Play has been discussed by mathematicians and mathematics educators as essential to mathematical progress and has been widely acknowledged to have a role in learning. Yet, play is rarely acknowledged, leveraged, or studied for mathematics learners beyond early childhood. Moreover, there are theoretical and empirical challenges with designing for…

Research results from this study reveal students have difficulties understanding and using of the concepts of average rate of change and the derivative function. Students in this study held multiple approach to understand the concepts that made it difficult to develop a strong understanding of the average rate of change and derivative function. In…

This dissertation investigates gender differences in (1) retrospective (i.e., measured after task completion) item-specific confidence judgments, and whether these judgments were warranted. Of particular interest was whether gender interacts with problem difficulty to explain confidence, calibration (speaks to the accuracy of confidence…

This dissertation explores the intricate dynamics between the self-perceptions of undergraduate mathematics (UM) educators and their conceptions of excellent teaching practices conducive to student learning. Employing a sequential mixed methods approach, the study addresses two primary research questions. First, it investigates educators'…

The purpose of this study was to examine the effects of a vocabulary tutoring intervention with defining key vocabulary terms and algebraic problem-solving skills of students who struggle with mathematics. Literature shows that there is a need to further explore how students with mathematical learning difficulties learn mathematics vocabulary at…

This study examined mathematics self-efficacy and the characteristics of flow in the context of performing mathematical tasks. In particular, it explored the subjective experiences of 113 undergraduate students enrolled in a developmental mathematics course while they were independently solving certain mathematical problems. This study…

As our society has become increasingly data dependent, statistics education has emerged as a field of study. Research has focused on statistics course content outcomes, showing most students struggle with statistical concepts, including variation and the standard deviation. Variation is a foundational concept in statistics. Without a firm grasp of…

Serving approximately 80% of the one million college students taking pre-college-level mathematics classes, community colleges perform an important function in providing access to advanced coursework and degrees. Low success rates in these classes has led mathematics educators to consider alternative forms of curriculum and instruction for these…

In this thesis, I study some aspects of how students learn to use math to make sense of physical phenomena. Solving physics problems usually requires dealing with algebraic expressions. That can take the form of reading equations you're given, manipulating them, or creating them. It's possible to use equations simply according to formal rules of…

This quantitative longitudinal study sought to highlight the difference between the proportion of men and women who planned to pursue a STEM major in the fields of mathematics, natural sciences, engineering, and computer and information sciences as freshmen, as well as to determine the proportion of men and women who changed their major choice by…

Past research has shown that students have difficulty developing a robust conception of function. However, little prior research has been performed dealing with student knowledge of function composition, a potentially powerful mathematical concept. This dissertation reports the results of an investigation into student understanding and use of…

The research literature has made calls for greater coherence and consistency with regard to the meaning and use of the term advanced mathematical thinking (AMT) in mathematics education (Artigue, Batanero, & Kent, 2007; Selden & Selden, 2005). Educators and researchers agree that students should be engaged in AMT but it is unclear…

The ability to succeed in Science, Technology, Engineering, and Mathematics (STEM) careers is contingent on a student's ability to engage in mathematical problem solving. As a result, there has been increased focus on students' ability to think critically by providing them more with problem solving experiences in the classroom. Much research has…

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…

Students experience difficulty learning and understanding chemistry at higher levels, often because of cognitive biases stemming from common sense reasoning constraints. These constraints can be divided into two categories: assumptions (beliefs held about the world around us) and heuristics (the reasoning strategies or rules used to build…