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Claremont Colleges

2019

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Full-Text Articles in Education

On Fall Break, Rachel Levy Jul 2019

On Fall Break, Rachel Levy

Journal of Humanistic Mathematics

A musing on Fall Break.


Book Review: What Is A Mathematical Concept? Edited By Elizabeth De Freitas, Nathalie Sinclair, And Alf Coles, Brendan P. Larvor Jul 2019

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 ...


Mathematics Out Of Nothing: Talking About Powerful Mathematical Ideas With Children, Matthew Oldridge Jul 2019

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.


Everyman's Climb, Charles A. Coppin Jul 2019

Everyman's Climb, Charles A. Coppin

Journal of Humanistic Mathematics

Hal and Verity represent two different philosophies of learning, one used by most of us. In today’s world, authentic teaching is indeed a heroic act, but may not be the most popular. This piece draws distinctions between these choices, each time we teach a course, each day we walk into the classroom, and even when working with an individual student; they are ever present.


Mathematics Students As Artists: Broadening The Mathematics Curriculum, Marshall Gordon Jul 2019

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 Jul 2019

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 ...


Visual Teaching Of Geometry And The Origins Of 20th Century Abstract Art, Stephen Luecking Jul 2019

Visual Teaching Of Geometry And The Origins Of 20th Century Abstract Art, Stephen Luecking

Journal of Humanistic Mathematics

As a group, the artists educated near the turn of the 19th and 20th centuries possessed greater mathematical knowledge than expected of artists today, especially regarding constructive skills in Euclidean geometry. Educational theory of the time stressed such skills for students in general, who needed these to enter the workplace of the time. Mathematics teaching then stressed the use of manipulatives, i.e., visual and interactive aids thought to better fix the student’s acquisition of mathematical skills. This visual training, especially in geometry, significantly affected the early development of abstraction in art. This paper presents examples of ...


Developing Stem Interest And Genre Knowledge Through Science Fiction Prototyping, Justin Nicholes Mar 2019

Developing Stem Interest And Genre Knowledge Through Science Fiction Prototyping, Justin Nicholes

The STEAM Journal

Upward Bound Math and Science, a federally funded initiative, aims to persuade U.S. high schoolers to become college STEM (science, technology, engineering, mathematics) majors. The program attempts this persuasion by developing students’ content and procedural knowledge so that students may succeed in high school and college STEM courses. Primary focus on knowledge acquisition, however, may cause missed opportunities to engage the imaginative dimensions of students’ science identities and students’ senses of wonder for science. In this reflective essay, I describe a science fiction prototyping assignment that meets the knowledge-based objectives of the Writing Skills course in a five-week Upward ...


Developing A Makerspace As A Vehicle For Partnership Building: The Role Of Teacher Education Programs In Guiding Teachers, Librarians, And Communities, Heejung An, Ellen Pozzi, Mar 2019

Developing A Makerspace As A Vehicle For Partnership Building: The Role Of Teacher Education Programs In Guiding Teachers, Librarians, And Communities, Heejung An, Ellen Pozzi,

The STEAM Journal

As schools consider new ways to enhance hands-on learning opportunities, many have focused on the emerging “Maker Movement.” As a means to support this trend, the authors share how the College of Education at a state university in northern New Jersey designed and facilitated a Makers Day event to help teacher candidates, teachers, and librarians, to develop insights into the activities for their own community based makerspaces. This article first describes the impetus for carrying out such activities, followed by a literature review, a description of how the event was designed, and our future plans for building on these activities.


Towards A Steam Underpinned Industrial Digitalisation Curriculum, Kamaran Fathulla Mar 2019

Towards A Steam Underpinned Industrial Digitalisation Curriculum, Kamaran Fathulla

The STEAM Journal

This article reports on an innovative approach for designing a STEAM curriculum aimed at giving graduates the necessary skills to meet the challenges set out by onset of the Fourth Industrial revolution (ID 4.0: Industrial Digitalisation). This curriculum has been developed as part of a hefce (Higher Education Funding Council, UK) funded project at the University of Lincoln, UK.


Design For Steam: Creating Participatory Art With Purpose, Nick Kamienski, Nicole M. Radziwill Mar 2019

Design For Steam: Creating Participatory Art With Purpose, Nick Kamienski, Nicole M. Radziwill

The STEAM Journal

Innovation is simultaneously reflected in the variety and diversity of art. Over the past century, art forms have progressed along a continuum from static to dynamic, and then to interactive and participatory. The therapeutic value of creating and engaging in all of these art forms has also been identified. Furthermore, educators have recognized the profound value of art and design within the context of scientific and technical learning, and STEAM (science, technology, engineering, art, and math) has emerged as an educational philosophy with a strong base of support. This paper defines and articulates participatory elements of STEAM projects, and provides ...


