Education Commons^™

Analyzing A Smartphone Battle Using Bass Competition Model, Maila Hallare, Alireza Hosseinkhan, Hasala Senpathy K. Gallolu Kankanamalage

CODEE Journal

Many examples of 2x2 nonlinear systems in a first-course in ODE or a mathematical modeling class come from physics or biology. We present an example that comes from the business or management sciences, namely, the Bass diffusion model. We believe that students will appreciate this model because it does not require a lot of background material and it is used to analyze sales data and serve as a guide in pricing decisions for a single product. In this project, we create a 2x2 ODE system that is inspired by the Bass diffusion model; we call the resulting system the Bass …

How To Intercept A High-Speed Rocket With A Pair Of Compasses And A Straightedge?, Yagub N. Aliyev

CODEE Journal

In this paper a nonlinear differential equation arising from an elementary geometry problem is discussed. This geometry problem was inspired by one of the proofs of the first remarkable limit discussed in a typical first semester undergraduate Calculus course. It is known that the involved differential equation can be reduced to Abel’s differential equation of the first kind. In this paper the problem was solved using an approximate geometric method which constructs a piecewise linear solution approximation for the curve. The compass tool of GeoGebra was extensively used for these constructions. At the end of the paper, some generalizations are …

Population Growth Models: Relationship Between Sustainable Fishing And Making A Profit, James Sandefur

CODEE Journal

In this paper, we develop differential equations that model the sustainable harvesting of species having different characteristics. Specifically, we assume the species satisfies one of two different types of density dependence. From these equations, we consider maximizing sustainable harvests. We then introduce a cost function for fishing and study how maximizing profit affects the harvesting strategy. We finally introduce the concept of open access which helps explain the collapse of many fish stocks.

The equations studied involve relatively simple rational and exponential functions. We analyze the differential equations using phase-line analysis as well as graphing approximate solutions using Euler's method, …

Fibonacci Differential Equation And Associated Spiral Curves, Mehmet Pakdemirli

CODEE Journal

The Fibonacci differential equation is defined with analogy from the Fibonacci difference equation. The linear second order differential equation is solved for suitable initial conditions. The solutions constitute spirals in the polar coordinates. The properties of the spirals with respect to the Fibonacci numbers and the differences between the new spirals and classical spirals are discussed.

A Generalized Solution Method To Undamped Constant-Coefficient Second-Order Odes Using Laplace Transforms And Fourier Series, Laurie A. Florio, Ryan D. Hanc

CODEE Journal

A generalized method for solving an undamped second order, linear ordinary differential equation with constant coefficients is presented where the non-homogeneous term of the differential equation is represented by Fourier series and a solution is found through Laplace transforms. This method makes use of a particular partial fraction expansion form for finding the inverse Laplace transform. If a non-homogeneous function meets certain criteria for a Fourier series representation, then this technique can be used as a more automated means to solve the differential equation as transforms for specific functions need not be determined. The combined use of the Fourier series …

The Conundrum Of Senior Thesis In The Library's Open Access Institutional Repository, Jennifer E. Beamer, Kenneth Cotich

Library Staff Publications and Research

Scholarship@Claremont (S@C) is the official institutional repository for the Claremont Colleges Consortium (a group of seven library arts colleges in Southern California) and is managed by The Claremont Colleges Library. For more than ten years, library staff has been assisting Seniors with posting their undergraduate theses as a part of the ETD program, and they are some of the most downloaded items numbering in the 300,000-plus range. Theses are accessible via Open access and on the Campuses only. This poster will share some challenges in hosting and posting workflows for students, policies, and procedures for library staff and our campus …

Undetermined Coefficients With Hyperbolic Sines And Cosines, Laurie A. Florio, George L. Fischer

CODEE Journal

The method of undetermined coefficients is commonly applied to solve linear, constant coefficient, non-homogeneous ordinary differential equations when the forcing function is from a selected class of functions. Often the hyperbolic sine and cosine functions are not explicitly included in this list of functions. Through a set of guided examples, this work argues that the hyperbolic sine and cosine ought to be included in the select class of functions. Careful explanation is provided for the necessary treatment of the cases where the argument of the hyperbolic sine and/or cosine functions matches one or both of the roots of the characteristic …

More Than Free Textbooks: Labor And Pedagogy In Implementing Open Resources In A Trigonometry Course, Caleb Holloway

