This reflection paper argues that the design and development of digital games teach essential 21st century skills. Intrinsic to application and game development is design thinking. Design thinking requires iterative development, which demands creativity, critical thinking and problem solving. Students are engaged through learning by doing in both…

Analysis of mathematical notations must consider both syntactical aspects of symbols and the underpinning mathematical concept(s) conveyed. We argue that the construct of "syntax template" provides a theoretical framework to analyse undergraduate mathematics students' written solutions, where we have identified several types of…

This piece explores conditions that stimulate classroom activities to facilitate creative habits of mind in an effort to motivate educators and students to better understand the complexities of creativity and how to promote it.

To understand better some of the classic knights and knaves puzzles, we count them. Doing so reveals a surprising connection between puzzles and solutions, and highlights some beautiful combinatorial identities.

In this article, I present and build on the ideas of John Threlfall ("Educational Studies in Mathematics" 50:29-47, 2002) about strategy development in mental mathematics contexts. Focusing on the emergence of strategies rather than on issues of choice or flexibility of choice, I ground these ideas in the enactivist theory of cognition,…

Many important problems require consideration of multiple constraints, such as choosing a job based on salary, location, and responsibilities. We used the Remote Associates Test to study how people solve such multiply-constrained problems by asking participants to make guesses as they came to mind. We evaluated how people generated these guesses…

This article describes how practice problems for the actuarial examination in probability can be used to encourage active, collaborative learning. (Contains 1 table.)

The purpose of this study was to investigate the relationship between what is currently understood about skills for school leadership and the need for a greater understanding of those skills. The importance of developing leadership skills to improve school performance and effectiveness is great. In the field of school leadership, most leaders…

Combinatorial topics have become increasingly prevalent in K-12 and undergraduate curricula, yet research on combinatorics education indicates that students face difficulties when solving counting problems. The research community has not yet addressed students' ways of thinking at a level that facilitates deeper understanding of how students…

Background: The ability to engage in a creative process to solve a problem or to design a novel artifact is essential to engineering as a profession. Research indicates a need for curricula that enhance students' creative skills in engineering. Purpose: Our purpose was to document current practices in engineering pedagogy with regard to…

Worldwide efforts are increasing to infuse thinking skills into the curriculum, which are part of cognitive behavior, and to include them in the instructional strategies, which will make the learner producer of knowledge and help to create a sense of responsibility among them. Metacognitive learning activities immerse students in challenging tasks…

This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…

Representations in physics possess both physical and conceptual aspects that are fundamentally intertwined and can interact to support or hinder sense making and computation. We use distributed cognition and the theory of conceptual blending with material anchors to interpret the roles of conceptual and material features of representations in…

Several types of converging evidence have suggested recently that skilled adults solve very simple addition problems (e.g., 2 + 1, 4 + 2) using a fast, unconscious counting algorithm. These results stand in opposition to the long-held assumption in the cognitive arithmetic literature that such simple addition problems normally are solved by fact…

The purpose of this paper is to provide an easy template for the inclusion of the Bayes factor in reporting experimental results, particularly as a recommendation for articles in the "Journal of Problem Solving." The Bayes factor provides information with a similar purpose to the "p"-value--to allow the researcher to make…