Diagnostic classification models (DCMs) are structured latent class models widely discussed in the field of psychometrics. They model subjects' underlying attribute patterns and classify subjects into unobservable groups based on their mastery of attributes required to answer the items correctly. The effective implementation of DCMs depends…

A key issue of cognitive diagnostic models (CDMs) is the correct identification of Q-matrix which indicates the relationship between attributes and test items. Previous CDMs typically assumed a known Q-matrix provided by domain experts such as those who developed the questions. However, misspecifications of Q-matrix had been discovered in the past…

1.2 billion users in Facebook, 17 million articles in Wikipedia, and 190 million tweets per day have demanded significant increase of information processing through Internet in recent years. Similarly life sciences and bioinformatics also have faced issues of processing Big data due to the explosion of publicly available genomic information…

Alternative high schools serve some of the most vulnerable students and their programs present a significant challenge to evaluate. Determining the impact of an alternative high school that serves mostly at-risk students presented a significant research problem. Few studies exist that dig deeper into the characteristics and strategies of…

High performance, massively-parallel multi-physics simulations are built on efficient mesh data structures. Most data structures are designed from the bottom up, focusing on the implementation of linear algebra routines. In this thesis, we explore a top-down approach to design, evaluating the various needs of many aspects of simulation, not just…

This Capstone project studied a pilot of the web-based homework system "Hawkes" in developmental mathematics classes at a mid-sized community college. The purpose of the study was to investigate how three instructors of developmental mathematics courses incorporated "Hawkes" in their classes, what obstacles they encountered,…

The growth of online programs has been substantial over the past decade; such growth has required that an equally substantial number of faculty become proficient in the pedagogy of online learning and the best practices in online course design. At the same time, universities are being called on to provide evidence of student learning and…

This thesis investigates and develops a few acceleration techniques for the search engine algorithms used in PageRank and HITS computations. PageRank and HITS methods are two highly successful applications of modern Linear Algebra in computer science and engineering. They constitute the essential technologies accounted for the immense growth and…

Like many colleges across the United States, Pipe Lake Community College (PLCC), (a pseudonym) has experienced a dramatic increase in enrollment of Latina/o students and is considered an emerging Hispanic Serving Institution (HSI). Other than Santiago & Andrade's (2010) survey, little research has been conducted on emerging HSIs. Also, little…

Combinatorial scientific computing plays an important enabling role in computational science, particularly in high performance scientific computing. In this thesis, we will describe our work on optimizing matrix-vector multiplication using combinatorial techniques. Our research has focused on two different problems in combinatorial scientific…

In this study, I considered the development of mathematical meaning related to the Invertible Matrix Theorem (IMT) for both a classroom community and an individual student over time. In this particular linear algebra course, the IMT was a core theorem in that it connected many concepts fundamental to linear algebra through the notion of…

Little is known about the variety of ways students conceptualize matrix multiplication, yet this is a fundamental part of most introductory linear algebra courses. My dissertation follows a three-paper format, with the three papers exploring conceptualizations of matrix multiplication from a variety of viewpoints. In these papers, I explore (1)…

Numerous procedures have been suggested for determining the number of factors to retain in factor analysis. However, previous studies have focused on comparing methods using normal data sets. This study had two phases. The first phase explored the Kaiser method, Scree test, Bartlett's chi-square test, Minimum Average Partial (1976&2000),…