Journal of Humanistic Mathematics

This paper reports the implementation of open educational resources (OER) in a university trigonometry class, with an emphasis on the pedagogical considerations and academic labor involved. To date these two matters have been underreported in the literature on OER. I provide an account of the work involved both in choosing an open textbook and in creating hundreds of accompanying homework exercises for an online learning platform. I also present the pedagogical lens that informed this implementation, discuss how it informed my adoption of an open textbook, and provide specific examples of how it guided the creation of these exercises. Based …

Synesthesia: 3.1415... Orange.Whiteperiwinklewhiteblue..., Shelly Sheats Harkness, Bethany A. Noblitt, Nicole Giesbers

Journal of Humanistic Mathematics

In this paper we address the questions: What is synesthesia? What support(s) can teachers provide for their students who have synesthesia? Nicole, a future mathematics teacher who possesses this synesthesia “superpower”, describes how it impacted her learning. We collected data for this case study through an audio-recorded and transcribed interview, as well as from subsequent email correspondence between the three authors. We asked Nicole three kinds of questions: questions she is frequently asked, questions she would like to be asked, and questions teachers (like Shelly and Beth) might ask. Results indicate that synesthesia may have helped Nicole learn English as …

“I Got You”: Centering Identities And Humanness In Collaborations Between Mathematics Educators And Mathematicians, Anne M. Marshall, Sarah Sword, Mollie Applegate, Steven Greenstein, Terrance Pendleton, Kamuela E. Yong, Michael Young, Jennifer A. Wolfe, Theodore Chao, Pamela E. Harris

Journal of Humanistic Mathematics

Existing literature widely reports on the value of collaborations between mathematicians and mathematics educators, and also how complex those collaborations can be. In this paper, we report on four collaborations that sought to address what mathematics is and who gets to do it. Drawing on the literature and from the careful and intentional work of the collaborators, we offer a framework to capture the richness of those collaborations – one that acknowledges the importance of acknowledging and welcoming the extensive personal and professional experience of each person involved in the collaboration – and a look at how collaborations built with …

Teaching Mathematics With Poetry: Some Activities, Alexis E. Langellier

Journal of Humanistic Mathematics

During the summer of 2021, I experimented with a new way of getting children excited about mathematics: math poetry. Math can be a trigger word for some children and many adults. I wanted to find a way to make learning math fun—without the students knowing they’re doing math. In this paper I describe some activities I used with students ranging from grades K-12 to the college level and share several poem examples, from students in grades two to eight.

Exploring Set-Theoretic Practices Of Youth Engagement In Connective Journalism: What We Lose In School-Mathematical Descriptions, Alexandra R. Aguilar, Emma C. Gargroetzi, Lynne M. Zummo, Emma P. Bene

Journal of Humanistic Mathematics

Analyzing youth video submissions regarding COVID-19 to KQED’s ‘Let’s Talk About the Election’ website, we explore the mathematics these youth engaged in through their submissions without creating any explicit connection to school mathematical concepts or standards. Our focus is the students’ construction of sets (e.g. sets of nurses, doctors, American workers), as a means of creating connection with voters and other media authors through Marchi and Clark’s (2021) construct of connective journalism. We observe these youth constructing sets of varying sizes and reflecting on how these sets are contextualized within a larger political dialogue. We also attempt to rewrite part …

Just Mathematics: Getting Started Teaching Postsecondary Math For Social Justice, Kenan A. Ince

Journal of Humanistic Mathematics

Following the summer 2020 civil rights movement and increasing attention to the intersections of mathematics with politics and power, many math educators have reported a desire to implement an antiracist pedagogy and to examine the intersections of their subject with issues of equity, inclusion, and social justice. Many resources exist for K-12 math educators interested in incorporating social justice into their curricula, but resources are comparatively scarce for college and university instructors (though this is changing quickly!). We discuss why one may want to teach mathematics for social justice, how to begin to implement issues of social justice into postsecondary …

No Simple Formula: Navigating Tensions In Teaching Postsecondary Social Justice Mathematics, Alexa W. C. Lee-Hassan

Journal of Humanistic Mathematics

Instructors of Social Justice Mathematics (SJM) have shared important insights into the powerful potential of connecting classroom mathematics with authentic data about social justice topics, but they have also warned about the harm such teaching can cause when done poorly. In this article, I consider what is necessary to teach SJM at the postsecondary level. I share research that has supported me in learning to teach SJM and highlight challenges that are particular to doing this work in postsecondary contexts. I then describe my experiences navigating the central tensions of this work while honoring its complexity.

