An English teacher and a math teacher collaborating to improve practices in classroom discussion develop a problem-solving method that steers students away from seeking simple solutions and into an understanding of the complexity and nature of problems.

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…

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…

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.

As society moves further into the 21st century and focuses on becoming more global, current and future learners will need to meet another set of requirements that are viewed as quality indicators and necessary dimensions for future success. These requirements are outlined by The National Education Association as the "Four Cs" of 21st…

The importance of so-called noncognitive skills--which include abilities and traits such as critical thinking skills, problem solving skills, social skills, persistence, creativity, and self-control--manifests itself in multiple ways throughout life. This policy brief, which focuses on a set of skills that can and should be taught in schools, is…

What is important for citizens to know and be able to do? The OECD Programme for International Student Assessment (PISA) seeks to answer that question through the most comprehensive and rigorous international assessment of student knowledge and skills. The PISA 2015 Assessment and Analytical Framework presents the conceptual foundations of the…

Creative leadership is basically about connecting people, and in a sense creative leadership is a form of servant leadership in which the leader's task is to connect different people, ideas, and ways of thinking. Leaders further develop the skills of their co-workers and co-create and co-sense problems of their organizations. Creative leadership…

Pythagoras' theorem in two and three dimensions appears in General Mathematics, Units 1-2, section 6 (Geometry and trigonometry: Shape and measurement) in the Victorian Certificate of Education Mathematics Study Design (Victorian Curriculum Assessment Authority, 2010). It also comes in Further Mathematics, Units 3-4 (Applications: Geometry and…