Digital Commons Network^™

Minimal Covers Of The Archimedean Tilings, Part Ii Appendices, Gordon Williams, Daniel Pellicer, Mark Mixer

Faculty

These files contain a full descriptions of the relations in the presentations of the monodromy groups for the (3.3.4.3.4), (3.3.3.4.4), (4.6.12), and (3.3.3.3.6) tilings. This material was prepared to provide additional material or the possibility of verification of our work for the interested reader of the associated article.

Brown, James Monroe, 1800-1886 (Sc 806), Manuscripts & Folklife Archives

Manuscript Collection Finding Aids

Finding aid only for Manuscripts Small Collection 806. Ciphering book, 1822-1827 (40 p.), of James M. Brown, Butler County, Kentucky, which also contains a few pages of account entries and other various notations, (806a). Photocopy of ciphering book is also included. Also letter, 1989, from donor relating family data.

Standards Based Education In Egypt And Singapore, Dara Akeal El Masri

Theses and Dissertations

Mathematics education is important for all members of modern societies. In Egypt, the importance of mathematics education needs greater emphasis because of its role in providing job opportunities and helping to understand and build new economies, as well as, reducing the gap between Egypt and other developing countries. In order to know the aspects that need improvement in the Egyptian mathematics educational system, this study analyzed both the national Egyptian and the national Singaporean eighth grade mathematics educational system; mainly the standards, curricula, and textbooks. The analysis of the standards was done by comparing them to the characteristics of high …

A Framework For Categorising Mobile Applications In Mathematics Education, Boris Handal, Joe El-Khoury, Chris Campbell, Michael Cavanagh

Education Conference Papers

New learning technologies have brought fresh challenges to teachers in selecting appropriate educational resources, particularly in regards to mobile devices. There are an impressive number of educational mobile learning applications, more commonly known as apps, that teachers need to understand before integrating them into the classroom. To make this process more effective, educational apps can be categorised according to their specific role in the teaching and learning of mathematics along with their media richness. A framework of nine distinct categories of apps emerged, grouped into three main clusters, namely, investigative, productivity and instructive tools. The framework was validated with examples …

The Arithmetical Hierarchy In The Setting Of $\Omega_1$, Jacob Carson, Jesse Johnson, Julia F. Knight, Karen Lange, Charles Mccoy Csc, John Walbaum

Faculty Research and Scholarship

We continue work from (Greenberg and Knight) on computable structure theory in the setting of $\omega_1$, where the countable ordinals play the role of natural numbers, and countable sets play the role of finite sets. In the present paper, we define the arithmetical hierarchy through all countable levels (not just the finite levels). We consider two different ways of doing this—one based on the standard definition of the hyperarithmetical hierarchy, and the other based on the standard definition of the effective Borel hierarchy. For each definition, we define computable infinitary formulas through all countable levels, and we obtain analogues of …

Scholarly Communications And The Role Of The Liberal Arts College Library, Diane J. Graves

Library Faculty Research

No abstract provided.

Behavior Of Solutions For Bernoulli Initial-Value Problems, Carlos Marcelo Sardan

Theses Digitization Project

The purpose of this project is to investigate blow-up properties of solutions for specific initial-value problems that involve Bernoulli Ordinary Differential Equations (ODE's). The objective is to find conditions on the coefficients and on the initial-values that lead to unbounded growth of solutions in finite time.

Language, Reading, And Math Learning Profiles In An Epidemiological Sample Of School Age Children., Lisa M D Archibald, Janis Oram Cardy, Marc F Joanisse, Daniel Ansari

Brain and Mind Institute Researchers' Publications

Dyscalculia, dyslexia, and specific language impairment (SLI) are relatively specific developmental learning disabilities in math, reading, and oral language, respectively, that occur in the context of average intellectual capacity and adequate environmental opportunities. Past research has been dominated by studies focused on single impairments despite the widespread recognition that overlapping and comorbid deficits are common. The present study took an epidemiological approach to study the learning profiles of a large school age sample in language, reading, and math. Both general learning profiles reflecting good or poor performance across measures and specific learning profiles involving either weak language, weak reading, weak …

Undergraduate Mathematics Students' Attitudes Toward Using E-Learning In Saudi Arabia, Bakheet Wasel Alrehaili

