At the K-12 level one assumes that mathematically gifted students identified by out-of-level testing are also creative in their work. In professional mathematics, "creative" mathematicians constitute a very small subset within the field. At this level, mathematical giftedness does not necessarily imply mathematical creativity but the…

Most school districts conduct annual leadership retreats for their school boards, central and site leadership teams and their business and community partners. Holding leadership development retreats for students, on the other hand, is a new and somewhat revolutionary idea. This article describes a series of leadership retreats where faculty worked…

School counseling literature indicates that school counselors experience isolation and frustration and that partnership projects between counselors and counselor educators are potentially valuable. The author describes the school counselor alumni peer consultation group, which provides (a) support and networking opportunities for new counselors…

In this article, the author presents lively and interesting ideas on renewing children's interest in group-time meetings. Come springtime, teachers usually find that interest is flagging at their class group-time meetings. It is at this time of year that children often need something extra special to inspire and motivate them in the classroom. The…

Plausibility has been implicated as playing a critical role in many cognitive phenomena from comprehension to problem solving. Yet, across cognitive science, plausibility is usually treated as an operationalized variable or metric rather than being explained or studied in itself. This article describes a new cognitive model of plausibility, the…

To immerse high school students in inquiry, as advocated by the National Science Education Standards (1996), and to take advantage of the Internet's power, students are engaged in a computer data-mining exercise to solve real science problems. After formulating their research question, students scour the Internet to locate raw data they can…

Peer-Led Team Learning (PLTL) is a method of student assisted learning in which a successful undergraduate student guides a team of 6-8 students engaged in solving problems developed by the course instructor. The peer leaders serve as role models for their students who want to become peer leaders and the leaders also recruit other students to…

Notwithstanding an impressive research tradition on key skills, no clear statistical criterion exists that is suitable to determine which skills may be considered key skills. This contribution proposes one possible methodology that can be used to identify key skills. Proposing an economic definition of the key skill concept and disentangling the…

Carry Groups are a wonderful collection of groups to introduce in an undergraduate Abstract Algebra course. These groups are straightforward to define but have interesting structures for students to discover. We describe these groups and give examples of in-class group projects that were developed and used by Miller.

In a time when nearly half the country's employees are currently working in self-directed work groups, successful team working within organizations is more important than ever. The Problem-Possibility-Pursuit-Presentation (PPPP) Portfolio Project is designed to give students an opportunity to experience teamwork in a meaningful fashion. This…

Groups are defined as a small, interdependent group of individuals who share a common identity and interact with one another, usually face to face over time. While groups can be an effective way to explore issues and provide creative solutions to problems, rarely do members in groups get through the process without encountering a difficult group…

Games like "Civilization III," a strategy game that allows players to create civilizations that stand the test of time, are attracting increasing attention in the educational community for their potential to support learning. A recent article in BBC news observed that "using "Civilisation III" to teach students about history showed that it could…

In this article, the authors describe their efforts to assess prospective K-8 teachers' knowledge of proportional reasoning. Based upon their analysis of prospective K-8 teachers' work on a mathematics performance task, they discuss the implications for preparing prospective teachers to teach proportional reasoning to their students. In general,…

This article discusses the four categories of triangles that are standard in most textbooks when "solving" triangles: (a) Given the lengths of two sides and the measure of an angle opposite one of the two given sides, (b) Given the lengths of two sides and the measure of the included angle, (c) Given the lengths of all three sides, d) Given the…

People spontaneously discover new representations during problem solving. Discovery of a mathematical representation is of special interest, because it shows that the underlying structure of the problem has been extracted. In the current study, participants solved gear-system problems as part of a game. Although none of the participants initially…