Education Commons^™

Finding Your Mathematical Roots: Inclusion And Identity Development In Mathematics, Linda Mcguire

Journal of Humanistic Mathematics

This paper details a semester-long course project that has been successfully adapted for use in mathematics courses ranging from introductory level, general-education classes to advanced courses in the mathematics major. Through creating aspirational mathematical family trees and writing mathematical autobiographies, this assignment is designed to help battle belonging uncertainty, to challenge students to self-situate in relation to the history of mathematical and scientific knowledge, and to make visible a student’s developing identity in mathematics and, more broadly, in STEM.

The construction and scaffolding of the project, assignments, examples of student work, foundational readings, assessment and outcomes, and adaptation strategies for …

Gödel's Theorem In The Continuing Education Of Mathematics Teachers, Ana J. Lemes

Journal of Humanistic Mathematics

The notion of dépaysement épistémologique (epistemological disorientation) aims to capture the sense of disorientation when a learner is led to question their prior assumptions and understandings, generating uncertainty in a context in which they thought they had certain knowledge. This article describes an activity used with a group of practicing mathematics teachers in Uruguay that integrates elements of the history of mathematics related to Gödel’s incompleteness theorem, with the aim of provoking in the participants the experience of dépaysement épistémologique. Results show that several of the teachers participating in the activity felt dépaysement épistémologique, and this feeling triggered …

Numeracy Tasks: Inspiring Transfer Between Concrete And Abstract Thinking Spaces, Taras Gula, Miroslav Lovric

Numeracy

In our paper we build a case for conceptualizing numeracy tasks as distinct from mathematical tasks (or at least as a special type of mathematical task), and for abstraction and interpretation as a set of key activities necessary for designating a numeracy task as being high-quality. We start with an attempt to tame the fuzziness of numeracy and its family members (including quantitative reasoning, quantitative literacy, mathematical literacy, and the word problem cousins) by outlining six areas of consensus gleaned from literature. These provide the foundation for a core mandate of numeracy. We then build our case for the distinctness …

The Effectiveness Of An Educational Program In Developing Mathematical Achievement As Well As Developing Productive Struggle Among Students Of Intermediate Stage, Ibrahim A. Khalil Ph.D.

International Journal for Research in Education

This study aimed to identify the effectiveness of an educational program in developing Mathematical Achievement and productive struggle among students of intermediate stage. To fulfil its goals the study used the quasi-experimental approach, based on the design of two equivalent groups. It also used the Teacher's Guide - an activity booklet as study material, in addition to the use of two tools to collect data. One of them is an achievement test that included (three levels of mathematical knowledge related to equation and inequalities) and the other is a productive struggle scale (divided into three axes). The study sample consisted …

Easy, Bright, Fluorescence Demonstration Of Buffer Action, Mariana Dykstra, Yejin Chung, Mark Muyskens

University Faculty Publications and Creative Works

We report an attractive update to the demonstration of acid–base buffer action that is appropriate for ease of use and getting attention in the classroom. The twist is based on new fluorophore information and the recent availability of UV flashlights serving as an ideal, portable excitation light source. The pH-dependent fluorescence comes from a choice among three natural sources, namely narra tree wood extract, kidneywood extract, and scopoletin, which is a purchasable coumarin, that all perform equally well. We provide practical details for performing the buffer demonstration at scales of 100 and 1000 mL and give background information for context.

“That Cross-Curricular Business”: The Engineering Design Process In Mathematics And Science Classrooms, Eugenia Vomvoridi-Ivanovic, Tonisha B. Lane, Leia K. Cain, Salam Ahmad, Selene Willis, Jonathan E. Gaines

The Qualitative Report

The engineering design process (EDP) is one tool teachers can use to facilitate STEM integration. As part of a larger three-year longitudinal research project regarding engineering identity development among middle school youth in a summer robotics outreach program, this study aims to understand teachers’ willingness to incorporate engineering design in their classrooms through an exploration of their perceptions of the EDP, its applications to their subject matter and classroom context, methods of enacting the EDP, and perceived challenges to and supports for doing so. We conducted a qualitative case study and drew our results from focus groups and semi-structured interviews …

Special Issue On Public Policy: Front Matter

CODEE Journal

The Front Matter contains the Editor-in-Chief's Foreword, a Dedicatory by Associate Editor Douglas Meade, a Preface by the Special Editors Bev West and Samer Habre, and the Table of Contents.

