Science and Mathematics Education Commons^™

A Visualization App On Proving Geometric Concepts, Ma. Louise Antonette N. De Las Peñas, Debbie Marie B. Verzosa, Maria Alva Q. Aberin, Agnes D. Garciano, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Juan Carlo F. Mallari

Mathematics Faculty Publications

This paper discusses the description, design and pedagogical basis of a mathematical app called Two Column Proof which provides students a framework for writing proofs of geometric statements. The app focuses on proving concepts on: properties of parallelograms, conditions that determine when a quadrilateral is a parallelogram, properties on trapezoids and kites for high school mathematics. It employs visual representations for students to understand the statement or reason of each given line in the proof, strengthening their logical and mathematical knowledge needed in the proof construction.

Population Growth Models: Relationship Between Sustainable Fishing And Making A Profit, James Sandefur

CODEE Journal

In this paper, we develop differential equations that model the sustainable harvesting of species having different characteristics. Specifically, we assume the species satisfies one of two different types of density dependence. From these equations, we consider maximizing sustainable harvests. We then introduce a cost function for fishing and study how maximizing profit affects the harvesting strategy. We finally introduce the concept of open access which helps explain the collapse of many fish stocks.

The equations studied involve relatively simple rational and exponential functions. We analyze the differential equations using phase-line analysis as well as graphing approximate solutions using Euler's method, …

A Modeling Framework For Minimizing Spread Of Mathematics Anxiety In College Students, Sara Sony, Majid Bani-Yaghoub

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modelling Impact Of Diverse Vegetation On Crop-Pollinator Interactions, Morgan N. Beetler

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Fibonacci Differential Equation And Associated Spiral Curves, Mehmet Pakdemirli

CODEE Journal

The Fibonacci differential equation is defined with analogy from the Fibonacci difference equation. The linear second order differential equation is solved for suitable initial conditions. The solutions constitute spirals in the polar coordinates. The properties of the spirals with respect to the Fibonacci numbers and the differences between the new spirals and classical spirals are discussed.

A Generalized Solution Method To Undamped Constant-Coefficient Second-Order Odes Using Laplace Transforms And Fourier Series, Laurie A. Florio, Ryan D. Hanc

CODEE Journal

A generalized method for solving an undamped second order, linear ordinary differential equation with constant coefficients is presented where the non-homogeneous term of the differential equation is represented by Fourier series and a solution is found through Laplace transforms. This method makes use of a particular partial fraction expansion form for finding the inverse Laplace transform. If a non-homogeneous function meets certain criteria for a Fourier series representation, then this technique can be used as a more automated means to solve the differential equation as transforms for specific functions need not be determined. The combined use of the Fourier series …

Undetermined Coefficients With Hyperbolic Sines And Cosines, Laurie A. Florio, George L. Fischer

CODEE Journal

The method of undetermined coefficients is commonly applied to solve linear, constant coefficient, non-homogeneous ordinary differential equations when the forcing function is from a selected class of functions. Often the hyperbolic sine and cosine functions are not explicitly included in this list of functions. Through a set of guided examples, this work argues that the hyperbolic sine and cosine ought to be included in the select class of functions. Careful explanation is provided for the necessary treatment of the cases where the argument of the hyperbolic sine and/or cosine functions matches one or both of the roots of the characteristic …

Synesthesia: 3.1415... Orange.Whiteperiwinklewhiteblue..., Shelly Sheats Harkness, Bethany A. Noblitt, Nicole Giesbers

Journal of Humanistic Mathematics

In this paper we address the questions: What is synesthesia? What support(s) can teachers provide for their students who have synesthesia? Nicole, a future mathematics teacher who possesses this synesthesia “superpower”, describes how it impacted her learning. We collected data for this case study through an audio-recorded and transcribed interview, as well as from subsequent email correspondence between the three authors. We asked Nicole three kinds of questions: questions she is frequently asked, questions she would like to be asked, and questions teachers (like Shelly and Beth) might ask. Results indicate that synesthesia may have helped Nicole learn English as …

“I Got You”: Centering Identities And Humanness In Collaborations Between Mathematics Educators And Mathematicians, Anne M. Marshall, Sarah Sword, Mollie Applegate, Steven Greenstein, Terrance Pendleton, Kamuela E. Yong, Michael Young, Jennifer A. Wolfe, Theodore Chao, Pamela E. Harris

Journal of Humanistic Mathematics

Existing literature widely reports on the value of collaborations between mathematicians and mathematics educators, and also how complex those collaborations can be. In this paper, we report on four collaborations that sought to address what mathematics is and who gets to do it. Drawing on the literature and from the careful and intentional work of the collaborators, we offer a framework to capture the richness of those collaborations – one that acknowledges the importance of acknowledging and welcoming the extensive personal and professional experience of each person involved in the collaboration – and a look at how collaborations built with …

An Introduction To The Algebra Revolution, Art Bardige

Numeracy

Bardige, Art. 2022. The Algebra Revolution: How Spreadsheets Eliminate Algebra 1 to Transform Education; (Bookbaby) 135 pp. UNSPSC 55111505.

