In his 1973 article "The Structure of ill structured problems", Herbert Simon proposed that solving ill-structured problems could be modeled within the same information-processing framework developed for solving well-structured problems. This claim is reexamined within the context of over 40 years of subsequent research and theoretical…

Creativity and innovation are frequently mentioned as key 21st-century skills for career and life success. Indeed, recent research provides evidence that the jobs of the future will increasingly require the ability to bring creative solutions to complex problems. And creativity is often the spice of life, that little extra something that makes the…

Background: A key feature of engineering design is collaborative, deliberate decision making that takes into account information about design options. K-12 students need opportunities for this kind of decision making if they are to meet the learning standards for engineering set out in the Next Generation Science Standards. Purpose: This…

Mathematicians commonly distinguish two modes of work in the discipline: "Problem solving," and "theory building." Mathematics education offers many opportunities to learn problem solving. This paper explores the possibility, and value, of designing instructional activities that provide supported opportunities for students to…

Despite significant scholarly attention, the literature on the existence and direction of gender differences in creativity has produced inconsistent findings. In the present paper, we argue that this lack of consensus may be attributable, at least in part, to gender-specific inconsistencies in the measurement of creative problem-solving. To…

The concept of intrinsic complexity explains why different problems of the same type, tackled by the same problem solver, can require different times to solve and yield solutions of different quality. This paper proposes a general four-step approach that can be used to establish a model for the intrinsic complexity of a problem class in terms of…

We present a method for finding partial fraction decompositions of rational functions with linear or quadratic factors in the denominators by means of repeated polynomial divisions. This method does not involve differentiation or solving linear equations for obtaining the unknown partial fraction coefficients, which is very suitable for either…

This study has identified factors stimulating creative ideas, transforming creative ideas to products, and continuing creative performance in the field of architecture based on interviews with 10 creative and successful architects. Having a penchant for liberal arts and reading books on a broad range of topics on arts, humanities, social sciences,…

Building students' understanding of cardinality is fundamental for working with numbers and operations. Without these early mathematical foundations in place, students will fall behind. Consequently, it is imperative to build on students' strengths to address their weaknesses with the notion of cardinality.

Regardless of what is intended by government curriculum specifications and advised by educational experts, the ICT competencies or skills taught and learned in and out of classrooms can vary considerably. In this paper, we explore how we can investigate the perceptions that individual teachers have of ICT as a subject, and how these and other…

Chuderski and Jastrzêbski (2017) found a positive relationship between working memory capacity and insight problem solving, and concluded that "people with less effective cognition" are therefore "less creative" (p. 2003). This interpretation discounts substantial evidence that devoting less executive control facilitates…

While the scientific investigation into creativity is a recent phenomenon, creative thinking has always been a crucial feature of humanity. The ability to creatively solve problems enabled early humans to survive and laid the foundation for the creative imagination that has resulted in our modern society. While most humans no longer face physical…

As a programmer when solving a problem, a number of conscious and unconscious cognitive operations are being performed. Problem-solving is a gradual and cyclic activity; as the mind is adjusting the problem to its schemas formed by its previous experiences, the programmer gets closer and closer to understanding and defining the problem. The…

This paper presents some critical perspectives regarding pedagogical approaches to the method of reversing the order of integration in double integrals from prevailing educational literature on multivariable calculus. First, we question the message found in popular textbooks that the traditional process of reversing the order of integration is…

Calculus has frequently been called one the greatest intellectual achievements of humankind. As a key transitional course to college mathematics, it combines such elementary ideas as rate with new abstract ideas--such as infinity, instantaneous change, and limit--to formulate the derivative and the integral. Most calculus texts begin with the…