The world has experienced rapid changes, leading to pressing issues such as environmental degradation, social inequality, and resource depletion. As a transdisciplinary field, evaluation has emerged as a crucial tool in addressing these challenges and promoting systemic change. However, concerns have been raised regarding the field's capacity to…

In the first main section of this thesis, I investigate superirreducible polynomials over fields of positive characteristic and also over [set of rational numbers] and [set of integers]. An n-superirreducible polynomial f(x) is an irreducible polynomial that remains irreducible under substitutions f(g(x)) for g of degree at most n. I find…

One expected outcome of physics instruction is that students develop quantitative reasoning skills, including evaluation of problem solutions. To investigate students' use of evaluation strategies, we developed and administered tasks prompting students to check the validity of a given expression. We collected written (N > 673) and interview (N…

It is common for students to make mistakes while solving mathematical problems. Some of these mistakes might be caused by the false ideas, or misconceptions, that students developed during their learning or from their practice. Calculus courses at the undergraduate level are mandatory for several majors. The introductory course of…

Computational thinking (CT) has been an increasing focus of research and practice since the seminal paper by Wing in 2006, especially in pre-college (K-12) education. Barr and Stephenson defined CT as a problem-solving methodology that can be automated, transferred, and applied across disciplines. With the challenges of fitting CT into already…

Problem-solving, collaboration, and adaptability to in-person and virtual environments are critical for success today. Therefore, brick-and-mortar and online instructional models have shifted to ensure that K-12 students are prepared with these skills for 21st-century challenges. Grounded in systems theory, the study examined the inputs,…

Some professional learning communities (PLC) are successful, and others are unsuccessful leading to questions about which characteristics of a group of people are important to the success of the community. The purpose of this qualitative case study was to understand the factors contributing to the presence of a community of practice between…

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…

The objective of this dissertation was to explore the paradoxical nature of Combinatorics as both a difficult and accessible domain in Mathematics, particularly for K-12 students. This paradox in Combinatorics' nature raised questions about how students interact with problems in this domain and the factors influencing their understanding and…

In this portfolio, I reflect on my efforts to provide professional development targeted to support teachers during the launch phase of their mathematics teaching, to elicit and respond to student ideas and experiences. I grounded my study in research on ambitious teaching practices for launching complex mathematical tasks using problem-based…

This convergent mixed methods study investigated the relationship between the assessment-capable learning (ACL) instructional model, John Hattie's influence referred to as "students driving their own learning," and math achievement in kindergarten. While Visible Learning literature has focused on secondary and higher education, this…

The issue of low math performance, particularly in schools serving historically marginalized communities, requires immediate attention. Despite implementing various interventions, including leadership changes, curriculum updates, and hiring consultants, student achievement in math has remained stagnant at Ida B. Wells Academy (Wells). This case…

Writing center consultations are built of writer and consultant relationships, interactions, and differences. Listening is a stance that facilitates navigation of these differences that are so inherent to writing centers. Yet listening has long been undervalued in Western society and in rhetoric and composition and writing center scholarship. To…

The purpose of this study was to identify perceived challenges that mentor and mentee teachers face within the teacher induction program in the rural school district of Greenway County. The different perceptions of mentor and mentee teachers will provide rich insight regarding the challenges teachers face within these programs. The challenges…

The purpose of this quantitative correlational study was to determine if, or to what extent, the soft skills of a principal, as perceived by their teachers, can predict a positive school climate at the middle school level in a large Independent School District (ISD) in southeast Texas. The theoretical constructs of attribution and emotional…