Education Commons^™

Sharing Four Biscuits Between Three People: An Illustrative Example Of How Mathematics Is Intertwined With Human Values, Lovisa Sumpter, David Sumpter

Journal of Humanistic Mathematics

Despite convincing arguments by mathematicians, philosophers, sociologists and machine learning practitioners to the contrary, there remains a widespread notion amongst many members of the general public (and some practitioners) that mathematics is neutral, that it is free from human values. One reason why this notion persists is that we lack clear-cut examples that demonstrate how mathematics and values are intertwined. In this paper, we offer one such example. In particular, we show that when sharing four biscuits between three people, several possible mathematical and ethical frameworks can be used. We demonstrate that different solutions—hiding one biscuit, arbitrarily sharing the extra …

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 …

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 …

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 …

“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 …

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 …

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.

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 …

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.

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 …

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 …

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 …

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.

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

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.

3ddp Engineering Design Intervention Impacts On Student Perceptions, Attitudes, And Interest Towards Engineering, James Robert Kane

Theses and Dissertations

The study, “3DDP Engineering Design Intervention Impacts on Student Perceptions, Attitudes, and Interest Towards Engineering” explored the impact of a culturally responsive, semi-formal 3D printing (3DDP) intervention on middle school students' perceptions, attitudes, and interest in engineering. The intervention aimed to broaden access to engineering education by providing formative experiences outside traditional classroom settings within the regular school day. A multifaceted approach was employed, utilizing quantitative analysis of assessments and surveys, qualitative analysis of written responses, follow-up interviews, and student-produced artifacts. The intervention functioned as a student-driven engineering club, integrating culturally relevant themes and hands-on activities spanning diverse engineering domains. …

Investigating Preservice Secondary Teachers’ Understanding And Enactment Of The Standards‑Based Practices During Microteaching, Deepika Menon, Diana S. Chang, Rosetta W. Ngugi

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

Reform efforts in K–12 science education have been gaining pace ever since the introduction of the Next Generation Science Standards (NGSS). The new vision calls for reconsidering teacher preparation programs to prepare future teachers who are confident and competent in delivering NGSS-based instruction. This study investigated the development of 27 preservice secondary science and mathematics teachers’ (PSTs’) knowledge and skills as they understand, interpret, and implement the NGSS, particularly science and engineering practices (SEPs), within the context of microteaching during a STEM methods course. Primary data sources include 12 videos of 40-minute-long microteaching lessons, self-reflections, semistructured and focus-group interviews, and …

Accessibility And Inclusivity In Marine Science Education: A Suite Of Collaborative Marine Science Lesson Plans, Amy Nicholson

Dissertations, Theses, and Masters Projects

Excerpt from capstone: "Marine science education is oftentimes sparse in formal education. This is due to a myriad of factors, including but not limited to: minimal state marine science curricula standards, geographic restraints, and lack of resources. This problem is not just unique to marine science, either. In 2018, it was found that only two states required environmental science in secondary education, with just eight requiring general earth and space science (American Geosciences Institute 2018). To further this disparity, marine science curricula are often focused on upper grade levels, with most marine science curricula being focused on the 10th grade …

Desarrollo Del Pensamiento Computacional A Través De Blockscad, Blockly Y La Resolución De Problemas En Matemáticas, Ángel-Alberto Magreñán-Ruiz, Rubén-Arístides González-Crespo, Cristina Jiménez-Hernández, Lara Orcos-Palma

Revista Española de Pedagogía

El desarrollo del pensamiento computacional se ha convertido en una de las prioridades educativas en varios países del mundo. En este artículo, se describen dos experiencias en el aula en las que se utilizan dos herramientas de programación por bloques. En la primera, solo se empleó BlocksCAD. En la segunda, se trabajó, además, con Blockly y con varios algoritmos matemáticos. El número de participantes en la experiencia fue de veintiocho en el grupo que solo utilizó Blockly y de trece en el que combinó el uso de ambas herramientas. Todos ellos cursaban tercero de educación secundaria (entre 14 y 15 …

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 …

Student Use Of Anchors And Metacognitive Strategies In Reflection, Anu Singh, Heidi A. Diefes-Dux

Department of Biological Systems Engineering: Papers and Publications

Context: Self-regulation, a skillset involving taking charge of one’s own learning processes, is crucial for workplace success. Learners develop self-regulation skills through reflection where they recognize weaknesses and strengths by employing metacognitive strategies: planning, monitoring, and evaluating. Use of anchors assists learners’ engagement in reflection. Purpose or Goal: The purpose of this work was to gain insight into students’ use of anchors when reflecting on their learning. The two research questions: (1) To what extent do students link their self-evaluation and learning objective (LO) self-ratings to their reflections? and (2) What dimensions and level of metacognitive strategies do students use …