Physical Sciences and Mathematics Commons^™

The Value Of Adding Nothing: A Call For Reform-Oriented Polynomial Division, Jonathan Clark, Jeneva Clark

Journal of Humanistic Mathematics

The call to implement reform practices in schools reflects the historical turn away from the behaviorist theory of learning in education. Yet the praxis of this turn remains a significant challenge, particularly within mathematics classrooms where procedural memorization is emphasized. In this article, we show one means of how to advance our pursuit of meaningful mathematics into polynomial division. Building on the literature for reform-based division methods, an alternative to the long division algorithm will be explored that relies solely on adding zero and fundamental algebraic principles.

Challenge-Based Learning & Steam Curriculum, Diana Lockwood

The STEAM Journal

STEAM education is being integrated into elementary schools as a way to engage more students in creativity, hands-on learning, and problem-based learning also referred to as Challenge-Based-Learning (CBL). This article focuses on elementary educators’ curriculum design for STEAM and presenting students with open-ended questions phrased as a challenge as a way to raise student interest and achievement (DeJarnette, 2018; Hunter-Doniger, 2018). When students received challenges to solve, they felt more open to sharing their ideas since there was more than one potential right answer (DeJarnette, 2018; Drake, 2012). When implementing CBL, teachers act as facilitators using a constructivist approach as …

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 …

Calculus Iii: Under The Influence Of Peer Instruction, Alan Von Herrmann, L. Jeneva Clark

Journal of Humanistic Mathematics

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 …

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 …

Changes And Deltas, Jim Wolper

Journal of Humanistic Mathematics

Lecturing about Mathematics is like playing Jazz.

A Study Of Problem Posing As A Means To Help Mathematics Teachers Foster Creativity, Deborah Moore-Russo, Amanda A. Simmons, Michael J.D. Tulino

Journal of Humanistic Mathematics

Research suggests that mathematical creativity often results from extended periods of mathematical activity and reflection based on the use of deep and flexible content knowledge [14, 15]. This implies that instruction can influence creativity. However, for teaching to foster creativity in mathematics, there should be purposefully designed instructional tasks. It is doubtful that routine, mechanical exercises would foster creativity. Moreover, mathematical creativity may neither be explicitly promoted, nor fully appreciated, by students when a learning space involves only problem solving, even if the problems are challenging and engaging. For students to get an authentic sense of mathematics and to develop …

Mathematics Out Of Nothing: Talking About Powerful Mathematical Ideas With Children, Matthew Oldridge

Journal of Humanistic Mathematics

Parents and educators have powerful opportunities to introduce children to big mathematical ideas, when those ideas become necessary. Children are capable and curious. They don’t need to be sheltered from big mathematical ideas. Bring out mathematical ideas when kids are ready, or when they are needed. This article describes one such instance, when I helped my six-year-old son move beyond zero in the negative direction when subtracting.

Mathematics Students As Artists: Broadening The Mathematics Curriculum, Marshall Gordon

Journal of Humanistic Mathematics

Mathematics has often been referred to as an art. For some it is “the purest of the arts”, where the mathematicians’ art is “asking simple and elegant questions about our imaginary creations, and crafting satisfying and beautiful explanations”. Yet with classroom time given primarily to “covering the curriculum”, testing, and practicing problem-solving procedures, students’ opportunities to appreciate the aesthetic dimension of mathematics are often limited. To promote a responsive environment in an effort to enable students to become artists of their own mathematics experience, I consider in this paper two facets of the mathematics classroom. Content-wise I make the argument …

Telling Women's Stories: A Resource For College Mathematics Instructors, Sarah Mayes-Tang

Journal of Humanistic Mathematics

Stereotypes about mathematicians that conflict with ``traditionally feminine" identities are widely held by people from middle-school-age onwards, and can influence their participation in mathematics and related fields. Simply being exposed to women in mathematics is not enough to change students' perceptions of mathematicians, and may even decrease girls' interest in mathematics. This paper proposes a storytelling strategy to help change students' perceptions of mathematicians. It includes several activities for intentionally incorporating women's stories into the post-secondary classroom and a list of resources for finding existing powerful stories. The diverse stories of women mathematicians, including details of their personal lives and …

Experiences Using Inquiry-Oriented Instruction In Differential Equations, Keith Nabb

CODEE Journal

Student-centered instruction can be a challenging endeavor for teachers and students. This article reports on the use of the Inquiry-Oriented Differential Equations (IO-DE) curriculum (Rasmussen, 2002) in an undergraduate differential equations course. Examples of student work are shared with specific reference to research in mathematics education.

Cmsc 2018: 4th Creative Mathematical Sciences Communication Conference, Frances Rosamond

Journal of Humanistic Mathematics

Join scientists, researchers, teachers, and artists in developing new ways of communicating mathematical and computational thinking. Welcome are contributions in art forms such as dance, graphic art, theatre, and the myriad of ways to communicate science to the public. The conference will feature keynote talks by leading researchers and communicators in the mathematical sciences, sharing their experience, new initiatives, and ideas. The conference will be held in Wellington, New Zealand, at The Learning Connexion (TLC) on 21--23 July 2018. The conference website is http://www.cmsc.nz.

