Science and Mathematics Education Commons^™

Special Case Of Partial Fraction Expansion With Laplace Transform Application, Laurie A. Florio, Ryan D. Hanc

CODEE Journal

Partial fraction expansion is often used with the Laplace Transforms to formulate algebraic expressions for which the inverse Laplace Transform can be easily found. This paper demonstrates a special case for which a linear, constant coefficient, second order ordinary differential equation with no damping term and a harmonic function non-homogeneous term leads to a simplified partial fraction expansion due to the decoupling of the partial fraction expansion coefficients of s and the constant coefficients. Recognizing this special form can allow for quicker calculations and automation of the solution to the differential equation form which is commonly used to model physical …

Modeling Immune System Dynamics During Hiv Infection And Treatment With Differential Equations, Nicole Rychagov

CODEE Journal

An inquiry-based project that discusses immune system dynamics during HIV infection using differential equations is presented. The complex interactions between healthy T-cells, latently infected T-cells, actively infected T-cells, and the HIV virus are modeled using four nonlinear differential equations. The model is adapted to simulate long term HIV dynamics, including the AIDS state, and is used to simulate the long term effects of the traditional antiretroviral therapy (ART). The model is also used to test viral rebound over time of combined application of ART and a new drug that blocks the reactivation of the viral genome in the infected cells …

Including The Literary Arts As The A In Steam, Lindsay E. Cunningham

The STEAM Journal

This article examines the integration of literature into secondary STEM (science, technology, engineering, mathematics) classes in British Columbia, Canada. Data were collected through interviews with nine secondary STEM subject teachers and focus on teachers’ perceptions of the effects of including literature, what/how literature has been included, as well as the barriers, both real and perceived, to doing so.

A review of the literature demonstrates that integrating literature into STEM can be appealing to a broad range of students and teachers and can help to engage students with a variety of interests, perspectives, and backgrounds. The arts, including the literary arts, …

Citizen Scientists And Artists: Integrating Arts And Technology To Teach The Effects Of Climate Change On Bird Migration, Laura Fattal Dr., Heejung An Dr.

The STEAM Journal

Ways to incorporate climate change into K-12 curricula are of growing interest to many science educators. The International Cooperation for Animal Research Using Space (ICARUS) examines animal and bird migrations as a lens to understand climate change aiding educators with its emphasis on technological imagining in science and visual arts teaching and learning. This article presents an interdisciplinary unit pertaining to bird migration and climate change that integrates the arts and technology by placing upper-elementary students in the position of being citizen scientists and artists, leading to a culminating art installation project. The unit shows how a variety of digital …

Students Arts Participation Increases Stem Motivation Via Self-Efficacy, Stephen M. Dahlem

The STEAM Journal

This work found that there exists a correlation between student motivation in science, technology, engineering and mathematics (STEM) and student participation in the arts during high school with self-efficacy being a mediator. STEM is an important component of student success from a broad, national, perspective, as well as from a domain-specific point of view. The results of this work may provide aid to teachers, parents, administrators, and even students seeking to find ways to increase student motivation and performance in the STEM subjects. Additionally, this work may be of interest to advocates of the arts. This quantitative correlational study was …

Challenge-Based Learning & Steam Curriculum, Diana Lockwood

The STEAM Journal

STEAM education is being integrated into elementary schools as a way to engage more students in creativity, hands-on learning, and problem-based learning also referred to as Challenge-Based-Learning (CBL). This article focuses on elementary educators’ curriculum design for STEAM and presenting students with open-ended questions phrased as a challenge as a way to raise student interest and achievement (DeJarnette, 2018; Hunter-Doniger, 2018). When students received challenges to solve, they felt more open to sharing their ideas since there was more than one potential right answer (DeJarnette, 2018; Drake, 2012). When implementing CBL, teachers act as facilitators using a constructivist approach as …

Creative Learning With Music And Mathematics: Reflections On Interdisciplinary Collaborations, Graham Johnson, Alesia M. Moldavan

The STEAM Journal

Culturally responsive content, accessible and inclusive tools, and meaningful interdisciplinary tasks can aid in developing equitable and creative learning environments. Music and mathematics are ideal disciplines for interdisciplinary creative learning. In this article, we reflect on our experiences engaging in interdisciplinary music and mathematics tasks with preservice teachers. In particular, we highlight specific efforts taken to design and implement a creative music and mathematics workshop for use in a mathematics methods course. Guided by these experiences, we offer examples of tools and practices that have helped preservice teachers collaborate, engage in inquiry, improvise, develop empathy, and take intellectual and social …

