Education Commons^™

Developing Awareness Around Language Practices In The Elementary Bilingual Mathematics Classroom, Gladys Krause, Melissa Adams Corral, Luz A. Maldonado Rodríguez

Teaching and Learning Faculty Publications and Presentations

This study contributes to efforts to characterize teaching that is responsive to children’s mathematical ideas and linguistic repertoire. Building on translanguaging, defined in this article as a pedagogical practice that facilitates students’ expression of their understanding using their own language practices, and on the literature surrounding children’s mathematical thinking, we present an example of a one-on-one interview and of the circulating portion of a mathematics class from a second grade classroom. We use these examples to foreground instructional practices, for researchers and practitioners, that highlight a shift from a simplified view of conveying mathematics as instruction in symbology and formal …

Applying Expansive Framing To An Integrated Mathematics-Computer Science Unit, Kimberly Evagelatos Beck, Jessica F. Shumway

Publications

In this research report for the National Council of Teachers of Mathematics 2022 Research Conference, we discuss the theory of Expansive Framing and its application to an interdisciplinary mathematics-computer science curricular unit.

Bbt Acoustic Alternative Top Bracing Cadd Data Set-Norev-2022jun28, Bill Hemphill

STEM Guitar Project’s BBT Acoustic Kit

This electronic document file set consists of an overview presentation (PDF-formatted) file and companion video (MP4) and CADD files (DWG & DXF) for laser cutting the ETSU-developed alternate top bracing designs and marking templates for the STEM Guitar Project’s BBT (OM-sized) standard acoustic guitar kit. The three (3) alternative BBT top bracing designs in this release are
(a) a one-piece base for the standard kit's (Martin-style) bracing,
(b) 277 Ladder-style bracing, and
(c) an X-braced fan-style bracing similar to traditional European or so-called 'classical' acoustic guitars.

The CADD data set for each of the three (3) top bracing designs includes …

Finding Approximate Pythagorean Triples (And Applications To Lego Robot Building), Ronald I. Greenberg, Matthew Fahrenbacher, George K. Thiruvathukal

Computer Science: Faculty Publications and Other Works

This assignment combines programming and data analysis to determine good combinations of side lengths that approximately satisfy the Pythagorean Theorem for right triangles. This can be a standalone exercise using a wide variety of programming languages, but the results are useful for determining good ways to assemble LEGO pieces in robot construction, so the exercise can serve to integrate three different units of the Exploring Computer Science high school curriculum: "Programming", "Computing and Data Analysis", and "Robotics". Sample assignment handouts are provided for both Scratch and Java programmers. Ideas for several variants of the assignment are also provided.

Using Magic To Teach Computer Programming, Dale F. Reed, Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

Magic can be used in project-based instruction to motivate students and provide a meaningful context for learning computer programming. This work describes several magic programs of the “Choose a Number” and “Pick a Card” varieties, making connections to underlying computing concepts.

Magic tricks presented as demonstrations and programming assignments elicit wonder and captivate students’ attention, so that students want to understand and replicate the work to show it to friends and family members. Capturing student interest and curiosity motivates them to learn the underlying programming concepts.

Two “Choose a Number” programs are shown where the computer is able to identify …

Understanding Compactness Through Primary Sources: Early Work Uniform Continuity To The Heine-Borel Theorem, Naveen Somasunderam

Analysis

No abstract provided.

Navigating Mathematics Teacher Preparation During A Time Of Crisis, Zareen G. Rahman, Rani Satyam, Younggon Bae

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper we highlight the experience of a mathematics teacher educator (MTE) and their preservice teachers (PTs) in a middle school mathematics methods course during the 2020 shift to online instruction due to the COVID-19 pandemic. We believe it is valuable to report how the MTE reflected on their instructional decision-making in response to this massive transition to remote instruction. We also report that PTs needed support and guidance to employ new teaching practices they had learned in the methods course instead of reverting to familiar teaching methods.