Special Case Of Partial Fraction Expansion With Laplace Transform Application, Laurie A. Florio, Ryan D. Hanc

CODEE Journal

Partial fraction expansion is often used with the Laplace Transforms to formulate algebraic expressions for which the inverse Laplace Transform can be easily found. This paper demonstrates a special case for which a linear, constant coefficient, second order ordinary differential equation with no damping term and a harmonic function non-homogeneous term leads to a simplified partial fraction expansion due to the decoupling of the partial fraction expansion coefficients of s and the constant coefficients. Recognizing this special form can allow for quicker calculations and automation of the solution to the differential equation form which is commonly used to model physical …

Modeling Immune System Dynamics During Hiv Infection And Treatment With Differential Equations, Nicole Rychagov

CODEE Journal

An inquiry-based project that discusses immune system dynamics during HIV infection using differential equations is presented. The complex interactions between healthy T-cells, latently infected T-cells, actively infected T-cells, and the HIV virus are modeled using four nonlinear differential equations. The model is adapted to simulate long term HIV dynamics, including the AIDS state, and is used to simulate the long term effects of the traditional antiretroviral therapy (ART). The model is also used to test viral rebound over time of combined application of ART and a new drug that blocks the reactivation of the viral genome in the infected cells …

Including The Literary Arts As The A In Steam, Lindsay E. Cunningham

The STEAM Journal

This article examines the integration of literature into secondary STEM (science, technology, engineering, mathematics) classes in British Columbia, Canada. Data were collected through interviews with nine secondary STEM subject teachers and focus on teachers’ perceptions of the effects of including literature, what/how literature has been included, as well as the barriers, both real and perceived, to doing so.

A review of the literature demonstrates that integrating literature into STEM can be appealing to a broad range of students and teachers and can help to engage students with a variety of interests, perspectives, and backgrounds. The arts, including the literary arts, …

An Undergraduate Consortium For Addressing The Leaky Pipeline To Computing Research, James C. Boerkoel Jr., Mehmet Ergezer

All HMC Faculty Publications and Research

Despite an increasing number of successful interventions designed to broaden participation in computing research, there is still significant attrition among historically marginalized groups in the computing research pipeline. This experience report describes a first-of-its-kind Undergraduate Consortium (UC; https://aaai-uc.github.io/about) that addresses this challenge by empowering students with a culmination of their undergraduate research in a conference setting. The UC, conducted at the AAAI Conference on Artificial Intelligence (AAAI), aims to broaden participation in the AI research community by recruiting students, particularly those from historically marginalized groups, supporting them with mentorship, advising, and networking as an accelerator toward graduate school, AI research, …

Integrating Theatre And Biology: How Embodied Performance Can Enhance Empathy Among College Science Students, Annika C. Speer, Begona Echeverria

The STEAM Journal

In these field notes, we examine the integration of the arts into a 20-person honors biology seminar at UC Riverside “Beyond Science: Being Humane Amid Human Rights Crises.” We held a four-hour workshop to examine the ways in which performance and theatrical storytelling can enhance science learning. The workshop provided a unique avenue for exploring how human activities result in downward consequences including refugee displacement, one of the course objectives. In addition to the workshop, we conducted surveys and a focus group with the students to better understand their experience incorporating the arts into their science class. A key concept …

Making Meaningful Connections With Steam For Elementary Aged Students In China, Francis Stonier

The STEAM Journal

This program included a summer STEAM experience for over 130 Chinese elementary aged children. During the week they constructed and tested an egg drop package, explored the local natural history museum, learned about animal footprints and the habitats they live in, dug up dinosaur fossils, and launched rockets. For many, this was their one of their first formal experiences with STEAM activities. The experiences provided a positive introduction or continued support for STEAM at the primary level.

Collaboration Between Science And Art Through A Special International Symposium For Ecosystem Health And Sustainability, Changwoo Ahn Dr.