All-Inclusive List of Electronic Theses and Dissertations

The main objective of this study was to investigate the attitudes of undergraduate mathematics students in Saudi Arabia towards online mathematicsEducation. Comparisons were made among male, female, underclassmen, and upperclassmen undergraduate mathematics students at the University of Tabuk (UT). Of 161 students enrolled in the mathematics program, 118 mathematics students responded to the survey. The sample consisted of 57 male and 61 female students. A 2 × 2 ANOVA test was used to reveal any statistically significant differences between the various groups based on gender andEducational level. The findings showed that underclassmen did not differ significantly from upperclassmen in their …

Inner City African American Girls' Learning Mathematics: Parental Influence And Classroom Experience As They Impact Mathematics Scores On The Act, Sharon Alicia Simeon

Wayne State University Dissertations

The objective of this study was to discover how parents (N=47), through their input at home, influence the mathematical performance of their daughters; how female African American students view their teachers' influence in their mathematical thinking; how critical is the mathematical classroom experience for African American girls; and can positive classroom experiences (teacher implementation of best practices) significantly add to the effect of the parental mathematical input at home. And lastly, how much can the two factors together predict higher mathematics scores on the ACT. Research instruments consisted of parent and student surveys. The participants were African American girls who …

Kam_Crk: Clustering And Ranking Knowledge For Reasonable Results Based On Behaviors And Contexts, Changhong Hu, Shufen Liu, Ramana Reddy, Sumitra Reddy, Mingyang Liu

Faculty & Staff Scholarship

A model named KaM_CRK is proposed, which can supply the clustered and ranked knowledge to the users on different contexts. By comparing the attributes of contexts and JANs, our findings indicate that our model can accumulate the JANs, whose attributes are similar with the user’s contexts, together. By applying the KaM_CLU algorithm and Centre rank strategy into the KaM_CRK model, the model boosts a significant promotion on the accuracy of provision of user's knowledge. By analyzing the users' behaviors, the dynamic coefficient BehaviorF is first presented in KaM_CLU. Compared to traditional approaches of K_means and DBSCAN, the KaM_CLU algorithm does …

Using Math Curriculum Based Assessments To Predict Student Performance On The Pennsylvania System Of School Assessment Math Test, Joseph H. Lucas

PCOM Psychology Dissertations

Today, a considerable emphasis is placed on students’ performance on state-wide achievement tests. In light of the mounting pressure for accountability for student academic achievement on state-wide tests, the use of curriculum-based measurement (CBM) methods for monitoring student progress, identifying students at risk for failing state tests, and identifying skill deficits to be addressed through interventions to increase student performance could prove beneficial. This study examined the relationship of the Measures of Academic Progress Math CBM (MAP) to performance on the Pennsylvania System of School Achievement (PSSA) with correlational analysis and the calculation of sensitivity and specificity indices and kappa …

Research Briefs: Improving College Students' Attitudes Toward Mathematics, Georgia Southern University

College of Education Research Briefs (2012-2019)

• Improving College Students’ Attitudes Toward Mathematics

What Do Students Do In Self-Formed Mathematics Study Groups?, Gillian E. Galle

Doctoral Dissertations

An implicit assumption of many university classes is that students will spend a large amount of time outside the classroom refining their understanding of the material to develop mastery of the concepts. This is especially true in first year mathematics courses at the undergraduate level. However, little is known about what students do to fulfill this didactical contract with their instructors. The currently available research relies primarily on self-reported data from the students collected through questionnaires or interviews. This study sought to start describing what students do while studying mathematics in a self-created group outside of the classroom setting through …

The Multifaceted Nature Of Mathematics Knowledge For Teaching: Understanding The Use Of Teachers' Specialized Content Knowledge And The Role Of Teachers' Beliefs From A Practice-Based Perspective, Lauren E. Provost

Doctoral Dissertations

This work investigates middle school teachers' mathematics knowledge for teaching (MKT) as defined by Hill (2007). Within this two-part dissertation, the level of MKT was considered as well as the role of teacher beliefs in actual specialized content knowledge (SCK) use, a specific type of mathematics knowledge for teaching vital in quality mathematics instruction. Additionally, the model of MKT knowledge was explored through confirmatory factor analysis on a large, national dataset of middle school mathematics teacher survey responses involving mathematics knowledge for teaching. SCK was found to be vital in quality mathematics instruction yet not sufficient. Teacher beliefs about the …

Factoring The Duplication Map On Elliptic Curves For Use In Rank Computations, Tracy Layden

Scripps Senior Theses

This thesis examines the rank of elliptic curves. We first examine the correspondences between projective space and affine space, and use the projective point at infinity to establish the group law on elliptic curves. We prove a section of Mordell’s Theorem to establish that the abelian group of rational points on an elliptic curve is finitely generated. We then use homomorphisms established in our proof to find a formula for the rank, and then provide examples of computations.