Steam Lessons From The Forest: Ingenuity, Instruments And Autonomy, Tracey Hunter-Doniger Mar 2019

Steam Lessons From The Forest: Ingenuity, Instruments And Autonomy, Tracey Hunter-Doniger

The STEAM Journal

This article discusses a case study of an environmental art camp that was modeled after choice-based pedagogies. At this camp the children were able to choose their activities, and taught how to think and work like an artist/scientist using a sketch/field book as a guiding instrument for their inquiry and empowerment. What was found was that three pillars of empowerment formed a foundational structure consisting of three interrelated factors that inspired the campers: 1) ingenuity, 2) a useful instrument, and 3) autonomy. Cultivating the artist/scientist habits gave the students the ingenuity or practical knowledge and understanding of ...


A Note On Equity Within Differential Equations Education By Visualization, Younes Karimifardinpour Feb 2019

A Note On Equity Within Differential Equations Education By Visualization, Younes Karimifardinpour

CODEE Journal

The growing importance of education equity is partly based on the premise that an individual's level of education directly correlates to future quality of life. Educational equity for differential equations (DEs) is related to achievement, fairness, and opportunity. Therefore, a pedagogy that practices DE educational equity gives a strong foundation of social justice. However, linguistic barriers pose a challenge to equity education in DEs. For example, I found myself teaching DEs either in classrooms with a low proficiency in the language of instruction or in multilingual classrooms. I grappled with a way to create an equity educational environment that ...


Kremer's Model Relating Population Growth To Changes In Income And Technology, Dan Flath Feb 2019

Kremer's Model Relating Population Growth To Changes In Income And Technology, Dan Flath

CODEE Journal

For thousands of years the population of Earth increased slowly, while per capita income remained essentially constant, at subsistence level. At the beginning of the industrial revolution around 1800, population began to increase very rapidly and income started to climb. Then in the second half of the twentieth century as a demographic transition began, the birth and death rates, as well as the world population growth rate, began to decline. The reasons for these transitions are hotly debated with no expert consensus yet emerging. It's the problem of economic growth. In this document we investigate a mathematical model of ...


Consensus Building By Committed Agents, William W. Hackborn, Tetiana Reznychenko, Yihang Zhang Feb 2019

Consensus Building By Committed Agents, William W. Hackborn, Tetiana Reznychenko, Yihang Zhang

CODEE Journal

One of the most striking features of our time is the polarization, nationally and globally, in politics and religion. How can a society achieve anything, let alone justice, when there are fundamental disagreements about what problems a society needs to address, about priorities among those problems, and no consensus on what constitutes justice itself? This paper explores a model for building social consensus in an ideologically divided community. Our model has three states: two of these represent ideological extremes while the third state designates a moderate position that blends aspects of the two extremes. Each individual in the community is ...


Modeling The Spread And Prevention Of Malaria In Central America, Michael Huber Feb 2019

Modeling The Spread And Prevention Of Malaria In Central America, Michael Huber

CODEE Journal

In 2016, the World Health Organization (WHO) estimated that there were 216 million cases of Malaria reported in 91 countries around the world. The Central American country of Honduras has a high risk of malaria exposure, especially to United States soldiers deployed in the region. This article will discuss various aspects of the disease, its spread and its treatment and the development of models of some of these aspects with differential equations. Exercises are developed which involve, respectively, exponential growth, logistics growth, systems of first-order equations and Laplace transforms. Notes for instructors are included.


A Model Of The Transmission Of Cholera In A Population With Contaminated Water, Therese Shelton, Emma Kathryn Groves, Sherry Adrian Feb 2019

A Model Of The Transmission Of Cholera In A Population With Contaminated Water, Therese Shelton, Emma Kathryn Groves, Sherry Adrian

CODEE Journal

Cholera is an infectious disease that is a major concern in countries with inadequate access to clean water and proper sanitation. According to the World Health Organization (WHO), "cholera is a disease of inequity--an ancient illness that today sickens and kills only the poorest and most vulnerable people\dots The map of cholera is essentially the same as a map of poverty." We implement a published model (Fung, "Cholera Transmission Dynamic Models for Public Health Practitioners," Emerging Themes in Epidemiology, 2014) of a SIR model that includes a bacterial reservoir. Bacterial concentration in the water is modeled by the Monod ...


