Are there developmental pathways for learning that provide continuity from early learning through adulthood with measurable intervals for assessment and with transitions for learning that are understandable, stable, identifiable, communicable, flexible, and affordable to implement? If so, what are the foundations for learning that enable students…

Cognitive development of eighth-grade students, as identified by Jean Piaget, occurs during a time when many of them are transitioning between concrete operations and formal operations where the ability to think in abstract concepts becomes possible. Because of this period of transition, many eighth-grade students find difficulty in demonstrating…

This dissertation describes an experiment to investigate how learners with different levels of background in computer science learn core concepts of computer science, in particular, algorithms. We designed a study to focus on cognitive task analysis for eliciting the empirical mental elements of learning two graph algorithms. Cognitive workload…

This dissertation documents a new way of conceptualizing vectors in college mathematics, especially in geometry. First, I will introduce three problems to show the complexity and subtlety of the construct of vectors with the classical vector representations. These highlight the need for a new framework that: (1) differentiates abstraction from a…

This research explored online graduate students' preferences using the Constructivist Internet-Based Learning Environment Survey (CILES) and how everyday learner attributes affected their preferences. The purpose of this study was to identify graduate students' preferences for various types of learning in order to aid designers with aligning…

Mathematics is an increasingly important aspect of education because of its central role in technology (Kuenzi, 2008). Mathematical achievement tests are universally applied throughout schooling in the US to assess yearly progress. The middle school years (e.g., Grade 6-Grade 8) are especially crucial to success in mathematics because students…

This mixed-methods study explored the influence and applicability of the Perry Scheme to students from mainland China studying in the U.S. The purpose of this mixed methods study was to explore the intellectual and ethical development of students from mainland China enrolled in a U.S graduate engineering program using the Perry Scheme of…