Digital Commons Network^™

On Not Teaching Addition: A Homeschooling Parent Teaches And Researches Math, Marion D. Cohen

Journal of Humanistic Mathematics

Interactions with the humans in one’s life can have bearings on the way one interacts with one’s work – and vice versa. In particular, the ways in which a math person who is also a parent interacts with their children can correlate with the ways that person interacts with students, colleagues, and with math itself. This article describes some of that correlation in one mathmom’s life. In particular, this mathmom worked toward balancing, both as a mom and as a teacher, her beliefs and feelings with societal mindsets and practices.

A Study Of Operators On The Discrete Analogue Of Hardy Spaces On Homogeneous Trees And On Other Structures., P. Muthukumar Dr.

Doctoral Theses

In analytic function theory, the study of multiplication and composition operators has a rich structure for various analytic function spaces of the unit disk D = {z ∈ C : |z| < 1} such as the Hardy spaces Hp, the Bergman spaces Ap and the Bloch space B. This theory connects the operator theoretic properties such as boundedness, compactness, spectrum, invertibility, isometry with that of the function theoretic properties of the inducing map (symbol) such as bijectivity, boundary behaviour and vise versa In Chapter 2, we define discrete analogue of generalized Hardy spaces (Tp) and their separable subspaces (Tp,0) on a homogenous rooted tree and study some of their properties such as completeness, inclusion relations with other spaces, separability and growth estimate for functions in these spaces and their consequences. In Chapter 3, we obtain equivalent conditions for multiplication operators Mψ on Tp and Tp,0 to be bounded and compact. Furthermore, we discuss point spectrum, approximate point spectrum and spectrum of multiplication operators and discuss when a multiplication operator is an isometry. In Chapter 4, we give an equivalent conditions for the composition operator Cφ to be bounded on Tp and on Tp,0 spaces and compute their operator norms. We have considered the composition operators induced by special symbols such as univalent and multivalent maps and automorphism of a homogenous tree. We also characterize invertible composition operators and isometric composition operators on Tp and on Tp,0 spaces. Also, we discuss the compactness of Cφ on Tp spaces and finally we prove that there are no compact composition operators on Tp,0 spaces. In Chapter 5, we consider the composition operators on the Hardy-Dirichlet space H2, the space of Dirichlet series with square summable coefficients. By using the Schur test, we give some upper and lower estimates on the norm of a composition operator on H2 , for the affine-like inducing symbol ϕ(s) = c1 + cqq −s , where q ≥ 2 is a fixed integer. We also give an estimate for approximation numbers of a composition operators in our H2 setting. In Chapter 6, we study the weighted composition operators preserving the class Pα. Some of its consequences and examples of certain special cases are presented. Furthermore, we discuss about the fixed points of weighted composition operators.

Agricultural Education And Mathematics Performance Among Secondary Students, Susan W. Githua, John C. Ricketts

Online Journal for Workforce Education and Development

The purpose of this study was to determine the effects of agricultural education, FFA involvement, and SAE participation on the mathematics performance of secondary students. The study explored these factors using an ex post facto research design. Respondents in the study were secondary students enrolled in Agricultural Education program (N=80) and non-agricultural education students (N=59). Results revealed that agricultural education students had a higher mathematics mean score (M=12.15, SD=4.61) than non-agricultural education students (M=10.67, SD=3.63). There were positive statistically significant differences between mathematics performance of the students and their FFA involvement as well as SAE participation.

Gwu Doctoral Student Pushes Past Language Barrier To Complete Curriculum And Instruction Degree, Office Of University Communications

Gardner-Webb NewsCenter Archive

Give Thanh-Thuy T. Nguyen a complicated mathematical problem, and she calculates the answer in a few minutes. But ask her to read a book on curriculum theory and practice, and the native of South Vietnam will pour over the material for hours, looking up definitions. Even after 24 years in America, Nguyen, a college math instructor, is not confident in her English skills.

Parts Of The Whole: The Having Of Wonderful Ideas: Eleanor Duckworth Introduces Us To Piaget, Dorothy Wallace

Numeracy

The small book of essays by Eleanor Duckworth has been a staple of teacher education for decades, serving as a bridge between Piaget’s observations of infants and the needs of the classroom. As her examples tend to be of young children, we consider more general ideas in the context of older grades and higher education. Several of her insights are discussed with an eye to application in the field of quantitative education, highlighting the need to integrate issues of pedagogy with those of content.

