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Full-Text Articles in Science and Mathematics Education

How To Calculate Pi: Buffon's Needle (Non-Calculus Version), Dominic Klyve Apr 2019

How To Calculate Pi: Buffon's Needle (Non-Calculus Version), Dominic Klyve

Pre-calculus and Trigonometry

No abstract provided.


Greatest Common Divisor: Algorithm And Proof, Mary K. Flagg Apr 2019

Greatest Common Divisor: Algorithm And Proof, Mary K. Flagg

Number Theory

No abstract provided.


Connectedness- Its Evolution And Applications, Nicholas A. Scoville Apr 2019

Connectedness- Its Evolution And Applications, Nicholas A. Scoville

Topology

No abstract provided.


Does Teaching The History Of Mathematics In High School Aid In Student Understanding?, Anne Campbell Apr 2019

Does Teaching The History Of Mathematics In High School Aid In Student Understanding?, Anne Campbell

Honors Thesis Projects

This research will study the effect teaching the history of mathematics in a high school classroom has on student understanding. To accomplish this, lessons both including and excluding historical background on different topics were taught in an Honors Algebra 2 class in the high school setting. This research aims to engage student learning and investigation of topics that normally do not draw a lot of student focus and spark a new or revived interest in mathematics for students by broadening lessons to include material of which students would not otherwise be exposed. The lessons themselves aim to engage other current ...


Context Is Critical: K-5th Grade Three-Act Math Tasks, Lindsey Herlehy Mar 2019

Context Is Critical: K-5th Grade Three-Act Math Tasks, Lindsey Herlehy

Publications & Research

Mathematicians view mathematics within interesting and natural contexts. In this session, participants will engage and explore Three-Act Math Tasks; a story-telling pedagogical strategy that elicits student curiosity, collaboration, and questioning while redefining the term “real-world context” and the role that students play in the learning process. Resources will be provided


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 ...


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.


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 ...


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 ...


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.


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 ...


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 ...


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.


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 ...


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.


The Second Decade Of Numeracy: Entering The Seas Of Literacy, H. L. Vacher Jan 2019

The Second Decade Of Numeracy: Entering The Seas Of Literacy, H. L. Vacher

Numeracy

This multipurpose editorial explores and tries to count the many types of literacy that are referred to by name in Wikipedia and Numeracy. Wikipedia’s Category:Literacy page identifies 44 kinds of literacy that are the subject of articles, ranging from numeracy and graphicacy to braille literacy and diaspora literacy. In addition, searching Google finds more than 30 adjective-literacy or noun-literacy collocations, including quantitative literacy, adult literacy, and document literacy, that do not have Wikipedia pages of their own but are mentioned on other Wikipedia pages. The sum puts this modest literacy count in line with the more than 70 ...


An Uncommon Textbook: Review Of Common Sense Mathematics By Ethan Bolker And Maura Mast, Bernard Madison Jan 2019

An Uncommon Textbook: Review Of Common Sense Mathematics By Ethan Bolker And Maura Mast, Bernard Madison

Numeracy

Ethan D. Bolker and Maura B. Mast. 2016. Common Sense Mathematics.(Washington DC.: Mathematics Association of America) ISBN-13: 978-1-93951-210-9.

Common Sense Mathematics is an integrative quantitative reasoning (QR) textbook that is built around scores of exercises derived from authentic circumstances from public media and other public sources. The exercises elicit responses from students requiring extensive communication and analyses and distinguish the book from ones typically encountered in a mathematics or science course. Responses to exercises often require one-half page or more of writing and can occupy considerable class time in discussion. The book has material for a one- or two-semester ...


