Computational thinking (CT) has been an increasing focus of research and practice since the seminal paper by Wing in 2006, especially in pre-college (K-12) education. Barr and Stephenson defined CT as a problem-solving methodology that can be automated, transferred, and applied across disciplines. With the challenges of fitting CT into already…

Learning engagement and career-relevant skills are both important elements in learning. Unfortunately, there is a lack of research related to learning engagement in massive open online courses (MOOCs) from MOOC instructors' point of view. Research is also needed on MOOC instructors' strategies to provide career-relevant content to the learners. In…

In the first part, we investigate Birman, Ko, and Lee's left canonical form of a braid and give a new diagrammatic approach. We use the left canonical form to characterize almost strongly quasipositive braids. In the second part, we investigate students' confidence in mathematics and problem solving skills. Every math instructor has heard students…

In the spring of 2020, many colleges and universities had to move their classes online due to COVID-19. This move to the virtual environment highlighted a growing problem in higher education, being increase failure rates for online students. This study addressed two research questions: 1) To what extent does the use of short lectures and small…

To make sense of our interconnected and algorithm driven world, students increasingly need proficiency with computational thinking (CT), systems thinking (ST), and computational modeling. One aspect of computational modeling that can support students with CT, ST, and modeling is testing and debugging. Testing and debugging enables students to…

This dissertation examines the development of combinatorial reasoning in high school students through an in-depth analysis of a problem-solving session involving the Pizza Problem. The study, part of the long-term Rutgers-Kenilworth longitudinal research project, focuses on four 11th-grade students as they explore and connect concepts related to…

One of the key challenges of Engineering Education is developing students' ability to navigate and solve problems that have multiple solution paths. In order to accomplish this, the process of solving these moderately- and ill-structured problems needs to be better understood. We used two approaches to achieve this. First, we performed problem…

As students with autism spectrum disorder (ASD) participate in the general education setting at greater rates, they are expected to meet rigorous grade-level academic standards. Students with ASD typically struggle with problem solving, higher-ordered thinking, and mathematical reasoning. When students enter middle school, mathematics becomes more…

This qualitative study was conducted to understand the instructional strategies used by high school integrated STEM (iSTEM) teachers to apply real-world problem solving in their classrooms in the state of Indiana. The problem addressed by this study was the need to understand the instructional strategies employed by iSTEM teachers in their…

This study investigated evidence of how students' mental models of fundamental kinematic relations evolved (i.e., developed cognitively over time) as observed during an introductory course in calculus-based classical mechanics. The core of the curriculum is based on a claim known as Galileo's principle of relativity. The course material comprised…

Through instructional tasks, teachers can present content in ways that require students to apply critical thinking, problem-solving, and other cognitive skills. The purpose of this mixed methods collective case study was to determine how teacher-assigned instructional tasks in mathematics impact students' learning of mathematical concepts. In this…

Uncertainties are inherent in education as learners encounter gaps in their awareness of topics, receive new information that potentially conflicts with prior understandings, and grapple with known unknowns in order to construct new knowledge. While researchers have shown that students productively struggling with problematized and uncertain…

It has been well-establishing in the field of educational research that traditional educational methods such as passive lectures and labs where students follow pre-designed procedures to verify information already told to them are not effective for promoting meaningful and lasting conceptual understanding. Alongside this knowledge have come a…

The purpose of this study was to evaluate the effect of an intervention utilizing modified schema-based instruction (MSBI) on the mathematical problem-solving ability of elementary school students with mild to moderate disabilities. Four participants were taught to solve percent of change word problems, which required them to calculate the…

This study examined the engagement of preservice elementary teachers (PSTs) with mathematics tasks that were open in various ways and to varying extents. In K-12 settings, practitioners who have implemented recently popular open tasks report increased engagement and from a wider variety of students. While these anecdotal reports and related…