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Differential Equations For A Changing World:How To Engage Students In Learning And Applying Differential Equations, Biyong Luo 2024 University of Massachusetts Dartmouth

Differential Equations For A Changing World:How To Engage Students In Learning And Applying Differential Equations, Biyong Luo

CODEE Journal

In this article, I share my decade-long experience teaching an intensive five-week summer Differential Equation course covering complex topics and tips for creating an interactive and supportive learning environment to optimize student engagement. This article provides my detailed approach to planning and teaching an asynchronous course with rigor and flexibility for each student. An interactive teaching approach and variety of learning activities will augment students’ mathematical fluency and appreciation of the importance of differential equations in modeling a wide variety of real-world situations with special attention to ways differential equations can be relevant to creating public policy.


Raising Student Awareness Of Environmental Issues Via Writing Assignments With Differential Equations, Michelle L. Ghrist 2024 Gonzaga University

Raising Student Awareness Of Environmental Issues Via Writing Assignments With Differential Equations, Michelle L. Ghrist

CODEE Journal

In this paper, I discuss two environmentally-focused writing assignments that I developed and implemented in recent integral calculus and differential equations courses. These models of carbon storage and PCB’s in a river provide interesting applications of one-compartment mixing problems. The assignments were intended to focus student attention on sustainability concerns while also developing other essential skills. I discuss these assignments and their effect on my students’ technical writing and environmental awareness. Detailed introductory instructions and mostly complete solutions to these assignments appear in the appendices, to include sample student work.


Blue Whale And Krill Populations Modeling, Li Zhang 2024 The Citadel

Blue Whale And Krill Populations Modeling, Li Zhang

CODEE Journal

We present an intriguing topic in an undergraduate mathematical modeling course where predator-prey models are taught to our students. We describe modeling activities and the use of technology that can be implemented in teaching this topic. Through modeling activities, students are expected to use the numerical and graphical methods to observe the qualitative long-term behavior of predator and prey populations. Although there are other choices of predators and prey, we find that using blue whales and krill as predator and prey, respectively, would be most beneficial in strengthening our students' awareness of protecting endangered species and its impact on climate …


Modeling Aircraft Takeoffs, Catherine Cavagnaro 2024 Sewanee University

Modeling Aircraft Takeoffs, Catherine Cavagnaro

CODEE Journal

Real-world applications can demonstrate how mathematical models describe and provide insight into familiar physical systems. In this paper, we apply techniques from a first-semester differential equations course that shed light on a problem from aviation. In particular, we construct several differential equations that model the distance that an aircraft requires to become airborne. A popular thumb rule that pilots have used for decades appears to emanate from one of these models. We will see that this rule does not follow from a representative model and suggest a better method of ensuring safety during takeoff. Aircraft safety is definitely a matter …


Ode Models Of Wealth Concentration And Taxation, Bruce Boghosian, Christoph Borgers 2024 Tufts University and American University of Armenia

Ode Models Of Wealth Concentration And Taxation, Bruce Boghosian, Christoph Borgers

CODEE Journal

We refer to an individual holding a non-negligible fraction of the country’s total wealth as an oligarch. We explain how a model due to Boghosian et al. can be used to explore the effects of taxation on the emergence of oligarchs. The model suggests that oligarchs will emerge when wealth taxation is below a certain threshold, not when it is above the threshold. The underlying mechanism is a transcritical bifurcation. The model also suggests that taxation of income and capital gains alone cannot prevent the emergence of oligarchs. We suggest several opportunities for students to explore modifications of the model.


Odes And Mandatory Voting, Christoph Borgers, Natasa Dragovic, Anna Haensch, Arkadz Kirshtein, Lilla Orr 2024 Tufts University, Medford, MA

Odes And Mandatory Voting, Christoph Borgers, Natasa Dragovic, Anna Haensch, Arkadz Kirshtein, Lilla Orr

CODEE Journal

This paper presents mathematics relevant to the question whether voting should be mandatory. Assuming a static distribution of voters’ political beliefs, we model how politicians might adjust their positions to raise their share of the vote. Various scenarios can be explored using our app at https: //centrism.streamlit.app/. Abstentions are found to have great impact on the dynamics of candidates, and in particular to introduce the possibility of discontinuous jumps in optimal candidate positions. This is an unusual application of ODEs. We hope that it might help engage some students who may find it harder to connect with the more customary …