Lessons From Human Experience: Teaching A Humanities Course Made Me A Better Math Teacher, Erin Griesenauer

Journal of Humanistic Mathematics

As a professor at a Liberal Arts college, I recently taught a General Education course called Human Experience. Far from my normal experiences in the mathematics classroom, in Human Experience I was tasked with teaching topics from the humanities, including art, philosophy, history, and political science. Teaching this course was challenging, but it was also transformative. Teaching a course so far from my background gave me the opportunity to experiment with different pedagogical techniques and to reflect on how I set up my math classes. I learned many lessons that I have brought back to my math classes—lessons that have …

Human-Machine Collaboration In The Teaching Of Proof, Gila Hanna, Brendan P. Larvor, Xiaoheng (Kitty) Yan

Journal of Humanistic Mathematics

This paper argues that interactive theorem provers (ITPs) could play an important role in fostering students’ appreciation and understanding of proof and of mathematics in general. It shows that the ITP Lean has three features that mitigate existing difficulties in teaching and learning mathematical proof. One is that it requires students to identify a proof strategy at the start. The second is that it gives students instant feedback while allowing them to explore with maximum autonomy. The third is that elementary formal logic finds a natural place in the activity of creating proofs. The challenge in using Lean is that …

Collapsing Spaces, Colliding Places: Leveraging Constructs From Humanistic Geography To Explore Mathematics Classes, Valentin A. B. Küchle, Shiv S. Karunakaran, Mariana Levin, John P. Smith Iii, Sarah Castle, Jihye Hwang, Yaomingxin Lu, Robert A. Elmore

Journal of Humanistic Mathematics

Humanistic geographers distinguish between space and place: “What begins as undifferentiated space becomes place as we get to know it better and endow it with value” (Tuan, 1977, page 6). In this essay, we seek to demonstrate how mathematics education researchers and mathematics instructors may find space and place illuminating for understanding important aspects of students’ learning experiences during the coronavirus pandemic—and possibly beyond. Specifically, after introducing the terms and relating them to the context of a university mathematics class, we exemplify how home and class places collided for three undergraduate mathematics students forced to deal with the abrupt …

The Roles Of Mathematical Metaphors And Gestures In The Understanding Of Abstract Mathematical Concepts, Omid Khatin-Zadeh, Zahra Eskandari, Danyal Farsani

Journal of Humanistic Mathematics

When a new mathematical idea is presented to students in terms of abstract mathematical symbols, they may have difficulty to grasp it. This difficulty arises because abstract mathematical symbols do not directly refer to concretely perceivable objects. But, when the same content is presented in the form of a graph or a gesture that depicts that graph, it is often much easier to grasp. The process of solving a complex mathematical problem can also be facilitated with the use of a graphical representation. Transforming a mathematical problem or concept into a graphical representation is a common problem solving strategy, and …

Introducing Systems Via Laplace Transforms, Ollie Nanyes

CODEE Journal

The purpose of this note is to show how to move from Laplace Transforms to a brief introduction to two dimensional systems of linear differential equations with only basic matrix algebra.

Undergraduates’ Preparedness For College-Level Work In Stem: The Importance Of Reading And Understanding Scientific Theories, Arguments, And Data, Ewa M. Burchard

CGU Theses & Dissertations

This study focuses on undergraduates’ preparation for college level courses. In recent international PISA results United States students fall behind seventeen countries on the computer-based reading proficiency test. They have scored low for over a decade, in spite of spending more than one hundred-thousand dollars per student on education. This US score is similar to, or lower than, the scores of other countries where spending is lower. Considering reading performance statistics from the international PISA assessment and the inconclusive results from reading comprehension studies across media, the concern arose whether today’s high school students are well prepared for college level …

Stem Education And Retention For Black Women Using High-Impact Practices: Historically Black Colleges And Universities Vs. Predominantly White Liberal Arts Colleges, Annette Njei

CMC Senior Theses

Black women are significantly underrepresented within the fields of science, technology, engineering, and mathematics (STEM). To address this, the Association of American Colleges & Universities crafted ten high-impact practices to increase student engagement and promote retention. This research paper examines how three specific high-impact practices (learning communities, mentoring, and undergraduate research experience) are utilized in STEM education.This research paper explores and compares the best high impact approaches that successfully teach and retain Black women within the various fields of STEM within the differing academic environments of historically Black colleges & universities ( HBCUs) and predominantly white liberal art colleges (PWLACs). …

