This qualitative study examines how playing levels of a fraction-themed videogame impacts students' thinking. The research question answered is: What do students' gestures reveal about the degree to which their thinking is embodied as they play a videogame that is constructed via a grounded metaphor for mathematical knowledge. Four soon-to-be…

Mathematical definitions are central to learning and doing mathematics. Research has uncovered significant differences between how mathematicians and non-mathematicians construct, reason about, and refine mathematical definitions. Various strands of research provide insight into the development of definitional practices, yet an integrated approach…

A solid foundation in mathematics is beneficial not only for individuals' concurrent and later academic achievement, but also for future career success and financial stability. Rational number knowledge plays a pivotal role in mathematical success, yet it is often regarded as a challenging area to grasp comprehensively. The dissertation aims to…

Deaf and hard of hearing (DHH) students' performance on fraction story problems is a cause for concern given that knowledge of fractions in the elementary grades is essential for learning Algebra in secondary school and advanced mathematics in college. Using grounded theory, the current study investigated DHH college students' cognitive strategies…

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…

Expertise in teacher noticing of children's thinking is central to a vision of responsive teaching in which teachers regularly elicit and build on children's thinking during instruction (Richards & Robertson, 2016). In mathematics classrooms, this core instructional practice of noticing children's mathematical thinking repeatedly occurs during…

The purpose of the study was to explore the cognitive profiles associated with inadequate responsiveness to fractions intervention on 3 fractions outcomes (calculations, ordering, and word problems). At the start of 3rd grade, 2 cohorts of students (N = 124) identified at the start of intervention as at-risk for mathematics difficulties were…

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…