Physical Sciences and Mathematics Commons^™

Mathematics And Society: Towards Critical Mathematics Research And Education, Tian An Wong, Carrie Diaz Eaton, Rachel Roca, Nancy Rodriguez

Journal of Humanistic Mathematics

No abstract provided.

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 …

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 …

Accidental World Teacher, Richard Delaware

Journal of Humanistic Mathematics

When the College Algebra and Calculus I video courses I created were posted on my university’s YouTube channel in 2009, I suddenly began to receive dozens of heartfelt emails from students around the world thanking me. Here I tell the story of the creation of those videos and sample the effect they seem to have had over the last decade, as I accidentally became a teacher available to the entire planet.

Fantasy At The Service Of Mathematics, Clara Ziskin, Esther Williams, Alla Shmukler

Journal of Humanistic Mathematics

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, …

Computational Thinking In Mathematics And Computer Science: What Programming Does To Your Head, Al Cuoco, E. Paul Goldenberg

Journal of Humanistic Mathematics

How you think about a phenomenon certainly influences how you create a program to model it. The main point of this essay is that the influence goes both ways: creating programs influences how you think. The programs we are talking about are not just the ones we write for a computer. Programs can be implemented on a computer or with physical devices or in your mind. The implementation can bring your ideas to life. Often, though, the implementation and the ideas develop in tandem, each acting as a mirror on the other. We describe an example of how programming and …

Surviving Mathematics, Nathalie M. Luna

Journal of Humanistic Mathematics

In this essay written in an informal voice, the author shares the ups and downs of her experience in academia. She shares her motivation to study mathematics, her undergraduate experience in Puerto Rico, and her graduate experience in South Texas.

Book Review: What Is A Mathematical Concept? Edited By Elizabeth De Freitas, Nathalie Sinclair, And Alf Coles, Brendan P. Larvor

Journal of Humanistic Mathematics

This is a review of What is a Mathematical Concept? edited by Elizabeth de Freitas, Nathalie Sinclair, and Alf Coles (Cambridge University Press, 2017). In this collection of sixteen chapters, philosophers, educationalists, historians of mathematics, a cognitive scientist, and a mathematician consider, problematise, historicise, contextualise, and destabilise the terms ‘mathematical’ and ‘concept’. The contributors come from many disciplines, but the editors are all in mathematics education, which gives the whole volume a disciplinary centre of gravity. The editors set out to explore and reclaim the canonical question ‘what is a mathematical concept?’ from the philosophy of mathematics. This review comments …

The Efficacy Of Mathematics Education, Eric Geimer

The STEAM Journal

Evidence supports the notion that mathematics education in the United States is inadequate. There is also evidence that mathematics education deficiencies extend internationally. The worldwide mathematics education deficit appears large enough that improving student performance in this educational problem area could yield great economic benefit. To improve the efficacy of mathematics education, education’s root problems must first be understood. Often supposed educational root problems are considered and contrasted against potential deficiencies of mathematics methodologies and curricula that are based on mainstream educational philosophies. The educational philosophies utilized to form early-grade mathematics methodologies and related curricula are judged to be the …

Adventures In Teaching: A Professor Goes To High School To Learn About Teaching Math, Darryl H. Yong

All HMC Faculty Publications and Research

During the 2009–2010 academic year I did something unusual for a university mathematician on sabbatical: I taught high school mathematics in a large urban school district. This might not be so strange except that my school does not have a teacher preparation program and only graduates a few students per year who intend to be teachers. Why did I do this? I, like many of you, am deeply concerned about mathematics education and I wanted to see what a typical high school in my city is like. Because I regularly work with high school mathematics teachers, I wanted to experience …

What Does It Take To Teach Nonmajors Effectively?, Feryal Alayont, Gizem Karaali, Lerna Pehlivan

Pomona Faculty Publications and Research

Most MAA members teach mathematics at the college level, and many often teach courses intended for nonmajors. Indeed this is one of the main responsibilities of a mathematics department: offering service courses for client departments and general education courses for nonmajors. The three of us have been thinking about the question of how to teach nonmajors successfully for a while now. Finally we decided on a time-tested method of figuring things out: if you don't know what to do, ask the experts. We organized a panel titled "Effective Strategies for Teaching Classes for Nonmajors" for MAA MathFest 2012 and invited …

Humanistic Mathematics: An Oxymoron?, Gizem Karaali

Pomona Faculty Publications and Research

Mathematics faculty are trained as mathematicians, first and foremost. If we did not experience the soul-expanding possibilities of liberal education during our own undergraduate years, we may hesitate to bridge disciplinary divides when pursuing our core human need to inquire and understand. Although most mathematicians I know are amazing teachers, communicators, and mentors, many still teach the same material that their professors and their professors’ professors taught. This time-tested approach can be powerful, fascinating, and even quite entertaining. But it can also seem far removed from the world we inhabit. Yes, we teach “real world applications” of mathematical concepts. Yet …

In Defense Of Frivolous Questions, Gizem Karaali

Pomona Faculty Publications and Research

Is there any reason for today's academic institutions to encourage the pursuit of answers to seemingly frivolous questions? The opinionated business leader who does not give a darn about your typical liberal arts classes "because they do not prepare today’s students for tomorrow's work force" might snicker knowingly here: Have you seen some of the ridiculous titles of the courses offered by the English / literature / history / (fill in the blank) studies department in the University of So-And-So? Why should any student take "Basketweaving in the Andes during the Peloponnesian Wars"? Just what would anyone gain from …

Medicine, Statistics, And Education: The Inextricable Link, Katharine K. Brieger '11, Johanna S. Hardin

Pomona Faculty Publications and Research

No abstract provided.