A Generalized Method Of Undetermined Coefficients, James S. Cook, William J. Cook

CODEE Journal

The method of undetermined coefficients is used to solve constant coefficient nonhomogeneous differential equations whose forcing function is itself the solution of a homogeneous constant coefficient differential equation. In this paper, we show that the classical methods for tackling constant coefficient equations, including the method of undetermined coefficients, generalize to much wider class linear differential equations which, for example, include Cauchy-Euler type equations. This general method includes an explicit construction of the fundamental solution sets of such equations. We also briefly consider where this method can be applied by producing the most general second and third order differential equations that …

Mathematics Education As Dystopia: A Future Beyond, Peter Appelbaum, Charoula Stathopoulou, Constantinos Xenofontos

Journal of Humanistic Mathematics

We argue that scholars and practitioners of mathematics education need to find new directions through recognition of its dystopic characteristics, and embrace these characteristics as both the source of challenges and method of response. This contrasts with the generally utopic approach of most scholarship in the field. We offer critical ethnomathematics education as a model, since it has its own origins in lingering dystopic legacies. A perpetual hopelessness and disempowerment is one implicit curriculum of contemporary mathematics education, where the mathematics one learns might help to describe things, yet hardly assists in transforming the reification of power and agency in …

Higher Meanings: A Speaker Series Connecting Mathematics And Religion, Lawrence M. Lesser, Patricia S. Barrientos, Ben Zeidman

Journal of Humanistic Mathematics

An innovative grant-funded general adult audiences international speaker series on connections between mathematics and religion yielded six 2021 (now archived) presentations. We share reflections and lessons learned, informed by two sets of surveys.

Live By The Research, Die By The Research, Szilárd Svitek

Journal of Humanistic Mathematics

The situation of doctoral students is a complex ethical issue. They are not really students any more, but they are not yet full members of the Academy, so they are less than it. PhD students focus primarily on research, since if they do not publish in quality scientific journals, their future (both career and financial) is very much in question. As most of the doctoral student's capacity is taken up by research and publication during the training period, another important task is relegated to the background: learning to teach and to supervise research. Will the student have the ambition to …

Benny, Barbara, And The Ethics Of Edtech, Geillan Aly

Journal of Humanistic Mathematics

Erlwanger (1973) shook the mathematics education world when he introduced Benny, a student who successfully worked through a behavioristic curriculum. Erlwanger showed how far removed Benny’s understanding of mathematics was from expectations. Erlwanger’s legacy is the basis for this comparative case study which explores students’ actions in the modern, in-class computer-centered emporium classroom. Many striking similarities are found between Pearson’s MyMathLabs (MML) and Benny’s Individually Prescribed Instruction curriculum. In this case study we meet Barbara, a student who succeeds in MML but shows little understanding of mathematical concepts and demonstrates that the legacy of Benny is his continued appearance in …

Analysis Of A Mathematical Model Of Real-Time Competitive Binding On A Microarray, Frank H. Lynch

CODEE Journal

A mathematical model of competitive binding on a microarray in real-time yields a planar system of nonlinear ordinary differential equations. This model can be used to explore dimensionless formulation, linear approximation, and reduction. Real-time competitive binding is proposed as an uncommon approach to advance the study of planar systems of differential equations.

An Urgent Plea For More Graduate Programs In Statistics Education, David Eli Drew, Sam Behseta, Cherie L. Ichinose

Journal of Humanistic Mathematics

Lately, much has been written about the importance of amplifying statistics-related content in the K-12 curricula. This can be viewed in parallel or as an addendum to the existing mathematics curricula in the United States. Nevertheless, a key component of this debate is the lack of robust and cutting-edge academic programs in statistics education. In this piece, we emphasize the urgent need for investing in creating strong statistics education programs, which would significantly contribute to nurturing quantitative literacy as well as preparing a more informed citizenry in the 21^st century.

In Search Of Star Clusters: An Introduction To The K-Means Algorithm, Marcio Nascimento

Journal of Humanistic Mathematics

This article is a gentle introduction to K-means, a mathematical technique of processing data for further classification. We begin with a brief historical introduction, where we find connections with Plato’s Timæus, von Linné’s binomial classification, and the star clustering concept of Mary Sommerville and collaborators. Artificial intelligence algorithms use K-means as a classification methodology to learn about data in a very accurate way, because it is a quantitative procedure based on similarities.