The STEAM Journal

The collaborations between ecosystem restoration and art practices was epitomized by the eco-artist Jackie Brookner who said: “it is not a matter of the scientists providing the hard-core research and artists the soft outreach; rather, the dynamics engendered in the space between disciplines is full of information necessary to solve complex problems at the systemic level”. This paper reviews and summaries the goals, activities, and lessons learned from a special symposium, which was held at the 12^th INTECOL (International Congress of Ecology) conference in Beijing, China, August 21 through 25, 2017, where about 3000 people attended from 70 countries. …

Constructing Kites To Integrate Mathematics And Arts Concepts, David Glassmeyer, Kevin Hsieh, Lieu Nguyen

The STEAM Journal

This article describes a tetrahedral kite activity that was implemented with grade 9 students (age 14-15). We detail how the three-part lesson provided opportunities to integrate mathematics and art concepts, with potential to also weave in science and engineering ideas. The first part primed students to consider tetrahedral kites, their cultural and historical significance, and the materials needed for constructing the kite. The second part had students create a prototype using nets of tissue paper decorated with mark making techniques. The third part had students create a tetrahedron kite containing cultural and geographical mark making techniques on the tissue paper …

Citizen Scientists And Artists: Integrating Arts And Technology To Teach The Effects Of Climate Change On Bird Migration, Laura Fattal Dr., Heejung An Dr.

The STEAM Journal

Ways to incorporate climate change into K-12 curricula are of growing interest to many science educators. The International Cooperation for Animal Research Using Space (ICARUS) examines animal and bird migrations as a lens to understand climate change aiding educators with its emphasis on technological imagining in science and visual arts teaching and learning. This article presents an interdisciplinary unit pertaining to bird migration and climate change that integrates the arts and technology by placing upper-elementary students in the position of being citizen scientists and artists, leading to a culminating art installation project. The unit shows how a variety of digital …

Cultivating Ingenuity In Art Through Steam Picture Books, Julia L. Hovanec

The STEAM Journal

In what creative ways can educators cultivate ingenuity? This article features ten STEAM picture books and their possibilities in the art room and beyond. It equips educators to take on STEAM armed with engaging and inspiring picture books that foster creativity, inventiveness, and more while inspiring students to create, experiment, problem-solve, and construct. There is a focus on one substantive, integrated Art and Science lesson built on the provocative book Summer Birds: The Butterflies of Maria Merian written by Margarita Engle and illustrated by Julie Paschkis. Readers will leave with one complete STEAM challenge-based lesson plan informed by this book …

Students Arts Participation Increases Stem Motivation Via Self-Efficacy, Stephen M. Dahlem

The STEAM Journal

This work found that there exists a correlation between student motivation in science, technology, engineering and mathematics (STEM) and student participation in the arts during high school with self-efficacy being a mediator. STEM is an important component of student success from a broad, national, perspective, as well as from a domain-specific point of view. The results of this work may provide aid to teachers, parents, administrators, and even students seeking to find ways to increase student motivation and performance in the STEM subjects. Additionally, this work may be of interest to advocates of the arts. This quantitative correlational study was …

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 …

Creative Learning With Music And Mathematics: Reflections On Interdisciplinary Collaborations, Graham Johnson, Alesia M. Moldavan

The STEAM Journal

Culturally responsive content, accessible and inclusive tools, and meaningful interdisciplinary tasks can aid in developing equitable and creative learning environments. Music and mathematics are ideal disciplines for interdisciplinary creative learning. In this article, we reflect on our experiences engaging in interdisciplinary music and mathematics tasks with preservice teachers. In particular, we highlight specific efforts taken to design and implement a creative music and mathematics workshop for use in a mathematics methods course. Guided by these experiences, we offer examples of tools and practices that have helped preservice teachers collaborate, engage in inquiry, improvise, develop empathy, and take intellectual and social …

Anneli Lax: They Think, Therefore We Are, Elena Anne Corie Marchisotto

Journal of Humanistic Mathematics

No abstract provided.

Lessons From Human Experience: Teaching A Humanities Course Made Me A Better Math Teacher, Erin Griesenauer

Journal of Humanistic Mathematics

As a professor at a Liberal Arts college, I recently taught a General Education course called Human Experience. Far from my normal experiences in the mathematics classroom, in Human Experience I was tasked with teaching topics from the humanities, including art, philosophy, history, and political science. Teaching this course was challenging, but it was also transformative. Teaching a course so far from my background gave me the opportunity to experiment with different pedagogical techniques and to reflect on how I set up my math classes. I learned many lessons that I have brought back to my math classes—lessons that have …

The Nothing That Really Matters, Szilárd Svitek

Journal of Humanistic Mathematics

Zero has (a) special role(s) in mathematics. In the current century, we take negative numbers and zero for granted, but we should also be aware that their acceptance and their emergence in mathematics, and their ubiquity today, have not come to happen as rapidly as, for example, that of natural numbers. Students can quickly become confused by the question: is zero a natural number? The answer is simple: a matter of definition. The history of zero and that of negative numbers are closely linked. It was in the calculations of debts that the negative numbers first appeared, where the state …