The Laplace equation has applications in several fields of physics, and problems involving this equation serve as paradigms for boundary value problems. In the case of the Laplace equation in a disc there is a well-known explicit formula for the solution: Poisson's integral. We show how one can derive this formula, and in addition two equivalent…

This study examined how instructional design (ID) experts used their prior knowledge and previous experiences to solve an ill-structured instructional design problem. Seven experienced designers used a think-aloud procedure to articulate their problem-solving processes while reading a case narrative. Results, presented in the form of four…

A key learning outcome in problem-solving domains is the development of flexible knowledge, where learners know multiple strategies and adaptively choose efficient strategies. Two interventions hypothesized to improve flexibility in problem solving were experimentally evaluated: prompts to discover multiple strategies and direct instruction on…

This study examines ways of approaching deductive reasoning of people involved in mathematics education and/or logic. The data source includes 21 individual semi-structured interviews. The data analysis reveals two different approaches. One approach refers to deductive reasoning as a systematic step-by-step manner for solving problems, both in…

Cochise College, Cochise County, and the Cochise Community Foundation partnered to create the Cochise County Quality of Life Index--the first to be developed in Arizona. The project brought together stakeholders to address shared problems in new ways, based on non-traditional partnerships. The college's Center for Economic Research provided…

Continuity in conflict behaviors from (a) adolescents' behavior with parents and their behavior with romantic partners and (b) from parents' marriage to adolescents' romantic relationships were examined in a sample of 58 mother-father-adolescent families and the adolescents' romantic partners. The social relations model was used to analyze…

This study examined achievement patterns of middle school students enrolled in Standards-based curricula, in particular those curricula that were funded from a solicitation of proposals through the National Science Foundation (NSF) in the early 1990s (NSF RFP 91-100). Approximately 1400 middle-grades students who had used either the Connected…

The goals of this study are to evaluate a relatively novel learning environment, as well as to seek greater understanding of why human tutoring is so effective. This alternative learning environment consists of pairs of students collaboratively observing a videotape of another student being tutored. Comparing this collaboratively observing…

This article uses diagrams that help the observer see how solutions of the wave equation and heat conduction equation are obtained. The analytical approach cannot necessarily show the mechanisms of the key to the solution without transforming the differential equation into a more convenient form by separation of variables. The visual clues based…

Whereas product-oriented worked examples only present a problem solution, process-oriented worked examples additionally explain the rationale behind the presented solution. Given the importance of understanding this rationale for attaining transfer, process-oriented worked examples would be expected to result in more efficient transfer. However, a…

Accurate and effective decision-making is one of the most essential skills necessary for organizational success. The problem-solving process provides a systematic means of effectively recognizing, analyzing, and solving a dilemma. The key element in this process is critical analysis of the situation, which can be executed by a taking a Socratic…

The extreme interval values and statistics (expected value, median, mode, standard deviation, and coefficient of variation) for the smallest (min) and largest (max) values of exponentially distributed variables with parameter ? = 1 are examined for different observation (sample) sizes. An extreme interval value g[subscript a] is defined as a…

To understand the issues of inquiry-based education, I adopted John Dewey's theory of inquiry as the analytical framework to examine science learning activities, students' interactions, and education standards. Educators have tried to engage students in meaningful learning, but the analysis revealed that the meaning of inquiry was diverse:…

The purpose of this study was to investigate the effect of using metacognitive strategy training on mathematical problem solving achievement. The study took place over a nine-week period with 47 fifth grade students. The experimental group (n = 24) instructed to improve their metacognitive skills. At the same time the students in the control group…

This study examines effective ways for teachers to interact with students when they are working collaboratively. Through prolonged daily engagement with one class of students working in groups, the nature and experience of one teacher's interventions are documented using practitioner action research. Specifically, small-group dynamics and teacher…