The Algebra Revolution: How Spreadsheets Eliminate Algebra 1 to Transform Education argues that Algebra 1 can be eliminated by teaching mathematics through spreadsheets. Such a change would eliminate the greatest roadblock to student achievement.

Lagrange’S Study Of Wilson’S Theorem, Carl Lienert

Number Theory

No abstract provided.

Lagrange’S Proof Of Wilson’S Theorem—And More!, Carl Lienert

Number Theory

No abstract provided.

Lagrange’S Proof Of The Converse Of Wilson’S Theorem, Carl Lienert

Number Theory

No abstract provided.

Lagrange’S Alternate Proof Of Wilson’S Theorem, Carl Lienert

Number Theory

No abstract provided.

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 …

Du Undergraduate Showcase: Research, Scholarship, And Creative Works, Caitlyn Aldersea, Justin Bravo, Sam Allen, Anna Block, Connor Block, Emma Buechler, Maria De Los Angeles Bustillos, Arianna Carlson, William Christensen, Olivia Kachulis, Noah Craver, Kate Dillon, Muskan Fatima, Angel Fernandes, Emma Finch, Colleen Cassidy, Amy Fishman, Andrea Francis, Stacia Fritz, Simran Gill, Emma Gries, Rylie Hansen, Shannon Powers, Jacqueline Martinez, Zachary Harker, Ashley Hasty, Mykaela Tanino-Springsteen, Kathleen Hopps, Adelaide Kerenick, Colin Kleckner, Ci Koehring, Elijah Kruger, Braden Krumholz, Maddie Leake, Lyneé Alves, Seraphina Loukas, Yatzari Lozano Vazquez, Haley Maki, Emily Martinez, Sierra Mckinney, Audrey Mitchell, Kipling Newman, Audrey Ng, Megan Lucyshyn, Andrew Nguyen, Stevie Ostman, Casandra Pearson, Alexandra Penney, Julia Gielczynski, Tyler Ball, Anna Rini, Christina Rorres, Simon Ruland, Helayna Schafer, Emma Sellers, Sarah Schuller, Claire Shaver, Kevin Summers, Isabella Shaw, Madison Sinar, Claudia Pena, Apshara Siwakoti, Carter Sorensen, Madi Sousa, Anna Sparling, Alexandra Revier, Brandon Thierry, Dylan Tyree, Maggie Williams, Lauren Wols

DU Undergraduate Research Journal Archive

DU Undergraduate Showcase: Research, Scholarship, and Creative Works

Curriculum Connectivity In Montclair State University’S Undergraduate Mathematics Program, Ana G. Da Silva Jesus

Theses, Dissertations and Culminating Projects

According to Piaget’s cognitive development theory and the constructivism learning theory of education, real learning occurs when students establish long term connections between disciplines by either adapting or redefining previously acquired knowledge. These ideologies have important teaching and learning implications that directly influence curriculum development and the design of a course of study. This thesis explores the interconnectedness of the subjects required for the successful completion of an undergraduate math program at Montclair State University. More specifically, it models students’ unique connections through a learning network and investigates the correlation between the interconnectivity of subjects and students’ overall performance. Results …

Propuesta De Un Modelo De Enseñanza En Las Matemáticas Enfocado En La Solución De Problemas En El Nivel Secundario En Puerto Rico, Carlos J. Colon Rivera

Theses and Dissertations

El propósito del estudio fue proponer un modelo educativo enfocado en la solución de problemas matemáticos en el nivel secundario, y se realizó la revisión sistemática para evaluarlo. El marco teórico incluyó teorías heurísticas y modelos educativos. La metodología de seis fases que se empleó en este estudio, incluyendo la formulación de preguntas investigativas, búsqueda de literatura, selección de investigaciones, levantamiento de información, análisis y resumen de resultados y exposición y discusión de estos. Se siguieron guías para revisiones sistemáticas y criterios de inclusión y exclusión para evaluar la efectividad de modelos didácticos en la disciplina de matemáticas con énfasis …

A Growth Mindset: Fostering Resilience And Success In The Middle School Mathematics Classroom, Mary Jicha

