial Volume: Extending A Toy Climate Model To A New Millennium, Samantha Secor, Jennifer Switkes

CODEE Journal

Starting with a toy climate model from the literature, we employ a system of two nonlinear differential equations to model the reciprocal effects of the average temperature and the percentage of glacial volume on Earth. In the literature, this model is used to demonstrate the potential for a stable periodic orbit over a long time span in the form of an attracting limit cycle. In the roughly twenty five years since this model appeared in the literature, the effects of global warming and human-impacted climate change have become much more well known and apparent. We demonstrate modification of initial conditions …

Analysis Of A Mathematical Model Of Real-Time Competitive Binding On A Microarray, Frank H. Lynch

CODEE Journal

A mathematical model of competitive binding on a microarray in real-time yields a planar system of nonlinear ordinary differential equations. This model can be used to explore dimensionless formulation, linear approximation, and reduction. Real-time competitive binding is proposed as an uncommon approach to advance the study of planar systems of differential equations.

Special Issue Call For Papers: Mathematics And Society, Carrie Diaz Eaton, Rachel Roca, Nancy Rodriguez, Tian An Wong

Journal of Humanistic Mathematics

The Journal of Humanistic Mathematics (http://scholarship.claremont.edu/jhm/) is pleased to announce a call for papers for a special issue on Mathematics and Society. Please send your initial proposal submissions via email to the guest editors by August 15, 2022. Initial submission of complete manuscripts is due December 15, 2022. The issue is currently scheduled to appear in July 2023.

Journal For Mathematics And The Arts Call For Papers: Special Issue On The Mathematics Of Fiber Arts, Carolyn Yackel, Sarah-Marie Belcastro

Journal of Humanistic Mathematics

The Journal for Mathematics and the Arts (https://www.tandfonline.com/journals/tmaa20) a peer-reviewed journal that focuses on connections between mathematics and the arts, is pleased to announce a call for papers for a special issue on Mathematics of Fiber Arts. Please send your queries via email to the guest editors. Initial submission of complete manuscripts is due August 1, 2022. The issue is currently scheduled to appear in Fall 2023.

A Non-Euclidean Story Or: How To Persist When Your Geometry Doesn’T, Rami Luisto

Journal of Humanistic Mathematics

Too little mathematics has been written in prose. Thus we prove here, via a fantasy novellette, that a locally L-bilipschitz mapping f : X → Y between uniformly Ahlfors q-regular, complete and locally compact path-metric spaces X and Y is an L-bilipschitz map when Y is simply connected. The motivation for such a result arises from studying the asymptotic values of BLD-mappings with an empty branch set.

As far as the author is aware, the result is new, even though it would not be hard for specialists in the field to prove. The proof is essentially a modest extension of …

So Long My Friend, Bryan Mcnair

Journal of Humanistic Mathematics

No abstract provided.

Heuristic Or Stochastic?, E Laura Golberg

Journal of Humanistic Mathematics

This is a poem about laying odds on the outcome of weddings.

The Solipsist’S First Paper, Sabrina Sixta

Journal of Humanistic Mathematics

The angst of a graduate student who has not yet written a paper, but really wants to.

Wrong Way, Joseph Chaney

Journal of Humanistic Mathematics

No abstract provided.

What's So Great About Non-Orientable Manifolds?, Michael Mccormick

Journal of Humanistic Mathematics

No abstract provided.

Poetry In The Glade: Bridges 2021 Fib Collection

Journal of Humanistic Mathematics

A Fibonacci poem follows the Fibonacci sequence to any length in its count of syllables per line, or words per line, or lines per stanza, or any other countable thing connected with the poem. A Fib is a special case of Fibonacci poem, a poem of 6 lines whose syllable line count follows the first 6 numbers of the Fibonacci sequence: 1; 1; 2; 3; 5; 8. The present collection of Fibs arose out of the Bridges poetry community in response to the Bridges organization’s efforts to make the Bridges 2021 conference more interactive.

Mathematics For The Masses: Door-To-Door Missionaries Of Math And Twelve-Step Recovery Programs, Daniel S. Helman

Journal of Humanistic Mathematics

Conversion of strangers, or proselytizing, is a feature of a range of groups for religious, organizational and other aims. In twelve-step recovery programs, such as Alcoholics Anonymous, belief in a higher power is a requirement for working the steps to recovery. People are encouraged to find a higher power of their own understanding. This paper presents a model for using mathematics as a higher power, and shows how recovery works with mathematics in that role instead of a more traditional higher power such as God. A contemplative definition of math is given along with a description of a three-categoried epistemology: …