Impact Of Pro-Based Learning On Student Performance In Elementary Mathematics, Emmanuela Remy

Theses and Dissertations

Elementary school students have been underperforming in mathematics at the city, state, and national level. The National Education Goals, adopted by the United States Congress in 1989, did not achieve the two math goals (Goal #3 and Goal #5) by the year 2000 as outlined in the Goals 2000 Legislation. The 2019 National Assessment of Educational Progress (NAEP) results indicated that grade 4 students were not proficient in mathematics. This exploratory study, not only sought to address the two National Education math goals, but also investigated whether Pro-Based Learning (ProBL) was an effective pedagogical practice for elementary school students of …

The Impact Of Universally Accelerating Eighth Grade Mathematics Students In Heterogeneously Grouped Classrooms: An Interrupted Time Series, Patrick Walsh

Theses and Dissertations

Traditionally, students are scheduled to take Algebra I in their first year of high school mathematics in New York State. However, in many schools, the “top” students in a cohort have access to this course in eighth grade, tracking these high-achieving students ahead of their lower-achieving peers. In response, some schools have adopted the policy of “Algebra for all” in eighth grade – called universal acceleration. A perceived benefit to the policy of universal acceleration is ensuring equal access to a challenging curriculum for all students, regardless of race, socioeconomic status, or prior achievement- mitigating one of the perceived limitations …

Recruitment Of Science And Mathematics Teachers: Analysis Of Findings From Three Years Efforts Of A Recruitment Program, Kadir Demir, Tugce Gul, Charlene Czerniak

Faculty Bibliography

No abstract provided.

First Grade Educators' Perceptions Of Their Confidence To Integrate The West Virginia Mathematical Habits Of Mind Into Classroom Practices, Monica Lynn Dellamea

Theses, Dissertations and Capstones

Mathematical proficiency during the early years is directly linked to later success in life, both regarding academics and economics. First grade educators must have the knowledge and skills to integrate the West Virginia Mathematical Habits of Mind (WV MHM) into their existing classroom instructional practices to help establish strong foundations for mathematical learning and thinking early on in children’s lives. This study investigated first grade educators’ perceptions of their confidence with integration of the WV MHM into their classroom instructional practices. Barriers to and supports for implementation, as well as educator demographics, were examined to determine any effect they may …

Eliminating Achievement And Opportunity Gaps: Supporting Black Girls As Mathematicians, Carolyn Fitzpatrick

Graduate Teacher Education

The research examined achievement and opportunity gaps for Black girls in the discipline of mathematics. Initiatives for mathematics programs were emphasized in secondary schools to encourage students to pursue degrees and careers in mathematics for economic advancement but failed to include certain minority groups. Researchers found underrepresentation of Black girls and women in mathematics programs, at the secondary and post-secondary level, and mathematics-related careers. Upon further investigation, researchers concluded there were achievement and opportunity gaps for Black girls in mathematics. This study was unique from other achievement studies that focused solely on gender or race because of Black girls’ double …

Communicating In Crisis Situations, Rick Gorvett, Chris Morse, Julie Volkman

Communication Faculty Journal Articles

Communicating technical information, especially in a crisis situation and particularly when the audience does not share the technical background, is a challenge that actuaries frequently face. This essay describes the dynamics and issues involved in crisis communications and provides some recommendations for actuaries confronting such a situation.

Math Department 2019-2020 Newsletter, Mathematics Department

Mathematics Newsletter

Welcome to our annual Mathematics Department Newsletter. This was an unusual year for our department as the coronavirus cut short our time on campus this year. Hence we were unable to have our usual events such as the Annual Mathematics Lecture, the Pi Mu Epsilon Induction and Awards Night, and there was no in-person commencement ceremony. But despite that, many great things happened in our department.

Discrepancy Inequalities In Graphs And Their Applications, Adam Purcilly

Electronic Theses and Dissertations

Spectral graph theory, which is the use of eigenvalues of matrices associated with graphs, is a modern technique that has expanded our understanding of graphs and their structure. A particularly useful tool in spectral graph theory is the Expander Mixing Lemma, also known as the discrepancy inequality, which bounds the edge distribution between two sets based on the spectral gap. More specifically, it states that a small spectral gap of a graph implies that the edge distribution is close to random. This dissertation uses this tool to study two problems in extremal graph theory, then produces similar discrepancy inequalities based …

Effectiveness Of Ilearn As A Formative Assessment Tool In Title I Middle Grade Mathematics, Christopher George Atkinson

Walden Dissertations and Doctoral Studies

Because students in two Georgia middle schools, Grades 6 through 8, performed poorly in standardized mathematics testing during the 2016-17 school term, the district sought improvements by using the computer-assisted formative assessment tool iLearn. The purpose of this quantitative project study was to determine whether the use of iLearn predicted increased mathematics achievement and to support professional development sessions for teachers to improve their pedagogy. With the theoretical framework of mastery learning theory, the study addressed the effectiveness of iLearn as a formative assessment tool, hypothesizing a positive relationship between iLearn and end-of-grade (EOG) assessment scores; a moderating effect of …

Third Grade Math Teachers’ Perceptions Of Their Preparedness To Teach The Standards For The Staar Math Test, Diana L. Everman

