The ideas of measurement and measurement comparisons (e.g., fractions, ratios, quotients) are introduced to students in elementary school. However, studies report that students of all ages have difficulty comparing two quantities in terms of their relative size. Students often understand fractions such as 3/7 as part-whole relationships or…

Science, Technology, Engineering, and Math (STEM) education is essential to the economic growth, health, and progress of the modern world. One cognitive ability that underpins thinking and learning in STEM, as well as other disciplines, is relational ability. This ability to spot common relations shared by different objects, events, ideas, or…

Adult humans are uniquely proficient in reasoning with abstract relations (relational reasoning) - a capacity which underpins much of human-unique cognition, including scientific analogies, artistic metaphors and many phrases in day-to-day language and thought. An important question for cognitive science, therefore, is exploring the nature of this…

Developing scientific literacy, which involves applying scientific knowledge to solve real-world problems, is a primary goal in science education. Socioscientific Issue (SSI) provides students opportunities to reason through authentic and complex scientific dilemmas that reflect real-world issues, thus fostering a deeper understanding of…

Mathematical reasoning, a fundamental aspect of human cognition, poses significant challenges for artificial intelligence (AI) systems. Despite recent advancements in natural language processing (NLP) and large language models (LLMs), AI's ability to replicate human-like reasoning, generalization, and efficiency remains an ongoing research…

Covariational reasoning is a cognitive activity that attends to two or more varying quantities and how their changes are related to each other. Previous studies indicate that covariational reasoning seems to have levels. Content analysis was used to examine the pedagogy and development of covariational reasoning levels in the sections that…

Data is everywhere, but not always accessible to everyone. Conventional data visualization tools and guidelines often assume a standard user, neglecting the neurodivergent needs of individuals with cognitive disabilities. These disabilities can create significant obstacles in data-driven reasoning, including difficulties in processing complex…

In this dissertation, I explore ways to support secondary school students' meaningful understanding of quadratic functions. Specifically, I investigate how students co-developed representational fluency (RF) and functional thinking (FT), when they gained meaningful understanding of quadratic functions. I also characterize students' co-emergence of…

Research has shown the majority of students who have completed a university calculus course reason about the definite integral primarily in terms of prototypical imagery or in purely algorithmic and non-quantitative ways. This dissertation draws on the framework of Emergent Quantitative Models to identify how calculus students might develop a…

In this dissertation study, I report on six middle school students' construction and interpretation of graphs and associated dynamic situations. Constructing and interpreting graphs represents a critical moment in middle school mathematics due to its opportunity to provide a powerful foundation for learning. Nevertheless, researchers have…

This research study explored robotics as the catalyst for computational thinking (CT) by sixth-grade students as they are engaged in a science lesson. The interactions, understandings, and applications are discussed, along with the participants' connections and implementations of CT concepts (decomposition, abstraction, pattern recognition, and…

Activity-based instructional strategies promote physical interaction with manipulatives to represent abstract concepts. As a means to improve student achievement in mathematics, educational researchers and practitioners often recommend instructional strategies that capitalize on the assumed benefits of manipulatives. Recent research has indicated…

The use of science classroom discourse analysis as a way to gain a better understanding of various student cognitive outcomes has a rich history in Science Education in general and Physics Education Research (PER) in particular. When students talk to each other in a collaborative peer instruction environment, such as in the CLASP classes…

Computational thinking aims to outline fundamental skills from computer science that everyone should learn. As currently defined, with help from the National Science Foundation (NSF), these skills include problem formulation, logically organizing data, automating solutions through algorithmic thinking, and representing data through abstraction.…

Video games have recently become a popular space for educational design due to their interactive and engaging nature and the ubiquity of the gaming experience among youth. Though many researchers argue video games can provide opportunities for learning, educational game design has focused on the classroom rather than the informal settings where…