Mathematics Commons^™

Nidus Idearum. Scilogs, Xii: Seed & Heed, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this twelfth book of scilogs – called seed & heed –, one may find topics on Neutrosophy, Superluminal Physics, Mathematics, Information Fusion, Philosophy, or Sociology – email messages to research colleagues, or replies, notes, comments, remarks about authors, articles, or books, spontaneous ideas, and so on.

New Types Of Soft Sets: Hypersoft Set, Indetermsoft Set, Indetermhypersoft Set, And Treesoft Set - An Improved Version, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This is an improved paper of [10], where we recall the definitions together with practical applications of the Soft Set and its extensions to HyperSoft Set, IndetermSoft Set, IndetermHyperSoft Set, and TreeSoft Set.

The Encyclopedia Of Neutrosophic Researchers, Vol. 6, Florentin Smarandache, Maikel Yelandi Leyva Vázquez, Jesús Estupiñán Ricardo

Branch Mathematics and Statistics Faculty and Staff Publications

Este es el Sexto volumen de la Enciclopedia de Investigadores Neutróficos, editados a partir de materiales ofrecidos por los autores que respondieron a la invitación del editor. Los autores se enumeran alfabéticamente. La introducción contiene una breve historia de la neutrosófica, y en especial se sus impacto en latinoamérica junto con enlaces a los principales artículos y libros. Conjunto neutrosófico, lógica neutrosófica, probabilidad neutrosófica, estadística neutrosófica, medida neutrosófica, precálculo neutrosófico, cálculo neutrosófico, psicología neutrosófica, sociología neutrosófica etc., están ganando una atención significativa en resolver muchos problemas de la vida real que implican incertidumbre, imprecisión, vaguedad, incompletitud, inconsistencia e indeterminación. En …

Inspection Assignment Form For Product Quality Control Using Neutrosophic Logic, Maissam Jdid, Florentin Smarandache, Said Broumi

Branch Mathematics and Statistics Faculty and Staff Publications

During the production process, production companies need to monitor the finished products and ensure their quality, which imposes on them the appointment of inspectors for auditing, and this appointment costs the company amounts that affect the general profit, so it strives to make this cost as low as possible and that the audit process is carried out with high accuracy because in case that the finished products do not conform to the basic specifications of the product, the company is required to pay a fine. In this research, we will formulate the text of the problem appropriately for such a …

150+1 Probleme (Și Soluțiile Lor) 150+1 / Problems (And Their Solutions) - Bilingual Romanian-English, Carina Maria Viespescu, Lucian Tutescu, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Cartea se adresează elevilor de gimnaziu și liceu, profesorilor și celor pasionați de matematică, conținând 150+1 probleme, urmate de soluții, pentru a fi mai ușor savurate de cititor. Ultima problemă (150+1) foarte interesantă lasă loc de comentarii și generalizări.

This book is written for middle and high school students, for teachers and for those with a passion for math, containing 150+1 problems (which are followed by solutions) to make it more accessible to the reader. The last problem (150+1), a very interesting one, leaves some space for comments and generalizations.

Neutrosophic Superhyperalgebra And New Types Of Topologies, Florentin Smarandache, Memet Sahin, Derya Bakbak, Vakkas Uluçay, Abdullah Kargı

Branch Mathematics and Statistics Faculty and Staff Publications

In general, a system S (that may be a company, association, institution, society, country, etc.) is formed by sub-systems Si { or P(S), the powerset of S }, and each sub-system Si is formed by sub-sub-systems Sij { or P(P(S)) = P^2(S) } and so on.

That’s why the n-th PowerSet of a Set S { defined recursively and denoted by P^n(S) = P(P^(n-1)(S) } was introduced, to better describes the organization of people, beings, objects etc. in our real world.

The n-th PowerSet was used in defining the SuperHyperOperation, SuperHyperAxiom, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom in order …

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 …

Interactive White Boards In A Secondary Mathematics Classroom, Leann Bolhuis

Mathematics Graduate Theses

"A Formal Portfolio Submitted to the Faculty of the DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE In Partial Fulfillment of the Requirements For the Degree of MASTER OF SCIENCE IN MATHEMATICS".