Liberty University Research Week

Undergraduate

Applied

Area Activity, Admin Stem For Success

STEM for Success Showcase

Lesson plan to teach students about area including an activity plan, activity description, activity video, and additional activity materials

Using Visual Imagery To Develop Multiplication Fact Strategies, Gina Kling

Dissertations

The learning of basic facts, or the sums and products of numbers 0–10 and their related differences and quotients, has always been a high priority for elementary school teachers. While memorization of basic facts has been a hallmark of elementary school, current recommendations focus on a more nuanced development of fluency with these facts. Fluency is characterized by the ability to demonstrate flexibility, accuracy, efficiency, and appropriate strategy use. Despite recommendations to focus on strategy use, there is insufficient information on instructional approaches that are effective for developing strategies, particularly for multiplication facts. Using visual imagery with dot patterns has …

Problem Of The Week: A Student-Led Initiative To Bring Mathematics To A Broader Audience, Jordan M. Sahs, Brad Horner

UNO Student Research and Creative Activity Fair

Problem of the Week (POW!) is a weekly undergraduate mathematics competition hosted by two graduate students from the UNO Math Department. It started with the goal to showcase variety, creativity, and intrigue in math to those who normally feel math is dry, rote, and formulaic. Problems shine light on both hidden gems and popular recreational math, both math history and contemporary research, both iconic topics and nontraditional ones, both pure abstraction and real-world application. Now POW! aims to increase availability and visibility in Omaha and beyond. Select problems from Fall 2021 to Spring 2023 are highlighted here: these received noteworthy …

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 …

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.

Broadening Views Of Mathematical Creativity: Inclusion Of The Undergraduate Student Perspective, Emily Cilli-Turner, V. Rani Satyam, Miloš Savić, Gail Tang, Houssein El Turkey, Gulden Karakok

Mathematics: Faculty Scholarship

Numerous conceptions of creativity exist in the literature; yet these are commonly based on the perspectives of professional mathematicians. Including students’ perspectives in creativity is crucial not only for a more robust picture of what it means to be creative but also to combat damaging dominant narratives about who can be creative. We examined calculus students’ views of mathematical creativity, a group not often considered in the creativity literature, to broaden future considerations of creativity. Interviews with N=55 calculus students across various institutions were conducted. Results show six emergent wide-ranging themes of these students’ creativity views: actions and attitudes, application, …

Math Department 2022-2023 Newsletter, Mathematics Department

Mathematics Newsletter

Welcome to our annual Mathematics Department Newsletter. We had an exciting year with many activities and accomplishments. Our students have received awards, attended conferences, conducted research, and have really contributed to the life of the department. Our faculty have had many accomplishments in teaching and scholarship. We conducted several events such as Alumni Night, hosted a guest speaker for the university community, had our Pi Mu Epsilon induction and awards ceremony, and much more. We have heard from several alumni and are happy to report what they are doing. Our Math Club has been becoming more active. On the curriculum …

Understanding And Advancing College Students' Mathematical Reasoning Using Collaborative Argumentation, Rachel Kay Heili

Graduate Theses/Dissertations

This study explored students’ mathematical reasoning skills and offered supports to advance them through a collaborative argumentation framework in a college intermediate algebra class. The goals of this study were to make observations about student reasoning, identify specific actions to address those observations, and document student growth in reasoning as a result of those actions. An iterative analysis, mixed method study was conducted in which the researcher engaged students in responding to questions that required conceptual understandings using a collaborative argumentation framework as a tool to identify and code components of their responses—claim, evidence, and reasoning. After coding and analyzing …

Mathematical Mobile Apps Via Rural Casting, Ma Louise Antonette N. De Las Peñas, John Chris T. Kwong, Peter Antonio B. Banzon, Philip A. Martinez, Wilbur Isaac G. Lapada, Julian N. Eballa, John Emil C. Sebastian, Miguel D. Asido, Jan Daryl M. San Juan, Debbie Marie B. Verzosa, Jumela F. Sarmiento, Agnes D. Garciano, Mark Anthony C. Tolentino, Maria Alva Q. Aberin, Juan Carlo F. Mallari

Mathematics Faculty Publications

This paper discusses the distribution, through a digital datacasting framework, of mathematical resources for Grades 1 to 7 to two schools in a community in the Philippines. Among the mathematical resources made available, are mathematical applications (apps), which run on mobile technologies, that have been created to help in the mathematical learning of students in a remote setting. The distribution is facilitated by the RuralCasting set-top box, a developed custom set-top box capable of receiving digital TV broadcasts and providing local content access through its Wi-Fi network. This paper presents the performance of the set-top box in distributing the mobile …