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…

A sample of 202 students filling in a student evaluation of teaching (SET) questionnaire were asked to complete another questionnaire asking about the specific reasons for awarding a score to the specific SET questionnaire items. The aim was to find out what influenced students' judgements on those items. It was found that students' interpretation…

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.

This article examines an innovative way of conceptualizing mentoring and develops the notion of a "distributed" model of mentoring, backed by snippets from professional development program that has sought to use the context of community to broaden the definition (and success) of mentoring for mathematical teachers. The author proposes a way of…

The study we present tries to explore how first year engineering students formulate hypotheses in order to construct their own problem solving structure when confronted with problems in physics. Under the constructivistic perspective of the teaching-learning process, the formulation of hypotheses plays a key role in contrasting the coherence of…

We employ tools of complexity theory to examine the effect of cognitive variables, such as working-memory capacity, degree of field dependence-independence, developmental level and the mobility-fixity dimension. The nonlinear method correlates the subjects' rank-order achievement scores with each cognitive variable. From the achievement scores in…

During one school year, data were collected for vocational education students while they worked collaboratively on open-ended mathematics problems. In collaboration with participating teachers, instructional activities were designed with a twofold goal of modelling the process of problem solving and improving collaboration. Instructional…

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…

Purpose: Knowledge management (KM) as a field has been characterized by great confusion about its conceptual foundations and scope, much to the detriment of assessments of its impact and track record. The purpose of this paper is to contribute toward defining the scope of KM and ending the confusion, by presenting a conceptual framework and set of…

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…

Interesting problems sometimes have surprising sources. In this paper we take an innocent looking problem from a calculus book and rediscover the radical axis of classical geometry. For intersecting circles the radical axis is the line through the two points of intersection. For nonintersecting, nonconcentric circles, the radical axis still…

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…