Using A Sand Tank Groundwater Model To Investigate A Groundwater Flow Model, Christopher Evrard, Callie Johnson, Michael A. Karls, Nicole Regnier 2024 Ball State University

Using A Sand Tank Groundwater Model To Investigate A Groundwater Flow Model, Christopher Evrard, Callie Johnson, Michael A. Karls, Nicole Regnier

CODEE Journal

A Sand Tank Groundwater Model is a tabletop physical model constructed of plexiglass and filled with sand that is typically used to illustrate how groundwater water flows through an aquifer, how water wells work, and the effects of contaminants introduced into an aquifer. Mathematically groundwater flow through an aquifer can be modeled with the heat equation. We will show how a Sand Tank Groundwater Model can be used to simulate groundwater flow through an aquifer with a no flow boundary condition.


To Open Or Not To Open: Developing A Covid-19 Model Specific To Small Residential Campuses, Christina Joy Edholm, Maryann Hohn, Nicole Lee Falicov, Emily Lee, Lily Natasha Wartman, Ami Radunskaya 2024 Scripps College

To Open Or Not To Open: Developing A Covid-19 Model Specific To Small Residential Campuses, Christina Joy Edholm, Maryann Hohn, Nicole Lee Falicov, Emily Lee, Lily Natasha Wartman, Ami Radunskaya

CODEE Journal

In May 2020, administrators of residential colleges struggled with the decision of whether or not to open their campuses in the Fall semester of 2020. To help guide this decision, we formulated an ODE model capturing the dynamics of the spread of COVID-19 on a residential campus. In order to provide as much information as possible for administrators, the model accounts for the different behaviors, susceptibility, and risks in the various sub-populations that make up the campus community. In particular, we start with a traditional SEIR model and add compartments representing relevant variables, such as quarantine compartments and a hospitalized …


Applying The Sir Model: Can Students Advise The Mayor Of A Small Community?, Carrin Goosen, Mark I. Nelson, Mahime Watanabe 2024 University of Wollongong

Applying The Sir Model: Can Students Advise The Mayor Of A Small Community?, Carrin Goosen, Mark I. Nelson, Mahime Watanabe

CODEE Journal

This is an account of a modelling scenario that uses the sir epidemic model. It was used in a third year applied mathematics subject. All students were enrolled in a mathematics degree of some type. Students are presented with the results of a test carried out on 100 individuals in a community containing 3000 people. From this they determined the number of infectious and recovered individuals in the population. Given the per capita recovery rate and making a suitable assumption about the number of infectious individuals at the start of the epidemic, they then estimate the infectious contact rate and …


Fitting A Covid-19 Model Incorporating Senses Of Safety And Caution To Local Data From Spartanburg County, South Carolina, D. Chloe Griffin, Amanda Mangum 2024 Brown University

Fitting A Covid-19 Model Incorporating Senses Of Safety And Caution To Local Data From Spartanburg County, South Carolina, D. Chloe Griffin, Amanda Mangum

CODEE Journal

Common mechanistic models include Susceptible-Infected-Removed (SIR) and Susceptible-Exposed-Infected-Removed (SEIR) models. These models in their basic forms have generally failed to capture the nature of the COVID-19 pandemic's multiple waves and do not take into account public policies such as social distancing, mask mandates, and the ``Stay-at-Home'' orders implemented in early 2020. While the Susceptible-Vaccinated-Infected-Recovered-Deceased (SVIRD) model only adds two more compartments to the SIR model, the inclusion of time-dependent parameters allows for the model to better capture the first two waves of the COVID-19 pandemic when surveillance testing was common practice for a large portion of the population. We find …


Nonlinear Dynamics Of Mountain Pine Beetle Populations: Discussion Of Forestry Policy, A Survey Of Existing Mathematical Models, And Code Base Demonstration, Scott A. Strong, Maya Maes-Johnson 2024 Colorado School of Mines

