Digital Commons Network^™

Digital Story-Based Problem Solving Applications: Preservice Primary Teachers’ Experiences And Future Integration Plans, Çiğdem Kilic, Hatice Sancar-Tokmak

Australian Journal of Teacher Education

This case study investigates how preservice primary school teachers describe their experiences with digital story-based problem solving applications and their plans for the future integration of this technology into their teaching. Totally 113 preservice primary school teachers participated in the study. Data collection tools included a questionnaire with three open-ended questions and focus group interviews. The data were analyzed using content analysis by combining manifest and latent techniques. Most of the preservice primary teachers described positive experiences about digital story-based problem solving applications by emphasizing on that they contribute to both their own and their students’ learning, development, and attitudes. …

A Beurling Theorem For Noncommutative Hardy Spaces Associated With A Semifinite Von Neumann Algebra With Various Norms, Lauren Beth Meitzler Sager

Doctoral Dissertations

We prove Beurling-type theorems for H-invariant spaces in relation to a semifinite von Neu-mann algebra M with a semifinite, faithful, normal tracial weight τ, using an extension of Arveson’s non-commutative Hardy space H-. First we prove a Beurling-Blecher-Labuschagne theorem for H-invariant subspaces of L p (M,τ) when 0 < p ≤ -. We also prove a Beurling-Chen-Hadwin-Shen theorem for H -invariant subspaces of L a (M,τ) where a is a unitarily invariant, locally k 1 -dominating, mutually continuous norm with respect to &\tau;. For a crossed product of a von Neumann algebra M by an action β, M o β Z, we are able to completely characterize all H-invariant subspaces of L a (Mo β Z,t) using our results. As an example, we completely characterize all H-invariant subspaces of the Schatten p-class, S p (H) (0 < p ≤ -), where H - is the lower tri-angular subalgebra of B(H). We also characterize the non-commutative Hardy space H -invariant subspaces in a Banach function space I(τ) on a semifinite von Neumann algebra M.

A Dynamical-Systems Approach To Understanding Turbulence In Plane Couette Flow, Mimi Szeto

Doctoral Dissertations

Dynamical systems theory is used to understand the dynamics of low-dimensional spatio-temporal chaos. Our research aimed to apply the theory to understanding turbulent fluid flows, which could be thought of as spatio-temporal chaos in a very-high dimensional space. The theory explains a system's dynamics in terms of the local dynamics of its periodic solutions; these are the periodic orbits in state space. We considered the development of a model for the dynamics of plane Couette flow based on the theory. The proposed model is essentially a set of low-dimensional models for the local dynamics of the periodic orbits of the …

The Role And Implications Of Executive Functions On Learning And Performing Math In High School Algebra I Students, Heather Lynn Rickmers Tacovsky

PCOM Psychology Dissertations

Current research is largely lacking in the areas of math, math learning deficits, and math-specific interventions. Even less available is research and interventions specific to high school learners. Some research addresses these areas with a specific focus on executive functions and how they may relate to student learning and performance. The present study sought to determine the relationship between three specific executive functions, Shift, Inhibit, and Working Memory, on learning and performance in math. Other executive functions, as measured by BRIEF rating scales and including Planning and Organization, Initiate, and Monitor, were also reviewed. Results of the present study found …

Pretending To Be Human: An Automated Theorem Prover To Write Mathematical Proofs, Khoa Nguyen

Senior Independent Study Theses

This project explores the theories of automated theorem proving and lambda calculus, and seeks to improve upon a current implementation of an automated theorem prover that produces human-like output. This software component is based on a published article titled “A Fully Automatic Theorem Prover with Human-Style Output” by M. Ganesalingam and W.T. Gowers [7], which outlines a program called robotone containing a first-order logic system (with a few modifications) able to automatically write simple direct proofs. It is designed to mimic different strategies that a human mathematician would use when facing a problem, and to write human-style proofs. The current …

Brauer-Picard Groups And Pointed Braided Tensor Categories, Costel Gabriel Bontea

Doctoral Dissertations

Tensor categories are ubiquitous in areas of mathematics involving algebraic structures. They appear, also, in other fields, such as mathematical physics (conformal field theory) and theoretical computer science (quantum computation). The study of tensor categories is, thus, a useful undertaking.