Bbt Side Mold Assy, Bill Hemphill

STEM Guitar Project’s BBT Acoustic Kit

This electronic document file set covers the design and fabrication information of the ETSU Guitar Building Project’s BBT (OM-sized) Side Mold Assy for use with the STEM Guitar Project’s standard acoustic guitar kit. The extended 'as built' data set contains an overview file and companion video, the 'parent' CADD drawing, CADD data for laser etching and cutting a drill &/or layout template, CADD drawings in AutoCAD .DWG and .DXF R12 formats of the centerline tool paths for creating the mold assembly pieces on an AXYZ CNC router, and support documentation for CAM applications including router bit specifications, feeds, speed, multi-pass …

Using Bayesian Networks To Provide Educational Implications: Mobile Learning And Ethnomathematics To Improve Sustainability In Mathematics Education, Jason D. Johnson, Linda Smail, Darryl Corey, Adeeb M. Jarrah

All Works

There are many Western apps that help students strengthen their mathematics skills through learning and game apps. A research project was designed to create an IOS Math App to provide Grade 6 Emirati students with the opportunity to explore mathematics, then, using Bayesian Networks, to examine the educational implications. The learning app was developed using ethnomathematics modules based on the Emirati culture. Students were required to navigate through several modules to examine various mathematical concepts in algebra and geometry. The survey was written for Grade 6 English language learners. Based on the Bayesian Networks, the findings suggested that if students …

Education In The Era Of Google, Wikipedia, And Deep Learning: Are We Humans Still Needed And If Yes For What?, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main purposes of education is to teach skills needed in future life and future jobs. What is important and what is useful changes with time. Before the industrial revolution, routine mechanical work was an important part of human activity – now machines can do it (and do it better). Before printing, copying was an important activity – now copy machines do it. Before computers, humans were needed for computing – now computer do it better. With Wikipedia and Google, there is not much need for scholars being erudite. Even extracting dependencies from data – one of the …

When Is Deep Learning Better And When Is Shallow Learning Better: Qualitative Analysis, Salvador Robles Herrera, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, deep neural networks work better than the traditional "shallow" ones, however, in some cases, the shallow neural networks lead to better results. At present, deciding which type of neural networks will work better is mostly done by trial and error. It is therefore desirable to come up with some criterion of when deep learning is better and when shallow is better. In this paper, we argue that this depends on whether the corresponding situation has natural symmetries: if it does, we expect deep learning to work better, otherwise we expect shallow learning to be more effective. …

Remotely Close: An Investigation Of The Student Experience In First-Year Mathematics Courses During The Covid-19 Pandemic, Sawyer Smith

Honors Theses

The realm of education was shaken by the onset of the COVID-19 pandemic in 2020. It had drastic effects on the way that courses were delivered to students, and the way that students were getting their education at the collegiate level. At the University of Nebraska – Lincoln, the pandemic dramatically changed the way that first-year mathematics courses looked for students. By Spring 2021, students had the opportunity to take their first-year math courses either in-person or virtually. This project sought to identify differences between the two methods of course delivery during the Spring 2021 semester, regarding interaction with peers …

Exploration Of Piccirillo's Trick On Low Crossing Number Knots, Gabriel Adams

Honors Theses

Piccirillo recently discovered a process that can be applied to an unknotting number one knot to convert it into a different knot called a Piccirillo dual. Piccirillo duals have been shown to have the same n-trace and the same sliceness. However, exploration and knowledge of this process is limited. We were able to generate the Piccirillo duals for several low-crossing number knots. We offer the foundation for and explain how to follow the Piccirillo process and generate Piccirillo duals. This talk assumes little knowledge of knot theory and concisely gives newcomers a clear introduction to get started working with Piccirillo …

Application Of Linear Algebra Within The High School Curriculum: Designing Activities To Stimulate An Interest In Upper-Level Math, Shelby Castle

Honors Theses

This senior project outlines potential lecture activities for a guest speaker or teacher in a high school classroom to present interesting applications of linear algebra. These applications are meant to be pertinent to things students at this age level are already learning or are interested in. The activities are designed such that the ideas of upper-level math are introduced in a very guided and non-intense way. The intent of the activities is mostly applications and interesting results rather than mathematical lecturing or instruction.

