Understanding fractions, especially their magnitude, is essential for success in mathematics. Unfortunately, fractions are one of the most challenging mathematics concepts to teach and learn. Several studies have examined preservice teacher (PST) knowledge of fractions, but very few studies have looked for ways to improve this knowledge. This…

With the changes in Common Core State Standards, it was essential to explore how elementary pre-service teachers' sense of fractions is developing and their thoughts about how to teach fractions. A gap in practice exists because it is unknown how pre-service elementary teachers, after student-teaching, perceive their level of in-practice knowledge…

Fractions are foundational for success in algebra and STEM, but they are notoriously difficult for students. In past work, two separate branches of research from psychology and math education have studied fractions knowledge using different, isolated approaches. In this dissertation, I synthesize research from both fields about proportional…

Research on fraction knowledge has revealed that prospective teachers' (PSTs) often lack fraction proficiency. The aim of this dissertation was to develop and test an intervention intended to increase PSTs' fraction proficiency by focusing on fraction comparison. I first adopted a five-dimensional framework to define PSTs' fraction proficiency. I…

This dissertation case study examines how teachers' levels of units coordination afford their ability to reason multiplicatively and fractionally, as well as use their mathematics knowledge for teaching to analyze student multiplicative and fractional reasoning, when a two-year intervention is put into place to evoke new mathematical reasoning.…

Twenty-five first-year preservice teachers attending a university in the Midwest of the United States of America participated in a whole-class-setting study aimed at investigating their knowledge of how they made sense of fraction concepts and operations, and how the development of this knowledge was facilitated during a mathematics education…

Fractions--their concepts, procedures, and symbolic notation--are well-known for the difficulty they present children, beginning in elementary school, and often, persisting long after. However, promoting children's development of flexible and robust conceptual knowledge in this content area is critical for their success both in and out of school.…

Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input, yet also requires cognitive supports. My dissertation sought to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning.…

Fractions are highly important. Therefore, it is crucial to understand the developmental trajectory of fraction knowledge and its main predictors and consequences. Our research team has proposed that we have a neurocognitive architecture dedicated to processing nonsymbolic ratios, which serves as a startup tool for fractions: the Ratio Processing…

Recent data from a cross-national assessment, the Programme for International Student Assessment (PISA), place the United States performance in mathematics at 38 out of 71 countries (OECD, 2016)--one clear indication of the ongoing need for the improvement of mathematics education. This improvement relies, in part, on improving undergraduate…

"A critical pillar of a strong PreK-12 education is a well-qualified teacher in every classroom" (Conference Board of Mathematical Sciences, 2012, p. 1). In order for teachers to help students build procedural fluency from conceptual understanding and meet the standards set forth by governing agencies, prospective teachers will need deep…

The purpose of this study was to examine adult developmental mathematics (ADM) students' knowledge of fraction addition and subtraction as it relates to their demonstrated fraction schemes and ability to disembed in multiplicative contexts with whole numbers. The study was conducted using a mixed methods sequential explanatory design. In the first…

The current study investigated college students' content knowledge and cognitive abilities as factors associated with their algebra performance, and examined how combinations of content knowledge and cognitive abilities related to their algebra performance. Specifically, the investigation examined the content knowledge factors of computational…

With the recent emergence of online professional development (PD), such opportunities are increasingly available to educators. It is important, then, to assess whether and how such options can be valuable and effective for them. The goal of this study was to assess whether and how a Massive Open Online Course for Educators (MOOC-Ed) can serve as…

Educational video games have the potential to be used as assessments of student understanding of complex concepts. However, the interpretation of the rich stream of complex data that results from the tracking of in-game actions is so difficult that it is one of the most serious blockades to the use of educational video games or simulations to…