Two classes of tensor categories arise naturally in this study. One consists of group-graded extensions and another of pointed tensor categories. Understanding the former involves knowledge of the Brauer-Picard group of a tensor category, while results about pointed Hopf algebras provide insights into the structure of the latter.

This work consists of two main parts. In the first one we …

Give Me A Formula Not The Concept! Student Preference To Mathematical Problem Solving, Manveer Mann, Mary C. Enderson

STEMPS Faculty Publications

Purpose of Study: The purpose of this study was to assess student preference for procedural (formula-driven) versus conceptual (concept-driven) approaches to solve mathematical problems. Additionally, we evaluated differences in preferences among students who performed above average and those who performed at or below average on simple arithmetic problems.

Methods/Design and Sample: We used a single-factor (Instructional Approach: conceptual vs. procedural) between-subjects experiment. Instructional approach was manipulated using short embedded instructional videos. Students evaluated each approach on a five-point scale.

Results: We found that students (above-average and average/below-average) preferred the procedural approach to the conceptual approach. Interestingly, however, although students preferred …

Comparative Spectral Analysis Of Flexible Structure Models: The Euler-Bernoulli Beam Model, The Rayleigh Beam Model, And The Timoshenko Beam Model, Anhhong Rose Nguyen

Master's Theses and Capstones

We derive herein approximate spectra for three dierent models of transversely vibrating, beams. Each model consists of a system of partial dierential equations (PDEs) with various, boundary conditions. The three models that we consider are the Euler-Bernoulli model, the, Rayleigh model, and the Timoshenko model. We rst discuss a brief history of the models, before delving into obtaining the spectral equations for each beam model under dierent, boundary conditions. Lastly, we present asymptotic approximations of some of the various, spectral equations we found from each model.

The Stem Dilemma: Skills That Matter To Regions, Fran Stewart

Upjohn Press

Fran Stewart dives into the murky waters where education and economic goals meet to confront several key issues facing policymakers and educators, including the role of public investment in human capital, the types of human capital investment that provide the greatest public return, and whether those investments should vary by region.

She shows that not all high-paying jobs require STEM skills; that not all good-paying, highly skilled STEM jobs require college degrees; and that "soft skills" are important for STEM as well as other high-paying jobs.

Emergence And Complexity In Music, Zoe Tucker

HMC Senior Theses

How can we apply mathematical notions of complexity and emergence to music, and how can these mathematical ideas then inspire new musical works? Using Steve Reich's Clapping Music as a starting point, we look for emergent patterns in music by considering cases where a piece's complexity is significantly different from the total complexity of each of the individual parts. Definitions of complexity inspired by information theory, data compression, and musical practice are considered. We also consider the number of distinct musical pieces that could be composed in the same manner as Clapping Music. Finally, we present a new musical …

Instructional Strategies Used By Effective Mathematics Teachers In Adventist Elementary Schools In Florida: An Mqi Analysis, Anna Adkins

Dissertations

The Problem

Teaching mathematics can be a difficult task. United States students on comparative international mathematics assessments consistently rank near the test averages. On a national assessment, commonly called the Nation’s Report Card, more than half of American students rank as ‘not proficient’ in mathematics. The purpose of this study was to describe the strategies used by teachers with at least average mathematical knowledge for teaching. This was evidenced by their scores on the Mathematical Knowledge Test for Teaching (MKT). In addition to teacher knowledge, the study sample was selected from among schools where the five-year average was above the …

The Influence Of Multiple Representations On Secondary Students' Understanding Of Trigononetric Functions, Mayra Lizeth Ortiz Galarza

