Energy is a critical concept in physics problem-solving, but is often a major source of confusion for students if the presentation is not carefully crafted by the instructor or the textbook. In the first three articles in this series we discussed several issues related to the teaching of energy concepts. We have saved a major single issue for this…

The mathematics methodology subjects the author undertook in the early 1980s encouraged him to adopt a very expository style of teaching in which each new concept is introduced by its formal definition. The teacher should then explain a few carefully chosen examples for students to copy into their books, and then provide plenty of graded practice…

This article presents a guided investigation into the spacial relationships between the centres of the squares in a Fibonacci tiling. It is essentially a lesson in number pattern, but includes work with surds, coordinate geometry, and some elementary use of complex numbers. The investigation could be presented to students in a number of ways…

In a general sense, the research interest of this article concerns the preschool class, which is an intermediate form of schooling for six-year-olds in Sweden, between preschool and school and their two traditions of "play" and "learning," respectively. In a more specific sense, the issue of learning one aspect of basic…

Although previous research has demonstrated the benefits of applying the Internet facilities to the learning process, problems with this strategy have also been identified. One of the major difficulties is owing to the lack of an online learning environment that can record the learning portfolio of using the Internet facilities in education, such…

Parent training is consistently highlighted as one of the most effective means of preventing delinquency and treating young children with conduct problems, and it has proven to be one of the most cost-effective interventions for doing so. There is, however, far less evidence supporting the efficacy of parent-training programs with adolescents and…

Students rarely see closed-form analytical rate equations derived from underlying chemical mechanisms that contain more than a few steps unless restrictive simplifying assumptions (e.g., existence of a rate-determining step) are made. Yet, work published decades ago allows closed-form analytical rate equations to be written quickly and easily for…

Objective: Faculty development has increasingly become a focus in medical education. Many models are employed around the United States. The authors present a group model process developed to train new educators to teach our medical students. Methods: The authors met monthly with a diverse faculty over the past 4 years and interacted in a…

Lecturers in mathematical modelling courses are always on the lookout for new examples to illustrate the modelling process. A physical phenomenon, documented as early as the nineteenth century, was recalled: when a wineglass "sings", waves are visible on the surface of the wine. These surface waves are used as an exercise in mathematical…

Obstructive sleep apnea (OSA) is a common disorder of upper airway obstruction during sleep. The effects of intermittent upper airway obstruction include alveolar hypoventilation, altered arterial blood gases and acid-base status, and stimulation of the arterial chemoreceptors, which leads to frequent arousals. These arousals disturb sleep…

This study is a cross-cultural comparison between the ideas of 49 Thai Grade 9 students and the 30 New Zealand Grade 9 students (approximately 15 years old), about energy related to technological and societal issues. Students' ideas were explored using the Questionnaire for exploring Students' ideas about Energy, Technological, and Societal issues…

This article discusses student difficulties in grasping concepts from linear algebra. Using an example from an interview with a student, we propose changes that might positively impact student understanding of concepts within a problem-solving context. In particular, we illustrate barriers to student understanding and suggest technological…

This article reports on 20 children's learning in arithmetic after teaching was adjusted to their conceptual development. The report covers periods from three months up to three terms in an ongoing intervention study of teachers and children in schools for the intellectually disabled and of remedial teaching in regular schools. The researcher…

Fermi problems, or order of magnitude estimates, are often used in introductory physics courses. In this paper I will show that first year students studying physics at university do not arrive with the skill set to solve these problems, and they have to be actively taught how to solve them. Once they have been shown how to solve Fermi problems,…

Project-based learning is a pedagogy that involves students in applying and developing theories, skills, and techniques to solve real world problems. Three faculty members used project-based learning to involve graduate students in an interdisciplinary seminar on sustainable development in Appalachian Ohio, which was convened under the auspices of…