In the first part, we investigate Birman, Ko, and Lee's left canonical form of a braid and give a new diagrammatic approach. We use the left canonical form to characterize almost strongly quasipositive braids. In the second part, we investigate students' confidence in mathematics and problem solving skills. Every math instructor has heard students…

The American School Counselor Association has placed an increased emphasis on school counselor leadership. School counselors play an essential role within the educational setting (ASCA, 2019). Leadership embodies the overarching role of a school counselor and is a key component of each school counselor's professional identity (McMahon et al.,…

In this dissertation, I explored students' expressed emotions as they worked on a problem-solving lab contextualizing the local lead poisoning issue in the city in which they attended college. I identified students' expressed emotions and their reasoning for expressing those emotions. I also looked at the change in students' emotions as they…

There is a strong need for fifth-grade students to become proficient in mathematical problem-solving using fractional computations because it will have a lasting impact on student achievement. Traditionally, mathematics is taught inside a brick-and-mortar classroom, grounded in rote memorization of facts, rules, and formulas. In recent years, more…

Dual-credit programs, also known in the state of Ohio as the College-Credit-Plus program, is an initiative across the United States to provide another method for high school students--and sometimes even younger students--to earn postsecondary credit before graduating from high school. This project investigates the experience of dual-credit…

Undergraduate students in an education program, or preservice teachers, are expected to practice and teach productive struggle in mathematics as they prepare for their career. Productive struggle in mathematics requires students to persevere in solving rigorous tasks, despite their frustration in doing so. Therefore, a student's level of…

Background: With around 200,000 autistic students set to enter universities and the workforce in the next decade, inclusive programs are receiving increased attention to helping educational systems carefully integrate these students' needs. Moreover, educational programs recognize that problem-solving is critical for school success and optimal…

SWLD are often underperforming in STEM courses compared to their peers without learning difficulties. Furthermore, how students perform in 9th grade is found to be a strong predictor of high school success, graduation, enrolling, and persisting in college (Easton et al., 2017). The study aimed to investigate whether the use of PBA, a…

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…

Methods of teaching differential equations (DE) have long focused on rote analytic solution methods that align poorly with more industry-relevant numerical and computational methods. Engineering and mathematics educators agree that there is a need to shape DE curricula to reflect the mathematical practices of the disciplines whose students take…

Non-formal STEM education programs can expose youth to STEM concepts outside the formal school environment. These programs employ education techniques such as hands-on learning, problem-solving, and connection to authentic science experiences. Youth participating in non-formal STEM programs are more likely to consider themselves science people and…

This explanatory sequential mixed methods study, which consisted of QUAN [right arrow] to qual investigated the impact of mathematics word problems among African American students in the seventh grade. This study applied a culturally relevant education (CRE) lens to examine how students solve mathematics word problems. Ladson-Billings (1997) and…

This study sought to compare the effectiveness of teaching with manipulatives versus algorithms and procedures. Assessment data were collected before instruction, after instruction with algorithms and procedures, and after instruction with modeling and manipulatives. Data were collected from 113 students from the 5th, 6th, and 7th grades within…