Open Access Theses & Dissertations

Trigonometry is a critical subject in mathematics that both high school and undergraduate students need to learn in order to be prepared for advanced mathematics. Despite the importance of trigonometry in the mathematics curriculum, little is known about best practices for teaching trigonometric functions and what difficulties students face when learning the topic. Using a Grounded Theory approach, this Dissertation presents the results of a design study (or teaching experiment) whose purpose was to examine the process by which students constructed the concept of trigonometric functions through multiple representations and how students developed meta-representational competence. The design study involved two …

Towards A Unified Theory Of Engineering Education, Oscar Humberto Salcedo

Open Access Theses & Dissertations

STEM education is an interdisciplinary approach to learning where rigorous academic concepts are coupled with real-world lessons and activities as students apply science, technology, engineering, and mathematics in contexts that make connections between school, community, work, and the global enterprise enabling STEM literacy (Tsupros, Kohler and Hallinen, 2009). The purpose of the Dissertation is to develop a unified theory of engineering education based on philosophies of mathematics, science, technology & engineering, and engineering education. Using purposive sampling methods, the Thesis constructs "representative" philosophy statements from the STEM fields based on the criteria of Constructivism, Progressivism, and/or Pragmatism. These statements are …

Knowledge Of Polymath Walks, Talks, Makes Waves, Turns Into Deeds, Hamlet Isaxanli, Waqas Ahmed

Khazar Journal of Humanities and Social Sciences

In this interview, Hamlet Isaxanli shares his opinion on polymathy. What makes a polymath? Isaxanli stresses the importance of two factors: a person’s nature may lead him/her to an insatiable thirst for knowledge and the desire to explore different fields simultaneously. On the other hand, the education system encourages polymathy from the perspective of the richness and diversity of the high school curriculum. Isaxanli also goes into the relationship between math and poetry as well as the art-science-humanities connections. He then calls attention to Omar Khayyam, Nasr al-Din Tusi and some polymaths of the 20th century. Finally yet importantly, Isaxanli …

On Degree Bound For Syzygies Of Polynomial Invariants, Zhao Gao

Senior Independent Study Theses

Suppose G is a finite linearly reductive group. The degree bound for the syzygy ideal of the invariant ring of G is given in [2]. We develop the theory of commutative algebra and give the proof from [2] that the ideal of relations of the minimal set of generators of invariant ring of a finite linearly reductive group G is generated in degree at most 2|G|.

The Search For Gto: Determining Optimal Poker Strategy Using Linear Programming, Stuart Young

Senior Independent Study Theses

This project applies techniques from game theory and linear programming to find the optimal strategies of two variants of poker. A set of optimal poker strategies describe a Nash equilibrium, where no player can improve their outcome by changing their own strategy, given the strategies of their opponent(s). We first consider Kuhn Poker as a simple application of our methodology. We then turn our attention to 2-7 Draw Poker, a modern variant onto which little previous research is focused. However, the techniques that we use are incapable of solving large, full-scale variants of poker such as 2-7 Draw. Therefore, we …

Building A Course Recommender System For The College Of Wooster, Nan Jiang

Senior Independent Study Theses

The goal of this project is to investigate the approaches for building recommender systems and to apply them to implement a course recommender system for the College of Wooster. There are three main objectives of this project. The first is to understand the mathematics and computer science aspects behind it. The mathematic concepts built into this project include probability, statistics and linear algebra. The final product is consist of two components: a collection of Python scripts containing the implementation code of the course recommender system, and a simple user interface allowing people to use the recommender system without typing commands. …

“I Learned Quite A Lot Of The Maths Stuff Now That I Think Of It”: Māori Medium Students Reflecting On Their Initial Teacher Education, Ngārewa Hāwera, Merilyn Taylor

Australian Journal of Teacher Education

Research involving preservice or initial teacher education (ITE) indicates that mathematics education is a vital component of study. Little is known however, of indigenous student views of their compulsory mathematics education courses for a teaching degree. This research contributes to that knowledge space as it explores Māori medium ITE students’ perceptions of mathematics education in Aotearoa New Zealand. A thematic and qualitative analysis of a focused group discussion provides insights into key factors that students reported as significant links between their university and practicum experiences (teaching practice in schools). Some suggestions for strengthening that programme were also expressed. Findings indicate …

