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…

Students come to their high school physics classroom with experiences and knowledge that can be used to help explain physics concepts, but those experiences may not fully align with the scientifically accepted science concept. When there is a misalignment between a student's prior knowledge and the scientifically accepted concept a misconception…

This study examined the engagement of preservice elementary teachers (PSTs) with mathematics tasks that were open in various ways and to varying extents. In K-12 settings, practitioners who have implemented recently popular open tasks report increased engagement and from a wider variety of students. While these anecdotal reports and related…

Epistemic beliefs, epistemic cognitions, and self-regulation processes have a significant role in students' learning. Through this study, I investigated the role of mechanical engineering students' epistemic beliefs and epistemic cognitions involved in self-regulation processes while working on tasks with different difficulty levels. In this…

This dissertation adopted the three-article format. The entire dissertation aims to explore Describing Critical Statistical Literacy Habits of Mind (CSLHM). The first article describes the creation of the CSLHM framework. The second describes how secondary preservice mathematics teachers enact CSLHM. The third article describes a common and an…

Broad exploration is often the best way to solve complex problems because the best solution might not come to mind first. Consequently, creative thinking, like simulated annealing, begins with a "hot" exploratory phase of broad solution search and gradually "cools" to exploitation and narrowing the search space. In solving…

As schools continue to focus on outcome-based instructional practices, less emphasis is placed on the creativity and reasoning necessary for students to become effective critical thinkers. As a result, students struggle to demonstrate creative problem-solving skills in the classroom. This study examines how the facilitation of an instructional…

This quantitative study, administered at a higher education institution, looked at what variation exists among immigrant students, domestic students, and international students as determined by analysis in the HERI CIRP Freshman Survey as measured by responses to Habits of Mind questions. Habits of Mind is a framework of attributes that focus on…

Problem solving is one of the most essential aspects of human life. Every day, people engage in problem solving any time they attempt to resolve uncertain issues or questions. Of utmost importance, in order to resolve problems effectively, people must "build them" by interacting with situations. In other words, people must actively…

I have created a general workflow that describes how students reason through non-trivial organic predict-the-product problems. This was accomplished through an iterative process that combined the experiences of instructors with holistic impressions of think-aloud interviews, incorporating feedback from both undergraduate focus groups and graduate…

A solid foundation in mathematics is beneficial not only for individuals' concurrent and later academic achievement, but also for future career success and financial stability. Rational number knowledge plays a pivotal role in mathematical success, yet it is often regarded as a challenging area to grasp comprehensively. The dissertation aims to…

This quantitative study examined the relationship between well-being and stages of the creative process, including problem identification and construction, idea generation, and idea evaluation among gifted young adults (n = 173). A sample of college honors students responded to multiple measures of well-being, creative problem-solving tasks, the…

Teaching and learning mathematics in an elementary classroom is a complex process in negotiating a balance in encouraging participation, responding to students, making connections between interactions, and planning for upcoming interactions. In a search for instructional models and structures that support and encourage student engagement in…

Information security practitioners and researchers who possess sufficient depth of conceptual understanding to reconstitute systems after attacks or adapt information security concepts to novel situations are in short supply. Education of new information security professionals with sufficient conceptual depth is one method by which this shortage…

National mathematics achievement results show that elementary students in the United States are not increasing in cognitive ability or critical thinking skills (NAEP, 2020). For this increase, mathematically promising students require more opportunities for cognitively demanding mathematics instruction. As a result, this descriptive study focused…