The article describes the harmonic mean and explores situations for using it. Activities that involve hands-on practice for students are provided. Students learn to recognize which mean, harmonic or arithmetic, is appropriate.

This note discusses some set equations, using set matrices, i.e. matrices whose entries are sets.

Choosing challenging problems to facilitate student learning of new mathematics is a difficult task so by using open-ended problems with prospective mathematics teachers, the potential solution characteristics were studied. It is shown that considering the conceptual diversity of solutions helps students develop a better sense of different…

Marion Walter, an internationally acclaimed mathematics educator discusses about problem posing, focusing on both the merits of problem posing and techniques to encourage problem posing. She believes that playful attitude toward problem variables is an essential part of an inquiring mind and the more opportunities that learners have, to change a…

Discourse, especially dialogic communication between students in collaborative problem-solving groups, plays a central role in educational reforms informed by learning science. This study examined the quality of discourse in problem-based learning groups in a university course. The study found a low incidence of high quality dialogue (dialogic…

The purpose of this research study was to examine the effectiveness of problem-based learning (PBL) on eleventh grade students' understanding of "The effects of temperature, concentration and pressure on cell potential" and also their social skills. Stratified randomly selected control and experimental groups with 20 students each were used in…

Some extant theory and empirical research suggests that youth problem behaviors, such as substance abuse and delinquency, reflect a single underlying dimension of behavior, whereas others suggest there are several different dimensions. Few studies have examined potential international differences in the structure of problem behavior, where…

The understanding that choice of words in an individual's language construction is a reflection of her or his perspective is not new. This article examines the mindful and intimate link between language and empathetic perspective--the language that the author, as an individual, employ's in her daily life to what she, as an individual, constructs…

It has been well recognized that problem-based learning (PBL) embraces the principles of what constitute good learning and teaching which encourage integrated, independent and experiential development of a number of skills including team work and communication. The question is how best can the PBL approach be implemented to ensure maximum gain of…

We introduce some concepts for analyzing proofs, including various structures, and for analyzing undergraduate and beginning graduate mathematics students' proving abilities. We then discuss how the coordination of these two analyses might be used to improve students' ability to construct proofs. For this purpose, we need a richer framework for…

Solution-focused applications are proposed to assist survivor employees to return to workplace homeostasis after co-workers voluntarily or involuntarily leave the organization. A model for transitional coping is presented as well as a potential case study illustrating the application of the model. Implications for the theory, practice, and…

This paper reviewed the research literature on graduation rates in U.S. high schools to evaluate and assess the findings. The methodology employed was to determine the measuring method that researchers used in reaching their findings. The strengths and weaknesses of the method employed were then analyzed. Flaws and inaccuracies were examined and…

The purpose of this experiment was to establish discriminative control of responding by an antecedent stimulus using differential punishment because the results of past studies on this topic have been mixed. Three adults with mental retardation who exhibited stereotypy not maintained by social consequences (i.e., automatic reinforcement)…

Campbell Loughmiller (1906-1993) is widely recognized as a leader in therapeutic work with troubled youngsters in outdoor settings. Rejecting punitive or institutional models of intervention, Loughmiller set out to demonstrate that every young person has strengths, desires to make positive changes, can grow in responsibility, and contribute to…

The purpose of this study was to produce a typology of behavior problems in preschool children. Distinct subtypes were identified through the use of cluster analytic techniques on data from the Behavior Assessment System for Children (BASC)--Parent Rating Scales. Analyses were based on archival data collected on a sample of 268 children, aged 2 to…