Commercially Available Digital Game Technology In The Classroom: Improving Automaticity In Mental-Maths In Primary-Aged Students., John O'Rourke, Susan Main, Susan M. Hill

Australian Journal of Teacher Education

In this paper we report on a study of the implementation of handheld game consoles (HGCs) in 10 Year four/five classrooms to develop student automaticity of mathematical calculations. The automaticity of mathematical calculations was compared for those students using the HGC and those being taught using traditional teaching methods. Over a school term, students (n=236) who used the HGCs and Dr Kawashima’s Brain Training showed significant improvement in both the speed and accuracy of their mathematical calculations. Data collected in interviews during the intervention period from students, staff and parents were analysed to provide further information on the implementation and …

Knight's Tours And Zeta Functions, Alfred James Brown

Master's Theses

Given an m × n chessboard, we get an associated graph by letting each square represent a vertex and by joining two vertices if there is a valid move by a knight between the corresponding squares. A knight’s tour is a sequence of moves in which the knight lands on every square exactly once, i.e., a Hamiltonian path on the associated graph. Knight’s tours have an interesting history. One interesting mistake regarding Knight’s Tours was made by the famous mathematician Euler. His mistake led to the further study of knight’s tours on 3 × n chessboards. We will explore and …

“I’M Not Good At Math”: Mathematical Illiteracy And Innummeracy In The United States, G. Wesley Rogers

College of Graduate Studies: Theses & Dissertations

Why do we view mathematics the way we do in the United States and how have these views created an environment where we consider mathematical illiteracy and innumeracy socially and culturally acceptable when a lack of this knowledge and ability can function to enslave, exploit, restrict, and oppress. Throughout this investigation, I have explored some of the possible reasons for why we view education, mathematics, and the learning of mathematics the way we do and the impact of these views on our motivation and desire to learn mathematics. Using my over 20 years of teaching experience and the review of …

Quantum Metrics On Approximately Finite-Dimensional Algebras, Konrad Aguilar

Electronic Theses and Dissertations

Our dissertation focuses on bringing approximately finite-dimensional (AF) algebras into the realm of noncommutative metric geometry. We construct quantum metric structures on unital AF algebras equipped with a faithful tracial state, and prove that for such metrics, AF algebras are limits of their defining inductive sequences of finite dimensional C*-algebras for the quantum Gromov-Hausdorff propinquity. We then study the geometry, for the quantum propinquity, of three natural classes of AF algebras equipped with our quantum metrics: the UHF algebras, the Effros-Shen AF algebras associated with continued fraction expansions of irrationals, and the Cantor space, on which our construction recovers traditional …

Banach Spaces From Barriers In High Dimensional Ellentuck Spaces, Gabriel Girón-Garnica

Electronic Theses and Dissertations

We construct new Banach spaces using barriers in high dimensional Ellentuck spaces following the classical framework under which a Tsirelson type norm is defined from a barrier in Ellentuck space. It is shown that these spaces contain arbitrary large copies of lⁿ_infinity and specific block subspaces isomorphic to l_p. We also prove that they are l_p-saturated and not isomorphic to each other. Finally, a study of alternative norms for our spaces is presented.

Students' Mathematics Self-Efficacy, Anxiety, And Course Level At A Community College, Scott Reiner Spaniol

Walden Dissertations and Doctoral Studies

Research suggests that student success in mathematics is positively correlated to math self-efficacy and negatively correlated to math anxiety. At a Hispanic serving community college in the Midwest, developmental math students had a lower pass rate than did college-level math students, but the role of math self-efficacy and math anxiety on these students' learning was unknown. This causal comparative, correlational study, guided by social cognitive theory and math anxiety research, hypothesized that students in developmental math would have lower levels of math self-efficacy and higher levels of math anxiety, and that significant correlations would exist between course level, self-efficacy, and …

Possibilities And Challenges Of Teaching Integrated Math And Social Studies For Social Justice: Two Teacher Educators' Collaborative Self-Study, Paula P. Guerra, Sohyun An

