The purpose of this study was to determine effects of implementing metacognitive practices on the engagement of students in secondary mathematics courses. The study was guided by two primary inquiry questions that focused on the current implementation of metacognitive practices in the mathematics courses as well as the perceived change in student…

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…

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…

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…

Given the well documented fact students often struggle with proof and proof-related activity for various reasons, more educators have shifted to incorporating pedagogies involving collaborative learning given their benefits to student learning. However, there is still surprisingly little research focused on the nature of students' collaborative…

Mathematics plays a crucial role in engineering education. Students who are good at math are often advised to consider engineering as a career. In this study, engineers, mathematics teachers, and engineering professors were asked about the type of mathematics representative of engineering, whether the engineering problems created by math…

The study examines the perspectives of using the Desmos calculator of Algebra I students' conceptual understanding and procedural fluency to write, graph, and solve linear equations in Algebra I STAAR. While the students have continuously used technology for mathematics assessment, emergent bilingual students in South Texas still need help passing…

Probabilistic simulations have long served as instructional tools in statistics and probability education. With advances in technology, computer simulation environments where large quantities of data can be collected and analyzed have been suggested as venues for problem solving in contexts involving both known and unknown probability…

Many questions have been asked about how to teach math, how to get students to like math, how to engage students in math and how to increase math scores. Metacognition and Self-Regulated Learning (SRL) have an impact on mathematics achievement in middle school students. In this quantitative study, the Self-Reflection Questionnaire, MKMQ was used…

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…

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…

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…

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,…

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…