This paper uses the hammer-and-nail metaphor to highlight the rigidity and impulsiveness that can be found in student mathematical behaviour. The hammer-and-nail phenomenon can be attributed to two plausible causes: (1) the way the human mind works; and (2) the way mathematics is traditionally taught in school. In this paper, the following aspects…

Social work is a profession that draws (or should draw) on available knowledge in the disciplines as well as other sources including other professions in the pursuit of "the betterment of life conditions of individuals, groups, and communities." An historical perspective illustrates opportunities taken and lost to harvest knowledge in pursuit of…

Creative achievements are the basis for progress in our world. Although creative achievement is influenced by many variables, the basis for creativity is held to lie in the generation of high-quality, original, and elegant solutions to complex, novel, ill-defined problems. In the present effort, we examine the cognitive capacities that make…

The study investigates medical students' ways of approaching a medical task. Fourteen medical students in their clinical years responded to a written patient case on chest pain. Variations in the students' responses to the task were analysed from a contextual and linguistic perspective. Students approached the task in two distinctly different…

One of Gardner's passions was to introduce puzzles into the classroom. From this point of view, polyomino dissections are an excellent topic. They require little background, provide training in geometric visualization, and mostly they are fun. In this article, we put together a large collection of such puzzles, introduce a new approach in solving…

The Spider and the Fly puzzle, originally attributed to the great puzzler Henry Ernest Dudeney, and now over 100 years old, asks for the shortest path between two points on a particular square prism. We explore a generalization, find that the original solution only holds in certain cases, and suggest how this discovery might be used in the…

Word problem solving involves the construction of two different mental representations, namely, mathematical and situational. Although educational research in word problem solving has documented different kinds of instruction at these levels, less is known about how both representational levels are evoked during word problem solving in day-to-day…

This paper presents a study of the opportunities presented to students that allow them to learn different types of mathematical reasoning during teachers' ordinary task solving presentations. The characteristics of algorithmic and creative reasoning that are seen in the presentations are analyzed. We find that most task solutions are based on…

In this article we report and discuss a contextual problem solving task that was proposed to a class of 8th grade (13-14-year-old) students. These students had been developing a reasonable experience in the use of the spreadsheet to model relations within contextual problems and chose to use this tool to solve the mentioned problem, engaging in…

This paper argues that academic development is a creative act. Creative acts have potential to inspire, critique, inform and in many cases to change. The creativity literature identifies a number of core features of creative acts that assist in developing independent creative practitioners. Those features are observing, attending to relationships,…

In this article a new parameterization of magic squares of order three is presented. This parameterization permits an easy computation of their inverses, eigenvalues, eigenvectors and adjoints. Some attention is paid to the Luoshu, one of the oldest magic squares.

Creativity, which is concerned with problem solving, is essential if we are to generate new solutions to the massive and complex problems in the unknown future. Our next generation needs an educational platform where they can be taught to possess creativity. Design education is such a way to foster students' creativity. Therefore, it is essential…

A visual proof of Ptolemy's theorem.

Multicriteria analysis constitutes a way to model decision processes, which allow the decision maker to assess the possible implications each course of action may entail. A multicriteria problem is chosen from the Programme for International Student Assessment 2003 Report and then extended to include questions involving a choice of preferences and…

This study investigates the internal structure and construct validity of Complex Problem Solving (CPS), which is measured by a "Multiple-Item-Approach." It is tested, if (a) three facets of CPS--"rule identification" (adequateness of strategies), "rule knowledge" (generated knowledge) and "rule application"…