Mathematics Commons^™

The Formal Presentation Language Of Mathematics And Communication Ethics, Marshall Gordon

Journal of Humanistic Mathematics

Mathematics employs a formal language where symbols, verbs, and nouns serve to express terms, concepts, and rules that concatenate to definitions, problem-solving procedures, and proofs. Taken together these constitute the expository language of mathematics found in journals, textbooks, and demonstrations. As a communication given to informing, there are epistemological and ethical considerations that deserve examination. For in keeping with the commitment to an aesthetic of concision promulgated by tradition, the formal presentation language and style of mathematics, while valuable in furthering the body of knowledge, provides only the conclusion of an inquiry, completely excluding the language of investigation that informed …

Propuestas Y Resultados De Investigación Transmoderna, Translocal Y Digital Desde Jóvenes Semilleristas, Xiomara Gonzalez Gaitan

Institucional

En el presente libro se recopilan las propuestas, avances y resultados de los proyectos en curso de los Semilleros de Investigación de la Universidad de Cundinamarca (Colombia), que se presentaron en el «II Encuentro de Semilleros de Investigación: ciencia, tecnología e innovación en la era digital» en su versión de 2020. Publicamos estos proyectos con la intención de difundir el conocimiento y como muestra del esfuerzo y del alcance de la labor investigadora de los semilleristas de la Universidad de Cundinamarca. Esperamos que los lectores encuentren en estas propuestas caminos para resolver problemas o inspiración para construir nuevas propuestas de …

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 & Statistical Sciences Faculty Publications

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.

Theoretical Features Of Foreign Systems Of Preschool Education, Ayjamal Bazarbaeva

Karakalpak Scientific Journal

This article analyzes the features of preschool education systems in foreign countries. The positive experience and features of some systems are highlighted. Comparison of domestic and foreign systems of preschool education is carried out.

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 …

Middle School Students Communicating Computational Thinking: A Systemic Functional Linguistics-Case Study Of Bilingual, Collaborative Teaching/Learning Of Computer Programming In Python, Jose Antonio Lecea Yanguas

Language, Literacy, and Sociocultural Studies ETDs

This dissertation presents the first Systemic Functional Linguistics-based analysis of the teaching/learning of computational thinking through computer programming and comprehensive analysis of discourse of a whole computer programming course at any educational level. The current educational research raises questions about the nature of authentic computational

vii

thinking teaching/learning environments and how they happen moment-to-moment. In one such environment, I examined the discourse of a facilitator, three students, and their Language Arts teacher in an introductory middle school after-school course (approximately 30 hours) in spring 2017 as students created a video in Python.

Methodologically, I show how a Systemic Functional Linguistics-based …

The Impact Of Academic Tracking And Mathematics Self-Concept On Mathematics Achievement., Kain M. Schow

Dissertations, Theses, and Projects

ABSTRACT

This study examines the effects of academic tracking, in high school math, on students’ mathematics self-concept (MSC) and how that correlates to students’ mathematics achievement. This study measured students’ MSC through a mathematics self-concept questionnaire and measured mathematics achievement by the students’ latest grade report. Participants included 60 students in grades 10-12 who had been or were currently enrolled in math courses in the researcher’s school district. The data collected will direct the researcher and school administration on the effects of academic tracking on students, allowing for further discussion about continuing tracking in the district.

Sheltered Math Curriculum For Middle School English Learners, Jasmine Ercink

Dissertations, Theses, and Projects

Language barriers have shown a need for differentiation and sheltered instruction in the classroom for English Learners (ELs) to be successful in the United States public school system. This project proposes a mathematics curriculum using SIOP so that both groups of students in the middle school level can increase their proficiency in the mathematics content area as well as experience opportunities for academic and social language development. The purpose of this report is to describe the processes, methods, data, and intent of the mathematics curriculum for these learners. The curriculum acts as an effective intervention to fill gaps in both …