Nonlinear Dynamics Of Mountain Pine Beetle Populations: Discussion Of Forestry Policy, A Survey Of Existing Mathematical Models, And Code Base Demonstration, Scott A. Strong, Maya Maes-Johnson

CODEE Journal

This article presents existing mathematical models associated with mountain pine beetle populations in lodgepole pine forests, whose reproductive cycle requires the destruction of colonized host trees, decreasing timber availability/quality, and providing fuel sources for wildfires. With the existence of a positive-feedback loop with environmental warming, the need for intervention and management is clear. However, the legislative responses to the focusing events from our 2000-2010 North American epidemics are characterized as under-leveraged. While the reasons for this are multifaceted, increasing the capacity of STEM-informed individuals to take part in quantitative modeling of the underlying ecosystem generates awareness and provides pathways connecting …


Solar Panels, Euler’S Method And Community-Based Projects: Connecting Differential Equations With Climate Change, Victor J. Donnay 2024 Bryn Mawr College

Solar Panels, Euler’S Method And Community-Based Projects: Connecting Differential Equations With Climate Change, Victor J. Donnay

CODEE Journal

How does mathematics connect with the search for solutions to the climate emergency? One simple connection, which can be explored in an introductory differential equations course, can be found by analyzing the energy generated by solar panels or wind turbines. The power generated by these devices is typically recorded at standard time intervals producing a data set which gives a discrete approximation to the power function $P(t)$. Using numerical techniques such as Euler’s method, one can determine the energy generated. Here we describe how we introduce the topic of solar power, apply Euler’s method to determine the energy generated, and …


Elementary Preservice Teachers' Conceptions And Ability To Develop And Assess Integrated Stem Lessons, Jelena Byers, Selina Bartels 2024 Valparaiso University

Elementary Preservice Teachers' Conceptions And Ability To Develop And Assess Integrated Stem Lessons, Jelena Byers, Selina Bartels

Indiana STEM Education Conference

Elementary teacher preparation programs prepare their pre-service teachers (PSTs) to teach STEM. In this study, two teacher educators in the disciplines of science and mathematics utilized a modified “Draw a Science Teacher” (DASTT-C) framework (Thomas et al., 2001) and the Understanding by Design (UbD) framework (Wiggins & McTighe, 2005) to understand PSTs' conceptions of integrated STEM and how they plan and assess their lessons. This research brief discusses some of the results of 16 PSTs’ pre- and post-DASTT-C results as well as analysis of STEM lesson plans written during their third-year pre-service program.


Harmonizing Stem And Social Justice Mathematics: A Path To Global Equity And Empowerment, Rose Mbewe 2024 Purdue University

Harmonizing Stem And Social Justice Mathematics: A Path To Global Equity And Empowerment, Rose Mbewe

Indiana STEM Education Conference

This study delves into the interconnectedness of science, technology, engineering, and mathematics (STEM) and social justice mathematics (SJM) to address pressing equitable global sustainable development and social justice issues. The research aims to understand how educators can effectively use SJM in STEM teaching to empower students as change agents for global equity by aligning mathematical tasks with the United Nations' 2030 agenda for Sustainable Development Goals (UN, 2015) and using them to address real-world injustices. The study unveils educators' pedagogical strategies for creating supportive learning environments and nurturing students' emotional well-being in STEM subjects. Educators who are conscious of social …


Proceedings Of The Ninth Annual Indiana Stem Education Conference: Resourcing Stem Education, William S. Walker III, Lynn A. Bryan, S. Selcen Guzey 2024 Purdue University

Proceedings Of The Ninth Annual Indiana Stem Education Conference: Resourcing Stem Education, William S. Walker Iii, Lynn A. Bryan, S. Selcen Guzey

Indiana STEM Education Conference

The Proceedings of the Ninth Annual Indiana STEM Education Conference are edited by the Center for Advancing the Teaching and Learning of STEM (CATALYST, https://www.education.purdue.edu/catalyst/) at Purdue University. The theme for the 2024 conference is Resourcing STEM Education. This year’s Indiana STEM Education Conference provides opportunities to learn about effective STEM education strategies, curriculum, and resources to engage students in integrated STEM learning opportunities and address the recently updated Indiana Academic Standards for Science and Computer Science, Indiana Academic Standards for Mathematics, and Indiana Academic Standards for Integrated STEM (https://www.in.gov/doe/students/indiana-academic-standards/).


