Single photon experiments involving a Mach-Zehnder interferometer can illustrate the fundamental principles of quantum mechanics, e.g., the wave-particle duality of a single photon, single photon interference, and the probabilistic nature of quantum measurement involving single photons. These experiments explicitly make the connection between the…

What are the nature, forms, and roles of metaphors in mathematics instruction? We present and closely analyze three examples of idiosyncratic metaphors produced during one-to-one tutorial clinical interviews with 11-year-old participants as they attempted to use unfamiliar artifacts and procedures to reason about realistic probability problems.…

This study examines how students solve problems that involve the concept of absolute value. One hundred seventeen students participated in the first (written) part of the study, 24 students participated in the second part (interview). Particular attention was paid to the actual process of problem solving and to the students' ability to establish…

Understanding key foundational principles is vital to learning chemistry across different contexts. One such foundational principle is the acid/base behavior of molecules. In the general chemistry sequence, the Bronsted-Lowry theory is stressed, because it lends itself well to studying equilibrium and kinetics. However, the Lewis theory of…

The purpose of this research was to investigate student conceptions of the topic of asymptotes of rational functions and to understand the connections that students developed between the closely related notions of asymptotes, continuity, and limits. The participants of the study were university students taking Calculus 2 and were mostly freshmen. …

While learning about the types of weather events that occur in the local area, students in grades 4-6 were asked to consider how structures can be built to withstand extreme weather conditions. Teams of students designed, constructed, and tested buildings to withstand hurricanes and designed the tests they would use to evaluate their structures.…

Background: Several studies have examined young primary school children's use of strategies when solving simple addition and subtraction problems. Most of these studies have investigated students' strategy use as if they were isolated processes. To date, we have little knowledge about how math strategies in young students are related to other…

In an empirical study, the use of knowledge by two groups of students and a group of professional engineers' use of knowledge when solving complex problems was investigated. The applied method was adopted from similar investigations within the field of medicine. Qualitative analysis of problem descriptions, solutions and interviews show…

While the existing research consistently points to the effectiveness of Dialectical Behavior Therapy (DBT) in treating borderline personality disorder, little qualitative research has been conducted to ascertain the reasons for its success, especially from the perspective of those undergoing the treatment. Our qualitative investigation was…

This paper reports on the mathematical thinking of participants of a long-term study, now in its 17th year, who did mathematics together through their public school and early university years. In particular, it describes how fundamental ideas and images of a cohort group of students are elaborated and presented in symbolic expressions of…

Concerns have been raised about the Department of Education's (Education) role in overseeing the lenders and schools that participate in the largest of the federal government's student loan programs, the Federal Family Education Loan Program (FFELP). GAO was asked to analyze Education's use of its oversight, guidance, and enforcement authorities…

Students nearing high school graduation need more than the skills and information given them in the past 12 years; they also need to know "how" to learn. The Senior Seminar, which is a program offering a semester of interdisciplinary experiential learning, teaches students to become independent, self-directed learners by first presenting…