The Art Of Teaching Mathematics, Garikai Campbell, Jon T. Jacobsen, Aimee S A Johnson, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

On June 10–12, 2007, Harvey Mudd College hosted A Conference on the Art of Teaching Mathematics. The conference brought together approximately thirty mathematicians from the Claremont Colleges, Denison, DePauw, Furman, Middlebury, Penn State, Swarthmore, and Vassar to explore the topic of teaching as an art. Assuming there is an element of artistic creativity in teaching mathematics, in what ways does it surface and what should we be doing to develop this creativity?

Mathematicians Playing A Role In Math Education: What We Learned At The Ime/Mime Workshop, Anna Bargagliotti, Rama Chidambaram, Gizem Karaali

Pomona Faculty Publications and Research

In Hollywood, some actors are regularly cast as mean, others as sweet and endearing, and some typically play innocent big-eyed youths who inevitably succeed after awakening to the particular facts of life that their producer wants them to awaken to. It is unusual and difficult for actors to cross the bridge between different types on a regular basis. However, there are always exceptions to the rule.

In the seemingly unrelated world of academics, mathematics faculty may find themselves playing different roles. People with different skills and interests strive to balance their careers in ways that will be uniquely fulfilling to …

Teaching Time Savers: The Exam Practically Wrote Itself!, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

When I first started teaching, creating an exam for my upper division courses was a genuinely exciting process. The material felt fresh and relatively unexplored (at least by me), and I remember often feeling pleasantly overwhelmed with what seemed like a vast supply of intriguing and engrossing exam-ready problems. Crafting the perfect exam, one that was noticeably inviting, exceedingly fair, and unavoidably illuminating, was a real joy.

Teaching Time Savers: Is Homework Grading On Your Nerves?, Lisette G. De Pillis, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

You have probably heard it said that we learn mathematics best when we do mathematics, or that mathematics is not a spectator sport. For most of our students, this means that their mathematics courses will involve a fair amount of homework. This homework is often used to evaluate individual student progress, but it can also be used, for example, as a catalyst for discussion, to emphasize a point made in class, and to identify common misunderstandings throughout the class as a whole. There is, however, the matter of grading homework.

Teaching Time Savers: Some Advice On Giving Advice, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

There are always a lot of questions that need to be answered at the beginning of a course. When are office hours? What are the grading policies? How many exams will there be? Will late homework be accepted? We have all seen the answers to these sorts of questions form the bulk of a standard course syllabus, and most of us feel an obligation (and rightly so) to provide such information.

Teaching Time Savers: Style Points, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

When I began as an assistant professor, I had a pretty good sense of how much time it would take for me to prepare for each class. After a few conversations with my new colleagues, I even had a good sense of how much time I should devote to tasks like office hours and committee work. Somewhere in the middle of grading my first exam, though, it became painfully clear that I had underestimated the amount of time I would need to grade exams!

Teaching Time Savers: A Recommendation For Recommendations, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

I admit it — I enjoy writing recommendation letters for my students. I like
learning about their hopes and dreams, where they have been and where they want to go. A recommendation letter is an opportunity to remind myself how much my students can grow while they are in college, and how much I have grown as an instructor, advisor, and mentor.

Communicating Applied Mathematics: Four Examples, Daniel E. Finkel, Christopher Kuster, Matthew Lasater, Rachel Levy, Jill P. Reese, Ilse C. F. Ipsen

All HMC Faculty Publications and Research

Communicating Applied Mathematics is a writing- and speaking-intensive graduate course at North Carolina State University. The purpose of this article is to provide a brief description of the course objectives and the assignments. Parts A–D of of this article represent the class projects and illustrate the outcome of the course:

• The Evolution of an Optimization Test Problem: From Motivation to Implementation, by Daniel E. Finkel and Jill P. Reese

• Finding the Volume of a Powder from a Single Surface Height Measurement, by Christopher Kuster

• Finding Oscillations in Resonant Tunneling Diodes, by Matthew Lasater

• …

Looking Beyond The Curriculum In Jamaica, Jon T. Jacobsen, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

In August 2004, we had the opportunity to travel to Jamaica to lead a pilot workshop for Jamaican high school math teachers. The workshop focused on the importance of mathematical context in the teaching of mathematics. It was sponsored by the Gibraltar Institute, a Jamaica-based nongovernmental organization led by Trevor Campbell (Pomona College) and Reginald Nugent (Cal State Pomona), Jamaica’s College of Agriculture, Science and Education, and Harvey Mudd College.