The Impact Of Geospatial Contexts And Out-Of-School Experiences On Students' Stem Identity Formation, Hillary Ongoyo Omoze, Abigail Erskine, Asenath Odondi 2024 Purdue University

The Impact Of Geospatial Contexts And Out-Of-School Experiences On Students' Stem Identity Formation, Hillary Ongoyo Omoze, Abigail Erskine, Asenath Odondi

Indiana STEM Education Conference

STEM teaching faces challenges in varied geospatial contexts (Mulvey et al., 2023), where place and space factors play a significant role. This research brief explores the influence of place and space in shaping students' STEM identities throughout their educational journey, with a specific emphasis on the role of out-of-school experiences in fostering student learning and interest in STEM careers, particularly among middle school students.


Applying A Sociopolitical Equity Framework To A Developmental Algebra Curriculum, Sarah Oppland-Cordell, Natalie McGathey, David Feikes, William S. Walker III, Brandon Sorge 2024 Northeastern Illinois University

Applying A Sociopolitical Equity Framework To A Developmental Algebra Curriculum, Sarah Oppland-Cordell, Natalie Mcgathey, David Feikes, William S. Walker Iii, Brandon Sorge

Indiana STEM Education Conference

The Thinking With Algebra (TWA) curriculum, a National Science Foundation Project (DUE 2021414), applies a sociopolitical equity framework (Gutiérrez, 2012) to strengthen student participants’ mathematics achievement outcomes and mathematics identity development. Instructor and student data indicate improvements in these two dimensions. This project also expands knowledge about creating equitable math learning environments that support underrepresented students’ mathematical success.


The Future Of Future City: A Stem Program, Jeffrey A. Nowak, Shelby Werling 2024 Purdue University Fort Wayne

The Future Of Future City: A Stem Program, Jeffrey A. Nowak, Shelby Werling

Indiana STEM Education Conference

The idea of integrating science, technology, engineering, and mathematics (STEM) is still an enigma for many educators (Dare et al, 2021). Recent academic standards favor curricula that interweave the principles of integrated STEM into all content areas. Finding a “one size fits all” curriculum is challenging, perhaps even impossible. Future City is a national program that specializes in hands-on cross-curricular STEM education. Students work collaboratively using an engineering and design process to showcase their solutions to citywide sustainability issues. This research brief examines how educators can utilize the Future City program as the cornerstone of their STEM curriculum.


Implementing Integrated Stem Forensic And Soil Sciences Lab Activities To Promote Interest In Stem Careers, Mariah K. Stollar Awan, Caroline J. Rakowski 2024 Purdue University

Implementing Integrated Stem Forensic And Soil Sciences Lab Activities To Promote Interest In Stem Careers, Mariah K. Stollar Awan, Caroline J. Rakowski

Indiana STEM Education Conference

We implemented forensic and soil science integrated STEM lab activities with 11 middle school youth at a 4-H day camp at Purdue University. STEM perceived knowledge increased overall for participants. However, the pre- and post-assessments did not show a statistically significant difference. More students also indicated STEM career interest after participating. Because this study was exploratory and had a small sample size, more research on these integrated STEM lab activities should be conducted with larger samples.


Does Stem Integration In High School Mathematics Classes In Underserved Schools Benefit Students' Standardized Testing Outcomes?, Steve Heinold 2024 Purdue University

Does Stem Integration In High School Mathematics Classes In Underserved Schools Benefit Students' Standardized Testing Outcomes?, Steve Heinold

Indiana STEM Education Conference

STEM education in Indiana has become increasingly popular with, among many other factors, the recent focus by the Indiana Department of Education on the STEM workforce pipeline and school STEM certification (IDoE, 2023b). Some previous research has shown that integrating STEM into science classes and afterschool spaces has helped students from low-income communities catch up to their higher-income peers on assessments like high-stakes standardized testing (Bartell et al., 2008; Hurley, 2001; Weissglass, 2011). However, regarding STEM integration into mathematics classes, it can be more challenging than integration into other classes like science (Walker, 2016) and large gaps remain in the …


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