Science and Mathematics Education Commons^™

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

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.

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.

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 …

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 writing, and …

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

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.

Ethnographic Narrative Project, Kimberly Goodwin

CGU Theses & Dissertations

This paper details the journey of a first-year teacher. It is a highly reflective exploration of their inner landscape – one that documents the development of the teaching self in relation to students and society at large. Separated into four distinct sections, this work serves as an account of personal motivation to teach, getting to know students beyond the classroom walls, immersion in the community to situate educational work, and a comprehensive reflection upon teaching effectiveness and the evolution of the educating self. Development as a professional educator as stated in Teacher Performance Expectation (TPE) 6 demands continual introspection and …

Hidden Cracks In The Leaking Stem Pipeline: Retention Within First-Generation Latinx Students In Baccalaureate Stem Programs At Predominately White Institutions, Kevin Kandamby

Pitzer Senior Theses

This thesis documents the lived experiences of first-generation Latinx students navigating

through predominately white institutions while attaining or attempting to attain a STEM degree. To examine this, twelve students from five different institutions were interviewed in semi- structured focus groups to better understand the educational trajectories of students in STEM. Inadequate high school preparation, educational disparities, mental health, and lack of institutional support were some of the reoccurring concerns students had across all focus groups. Students also highlighted that cultural competency across faculty in STEM, support from identity groups, and returning back to their Latinx community to serve as professionals …

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, spending …

Find, Process, And Share: An Optimal Control In The Vidale-Wolfe Marketing Model, Michael C. Barg

CODEE Journal

The Vidale-Wolfe marketing model is a first-order, linear, non-homogeneous ordinary differential equation (ODE) where the forcing term is proportional to advertising expenditure. With an initial response in sales as the initial condition, the solution of the initial value problem is straightforward for a first undergraduate ODE course. The model serves as an excellent example of many relevant topics for those students whose interests lie in economics, finance, or marketing. Its inclusion in the curriculum is particularly rewarding at an institution without a physics program. The model is not new, but it was novel to us when a group of students …

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.

Teaching Differential Equations Without Computer Graphics Solutions Is A Crime, Beverly H. West

CODEE Journal

In the early 1980s computer graphics revolutionized the teaching of ordinary differential equations (ODEs). Yet the movement to teach and learn the qualitative methods that interactive graphics affords seems to have lost momentum. There still exist college courses, even at big universities, being taught without the immense power that computer graphics has brought to differential equations. The vast majority of ODEs that arise in mathematical models are nonlinear, and linearization only approximates solutions sufficiently near an equilibrium. Introductory courses need to include nonlinear DEs. Graphs of phase plane trajectories and time series solutions allow one to see and analyze the …

Motherhood And Teaching: Radical Care, Ksenija Simic-Muller

Journal of Humanistic Mathematics

This essay is a personal reflection on how I leverage my positioning as a caregiver in my roles of a mathematician, teacher, and mother, to advance a vision for a more just and equitable society. I argue that care at home and in the classroom takes similar forms, and can be liberating instead of oppressive.

Revealing Luz: Illuminating Our Identities Through Duoethnography, Carrie Diaz Eaton, Luz Marizza Bailey

Journal of Humanistic Mathematics

Hispanic Americans make up 15% of the current US workforce, but they only account for 7% of the STEM Education workforce [8]. One effective way to reach this population, particularly Latinas, is by providing stories and ethnographic biographies of successful Latinas they can relate to. It is important to note that Latinas have been earning PhDs in STEM disciplines outside of the US much longer than US-born Latinas have been earning them inside. Thus we offer the story of a mathematics educator, from Peru, Dr. Luz Antonia Mendizábal Gálvez de Rodriguez, a girl who was given a chance to be …

Stumbling Into The Spiral: A Serendipitous Steam Exploration, David Rufo

The Transdisciplinary STEAM+ Journal

An artist-educator discovers how a STEAM-based approach to making art brings together a variety of subject areas in surprising ways.