The Mathematics Of Gossip, Jessica Deters, Izabel P. Aguiar, Jacquie Feuerborn Feb 2019

The Mathematics Of Gossip, Jessica Deters, Izabel P. Aguiar, Jacquie Feuerborn

CODEE Journal

How does a lie spread through a community? The purpose of this paper is two-fold: to provide an educational tool for teaching Ordinary Differential Equations (ODEs) and sensitivity analysis through a culturally relevant topic (fake news), and to examine the social justice implications of misinformation. Under the assumption that people are susceptible to, can be infected with, and recover from a lie, we model the spread of false information with the classic Susceptible-Infected-Recovered (SIR) model. We develop a system of ODEs with lie-dependent parameter values to examine the pervasiveness of a lie through a community.

The model presents the opportunity ...


Climate Change In A Differential Equations Course: Using Bifurcation Diagrams To Explore Small Changes With Big Effects, Justin Dunmyre, Nicholas Fortune, Tianna Bogart, Chris Rasmussen, Karen Keene Feb 2019

Climate Change In A Differential Equations Course: Using Bifurcation Diagrams To Explore Small Changes With Big Effects, Justin Dunmyre, Nicholas Fortune, Tianna Bogart, Chris Rasmussen, Karen Keene

CODEE Journal

The environmental phenomenon of climate change is of critical importance to today's science and global communities. Differential equations give a powerful lens onto this phenomenon, and so we should commit to discussing the mathematics of this environmental issue in differential equations courses. Doing so highlights the power of linking differential equations to environmental and social justice causes, and also brings important science to the forefront in the mathematics classroom. In this paper, we provide an extended problem, appropriate for a first course in differential equations, that uses bifurcation analysis to study climate change. Specifically, through studying hysteresis, this problem ...


The Ocean And Climate Change: Stommel's Conceptual Model, James Walsh Feb 2019

The Ocean And Climate Change: Stommel's Conceptual Model, James Walsh

CODEE Journal

The ocean plays a major role in our climate system and in climate change. In this article we present a conceptual model of the Atlantic Meridional Overturning Circulation (AMOC), an important component of the ocean's global energy transport circulation that has, in recent times, been weakening anomalously. Introduced by Henry Stommel, the model results in a two-dimensional system of first order ODEs, which we explore via Mathematica. The model exhibits two stable regimes, one having an orientation aligned with today's AMOC, and the other corresponding to a reversal of the AMOC. This material is appropriate for a junior-level ...


Sir Models: Differential Equations That Support The Common Good, Lorelei Koss Feb 2019

Sir Models: Differential Equations That Support The Common Good, Lorelei Koss

CODEE Journal

This article surveys how SIR models have been extended beyond investigations of biologically infectious diseases to other topics that contribute to social inequality and environmental concerns. We present models that have been used to study sustainable agriculture, drug and alcohol use, the spread of violent ideologies on the internet, criminal activity, and health issues such as bulimia and obesity.


An Epidemiological Math Model Approach To A Political System With Three Parties, Selenne Bañuelos, Ty Danet, Cynthia Flores, Angel Ramos Feb 2019

An Epidemiological Math Model Approach To A Political System With Three Parties, Selenne Bañuelos, Ty Danet, Cynthia Flores, Angel Ramos

CODEE Journal

The United States has proven to be and remains a dual political party system. Each party is associated to its own ideologies, yet work by Baldassarri and Goldberg in Neither Ideologues Nor Agnostics show that many Americans have positions on economic and social issues that don't fall into one of the two mainstream party platforms. Our interest lies in studying how recruitment from one party into another impacts an election. In particular, there was a growing third party presence in the 2000 and 2016 elections. Motivated by previous work, an epidemiological approach is taken to treat the spread of ...


Linking Differential Equations To Social Justice And Environmental Concerns Feb 2019

Linking Differential Equations To Social Justice And Environmental Concerns

CODEE Journal

Special issue of the CODEE Journal in honor of its founder, Professor Robert Borrelli.


Academia Will Not Save You: Stories Of Being Continually “Underrepresented”, Lynette Deaun Guzmán Jan 2019

Academia Will Not Save You: Stories Of Being Continually “Underrepresented”, Lynette Deaun Guzmán

Journal of Humanistic Mathematics

My entire life I have had to navigate educational structures labeled (by other people) as “underrepresented” in my fields—mathematics and mathematics education. As many people who are similarly labeled in this way know, this meant I had to navigate oppressive structures that positioned me as lesser (e.g., white supremacy, patriarchy). Making sense of these repeated interactions, I wrote my dissertation as a series of three articles, each prefaced with an essay that situated a broader social, cultural, and political context and also connected to my lived experiences navigating academia. These essays were some of my most personal academic ...