Teaching Preservice Teachers In The Time Of Covid: What’S Worth Keeping?, Kathy Liu Sun, Jennifer L. Ruef, Kathleen Jablon Stoehr, Madeline Ahearn

Journal of Humanistic Mathematics

As we begin to transition from online instruction to in-person, we (four mathematics teacher educators) reflect on how COVID-19 impacted our instruction and address the question: what will we take back to in-person instruction? This article includes our individual reflections and an analytical synthesis of them. Findings reveal that there were unanticipated ways that human connection and consideration arose from teaching online, much of which we want to maintain in some form when returning to brick and mortar classrooms. We conclude by highlighting the value and importance of reflection for our own well-being.

Middle School Students Generating Mathematical Problems From A Real-Life Situation, David Coffland, Ying Xie

Journal of Humanistic Mathematics

In this study, we examined the effect of different presentation formats of a realistic situation on students’ mathematical problem-posing behavior. We divided thirty-six middle school students into two groups, gave them a pretest, and then showed them a realistic, problem-posing situation in Artifact or Video format. We used Silver’s core dimensions of creativity, namely fluency, flexibility, and originality, to measure participants’ problem-posing activity. The results for the fluency measures showed that the Artifact group wrote more questions than the Video group but the same number of mathematics problems. The Video group posed problems in more mathematical domains than the Artifact …

Plane Figurate Number Proofs Without Words Explained With Pattern Blocks, Gunhan Caglayan

Journal of Humanistic Mathematics

This article focuses on an artistic interpretation of pattern block designs with primary focus on the connection between pattern blocks and plane figurate numbers. Through this interpretation, it tells the story behind a handful of proofs without words (PWWs) that are inspired by such pattern block designs.

Teacher Self-Efficacy And Mathematics Achievement Among Racial And Ethnic Minority Students: Evidence From The High School Longitudinal Study Of 2009, Eliud Partida

CGU Theses & Dissertations

Current data suggests that for every 1000 U.S. high school students only about a dozen from Racial and Ethnic Minority (REM) groups will obtain a STEM degree and pursue a STEM occupation. These numbers underscore the wealth of untapped talent in our high schools and the pressing need to broaden participation among REM students in STEM. Yet, policies aimed at improving teacher quality as a vehicle for broadening participation of REM students in STEM use measures that at best, are only weakly associated with positive educational outcomes for REM students. This study contributes an ecological perspective and analysis to advance …

Public Perception Of Socio-Scientific Issues Do You Decide Based On Your Education, Your Experience Or Reading The News?, Burcu Demiralp

CGU Theses & Dissertations

One of the challenges humans face is making collective decisions with regards to controversial issues related to science, namely socio-scientific issues (SSIs). Genetic modification, nuclear energy, experimental drugs, 5G technology are a few examples of SSIs. Some of the concerns posed by such issues are compromise to privacy and identity, threat to the workforce due to automation, and potential changes to the human genome. To better understand SSI-related decision making, it is important to understand the public perception of SSIs, while also including opinions of rural areas.This research investigated the perception of SSIs for the U.S. public both in a …

Can We Science The Poop, Too?, Nat Banting

Journal of Humanistic Mathematics

This article describes how an innocuous question from a primary schooler taught me to pay attention to the dynamic meaning making activities of children—particularly, those of my young daughter. Through this lens, I examine how the verb-based world of children might compel us to think differently about the largely nominalized project of schooling and, more specifically, about the craft of teaching mathematics.

The Math Games Seminar: A Mathematical Learning Community, Anthony Delegge, Ellen Ziliak

Journal of Humanistic Mathematics

Learning communities can be an effective means of engaging university students across disciplines. Games have always been a source of both enjoyment and interesting mathematics. Based on our own interest in games, and the deep, strategic discussions we found ourselves having with students when we played games with them, we decided to design a learning community around the mathematics of games. We hoped in particular that such a community could be a great pathway to introducing mathematical thinking to students not majoring in mathematics, and that they would gain a greater appreciation for our field. In this paper, we describe …

Engaging Students Early By Internationalizing The Undergraduate Calculus Course, Chinenye Ofodile

CODEE Journal

Today's world is global. However, despite increasing numbers and diversity of participants in Study Abroad programs, only 10% of U. S. college students get that experience. There is an ever-growing need for students to become aware of and experience other cultures, to understand why others think and act differently. Internationalization is the conscious effort, begun nearly 40 years ago, to integrate an international, intercultural, and global dimension into the purpose, functions, and delivery of post-secondary education.

Albany State University began a Global Program Initiative in the 1990s. In 2016, we extended into mathematics the curriculum innovations of this program. The …