The high school level courses explored in this project are chemistry, economics, and health/physical education. For these …

Existence And Uniqueness Of Minimizers For A Nonlocal Variational Problem, Michael Pieper

Honors Theses

Nonlocal modeling is a rapidly growing field, with a vast array of applications and connections to questions in pure math. One goal of this work is to present an approachable introduction to the field and an invitation to the reader to explore it more deeply. In particular, we explore connections between nonlocal operators and classical problems in the calculus of variations. Using a well-known approach, known simply as The Direct Method, we establish well-posedness for a class of variational problems involving a nonlocal first-order differential operator. Some simple numerical experiments demonstrate the behavior of these problems for specific choices of …

A Phenomenological Study Of Perceived Factors Influencing Math Teachers' Technology Self-Efficacy, Jenna Finnegan

Doctoral Dissertations and Projects

The purpose of this study was to explore how a teacher's technology self-efficacy influences decisions they make about the use of technology in their classrooms. The factors influencing teachers' technology self-efficacy were examined through a qualitative transcendental phenomenological research design. This study's theoretical framework was based on the combination of social cognitive theory and self-efficacy theory; both provide insight into how external and internal factors can influence a person's perception of their abilities. Using these theories helped identify and describe the self-efficacy experiences of high school math teachers. This research was conducted during the 2020-2021 school year using a qualitative …

A Natural Causality-Motivated Description Of Learning, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Teaching is not easy. One of the main reasons why it is not easy is that the existing descriptions of the teaching process are not very precise -- and thus, we cannot use the usual optimization techniques, techniques which require a precise model of the corresponding phenomenon. It is therefore desirable to come up with a precise description of the learning process. To come up with such a description, we notice that on the set of all possible states of learning, there is a natural order s ≤ s' meaning that we can bring the student from the state s …

Video Or Text? Bullets Or No Bullets? Why Not Both?, Olga Kosheleva, Vladik Kreinovich, Christian Servin

Departmental Technical Reports (CS)

Some students – which are, in terms of pop-psychology – more left-brain – prefer linear exposition, others – more right-brain ones – prefer 2-D images and texts with visual emphasis (e.g., with bullets). At present, instructors try to find a middle grounds between these two audiences, but why not prepare each material in two ways, aimed at both audiences?

A Phenomenological Study: The Lived Experience Of Self-Described Math-Anxious Students Attending College Online, Toni Nicole Sawhill

Doctoral Dissertations and Projects

The purpose of this transcendental phenomenological study is to describe the lived experience of mathematics anxiety for self-described math-anxious students who completed an undergraduate mathematics course online at a university in the Pacific Northwest part of the United States. The theory guiding this study is community of inquiry (COI) introduced by early pragmatist philosophers C. S. Peirce and John Dewey and further developed by D. Randy Garrison, Terry Anderson, and Walter Archer as mathematics anxiety is a learned behavior based on students’ experiences. This research study answers the central research question: What are the lived experiences of mathematics anxiety for …

Affect Graphing: Leveraging Graphical Representations In The Study Of Students’ Affect In Mathematics, V. Rani Satyam, Younggon Bae, John P. Smith Iii, Mariana Levin

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Affect (e.g., beliefs, attitudes, emotions) plays a crucial role in mathematics learning, but reliance on verbal and written responses (from surveys, interviews, etc.) limits students’ expression of their affective states. As a complement to existing methods that rely on verbal reports, we explore how graphing can be used to study affect during mathematical experiences. We analyze three studies that used graphing to represent, stimulate recall, and reflect on affect. In each, students were asked to draw their perception of an affective construct, such as confidence or intensity of emotion, against time. The studies differed in participant populations, target affect, timescales …

Math Department 2021-2022 Newsletter, Mathematics Department

Mathematics Newsletter

Welcome to our annual Mathematics Department Newsletter. As we are slowly coming out of the pandemic, we were able to resume many of our normal events.