Finding Teaching Inspiration From Gorgias: Mathematics Lessons From A Sophist, Ann L. Von Mehren Jan 2019

Finding Teaching Inspiration From Gorgias: Mathematics Lessons From A Sophist, Ann L. Von Mehren

Journal of Humanistic Mathematics

The logos or rational language of the fifth-century BCE teacher, Gorgias, as contained in the fragment On the Nonexistent, challenges a reader to understand the relationship between the existent and the nonexistent; yet the text also offers an accessible idea of logos. Inspired by William M. Priestley's approach to the study of logos through ratios, and by Ivor Grattan-Guinness's recommendation to broaden the study of historical texts in the history of mathematics and mathematics education, and pursue their significance in a heritage sense, this article suggests that this ancient non-mathematics text by Gorgias may inspire and refresh elementary ...


Fun With Math On Valentine's Day, Kristin T. Kennedy Jan 2019

Fun With Math On Valentine's Day, Kristin T. Kennedy

Journal of Humanistic Mathematics

This article describes various love-themed activities the department of mathematics at Bryant University hosted during a college-wide celebration of love called "The Arts and Science of Love", held during Valentine's Day 2018. Inspired by Susan D'Agustino's article "To Fall in Love with Math, Do This" [1], Bryant mathematicians came up with many creative and engaging activities that brought mathematics and its practitioners closer to the students on campus. Much fun was had.


What Is Humanistic Stem And Why Do We Need It?, Debra T. Bourdeau, Beverly L. Wood Jan 2019

What Is Humanistic Stem And Why Do We Need It?, Debra T. Bourdeau, Beverly L. Wood

Journal of Humanistic Mathematics

Getting students who are planning on technical careers to value their general education courses, particularly in the humanities, is not an easy task. The experiences of two professors from disciplines that cross the so-called divide between STEM and Humanities motivate not only a series of courses blending the two to the advantage of their own students but also a virtual pedagogical community to support efforts taking place elsewhere.


Symmetry And Measuring: Ways To Teach The Foundations Of Mathematics Inspired By Yupiaq Elders, Jerry Lipka, Barbara Adams, Monica Wong, David Koester, Karen Francois Jan 2019

Symmetry And Measuring: Ways To Teach The Foundations Of Mathematics Inspired By Yupiaq Elders, Jerry Lipka, Barbara Adams, Monica Wong, David Koester, Karen Francois

Journal of Humanistic Mathematics

Evident in human prehistory and across immense cultural variation in human activities, symmetry has been perceived and utilized as an integrative and guiding principle. In our long-term collaborative work with Indigenous Knowledge holders, particularly Yupiaq Eskimos of Alaska and Carolinian Islanders in Micronesia, we were struck by the centrality of symmetry and measuring as a comparison-of-quantities, and the practical and conceptual role of qukaq [center] and ayagneq [a place to begin]. They applied fundamental mathematical principles associated with symmetry and measuring in their everyday activities and in making artifacts. Inspired by their example, this paper explores the question: Could symmetry ...


The Mathematics Orientation Seminar: A Tool For Diversity And Retention In The First Year Of College, Salvatore J. Petrilli Jan 2019

The Mathematics Orientation Seminar: A Tool For Diversity And Retention In The First Year Of College, Salvatore J. Petrilli

Journal of Humanistic Mathematics

In this article I describe Adelphi University's Mathematics Orientation Seminar, a new course that was introduced into the mathematics major to help students find their passion in mathematics and to strengthen the educational community within our department. I discuss quantitative and qualitative results of surveys among students in the Mathematics Orientation Seminar in Fall 2016 and Fall 2017, which suggest that this might be a useful course for other institutions to utilize within any major. Finally, I explore faculty perspectives and describe what I believe to be the final version of this course.


Putting Educational Reform Into Practice: The Impact Of The No Child Left Behind Act On Students, Teachers, And Schools, Timothy Song Jan 2019

Putting Educational Reform Into Practice: The Impact Of The No Child Left Behind Act On Students, Teachers, And Schools, Timothy Song

CMC Senior Theses

This thesis seeks to investigate the effects of the No Child Left Behind Act (NCLB) on U.S. student achievement and teacher effectiveness. By combining the results from various data sources, I am able to indicate the levels of student preparedness, school spending, and specific classroom practices. After an analysis of my results, I suggest that NCLB has found moderate success in increasing the level of math preparedness for younger students from historically disadvantaged backgrounds. On the other hand, the data also suggests that there have been no statistically significant gains in reading achievement after the implementation of NCLB. Additionally ...