When, how, and why students use conceptual knowledge during math problem solving is not well understood. We propose that when solving routine problems, students are more likely to recruit conceptual knowledge if their procedural knowledge is weak than if it is strong, and that in this context, metacognitive processes, specifically feelings of…

The purpose of this study was to describe students' thinking processes in relating quantities to the problem of covariation in the process of solving mathematical problems. This study used a descriptive exploratory approach within the scope of qualitative research involving 87 students as prospective subjects from three different high schools. The…

We studied the impact of metacognitive reflections on recently-completed work as a way to improve the retention of newly learned problem-solving techniques. Students video recorded themselves talking through problems immediately after finishing them, completed ongoing problem-solving strategy maps or problem-sorting exercises, and filled out…

The purpose of this study was to gain insight into 30, first year calculus students' understanding of the relationship between the concept of vertex of a quadratic function and the concept of the derivative. APOS (action-process-object-schema) theory was applied as a guiding framework of analysis on student written work, think-aloud and follow up…

We previously reported that students' concept-building approaches, identified a priori using a cognitive psychology laboratory task, extend to learning complex science, technology, engineering, and mathematics topics. This prior study examined student performance in both general and organic chemistry at a select research institution, after…

On the basis of the results of two prior studies at the US Naval Academy (USNA), which described the choice of study resources and the self-reported learning approaches of students of differing achievement levels, the current investigation examines how students of differing achievement levels in general chemistry actually solve multiple-choice…

Research on problem solving typically does not address tasks that involve following detailed and/or illustrated step-by-step instructions. Such tasks are not seen as cognitively challenging problems to be solved. In this paper, we challenge this assumption by analyzing verbal protocols collected during an Origami folding task. Participants…

The Dirac delta function is a standard mathematical tool that appears repeatedly in the undergraduate physics curriculum in multiple topical areas including electrostatics, and quantum mechanics. While Dirac delta functions are often introduced in order to simplify a problem mathematically, students still struggle to manipulate and interpret them.…

The internal design thinking behaviour of designers in the concept development has been an important issue of cognitive psychology. In this study, the design thinking process designers have in applying digital media and traditional paper in the early concept development stage was explored. Special focus was made on the structure and procedure of…

This thesis explores the role of multiple representations in introductory physics students' problem solving performance through several investigations. Representations can help students focus on the conceptual aspects of physics and play a major role in effective problem solving. Diagrammatic representations can play a particularly important role…

The ability to reason with formal logic is a foundational skill for computer scientists and computer engineers that scaffolds the abilities to design, debug, and optimize. By interviewing students about their understanding of propositional logic and their ability to translate from English specifications to Boolean expressions, we characterized…

This exploratory study highlights certain differences in the way an expert and a novice engineer used their analyzing and generating skills while solving a fairly ill-structured design problem. The expert tends to use more inferences and elaboration when solving the design problem and the novice tend to use analysis that is focused on the…

This study examined the representational competence of students as they solved problems dealing with the temperature-pressure relationship for ideal gases. Seven students enrolled in a first-semester general chemistry course and two advanced undergraduate science majors participated in the study. The written work and transcripts from videotaped…

The role of planning in the design of digital circuits was studied in two experiments. One compared the planning-related activities of expert designers and beginning students of design, and the other looked at the effect on circuit-design processes of forcing students to construct a global plan. In experiment 1, five undergraduate students…

Explores how a set of possible student misconceptions about solving a complex problem can be used in computer-based intelligent tutoring systems and in computer-based exercise and test generation. Topics discussed include expert systems, misconception covers, discrimination trees, methods of acquiring the set of misconceptions, and protocol…