Kids Inspire Kids For Steam, Kristof Fenyvesi, Tony Houghton, José Manuel Diego-Mantecón, Elizabeth Crilly, Adrian Oldknow, Zsolt Lavicza, Teresa F. Blanco

The Transdisciplinary STEAM+ Journal

The goal of the Kids Inspiring Kids in STEAM (KIKS) project was to raise students’ awareness towards the multi- and transdisciplinary connections between the STEAM subjects (Science, Technology, Engineering, Arts & Mathematics), and make the learning about topics and phenomena from these fields more enjoyable. In order to achieve these goals, KIKS project has popularized the STEAM-concept by projects based on the students inspiring other students-approach and by utilizing new technologies, tools, open educational resources, and everyday items and materials. Through the students-inspiring-other-students-approach, we have aimed to get participating students developing STEAM activities for other students in their own local …

Science Theater As Steam: A Case Study Of "Save It Now", Christopher D. Davidson, Willard Simms

The Transdisciplinary STEAM+ Journal

What are the markers of a successful STEAM program? How and when can educators be reasonably sure that an interdisciplinary unit or project, rich in both the sciences and the arts, has delivered on its implicit promise – by adding value to a student’s education in ways that are beyond the scope of traditional discipline-specific learning? I attempt to address this question with a case study of Theatre of Will’s “Save It Now,” a pilot program for 4^th, 5^th and 6^th graders at eight Los Angeles public schools that integrates theater arts, music and the STEM …

A Brief History Of Stem And Steam From An Inadvertent Insider, Lisa G. Catterall

The Transdisciplinary STEAM+ Journal

This article traces a history of STEM and STEAM from the perspective of someone involved in arts integration research for the last 35 years, and proposes a vision for the next steps. It also provides an assessment of the risks inherent in current trends of STEAM roll-out in schools, from the lack of resources for professional development to the burgeoning market in STEAM kits and activity books that do not lead to the original learning goals of STEAM.

Special Issue Call For Papers: Mathematics And Motherhood, Pamela E. Harris, Becky Hall, Carrie Diaz Eaton, Emille Davie Lawrence

Journal of Humanistic Mathematics

The Journal of Humanistic Mathematics is pleased to announce a call for papers for a special issue on Mathematics and Motherhood. Please send your abstract submissions via email to the guest editors by October 1, 2017. Initial submission of complete manuscripts is due January 1, 2018. The issue is currently scheduled to appear in July 2018.

I Love You Fifty, Nat Banting

Journal of Humanistic Mathematics

This article chronicles the merging of my roles of teacher and learner of mathematics with that of a relatively new pursuit: parenthood. Amidst my attempts to dutifully provide opportunities for my son to interact with various mathematical ideas and artifacts, it was an unanticipated moment of epiphany that allowed me to enter into his emerging world of mathematical significance and rediscover what first drew me to the teaching and learning of mathematics. My son’s innocent, yet potent, understanding of number provides an image of the power of mathematics to organize experience, structure significance, and communicate meaning.

Inquiry Based Learning From The Learner’S Point Of View: A Teacher Candidate’S Success Story, Caroline Johnson Caswell, Derek J. Labrie

Journal of Humanistic Mathematics

The goal of this paper is to review current research on Inquiry Based Learning (IBL) and shed some light, from a student's perspective, on the challenges and rewards of this pedagogy. The first part of the article provides an extensive review of the literature on IBL. The second part focuses on one student's experiences in an IBL classroom.

In particular, a graduate secondary mathematics student reflects upon his experiences in a college mathematics class where the instructor implemented an Inquiry Based Learning model. His experience is validated by current research on IBL educational methodology which structures the classroom environment for …

16, Dan Mcquillan

Journal of Humanistic Mathematics

This 15 word poem suggests that the reader count the words of the poem. Since every line has half as many words as the previous line, and since the poem urges the reader to keep counting forever, one imagines a total of 16 words.