Walden Dissertations and Doctoral Studies

Teacher professional development (PD) is acknowledged as an effective approach for changing teachers’ beliefs, practices, and behaviors to raise student academic achievement. A rural school district identified that 3rd grade math teachers felt inadequately prepared to teach the College and Career Readiness and Academic Standards (CCRS) standards for the state math assessment (STAAR). The purpose of this basic qualitative study was to explore third grade math teachers’ perceptions of their preparedness to meet the demands of the new third grade STAAR math test. Vygotsky’s constructivist theory from an adult learning perspective and Bandura’s self-efficacy theory guided the study. The research …

Community College Students' Perceptions Of Developmental Mathematics And Influences On Persistence, Sumithra S. Iyer

Walden Dissertations and Doctoral Studies

The increase in the dropout rates associated with developmental mathematics classes in 1 Texas community college provoked the need for this study. The purpose of this case study was to explore students' reasons for dropping out of developmental mathematics and what might have helped them be successful. Tinto's model of student attrition, which is characterized by students' social and academic integration affecting their retention in the college, provided the conceptual framework for the study. The research questions addressed the students' perceptions of both why they dropped out of developmental mathematics courses and what might have helped them to successfully complete …

Instructional Leadership Of Elementary School Principals Regarding Proficiency In Mathematics, Melvinia Robinson

Walden Dissertations and Doctoral Studies

Elementary school principals, as instructional leaders, are critical to improving

mathematics proficiency. The research problem was that elementary school principals are

inconsistently applying instructional leadership to support mathematics teachers' efforts

to improve students' proficiency. The purpose of this qualitative case study was to

understand how elementary school principals apply instructional leadership to support

mathematics teachers in their efforts to improve student proficiency in mathematics. The

conceptual framework was the instructional leadership model of Hallinger and Murphy,

which defines three main dimensions of instructional leadership: (a) the school mission,

(b) the instructional program, and (c) the school climate. The research question …

Math Across The Curriculum, Kelsey Mason

Masters Essays

No abstract provided.

Good Teachers Borrow, Great Teachers Steal: A Case Study In Borrowing For A Teaching Project, Mike May, Rebecca Segal, Victor Piercey, Tao Chen

Publications and Research

Very few great ideas in teaching are without ancestors or descendants. This paper presents a case study in how one particular pedagogical project, the work at Saint Louis University as part of the National Science Foundation supported SUMMIT-P consortium, borrowed from other sources. The particular project was an interdisciplinary collaboration to make mathematics education more effective for business students. The various borrowings are treated in roughly chronological order from initial inspiration through planned adoption and adaptation of the work of others to the addition of features that only became available mid-project. The kinds of sources include a particular business calculus …

Final Report: Incorporating Open Educational Textbook Into Business Math Co-Requisite Model, Aida Allen

Mavs Open Press Open Educational Resources - Archive

Aida Allen's final report for the UTA CARES Grant Program

A Cool Brisk Walk Through Discrete Mathematics, Stephen Davies

Computer Science Articles

A Cool Brisk Walk Through Discrete Mathematics - and its companion site "allthemath" - are completely-and-forever-free-and-open-source educational materials dedicated to the mathematics that budding computer science practitioners actually need to know. They feature the fun and addictive teaching of award-winning lecturer Dr. Stephen Davies of the University of Mary Washington in Fredericksburg, Virginia!

The Elements Of Input-Output Analysis, William H. Miernyk

Web Book of Regional Science

The first writers to treat economics systematically — Adam Smith and his immediate successors — dealt with the economy as a whole. In today’s terminology they were concerned with macroeconomics. Later economists, notably Alfred Marshall and his followers in the Neo-classical school, focused upon the household and the firm. They inaugurated the era of microeconomics which led to Chamberlin’s theory of monopolistic competition and Mrs. Robinson’s theory of imperfect competition. The Neo-classical economists and their successors analyzed the forces which result in economic equilibrium, but their approach was that of partial equilibrium, or the method of examining "one thing at …

Teacher-Perceived Barriers To Math Achievement And Implementation Of Literature-Based Recommendations For Change In Math Instruction In Grades 4 Through 8, Kimberly Summey

Ed.D. Dissertations

The purpose of this research was to identify teachers’ perceptions of barriers to math achievement below Grade 10, if any, to determine which, if any, of the identified barriers teachers reported, and to determine which, if any, previous recommendations for positive changes in mathematics classrooms teachers reported, as well as identify any teacher reports of resistance to change. I conducted research on 19 participants by collecting questionnaires online due to the COVID-19 pandemic. Participants were teachers of mathematics from Grade 4 through Grade 8. I compared participants’ responses to literature-based components using predetermined coding along with emergent coding to identify …