Georgia Educational Researcher

In this paper, we—one mathematics teacher educator and one social studies teacher educator—describe a project where we collaborated to model teaching integrated mathematics and social studies for social justice in our methods courses. We encountered varied challenges in our efforts to prepare teacher candidates for social-justice-oriented lessons. These challenges included teacher candidates’ perception of authority/credibility of their professors who were foreign females from the “Third World”, teacher candidates’ deficit views on minoritized students, and the limited time and resources for teacher collaboration in teacher education. Despite these challenges, we believe this kind of project is necessary to move forward in …

Winner's Curse Correction And Variable Thresholding Improve Performance Of Polygenic Risk Modeling Based On Genome-Wide Association Study Summary-Level Data, Jianxin Shi, Ju-Hyun Park, Jubao Duan, Sonja T. Berndt, Winton Moy, Kai Yu, Lei Song, William Wheeler, Xing Hua, Debra Silverman, Montserrat Garcia-Closas, Chao Agnes Hsiung, Jonine D. Figueroa, Victoria K. Cortessis, Nuria Malats, Margaret R. Karagas

Dartmouth Scholarship

Recent heritability analyses have indicated that genome-wide association studies (GWAS) have the potential to improve genetic risk prediction for complex diseases based on polygenic risk score (PRS), a simple modelling technique that can be implemented using summary-level data from the discovery samples. We herein propose modifications to improve the performance of PRS. We introduce threshold-dependent winner’s-curse adjustments for marginal association coefficients that are used to weight the single-nucleotide polymorphisms (SNPs) in PRS. Further, as a way to incorporate external functional/annotation knowledge that could identify subsets of SNPs highly enriched for associations, we propose variable thresholds for SNPs selection. We applied …

Associating Mathematics To Its History: Connecting The Mathematics We Teach To Its Past, Joseph M. Furner, Ernest A. Brewer

Transformations

Across the USA and around the world now, globalization has taken a strong hold. The purpose of this paper is to explore the historical considerations that can be incorporated in the teaching of mathematics. The paper will also provide suggestions for teaching math by interweaving historical elements into the mathematics instruction. Teachers should strive to bridge the cultural and historical gap among all students by incorporating innovative ideas as well as historical and cultural connections into their teaching so to foster understanding, appreciation, and tolerance for the richness inherent in diversity and a sound understanding of mathematics and appreciation for …

Three A&S Faculty Recognized In Ohio Magazine, Ohio University College Of Arts & Sciences

All Forum Articles

No abstract provided.

Art-Integration Through Making Dioramas Of Women Mathematicians’ Lives Enhances Creativity And Motivation, Audrey C. Rule, Dana L. Atwood-Blaine, Clayton M. Edwards, Mindy M. Gordon

Journal of STEM Arts, Crafts, and Constructions

Creativity is essential for solving problems in the workplace, natural environment, and everyday life, necessitating that creativity be nurtured in schools. Identification of factors that intrinsically motivate students to learn difficult or initially unappealing content is also important. This project, in which 24 racially diverse fifth grade girls created dioramas of the lives of diverse successful women mathematicians, explored the girls’ reactions to art integration into mathematics through a phenomenological qualitative analysis of their products, essays, and responses to questionnaires. The project supported the Next Generation Science Standard for engineering design, Standard 3-5-ETS1-1 and two National Core Arts Standards for …

Differentiating Instruction Through Math Stations And Literacy Centers, Olivia Bates

Faculty Curated Undergraduate Works

Differentiating instruction based on students’ readiness, interests, and learning profiles is essential for creating effective and meaningful learning activities. Identifying these characteristics allows teachers to meet students’ needs and engage them in learning. By differentiating instruction, educators target specific students’ strengths and challenges in developing lessons to support their understanding of content. Two useful strategies for differentiating math and literacy instruction include stations and centers. In stations and centers, students work on specific skills catered to their educational needs while rotating activities in flexible groups. This guide supports teachers in identifying strategies and understanding the benefits of differentiating math and …