Neuromatch Academy: A 3-Week, Online Summer School In Computational Neuroscience, Bernard Marius 'T Hart, Titipat Achakulvisut, Ayoade Adeyemi, Athena Akrami, Bradly Alicea, Alicia Alonso-Andres, Diego Alzate-Correa, Arash Ash, Jesus J. Ballesteros, Aishwarya Balwani, Eleanor Batty, Ulrik Beierholm, Ari S. Benjamin, Upinder Bhalla, Gunnar Blohm, Joachim C. H. Blohm, Kathryn Bonnen, Marco Brigham, Bingni W. Brunton, John Butler, Brandon Caie, N Alex Cayco Gajic, Sharbatanu Chatterjee, Spyridon Chavlis, Ruidong Chen, You Cheng, H. M. Chow, Raymond Chua, Yunwei Dai, Isaac David, Eric E. J. Dewitt, Julien Denis, Alish Dipani, Arianna Dorschel, Jan Drugowitsch, Kshitij Dwivedi, Sean Escola, Haoxue Fan, Roozbeh Farhoodi, Yicheng Fei, Pierre-Étienne Fiquet, Lorenzo Fontolan, Jeremy Forest, Yuki Fujishima, Byron V. Galbraith, Mario Galdamez, Richard Gao, Julijana Gjorgjieva, Alexander Gonzalez, Qinglong Gu, Yueqi Guo, Ziyi Guo, Pankaj K. Gupta, Busra Tugce Gurbuz, Caroline Haimerl, Jordan B. Harrod, Alexandre Hyafil, Martin Irani, Daniel Jacobson, Michelle Johnson, Ilenna Simone Jones, Gili Karni, Robert E. Kass, Hyosub Edward Kim, Andreas M. Kist, Randal Koene, Konrad Kording, Matthew R. Krause, Arvind Kumar, Norma K. Kühn, Ray Lc, Matthew L. Laporte, Junseok Lee, Songting Li, Sikun Lin, Yang Lin, Shuze Liu, Tony Liu, Jesse A. Livezey, Linlin Lu, Jakob H. Macke, Kelly Mahaffy, A. Lucas Martins, Nicolás Martorell, Manolo Martínez, Marcelo G. Mattar, Jorge Aurelio Menendez, Kenneth D. Miller, Patrick J. Mineault, Nosratullah Mohammadi, Yalda Mohsenzadeh, Elenor Morgenroth, Taha Morshedzadeh, Alice Claudia Mosberger, Madhuvanthi Muliya, Marieke Mur, John D. Murray, Yashas Nd, Richard Naud, Prakriti Nayak, Anushka Oak, Itzel Olivos Castillo, Seyedmehdi Orouji, Jorge Otero-Millan, Marius Pachitariu, Biraj Pandey, Renato Paredes, Jesse Parent, Il Memming Park, Megan A. K. Peters, Xaq Pitkow, Panayiota Poirazi, Haroon Popal, Sandhya Prabhakaran, Tian Qiu, Srinidhi Ragunathan, Raul Rodriguez-Cruces, David Rolnick, Ashish Kumar Sahoo, Saeed Salehinajafabadi, Cristina Savin, Shreya Saxena, Paul Schrater, Karen Schroeder, Alice C. Schwarze, Madineh Sedigh-Sarvestani, K. Yuvaraj Sekhar, Reza Shadmehr, Maryam M. Shanechi, Siddhant Sharma, Eric Shea-Brown, Krishna V. Shenoy, Carolina L. Shimabukuro, Sergey Shuvaev, Man Ching Alison Sin, Maurice Smith, Nicholas A. Steinmetz, Karolina Stosio, Elizabeth Straley, Gabrielle Strandquist, Carsen Stringer, Rimjhim Tomar, Ngoc Tran, Sofia Triantafillou, Lawrence Udeigwe, Davide Valeriani, Vincent Valton, Maryam Vaziri-Pashkam, Peter Vincent, Gal Vishne, Pascal Wallisch, Peiyuan Wang, Claire Ward, Michael Waskom, Kunlin Wei, Anqi Wu, Zhengwei Wu, Brad Wyble, Lei Zhang, Daniel Zysman, Federico D’Oleire Uquillas, Tara Van Viegen

Articles

No abstract provided.

Making Upper-Level Math Accessible To A Younger Audience, Allyson Roller

WWU Honors College Senior Projects

Symmetry is all around us. It appears on fabrics and on the buildings that surround us. Believe it or not, there is actually quite a bit of math that goes into generating these patterns, which are known as the seven frieze patterns. In my work, I explain how each unique pattern is generated using different types of symmetries. I also created a PDF of a children’s book about frieze patterns to ensure that people of all ages have the opportunity to learn about seemingly complex patterns.