The Role Of Sequence In The Experience Of Mathematical Beauty, Leslie Dietiker

Journal of Humanistic Mathematics

In this article, I analyze the aesthetic dimensions of a sequence of mathematical events found in an unusual first grade lesson in order to demonstrate how sequencing may affect an individual’s experience of mathematical beauty. By approaching aesthetic as a sense or felt quality of an experience in context (Sinclair, 2001, 2011), this analysis explains how sequence can affect the way mathematical objects or actions are experienced by an individual. Thus, rather than questioning whether or in what ways a set of mathematical objects are beautiful or not, this paper addresses under what conditions is the mathematics in play beautiful. …

Ecoscience + Art Initiative: Designing A New Paradigm For College Education, Scholarship, And Service, Changwoo Ahn

The STEAM Journal

The paper presents a new initiative, EcoScience + Art, which blooms at George Mason University. The creator explains the background, history, and recent activities of the initiative, and also introduces an on-going special project called “The Rain Project”, a student participatory project to design, construct, and monitor a green infrastructure (i.e., floating wetland) for sustainable stormwater management on campus. The special project is geared to design and present a new paradigm to integrate college education, scholarship, and service. The relevance of the initiative and the special project to STEAM education is discussed.

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 …

Using Topology To Explore Mathematics Education Reform, Carling Sugarman

HMC Senior Theses

Mathematics education is a constant topic of conversation in the United States. Many attempts have been made historically to reform teaching methods and improve student results. Particularly, past ideas have emphasized problem-solving to make math feel more applicable and enjoyable. Many have additionally tackled the widespread problem of “math anxiety” by creating lessons that are more discussion-based than drill-based to shift focus from speed and accuracy. In my project, I explored past reform goals and some added goals concerning students' perceptions of mathematics. To do so, I created and tested a pilot workshop in topology, a creative and intuitive field, …

Towards A “Cloud Curriculum” In Art And Science?, Roger Malina

The STEAM Journal

Recently an email hit my desk from Paul Thomas in Australia with a proposal to work together on a “Cloud Curriculum for Art and Science”. I immediately agreed to collaborate. I don’t yet have a clue of what a cloud curriculum is, but what I do know is that we are ‘backing into the future’ in educational institutions and we desperately need a ‘cloud curriculum.’ We need to look over the ten year horizon. And in the emerging art-science field I doubt that the usual approach to curriculum development will work.

San Antonio High School Food Justice Program: A Handbook And Evaluation Of Edible Education, Katherine B. Tenneson

Pitzer Senior Theses

This senior environmental studies thesis explains and analyzes edible education through a food and gardening program at a continuation high school in Claremont, California. The first chapter situates the program-specific analysis by providing background information of the edible education movement, a history of the Edible Schoolyard in Berkeley, California, and an explanation of why food is a powerful teaching tool. The second chapter delineates the program by describing all of its components and compiling essential resources and teaching documents. The third chapter is based on interviews with 9 of 12 involved students and 7 teachers, and thoroughly explains the outcomes …

Exploring German And American Modes Of Pedagogical And Institutional Sustainability: Forging A Way Into The Future, Lindon N. Pronto

Pitzer Senior Theses

Rooted deep in Germany's past is its modern socio-political grounding for environmental respect and sustainability. This translates into individual and collective action and extends equally to the economic and policy realm as it does to educational institutions. This thesis evaluates research conducted in Germany with a view to what best approaches are transferable to the United States liberal arts setting. Furthermore, exemplary American models of institutional sustainability and environmental education are explored and combined with those from abroad to produce a blueprint and action plan fitting for the American college and university.

Imagine Math Day: Encouraging Secondary School Students And Teachers To Engage In Authentic Mathematical Discovery, Darryl H. Yong, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

Research mathematicians and school children experience mathematics in profoundly different ways. Ask a group of mathematicians what it means to “do mathematics” and you are likely to get a myriad of responses: mathematics involves analyzing and organizing patterns and relationships, reasoning and drawing conclusions about the world, or creating languages and tools to describe and solve important problems. Students of mathematics often report “doing mathematics” as performing calculations or following rules. It’s natural that they see mathematics as monolithic rather than an evolving, growing, socially constructed body of knowledge, because most mathematical training in primary and secondary schools consists of …

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?

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: 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.

Humanistic Mathematics: Personal Evaluation And Excavations, Stephen I. Brown

Humanistic Mathematics Network Journal

No abstract provided.

Innumeracy And Its Perils, Numeracy And Its Promises, Ramakrishnan Menon

Humanistic Mathematics Network Journal

No abstract provided.

When Is A Math Problem Really "Real"?, Michael E. Goldberg

Humanistic Mathematics Network Journal

No abstract provided.

"Magic In A Box", Lacie Juris

Humanistic Mathematics Network Journal

No abstract provided.