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.

The research paradigm invented by Allen Newell and Herbert A. Simon in the late 1950s dominated the study of problem solving for more than three decades. But in the early 1990s, problem solving ceased to drive research on complex cognition. As part of this decline, Newell and Simon's most innovative research practices--especially their method for…

We investigated human performance on the Euclidean Traveling Salesperson Problem (TSP) and Euclidean Minimum Spanning Tree Problem (MST-P) in regards to a factor that has previously received little attention within the literature: the spatial distributions of TSP and MST-P stimuli. First, we describe a method for quantifying the relative degree of…

The use of the curved-arrow notation to depict electron flow during mechanistic processes is one of the most important representational conventions in the organic chemistry curriculum. Our previous research documented a disturbing trend: when asked to predict the products of a series of reactions, many students do not spontaneously engage in…

The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…

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,…