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 …

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 …

How To Guard An Art Gallery: A Simple Mathematical Problem, Natalie Petruzelli

The Review: A Journal of Undergraduate Student Research

The art gallery problem is a geometry question that seeks to find the minimum number of guards necessary to guard an art gallery based on the qualities of the museum’s shape, specifically the number of walls. Solved by Václav Chvátal in 1975, the resulting Art Gallery Theorem dictates that ⌊n/3⌋ guards are always sufficient and sometimes necessary to guard an art gallery with n walls. This theorem, along with the argument that proves it, are accessible and interesting results even to one with little to no mathematical knowledge, introducing readers to common concepts in both geometry and graph …

Meas: Exploring Links Between Implementation And Standards Mastery, Noah Silver

Honors Projects

In order to effectively enhance a student’s mathematical understanding and development in the field of mathematics, students need to engage in problem solving. Model eliciting activities, or MEAs, provide students with tasks that promote higher level thinking and the ability to utilize mathematics outside of the classroom; they also align and promote the utilization of the Common Core State Standards and Standards for Mathematical Practice. Research suggests that the language and motivation promoted by MEAs enriches engagement and increases student ability and performance of traditional and real-world mathematics. Use of technology further supports these goals. Through the analysis of checkpoint …

Machine Learning In Support Of Student Success, Rachel Rucker

Undergraduate Research Conference

Our goal is to predict whether a student will finish the semester on academic probation by mid-term using university data.

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 Program: Senior Projects (Public)

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 …

Proceedings State Of Stem 2022: How Does Virtual Hands-On Stem Work?, Cristo Leon, James Lipuma, Michele Rittenhouse, Louis Wells, Edgar Meritano, Ricardo Morales-Carbajal, Miguel Angel Bastarrachea Magnani, Ten80 Education, Llc, New Jersey School Boards Association, International Stem League, Inc (Insl), Red De Investigadores De Juegos De Rol

STEM for Success Resources

Proceedings of the "State of STEM 2022: How does virtual hands-on STEM work?"

Learning Mathematics From The Master: A Collection Of Euler-Based Primary Source Projects For Today’S Students, Part I, Janet Heine Barnett, Dominic Klyve, Kenneth M. Monks, Adam E. Parker

Euleriana

This article and its sequel will together highlight a set of nine classroom ready projects that draw on the remarkable writing of Leonhard Euler (1707–1783) as a means to help students develop an understanding of standard topics from today’s undergraduate mathematics curriculum. Part of a larger collection of primary source projects intended for use in a wide range of undergraduate mathematics courses, these projects are freely available to students and their instructors. We provide a general description of the pedagogical design underlying these projects, more detailed descriptions of the individual projects themselves, and instructions for obtaining downloadable copies for classroom …

High School Student Perspective: My Njit Stem For Success Internship Experience, Michael Mora

STEM Month

During the 2020-2021 school year, I was a senior at the Academy for Mathematics, Science, and Engineering (AMSE) in Rockaway, NJ. At AMSE, a STEM-focused four-year magnet high school program hosted at Morris Hills High School, participating in an extended internship senior year is a cornerstone of the learning process. Required to complete a STEM-related internship to graduate, Academy students are encouraged to seek out an internship they’re passionate about in a field of their choice. The internship, which must be conducted under the mentorship of an industry professional, must meet the New Jersey-approved standards for a work-based learning experience …

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

Honors Program: Senior Projects (Public)

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 …

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.

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

Honors Program: Senior Projects (Public)

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 …

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 …

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

Honors Program: Senior Projects (Public)

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 …

Revisiting Prejudiced Polygons: Adapting A Familiar Activity During A Time Of Unknowns, Anne M. Ho, Jaime J. Mccauley, Tara T. Craig

Journal of Math Circles

This article describes the design process behind various iterations of Prejudiced Polygons, a Math Circles activity about segregation. In particular, we frame our discussion around two guiding principles from User Experience (UX) Design in thinking about the interconnected components of a Math Circles session, which includes all the people, the physical or virtual setting, the technology, and the world context. Additionally, we describe how we think about developing a “low floor" and “high ceiling" for math content, social issues content, as well as technology and access.

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?