Ambientes De Inclusión Para El Desarrollo Del Pensamiento Numérico Con Población Con Síndrome De Down, Luisa Valeria Escobar Buitrago, Ingry Yuliana Torres Garzón, Juan David Firigua Bejarano

Educación

La importancia de tratar sobre una educación inclusiva es hacer que la humanidad obtenga la aceptación hacia la diversidad, donde se encuentre un mundo lleno de posibilidades reconociendo todos los tipos de población entre ella las personas con Síndrome de Down, lo cual consiste en que la educación esté centrado en el respeto y la valoración de la diversidad, haciendo un enfoque general en las necesidades que esta población tiene, desarrollando habilidades para su desenvolvimiento tanto personal como laboral en determinada sociedad, por lo tanto el objetivo principal de este trabajo es desarrollar el pensamiento numérico de los estudiantes de …

A View Into Secondary Education Mathematics, Thomas Krieger Jr.

Honors Theses

Teaching methods, and the effects they can have on students, are important to consider for a classroom because when teaching you should allow for every student to have an opportunity. Every student should feel encouraged in the classroom, however not every method may allow for that. An important task for a teacher is to find out how to reach their students in their classroom; be it adapting methods or choosing when to implement one item over another. This task differs with every student that enters the classroom as no student is the same. Every students’ differences stem from their academic …

Financial Literacy Among Buffalo State College Undergraduate Students, Toni Martinucci

Public Administration Master’s Projects

Financial literacy can be complex and difficult for college students to comprehend. Many students struggle to afford college and are faced with large amounts of student loan debt. Financial awareness needs to be addressed early on for students to make informed decisions about college costs, student debt, and financial aid. However, financial aid applications, terms and conditions, and eligibility requirements are difficult for many students to comprehend on their own. The purpose of this study is to access financial literacy among undergraduate students at Buffalo State College. A quantitative approach is used in this study by implementing a web-based cross-sectional …

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

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 …

College Algebra Slide Decks, Bader Abukhodair, Michelle Zeng

All Open Educational Resources

This collection of slide decks is designed to be used in concert with the following Open Eduational Resources:

- OpenStax College Algebra 2e Open Texbook

- Department of Mathematics Video Playlist

- Homework questions from myOpenMath

Concepts include are: A study of equations, graphs, and inequalities for linear, quadratic, polynomial, rational, logarithmic, exponential, and absolute value functions. Transformations on graphs, complex numbers, circles, systems of inequalities, and systems of equations including matrices.

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 …

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.

“Math Talks Are Like An Alarm Clock Waking You Up”: Language’S Crucial Role In Mathematics, Gabriella M. Wasser

Journal of Practitioner Research

Whole group math talks, or number talks, are a common practice to get students talking about their own understanding of mathematical concepts. The purpose of this study was to implement math talks in small group settings to see what would happen, specifically to students’ conceptual understanding as well their general perceptions of math talks. This study took place in a fourth-grade math classroom, and math talks were implemented with the whole class for a week and then moved to small groups for the remaining three weeks of the study. During the study, a pre-and post-assessment was given, field notes were …

Teaching Euclidean Geometry Using Proof And Dynamic Geometry Software, Cheryl Stoddard

Mathematics Graduate Theses

This paper examines incorporating proofs and dynamic geometry software when teaching Euclidean geometry to produce deeper understanding of geometric relationships for middle and secondary level students. The utilization of technology through classroom investigations and activities has shown to have an impact on the achievement scores on posttests and in the development of mathematical proof.

Mathspark: Sparking Student Curiosity Through Hands-On, Inquiry-Based Mathematics Explorations Inspired By Funds Of Knowledge, Katrina Baha, Kaliyah Clyde, Mikaela Morris, Perla Myers Phd, Amanda Ruiz Phd

Creative Collaborations: Annual Showcase of Undergraduate Research

Abstract: Much of the existing research focuses on the questions teachers ask students, but there is very little information about the questions students ask. The main purpose of this research was to explore ways to engage students in asking their own questions in the learning of mathematics, and to create a scale to help educators categorize the types of questions students ask. We created and used inquiry-based, funds of knowledge-rich lessons with productive struggle opportunities to promote curiosity (Calleja, 2016) and elicit student questions to develop and test our question categorization scale.

Recognizing And Reducing Ambiguity In Mathematics Curriculum And Relations Of Θ-Functions In Genus One And Two: A Geometric Perspective, Shantel Spatig

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Anxiety and mathematics come hand in hand for many individuals. This is due, in
part, to the fact that the only experience they have with mathematics is what some
mathematics educators refer to as "schoolmath," which uses a somewhat different
language than real mathematics. The language of schoolmath can cause individu-
als to have confusion and develop misconceptions related to several mathematical
concepts. One such concept is a fraction. In chapter one of this report, one possible
reason for this is discussed and a possible solution is purposed.
In chapter three of this report, genus-two curves admitting an elliptic involution …