Full Issue - Engaging The World: Differential Equations Can Influence Public Policies

CODEE Journal

This is the full issue (front matter and all papers) of the Third CODEE Special Issue, with the theme, "Engaging the World: Differential Equations can Influence Public Policies."

Seeing Eye To Eye? Comparing Faculty And Student Perceptions Of Biomolecular Visualization Assessments, Josh T. Beckham, Daniel R. Dries, Bonnie L. Hall, Rarchel M. Mitton-Fry, Shelly Engelman, Charmita Burch, Roderico Acevedo, Pamela S. Mertz, Didem Vardar-Ulu, Swati Agrawal, Kristin M. Fox, Shane Austin, Margaret A. Franzen, Henry V. Jakubowski, Walter R. P. Novak, Rebecca Roberts, Alberto I. Roca, Kristen Procko

Chemistry Faculty Publications

While visual literacy has been identified as a foundational skill in life science education, there are many challenges in teaching and assessing biomolecular visualization skills. Among these are the lack of consensus about what constitutes competence and limited understanding of student and instructor perceptions of visual literacy tasks. In this study, we administered a set of biomolecular visualization assessments, developed as part of the BioMolViz project, to both students and instructors at multiple institutions and compared their perceptions of task difficulty. We then analyzed our findings using a mixed-methods approach. Quantitative analysis was used to answer the following research questions: …

How Mathematicians Characterize And Attempt To Develop Understanding Of Concepts And Definitions In Proof-Based Courses, Rachel Rupnow, Timothy Fukawa-Connelly

Faculty Peer-Reviewed Publications

Mathematics education research has long focused on students’ conceptual understanding, including highlighting conceptions viewed as problematic and looking for ways to develop more desirable conceptions. Nevertheless, limited research has examined how mathematicians characterize understanding of concepts and definitions or promote activities beneficial for students. Based on interviews with 13 mathematicians, we present thematic characterizations of what it means to understand a concept and definition, highlight activities mathematicians believe assist students’ learning, and examine their reasons for promoting these activities.

Results include mathematically grounded descriptions of what it means to understand a concept but general descriptions of approaching and supporting learning. …

Instructional Decision Making In A Gateway Quantitative Reasoning Course, Deependra Budhathoki, Gregory D. Foley, Stephen Shadik

Numeracy

Many educators and professional organizations recommend Quantitative Reasoning as the best entry-level postsecondary mathematics course for non-STEM majors. However, novice and veteran instructors who have no prior experience in teaching a QR course often express their ignorance of the content to choose for this course, the instruction to offer students, and the assessments to measure student learning. We conducted a case study to investigate the initial implementation of an entry-level university quantitative reasoning course during fall semester, 2018. The participants were the course instructor and students. We examined the instructor’s motives and actions and the students’ responses to the course. …

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 …

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

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 …

Pre-Service Teachers Notice Student Thinking: Then What?, Tara Barnhart, Heather J. Johnson, Miray Tekkumru-Kisa

Education Faculty Articles and Research

Research has demonstrated that pre-service teachers (PSTs) can learn to notice students’ thinking in sophisticated ways by analyzing videos of classroom interactions. What is less clear is how PSTs use what they notice about student thinking to inform how they respond. Secondary math and science PSTs from three teacher preparation programs were invited to analyze a video clip identifying noteworthy moments of student thinking and describing an instructional move they might make and why. A qualitative analysis of their responses indicates that the PSTs overwhelmingly noticed both the substance and the source of students’ ideas. However, the patterns in their …

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 …

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 …

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 …

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.

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 …

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 …

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.

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.

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.

