Polyiamonds are the 'and so on' when unit-squares are replaced with unit-equilateral triangles. Polyiamonds are used to play the satisfying Blokus variant, Blokus Trigon, where the playing grid is also hexagonal, and the playing pieces are all the polyiamonds from mono- to hex. This article discusses the use of polyiamonds in puzzles.

Problem posing engages students in generating new problems based on given situations (including mathematical expressions or diagrams) or changing (i.e., reformulating) existing problems. Problem posing has been at the forefront of discussion over the past few decades. One of the important topics studied is the process of problem posing as…

In this study, effects of asking participants to make different types of considerations when solving a realistic word problem were investigated. A two-factorial experiment with the factors "addressing realistic considerations" (with vs. without) and "addressing mathematical operations" (with vs. without) was conducted. It was…

This article provides an update on the blind-variation and selective-retention theory of creativity (BVSR), beginning with an overview of its historical development. That brief narrative is then followed by a more extensive summary of recent enhancements in BVSR's conceptual foundations, including formal definitions of creative, sighted, and blind…

The growing use of programming in mathematics classrooms presents a challenge linked to implementation in general and task design in particular. This article presents design ideas for mathematical problems incorporating programming in which the focus remains mainly on learning mathematics and less on learning programming. The article starts by…

The main aim of this paper is to propose a critical view of the application of Toulmin's model of argument to mathematics education, focusing on aspects that have strong teaching implications. It is claimed that Toulmin's description of arguments in mathematics, in particular as regards the relations between form and meaning, is misleading and out…

Various theories and models discuss how instructional designers can develop systems that allow learners to engage in problem-solving. To date, many of these theories and models that guide design often describe how learners engage in meaning-making within a situated context; however, they do not address strategies instructional designers can use to…

This article reviews literature on worked examples in the context of programming activities. We focus on two types of examples, namely, code-tracing and code-generation, because there is sufficient research on these to warrant a review. We synthesize key results according to themes that emerged from the review. This synthesis aims to provide…

The goal of this article is to propose a framework for understanding the nature of "how people construct problems" by interacting with situations and subsequently to offer implications for instructional design and future research. We propose that people must interactively frame the components of a situation in order to establish the…

Clinical supervision is crucial for the professional learning and development of practitioners in many fields. While many have articulated what should happen in clinical supervision, and evaluative research has been undertaken, little is known about the details of what actually happens in clinical supervision. This study addresses this gap,…

Combinatorial proofs of binomial identities involve establishing an identity by arguing that each side enumerates a certain set of outcomes. In this paper, we share results from interviews with experienced provers (mathematicians and upper-division undergraduate mathematics students) and examine one particular aspect of combinatorial proof, namely…

Comprehending and formulating strategies for geometry problems that require higher-order thinking skills (HOTS) is crucial in enhancing mathematics education. This study implements a qualitative case study approach to comprehend how prospective mathematics teachers with varying Adversity Quotients (AQ) solve geometry Higher-Order Thinking Skill…

Mathematical flexibility is thought to be a critical component of mathematical proficiency, and the term "mathematical flexibility" has been used by teachers, researchers, and policy makers for more than 2 decades. Although there seems to be consensus on the importance of mathematical flexibility as a construct, the way it is defined and…

Problem solving is a common activity for engineering students and practicing engineers as they learn and practice the use of engineering concepts. Understanding the approach to a problem provides a glimpse at unique problem-solving behaviors that can be used as a means to compare different problem solvers. Engineering education research has…

In this article, we delve into a hermeneutic process that analyzes the term "Computational Thinking" as it was constructed through Wing's series of iterations in conceptualization attempts (2006, 2008, 2011 and 2014). On the one hand, this brings us to analyze the relations and intersections between different process of thought…