Mathematics Teachers’ Working With Cooperative Learning, Jaime Gomez

Theses and Dissertations

Teaching styles vary greatly amongst educators. One being extensively researched and highly discussed is the method of cooperative learning. Although many studies have shown the benefits of incorporating cooperative learning into classrooms, it has not been a widely used method of teaching in high school mathematics classrooms. This study explores some of the efforts that teachers, who utilize cooperative learning in their classrooms, make to implement cooperative learning lessons successfully. Furthermore, this study also explores the challenges these teachers have encountered when using cooperative learning. Data was collected qualitatively by interviews and surveys from six in-service high …

Using Teacher Noticing And Video-Mediated Professional Learning To Develop Preservice Teachers’ Knowledge For Teaching The Derivative, Alfred M. Limbere

Theses, Dissertations and Culminating Projects

This study investigated how problem-solving videos can be used in video-mediated professional learning to support secondary preservice mathematics teachers (PMTs) in developing teacher knowledge for noticing student thinking in the context of the derivative concept in calculus. A model of the trajectory of PMTs’ noticing was constructed as six PMTs viewed and analyzed videos of students’ problem solving. At the same time, the nature of video-mediated interactions that were found to be productive in supporting this knowledge development was examined. A design experiment was used as the research methodology. Data was collected from video recordings of eight semi-structured teaching episodes …

Investigating Elementary School Students’ Reasoning About Dynamic Angles, Erell Germia

Theses, Dissertations and Culminating Projects

Angle measurement is a significant topic in almost all areas of mathematics learning and also in many disciplines outside mathematics education, such as engineering and architecture. According to the literature, there are three common conceptions of angles – as union of rays, rotations, and wedges. Researchers argued that students must consider these three angle concepts together to construct a meaningful understanding of angles. However, the curriculum standards for mathematics often present these angle conceptions separately to students, probably resulting in a fragmented understanding of the angle concept. In addition to this problem, the research literature documents multiple alternative conceptions 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 …

Calculus Iii: Under The Influence Of Peer Instruction, Alan Von Herrmann, L. Jeneva Clark

Journal of Humanistic Mathematics

In peer Instruction, students engage with core course concepts and then explain those concepts to one another in small groups. Unlike in lecture format, peer instruction involves every student in the class. In Spring 2019, the first authot began using a modified version of peer instruction in Calculus III classes. He started each class by discussing important Calculus III concepts from three standpoints (the formula, the geometry behind the formula, and the physics behind the formula). During the last 20 minutes of each 50-minute class session, he polled the students using questions in the “Goldilocks Zone” – not too hard …

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.

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

Journal of Humanistic Mathematics

In this paper we highlight the experience of a mathematics teacher educator (MTE) and their prospective 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.

Stewardship Of Mathematics: Essential Training For Contributors To, And Users Of, The Practice Of Mathematics, Rochelle E. Tractenberg

Journal of Humanistic Mathematics

A steward of the discipline was originally defined as an individual to whom “we can entrust the vigor, quality, and integrity of the field”, and more specifically, as “someone who will creatively generate new knowledge, critically conserve valuable and useful ideas, and responsibly transform those understandings through writing, teaching, and application” [8]. Originally articulated for doctoral education, in 2019 the construct of stewardship was expanded so that it can also be applied to non-academic practitioners in any field, and can be initiated earlier than doctoral education [18]. In this paper, we apply this construct to the context of mathematics, and …

Towards Pedagogy Supporting Ethics In Modelling, Marie Oldfield

Journal of Humanistic Mathematics

Education for concepts such as ethics and societal responsibility that are critical in building robust and applicable mathematical and statistical models do currently exist in isolation but have not been incorporated into the mainstream curricula at the school or university level. This is partially due to the split between fields (such as mathematics, statistics, and computer science) in an educational setting but also the speed with which education is able to keep up with industry and its requirements. I argue that principles and frameworks of socially responsible modelling should begin at school level and that this would mean that ethics …

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 …

Violence In Mathematics Teaching. Reflections Inspired By Levinas’ Totality And Infinity, Adriano Demattè

Journal of Humanistic Mathematics

In mathematics class, violence is carried out in some usually not recognized situations. In this article, I share some reflections on the topic inspired by some passages of Totality and Infinity, work of the French-Lithuanian philosopher Emmanuel Levinas (1906-1995). I find violence by the teacher in not promoting students’ understanding of mathematics, in a distorted use of rhetoric, and in interrupting an ethical relation. This article analyses situations taken from class activities, focusing on the teacher’s presentation of mathematical content and students’ interventions. I also propose that the improvement of interventions in mathematics education is possible and suggest theoretical …