Equitable Mathematics Education Through Pursuing Quantitative Reasoning, Kyle Kimball

Honors Capstones

The purpose of this project is to develop means of addressing discrepancies between the mathematics education of students from different socioeconomic backgrounds. The central question of the project is: How can I as a teacher foster quantitative reasoning so that underrepresented students gain access to meaningful understanding of mathematics? Access to mathematics is important in order to gain access to economic opportunities, meaning it is essentially a social justice issue. The project entailed secondary research of existing paradigms and research projects. The major finding of the project is that some of the classroom causes of inequity in mathematics education can …

Investigating Latina/O Mathematics Students' Perceptions Of Interpersonal Relationships In College Mathematics, Victoria Rose Larabell

Open Access Theses

It is known that interpersonal relationships are significant to the success of the Latina/o mathematics learner. Unfortunately, interpersonal relationships in mathematics are understudied. For this reason, this study seeks to answer the following question: How do Latina/o mathematics students perceive their interpersonal relationships with their mathematics professors, peers in mathematics, and families with respect to mathematics? To explore the role of such relationships in Latinas/os experiences in mathematics, I define a meaningful relationship in mathematics education (MRIME) as interactions between two parties in which one party acknowledges the other party as a sociocultural being and fosters their mathematics identity. This …

Math Education At Its Prime?, Natalie Benet

Senior Honors Theses

Three main problems with current math education are negative mindsets toward math, the lagging comparison with advanced education in other countries, and ill-equipped teachers and school systems. The consequences of these problems have impacted math education by convincing students that they do not need to try at math, filling countless classrooms with ill-qualified teachers, and overall lowering the quality of U.S. math education compared to the education of rest of the world. In order to correct these problems and reverse the present and future consequences, the quality of math education must be increased. This can be done by changing the …

Dismantling The Birdcage : Adolescent Girls' Attitudes Towards Learning Mathematics With A Relational Pedagogy In A Problem-Based Environment, Carmel Schettino

Legacy Theses & Dissertations (2009 - 2024)

Although the Gender Achievement Gap is closing in mathematics, the "interest gap" in pursuing STEM fields is not. Mathematics education research has discussed constructivist, student-centered and inclusive methods of teaching that have been found to encourage students that have underachieved and been underrepresented in STEM fields. One recommendation for encouraging young women to continue in their mathematical studies is to find instructional methods that allow them to feel included in the learning process and "unfix" the dichotomous, gendered socio-cultural view of mathematics and the mathematics classroom fostering positive attitudes such as self-confidence, empowerment and agency.

The Impact Of Teachers' Characteristics And Self-Reported Practices On Students' Algebra Achievement, Liza Cope

Legacy Theses & Dissertations (2009 - 2024)

This study examined the impact of teachers' characteristics and self-reported practices on students' Algebra achievement while controlling for students' characteristics. This study is based on the secondary analysis of data collected from a nationally representative sample of 9th grade students and their mathematics teachers during the base year of the High School Longitudinal Study of 2009 (HSLS). Student and teacher data were obtained through questionnaires and students' Algebra achievement was measured by an ability-adaptive assessment designed to measure a cross-section of understandings representative of the six major Algebraic content domains (The language of algebra; Proportional relationships and change; Linear equations, …

Coloring Pythagorean Triples And A Problem Concerning Cyclotomic Polynomials, Daniel White

Theses and Dissertations

One may easily show that there exist $O( \log n)$-colorings of $\{1,2, \ldots, n\}$ such that no Pythagorean triple with elements $\le n$ is monochromatic. In Chapter~\ref{CH:triples}, we investigate two analogous ideas. First, we find an asymptotic bound for the number of colors required to color $\{1,2,\ldots ,n\}$ so that every Pythagorean triple with elements $\le n$ is $3$-colored. Afterwards, we examine the case where we allow a vanishing proportion of Pythagorean triples with elements $\le n$ to fail to have this property.