Deployment Of Mathematical Resources To A Philippine High School Through A Community Lte Network, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Juan Carlo F. Mallari, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Debbie Marie Verzosa

Mathematics Faculty Publications

In the Philippines, one challenge that continues to be faced by the Department of Education in bringing educational content in a blended learning modality is the lack of internet access of the learners. This paper discusses the distribution, through a community LTE network, of mathematical resources for Grades 7 to 10 to teachers and students of a particular high school in the Philippines. It also gives details on particular technological tools (mathematical applications) that were created to help the mathematical learning of students in a remote setting.

Linguistic Matrices, W. B. Vasantha Kandasamy, K. Ilanthenral, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The authors build linguistic matrices only for those linguistic variables which yield a linguistic continuum or an ordered linguistic set. Most of the properties enjoyed by real and complex matrices are satisfied by these linguistic matrices. However, we see when we try to define operations on linguistic matrices that they behave in different ways. The possible operations defined on linguistic matrices are only the maximum and minimum. Further, we have different identities for min and max operations on these matrices for linguistic variable and its associated linguistic words.

Collected Papers (On Neutrosophic Theory And Its Applications In Algebra), Volume Ix, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This ninth volume of Collected Papers includes 87 papers comprising 982 pages on Neutrosophic Theory and its applications in Algebra, written between 2014-2022 by the author alone or in collaboration with 81 co-authors from 19 countries.

نيوتروسوفيك أوفرسيت ، نيوتروسوفيك أونديرست ، وإزاحة نيوتروسوفيك [Neutrosophic Overset, Neutrosophic Underset, And Neutrosophic Offset], Florentin Smarandache, Riad K Al-Hamido (Translator From English To Arabic)), Khaled Adnan Alabdullah (Translator From English To Arabic)

Branch Mathematics and Statistics Faculty and Staff Publications

تم تعريف Neutrosophic Over-/ Under- / Off-Set and -Logic لأول مرة بواسطة Smarandache في عام 1995 ونشر في عام 2007. وهي مختلفة تمامًا عن المجموعات / المنطق / الاحتمالات الأخرى. قام بتمديد مجموعة العدلات على التوالي إلى Neutrosophic Overset {عندما يكون بعض مكونات neutrosophic> 1} ، Neutrosophic Underset {عندما يكون بعض مكونات neutrosophic <0} ، وإلى إزاحة Neutrosophic {عندما تكون بعض مكونات العدلات خارج الفاصل الزمني [0 ، 1] ، أي بعض مكونات العدلات> 1 ومكونات أخرى نيوتروسوفيك <0}. هذا ليس مفاجئًا فيما يتعلق بالمجموعة / المنطق الغامض الكلاسيكي ، أو المجموعة / المنطق الغامض الحدسي ، أو الاحتمال الكلاسيكي / غير الدقيق ، حيث لا يُسمح بالقيم خارج الفاصل الزمني [0 ، 1] ، نظرًا لأن عالمنا الحقيقي به العديد من الأمثلة و تطبيقات المكونات الزائدة / السفلية / البعيدة عن العدلات

Neutrosophic Over-/Under-/Off-Set and -Logic were defined for the first time by Smarandache in 1995 and published in 2007. They are totally different from other sets/logics/probabilities. He extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is > 1}, Neutrosophic Underset {when …

Collected Papers (On Neutrosophic Theory And Applications), Volume Viii, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This eighth volume of Collected Papers includes 75 papers comprising 973 pages on (theoretic and applied) neutrosophics, written between 2010-2022 by the author alone or in collaboration with 102 co-authors from 24 countries.

Development Of An App And Videos To Support The Fraction Learning Trajectory From Grades 1-7, Debbie Marie Verzosa, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Jumela F. Sarmiento, Juan Carlo F. Mallari, Mark Anthony C. Tolentino

Mathematics Faculty Publications

Lack of procedural fluency in fractions impedes access to advanced mathematical courses and limits opportunities for entry into STEM-related fields. This paper describes the design and pedagogical basis of the Moving Fractions app and supplementary fraction videos for promoting fraction learning. Moving Fractions utilizes game-design factors to draw students through a trajectory of fraction learning from part-whole comparisons to a more robust understanding of the measurement concept of fractions. The supplementary video immerses students in a broad range of fraction representations. The app and video are intended to form a fraction learning package for distribution in Philippine schools. Future work …

The Reciprocal Of The Butterfly Theorem, Ion Patrascu, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.