Knowledge assessments in undergraduate mathematics education commonly evaluate response correctness to determine learner proficiency. However, simultaneous evaluation of learner metacognition more accurately assesses the multiple dimensions of knowledge and has been shown to increase assessment validity and reliability. Research into…

This study sought to explore whether access to definitions and general representations influences the construction of general direct arguments. Data was collected in college mathematics courses for prospective elementary school teachers. Participant arguments were analyzed along two variables: the generality of the representations and the…

Analogical reasoning has played a significant role in the development of modern mathematical concepts. Although some perspectives in mathematics education have argued against the use of analogies and analogical reasoning in instructional contexts, some attempts have been made to leverage the pedagogical power of analogies. I assert that with a…

Inquiry-oriented teaching is a specific form of active learning gaining popularity in teaching communities. The goal of inquiry-oriented classes is to help students in gaining a conceptual understanding of the material. My research focus is to gauge students' performance and conceptual understanding in inquiry-oriented linear algebra classes. This…

The role of the community college is constantly evolving. At its inception in the early 1900's, the community college's broad focus was to provide quality, affordable education to the members of the community the college serves. Today, that focus remains the same, but has also morphed into one that meets the specific needs of its students. One of…

In this research, I set out to elucidate the relationships that might exist between students' conceptual understanding upon which they draw in their proof activity. I explore these relationships using data from individual interviews with three students from a junior-level Modern Algebra course. Each phase of analysis was iterative, consisting of…

The purpose of this research is to provide information about the psychometric properties of technology-enhanced (TE) items and the effects these items have on the content validity of an assessment. Specifically, this research investigated the impact that the inclusion of TE items has on the construct of a mathematics test, the technical properties…

This dissertation consisted of three different, but conceptually related manuscripts. The series of manuscripts examined psychosocial factors of learning including attitude towards mathematics, motivation to learn mathematics, and satisfaction from the mathematics instruction in both redesigned and traditionally- taught college algebra courses at…

Over the past thirty years, policies have been enacted at the local and state levels to reform mathematics instruction to be student-centered (see Cohen & Ball, 1990; Resnick, Stein, & Coon, 2008). Despite the wave of instructional reforms, several critical gaps remain in our understanding of student-centered mathematics instruction.…

The purpose of this study was to determine the extent to which the modeling of deductive reasoning and proof-type thinking occurs in a mathematics course in which students are not explicitly preparing to write formal mathematical proofs. Algebra was chosen because it is the course that typically directly precedes a student's first formal…

Becoming a skillful prover is critical for success in advanced undergraduate and graduate mathematics courses. In this dissertation, I report my investigations of proof and the proving process in three separate studies. In the first study, I examined the amount of logic used in student-constructed proofs to help in the design of…

In this thesis, our aim is the study the Vanishing of Maps of Tor Conjecture of Hochster and Huneke. We mainly focus on an equivalent characterization called the Strong Direct Summand Conjecture, due to N. Ranganathan. Our results are separated into three chapters. In Chapter 3, we prove special cases of the Strong Direct Summand Conjecture in…

The purpose of this study was to examine the impact of the number of transitions by students from school to school on their mathematics achievement. Transition is defined as the number of times a student has changed schools from Kindergarten to the current school year. This study also looked at the relationship between the students' perceived…

Current reforms in undergraduate mathematics education devoted to proof and counterexample highlight its importance in teaching and learning mathematics. While undergraduate students who have taken a number of upper-level mathematics courses are expected to have mastered the skills required to verify statements as well as to read and write proofs…

The purpose of the study was to determine the technical adequacy of the Core Skills Algebra curriculum-based measure for students enrolled in algebra I courses at the high school level. Due to the dearth of curriculum-based measures available to educators at the secondary school level, the Core Skills Algebra curriculum-based measure was developed…