Unrelated, in 1908, Schur raised the question of the irreducibility over $\Q$ of polynomials of the form …

On A Theorem Of Livsic, William T. Ross, Alexandru Aleman, R. T. W. Martin

Department of Math & Statistics Faculty Publications

The theory of symmetric, non-selfadjoint operators has several deep applications to the complex function theory of certain reproducing kernel Hilbert spaces of analytic functions, as well as to the study of ordinary differential operators such as Schrodinger operators in mathematical physics. Examples of simple symmetric operators include multiplication operators on various spaces of analytic functions such as model subspaces of Hardy spaces, deBranges-Rovnyak spaces and Herglotz spaces, ordinary differential operators (including Schrodinger operators from quantum mechanics), Toeplitz operators, and infinite Jacobi matrices.

In this paper we develop a general representation theory of simple symmetric operators with equal deficiency indices, and …

Direct And Reverse Carleson Measure For Hb Spaces, William T. Ross, Alain Blandigneres, Emmanuel Fricain, Frederic Gaunard, Andreas Hartmann

Department of Math & Statistics Faculty Publications

In this paper we discuss direct and reverse Carleson measures for the de Branges-Rovnyak spaces H(b), mainly when b is a non-extreme point of the unit ball of H^∞.

Oddification Of The Cohomology Of Type A Springer Varieties, Heather M. Russell, Aaron D. Lauda

Department of Math & Statistics Faculty Publications

We identify the ring of odd symmetric functions introduced by Ellis and Khovanov as the space of skew polynomials fixed by a natural action of the Hecke algebra at q = −1. This allows us to define graded modules over the Hecke algebra at q = −1 that are ‘odd’ analogs of the cohomology of type A Springer varieties. The graded module associated to the full flag variety corresponds to the quotient of the skew polynomial ring by the left ideal of nonconstant odd symmetric functions. The top degree component of the odd cohomology of Springer varieties is identifiedwith the …

Model Spaces: A Survey, William T. Ross, Stephan Ramon Garcia

Department of Math & Statistics Faculty Publications

This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.

Undergraduate And Graduate Teaching Assistants' Perceptions Of Their Responsibilities - Factors That Help Or Hinder, Alena Moon, Hyunyi Jung, Farshid Marbouti, Kelsey Joy Rodgers, Heidi A. Diefes-Dux

Mathematics, Statistics and Computer Science Faculty Research and Publications

Effective teaching assistants (TAs) are crucial for effective student learning. This is especially true in science, technology, engineering, and mathematics (STEM) programs, where TAs are enabling large programs to transition to more student-centered learning environments. To ensure that TAs are able to support these types of learning environments, their perspectives of training, their abilities, and other work related aspects must be understood. In this paper a survey that was created based on interviews conducted with eight TAs is discussed. The survey has four primary categories of content that are critical for understanding TAs' perspectives: (1) background, (2) motivation, (3) training, …

Numerical And Analytical Methods For Variational Inequalities And Related Problems 2013, Zhenyu Huang, Ram N. Mohapatra, Shih-Sen Change, Qingzhi Yang

Faculty Bibliography 2010s

No abstract provided.

A Case Study Exploring The Relationship Between Culturally Responsive Teaching And A Mathematical Practice Of The Common Core State Standards, Tashana Howse

Electronic Theses and Dissertations

This collective case study explores the nature of the relationship between teachers’ use of culturally responsive teaching (CRT) practices and students’ engagement in constructing viable arguments and critiquing the reasoning of others (SMP3). This study was informed by the Common Core State Standards Initiative related to developing mathematically proficient students through the use of student engagement practices consistent with the standards for mathematical practice. As a means to support teachers’ facilitating specific student engagement practices, professional development was provided. This study is situated in the growing body of research associated with student engagement and cultural identity. The case of two …

A Statistical Analysis For Estimating Fish Number Density With The Use Of A Multibeam Echosounder, Madeline L. Schroth-Miller

Master's Theses and Capstones

Fish number density can be estimated from the normalized second moment of acoustic backscatter intensity [Denbigh et al., J. Acoust. Soc. Am. 90, 457-469 (1991)]. This method assumes that the distribution of fish scattering amplitudes is known and that the fish are randomly distributed following a Poisson volume distribution within regions of constant density. It is most useful at low fish densities, relative to the resolution of the acoustic device being used, since the estimators quickly become noisy as the number of fish per resolution cell increases. New models that include noise contributions are considered. The methods were applied to …