Physics experts and students commonly use a variety of representations when working with partial derivatives, including symbols, graphs, and words. One especially powerful representation is the contour graph. In open-ended problem-solving interviews with nine upper-division physics students, we asked students to determine derivatives from contour…

In the evolving landscape of higher education, challenges such as the COVID-19 pandemic have underscored the necessity for innovative teaching methodologies. These challenges have catalyzed the integration of technology into education, particularly in blended learning environments, to bolster self-regulated learning (SRL) and higher-order thinking…

"When you hear hoofbeats, look for horses, not zebras." This common saying in medicine (often attributed to Theodore Woodward, MD, of the University of Maryland School of Medicine) advises doctors to stick to the expected or likely diagnosis, rather than anticipating an unusual or atypical one. As a result, uncommon medical diagnoses are…

With the increasing attention and surge of empirical research in providing academic instruction for students with autism spectrum disorder (ASD) comes the need to provide teachers with research-supported strategies. Using one evidence-based strategy for teaching mathematics to students with high incidence disabilities, and another for teaching…

Background: We tested the effects of an intervention on the learning of introductory thermodynamics principles. This intervention, OEM-Thermo, is designed to prompt the cognitive operations of meaningful learning: organization, elaboration, and monitoring. We also sought evidence to show that execution of these operations was associated with…

Findings from the fields of cognitive science and cognitive development propose a variety of evidence-based principles for improving learning. One such recommendation is that instead of having students practice solving long strings of problems on their own after a lesson, worked-out examples of problem solutions should be incorporated into…

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.…

In a series of two in vivo experiments, we examine whether correct and incorrect examples with prompts for self-explanation can be effective for improving students' conceptual understanding and procedural skill in Algebra when combined with guided practice. In Experiment 1, students working with the Algebra I Cognitive Tutor were randomly assigned…

In teaching geometry, most instructors opt for direct demonstration with detailed explanations; however, under this kind of instruction students face considerable difficulties in the development of the reasoning skills required to deal with problems of a geometric nature. This study adopted a nonequivalent pretest-postest quasi-experimental design…

Learn the 5 practices for facilitating effective inquiry-oriented classrooms: (1) Anticipating what students will do--what strategies they will use--in solving a problem; (2) Monitoring their work as they approach the problem in class; (3) Selecting students whose strategies are worth discussing in class; (4) Sequencing those students'…

THIS EXPERIMENT WAS DESIGNED TO INVESTIGATE (1) THE AMOUNTS OF INFORMATION COMMUNICATED BY THE KNOWLEDGE OF A PRINCIPLE AS OPPOSED TO THE KNOWLEDGE OF CUES AND (2) THE EFFECTIVENESS OF THE KNOWLEDGE OF A PRINCIPLE AS OPPOSED TO THE KNOWLEDGE OF CUES AT DIFFERENT STAGES OF LEARNING. THE FOUR GROUPS MAKING UP THE EXPERIMENTAL DESIGN WERE A CUE GROUP…

This study investigated several questions generated by cueing system research. The cueing system is perceived as a means of directing our categorizing behaviors in the processing and recall of information. Experiments involved a comparison of categorical cueing systems on a given task in relation to two control areas: (1) subjects using a free…

Students in Grades six, seven, and eight were asked to integrate existing information and initially unknown answers to prose-related questions for answering superordinate questions. Results suggest that grade level development of hypothetico-deductive skills interacts with instructional prompt levels and that these skills are essential to…