The Battle Against Malaria: A Teachable Moment, Randy K. Schwartz

Journal of Humanistic Mathematics

Malaria has been humanity’s worst public health problem throughout recorded history. Mathematical methods are needed to understand which factors are relevant to the disease and to develop counter-measures against it. This article and the accompanying exercises provide examples of those methods for use in lower- or upper-level courses dealing with probability, statistics, or population modeling. These can be used to illustrate such concepts as correlation, causation, conditional probability, and independence. The article explains how the apparent link between sickle cell trait and resistance to malaria was first verified in Uganda using the chi-squared probability distribution. It goes on to explain …

Aesthetics In A Mathematics For Liberal Arts Project, Jason Callahan, Carol Gee

Journal of Humanistic Mathematics

We present and assess a project and its rubric developed and assigned in Mathematics for Liberal Arts, a general education course for non-science and non-business majors, to incorporate different skills including aesthetic design, written and oral communication, and mathematical analysis to tackle a common optimization problem with an aesthetic slant: construct a beverage can (i.e., right circular cylinder) of a given volume while taking into account the cost of materials (i.e., surface area) and aesthetic qualities (e.g., the golden ratio).

Struggles And Growth In Mathematics Education: Reflections By Three Generations Of Mathematicians On The Creation Of The Computer Game E-Brock Bugs, Laura Broley, Chantal Buteau, Eric Muller

Journal of Humanistic Mathematics

In the Fall of 2013 our team of three different generations of mathematicians launched the free, online E-Brock Bugs© mathematics computer game [5] which we developed from an original probabilistic board game, Brock Bugs, and its digital learning object version. We constructed E-Brock Bugs using Devlin’s [9] mathematics computer game design principles for games that prompt players’ development of mathematical thinking. As we created E-Brock Bugs we found it necessary to go through an evolving cyclic process of design, implementation, and analysis. In this paper we reflect upon the main struggles we faced in this process and the …

Metaphors And Mathematical Identity: Math Is Like A Tornado In Kansas, Carmen M. Latterell, Janelle L. Wilson

Journal of Humanistic Mathematics

Mathematical identity is an individual’s concept of who he or she is mathematically. In this paper, metaphors for mathematics from elementary education majors are compared to metaphors created by secondary mathematics teaching majors. The analysis demonstrates a basic difference in the mathematical identity of the two groups, with the latter group having more holistic conceptions of mathematics than the first group. Elementary education majors describe mathematics as an ongoing struggle in which the mathematics is active, and they are the victims. The secondary teaching mathematics majors describe mathematics as an ongoing struggle in which they are active.

Mathematics For Human Flourishing, Francis Su

All HMC Faculty Publications and Research

Why does the practice of mathematics often fall short of our ideals and hopes? How can the deeply human themes that drive us to do mathematics be channeled to build a more beautiful and just world in which all can truly flourish?

Mom, Dad, Help Please: The Home Environment’S Influences On A Child’S Math Ability, Nicole Kerkhof

CMC Senior Theses

Recently, there has been a big surge of research and public interest in increasing the math capabilities and skills of American children. This paper serves as a literature review examining how the home environment, specifically parents, can help with that. This meta-analysis delves into the factors of maternal math talk, a parent’s own math anxiety, and the relationship between a parent and child in the context of a parent’s gender stereotypes and a parent’s perception on his or her child’s math abilities. Interventions, suggestions, and future implications are also discussed. This paper will hopefully bring needed awareness to parents about …

Engaging The Community: Reflections On A Steam Institute, Dennis Doyle, Yat-Long Sam Poon

The Transdisciplinary STEAM+ Journal

Staff at an elementary school working with artists from a non-profit arts integration professional development organization developed a highly engaging full day STEAM Institute to engage the community in experiential STEAM learning practices and to leverage the experience for systemic impact. This reflection considers the outcomes that went well beyond the original goals.