In this dissertation, I utilize the post-structural philosophy of Gilles Deleuze and Fe´lix Guattari as a lens for investigating the proof process. Deleuze and Guattari were both post- structural philosophers who, like many in this tradition, troubled traditional notions related to stable identities, meaning, language, and mathematics. For…

Undergraduate students' choices and success in their career and life is influenced by their mathematics achievement and perception of themselves in life. Conceptual understanding of topics in undergraduate mathematics such as quantitative reasoning can be difficult for students with less sophisticated multiplicative reasoning than others. This…

This dissertation develops and evaluates the validity and reliability of the Skills Self-Efficacy Scale for Adolescents (SSES-A), a measure designed to assess adolescents' self-efficacy in critical future skills: problem-solving, communication, creativity, collaboration, and critical thinking. Anchored in Social Cognitive Theory and Psychometric…

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 purpose of this study is to explore elementary educators' perceptions regarding what it means to conceptually understand mathematics, the emphasis teachers place on utilizing evidence-based teaching processes, as identified as effective by National Council of Teachers of Mathematics (NCTM), and how these perceptions influence their…

The purpose of this non-experimental research study was three-fold: (1) to investigate the relationships among the attributes of creative problem solving ability (divergent thinking, convergent thinking, motivation, general knowledge and skills, and environment) and their relationships in the humanities (specifically those that took enrichment…

Human-centered design requires thorough understanding of people (e.g. customers, designers, engineers) in order to better satisfy the needs and expectations of all stakeholders in the design process. Designers are able to create better products by incorporating customers' subjective evaluations on products. Engineers can also build better tools…

Higher order thinking skills have been embedded into state teaching standards, including Standard 9 of the New Jersey Core Curriculum Content Standards (NJCCCS) for 21st Century Life and Careers. These standards aim to encourage problem solving, critical thinking, reasoning, and real-world application in order to prepare students for the workplace…

Institutions of higher education often promise to graduate individuals capable not only of excelling in their area of expertise but also qualified as exceptional leaders and citizens. Yet, what are the competencies needed from leaders in order to address the most challenging issues facing society? How would higher education cultivate the next…

Rapid advancements in technology, global competitiveness, and an increasing demand for 21st-century skills, such as problem-solving, underscore the pivotal role teachers play to prepare our youth for an era of exponential change. Those at the forefront of education are challenged to equip students with skills and strategies necessary to think…

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 study, I examined the relation between various construct relevant and irrelevant variables and a math problem solving assessment. I used independent performance measures representing the variables of mathematics content knowledge, general ability, and reading fluency. Non-performance variables included gender, socioeconomic status,…

Topics in trigonometry have not been well-studied, especially with college-level students. Thus, despite providing a venue for important concepts such as notions of proof and algebraic skill, the process of verifying trigonometric identities, or VTI, has not been thoroughly explored. This study attempts to remedy this gap in the literature by…

The purpose of this research is to find the relationships among attributes of creative problem solving ability and their relationships with the Math Creative Problem Solving Ability. In addition, the attribute patterns of high, medium, and low mathematical creative groups were identified and compared. There were 409 fifth and sixth graders…

This study was designed to investigate the predictive relationships of creative problem-solving attributes, which comprise divergent thinking, convergent thinking, motivation, general and domain knowledge and skills, and environment, with mathematical creativity of sixth grade students in Thai Nguyen City, Viet Nam. The study also aims to revise…