Assessing The Relationship Between Neighborhood Inequality And Stem Employment For Underrepresented Minorities With Stem Degrees, Brian P. Hurley

Graduate Research Theses & Dissertations

The purpose of this study is to assess whether there is a relationship between neighborhood inequality in which underrepresented minorities (URMs) with STEM degrees reside and their employment in STEM fields. The current study deploys an Intersectional Theory (IT) research framework and Bourdieu’s Theory of Practice to identify the influence of neighborhood capital on successful matriculation through the STEM pipeline as well as variables that elucidate latent inequities in the STEM pipeline which lead to unequal outcomes for URMs. Generalized Linear Multilevel Models (GLMMs) are used to answer the research questions where the individual variables of gender, race, and age …

Mapping With The Land: Co-Developing A Cumulative Impact Monitoring And Land Stewardship Framework With Sambaa K’E First Nation, Northwest Territories, Canada, Michael S. Mcphee

Theses and Dissertations (Comprehensive)

Across the Northwest Territories (NWT), Canada, Indigenous populations are striving to achieve effective environmental protection, whilst navigating complex methods, policies, and research relationships within co-management contexts. This thesis seeks to identify how differing cultural systems, environmental change, and fractured partnerships may be unified to align with the needs of the Sambaa K’e First Nation (SKFN), a remote Dehcho Dene community. Indigenous methodologies guided co-development of research questions with SKFN leadership which yielded objectives a) develop a GIS-based method to manage, organize and mobilize cultural and environmental data; b) develop a new stewardship monitoring procedure so that users can apply the …

An Expository Analysis Of Textbook Usage In Classical Settings For High School Biology, Kristen Bissontz

Master of Arts in Classical Studies

AN EXPOSITORY ANALYSIS OF TEXTBOOK USAGE IN CLASSICAL SETTINGS FOR HIGH SCHOOL BIOLOGY

Kristen Bissontz

Southeastern University, Lakeland FL

The classical model of education has reemerged as a viable alternative to the modern education system. Many of the disciplines taught in a classical school, program or home education scenario appear to align with the classical philosophy with the exception of the sciences. This paper serves to uncover if textbooks are the primary source in classical settings, what resources are utilized, and offers suggestions to better align with the classical pedagogy.

A small sample of classical schools and programs in a …

A Meta-Synthesis Of The Literature On Science And Engineering Teaching Self-Efficacy: Current Gaps And Future Research Directions, Deepika Menon, Jeanna R. Wieselmann, Sarah Haines, Sumreen Asim

Department of Teaching, Learning, and Teacher Education: Faculty Publications

Self-efficacy is a topic of great interest in elementary preservice and inservice teacher education given that elementary teachers often have low self-efficacy for STEM teaching. In this article, we synthesize the existing literature on science and engineering teaching self-efficacy to (1) explore trends in science and engineering teaching self-efficacy research, (2) identify current gaps that exist in the literature, and (3) propose a visual model to provide future direction in research. Utilizing a qualitative meta-synthesis, we analyzed 88 articles focused on science and engineering teaching self-efficacy. Of these articles, 66 studied preservice teachers, 21 studied inservice teachers, and one included …

The Effect Of Learning Environment And Student Groupings On Math Skill Mastery, Erin Marr

Electronic Theses & Dissertations (2024 - present)

This study was designed to evaluate the impact of instructional group size and composition on student progress within a classwide math intervention. In terms of group size, groupings of greater than and less than 10 students were compared. In terms of group composition, homogeneous and heterogeneous groups were compared, defined by grouping the classes with standard deviations of student performance within the upper quartile (heterogeneous) and lower quartile (homogeneous) on a pre-intervention measure. The outcome measure used to evaluate student progress was the number of trials required for students to reach mastery on a specific skill within the 16-skill intervention …

Enhancing Rural Science Education Through School District-University Partnership, Venicia A. Ferrell, Alexis S. Tharpe

Center for Educational Partnerships Publications

This instrumental case study describes the steps taken to establish and implement a university–school partnership to improve rural science teachers’ content knowledge and teaching practices and students’ achievement in elementary science and high school biology courses. Our research questions explored the impact of professional development and place-based learning on student outcomes, with the study’s methodology involving needs assessments, teacher training, and continuous support through modeling and coaching. The findings include gains in achievement and substantial gains in science education. The findings have implications for the design, implementation, and evaluation of university–school partnerships designed to build teachers’ capacity to deliver high-quality …