Meichen Liu, Meichen Liu

UNBOUND 2020 Archive (Virtual)

Meichen Liu, PRINT 22 makes larger-than-human-size installations, picture books and zines to present personal understandings of human emotions as well as relationships, and also to resonate with her audience. She seeks a deeper meaning behind ordinary things, and her seekings are reflected in her arts. She is searching for a way to combine maths with fine arts. She hasn’t found the one she likes yet, but she never gives up on things she values, and she gains better comprehension in both fields through this process. View Meichen's Baker & Whitehill Annual Student Artists' Book Contest entries Pockets, 2020 and …

Validity Of A Special Education Teacher Observation System, Evelyn S. Johnson, Angela Crawford, Laura A. Moylan, Yuzhu Zheng

Early and Special Education Faculty Publications and Presentations

This manuscript describes the comprehensive validation work undertaken to develop the Recognizing Effective Special Education Teachers (RESET) observation system, which was designed to provide evaluations of special education teachers’ ability to effectively implement evidence-based practices and to provide specific, actionable feedback to teachers on how to improve instruction. Following the guidance for developing effective educator evaluation systems, we employed the Evidence-Centered Design framework, articulated the claims and inferences to be made with RESET, and conducted a series of studies to collect evidence to evaluate its validity. Our efforts and results to date are described, and implications for practice and further …

Trigonometry: A Brief Conversation, Carolyn D. King Phd, Tam Evelyn, Fei Ye Phd, Beata Ewa Carvajal

Open Educational Resources

These five units are specifically tailored to foster the mastery of a few selected trigonometry topics that comprise the one credit MA-121 Elementary Trigonometry course. Each unit introduces the topic, provides space for practice, but more importantly, provides opportunities for students to reflect on the work in order to deepen their conceptual understanding.

These units have also been assigned to students of other courses such as pre-calculus and calculus as a review of trigonometric basics essential to those courses. This is the second edition of the materials. Units 4 and 5 have been edited to reflect suggestions from instructors who …

Teacher Perception Of Inquiry-Based Teaching In Mathematics In Early Childhood, Nadim Farooqi

CUP Ed.D. Dissertations

Inquiry-based instruction has been pivotal in transforming classrooms into engaging student-centered learning environments. Utilizing inquiry-based instruction in mathematics in early childhood can help build a strong foundation in mathematics. This qualitative study examined the perceptions of teachers and administrators on inquiry-based instruction in early childhood mathematics. This study was guided by three research questions. This study took place at two public schools in NYC. Data was collected through a preinterview survey and interviews. The participants included nine teachers and three administrators. During the analysis process five themes were revealed: professional development, planning and preparation, student engagement, building foundational skills, and …

Recognizing And Addressing Mathematics Anxiety In Female Students, Amanda Sost

West Chester University Master’s Theses

Mathematics anxiety is a prevalent concern in the world of education. As a female mathematician myself, my own personal experiences led me to research the reasons why mathematics anxiety affects more girls than boys. Specifically this paper explores the basics of anxiety including its definition and causes. This definition provides a meaning behind discussing the authoritarian model of education and the importance behind creating a free democratic society, not only in the classroom but in the world. Specifically, the authoritarian style of pedagogy has many affects on students who are learning mathematics, which will be explored as one of the …

A Natural Rank Problem For Homogeneous Polynomials And Connections With The Theory Of Functions Of Several Complex Variables, Kevin A. Palencia Infante

Graduate Student Theses, Dissertations, & Professional Papers

We study a natural extremal problem about the vector space consisting of all homogeneous polynomials of degree $d$ in $n+1$ variables with real coefficients, together with the zero polynomial. We define the {\it rank} of a polynomial to be the number of distinct monomials appearing in the polynomial with non-zero coefficient. We are particularly interested in those homogeneous polynomials whose quotient with the homogeneous polynomial $x_0+x_1+\cdots+x_n$ is a polynomial of degree $d-1$ with maximal rank. For each degree $d$, we seek the minimum rank for an element of this subfamily and we seek to describe those polynomials with minimum rank. …

Using A Faculty Learning Community To Promote Interdisciplinary Course Reform, Rhonda Bishop, Victor Piercey, Mischelle Stone

Journal of Mathematics and Science: Collaborative Explorations

As part of a multi-institution, National Science Foundation (NSF) grant-funded project, Ferris State University (FSU) joins a national effort to reform mathematics curricula. Researchers from FSU developed and facilitated a faculty learning community (FLC) as one strategy to redesign the traditional approach to the quantitative reasoning skill development of students in the departments of mathematics, nursing, social work, and the College of Business. Over the course of one academic year, the FLC provided an interdisciplinary faculty connection to develop pedagogical approaches that integrated cross-curricular concepts and context from each discipline. The FLC not only produced uniquely designed, learning-centered approaches to …