Student Help-Seeking Behaviors And Teacher Instructional Practices: Examining Their Relationship With U.S. Student Mathematics Achievement, Michael C. Osborne Jan 2019

Student Help-Seeking Behaviors And Teacher Instructional Practices: Examining Their Relationship With U.S. Student Mathematics Achievement, Michael C. Osborne

Theses and Dissertations--Curriculum and Instruction

Even though the United States (U.S.) spends, on average, more money per student than most Organisation for Economic Co-operation and Development (OECD) countries, it continues to lag behind its international peers in mathematics achievement. This study, which responded to the call for educational reforms that improve the mathematics achievement of U.S. students, aimed to examine the issue of student help-seeking behaviors and teacher instructional practices as they interact to affect student mathematics achievement. The Programme for International Student Assessment (PISA) defines student help-seeking behaviors as the ways in which students have a propensity to depend on the knowledge ...


Aligning Best Practices In Student Success And Career Preparedness: An Exploratory Study To Establish Pathways To Stem Careers For Undergraduate Minority Students, Kimberly D. Kendricks, Anthony A. Arment, K. V. Nedunuri, Cadance A. Lowell Jan 2019

Aligning Best Practices In Student Success And Career Preparedness: An Exploratory Study To Establish Pathways To Stem Careers For Undergraduate Minority Students, Kimberly D. Kendricks, Anthony A. Arment, K. V. Nedunuri, Cadance A. Lowell

Journal of Research in Technical Careers

Undergraduate minority retention and graduation rates in STEM disciplines is a nationally recognized challenge for workforce growth and diversification. The Benjamin Banneker Scholars Program (BBSP) was a five-year undergraduate study developed to increase minority student retention and graduation rates at an HBCU. The program structure utilized a family model as a vehicle to orient students to the demands of college. Program activities integrated best K-12 practices and workforce skillsets to increase academic preparedness and career readiness. Findings revealed that a familial atmosphere improved academic performance, increased undergraduate research, and generated positive perceptions of faculty mentoring. Retention rates among BBSP participants ...


Assimilating Mathematical Thinking To The Learning Of Shadows, Taheeda Shwana Street-Conaway Jan 2019

Assimilating Mathematical Thinking To The Learning Of Shadows, Taheeda Shwana Street-Conaway

Theses, Dissertations and Culminating Projects

This study focuses on a teaching experiment with 33 six-graders in a Kearny public school in Hudson County, New Jersey, during the 2017-2018 academic year. More specifically, this study explored a) the types of tasks and tools that can be used to develop students’ covariational and correspondence reasoning in learning about shadows and b) the nature of students’ reasoning about covariation and correspondence relationships as students engage in the use of tools and tasks. The results showed that the simulation and the tasks I designed had the students engaged in the learning process. Students were able to reason about the ...


Find, Process, And Share: An Optimal Control In The Vidale-Wolfe Marketing Model, Michael C. Barg Dec 2018

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 Nov 2018

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 Nov 2018

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 ...


Dual Perspectives On Desargues' Theorem, Carl Lienert Oct 2018

Dual Perspectives On Desargues' Theorem, Carl Lienert

Geometry

No abstract provided.


The Origin Of The Prime Number Theorem, Dominic Klyve Oct 2018

The Origin Of The Prime Number Theorem, Dominic Klyve

Number Theory

No abstract provided.


Otto Holder's Formal Christening Of The Quotient Group Concept, Janet Heine Barnett Oct 2018

Otto Holder's Formal Christening Of The Quotient Group Concept, Janet Heine Barnett

Abstract Algebra

No abstract provided.


The Effects Of Metacognitive Training On Algebra Students’ Calibration Accuracy, Achievement, And Mathematical Literacy, Deana J. Ford Oct 2018

The Effects Of Metacognitive Training On Algebra Students’ Calibration Accuracy, Achievement, And Mathematical Literacy, Deana J. Ford

Teaching & Learning Theses & Dissertations

This dissertation describes an empirical study that investigated how metacognitive training influenced lower achieving Algebra students’ calibration accuracy, achievement, and development of mathematics literacy. Multiple methods were used to collect and analyze the data. Close analysis of students’ work and classroom observations revealed that students that were exposed to the metacognitive training had significantly higher prediction accuracy and made gains in their understanding of the mathematics word problems than did students who did not receive the metacognitive training. Overall, however, both the intervention and comparison groups improved in their academic performance and became more mathematically literate and accurate in their ...