The solution of problems and the provision of proofs have always played a crucial part in mathematics. In fact, they are the heart and soul of this discipline. Moreover, the use of different techniques and methods of proof in the same mathematical field, or by combining fields, for the same specific problem, can show the interrelations between the…

Since the first descriptions of design research (DR), there have been calls to better define it to increase its rigour. Yet five uncertainties remain: (1) the processes for conducting DR, (2) how DR differs from other forms of research, (3) how DR differs from design, (4) the products of DR, and (5) why DR can answer certain research questions…

One way to ease the solution of physics problems is to visualize the situation. However, by visualization we do not mean the pictorial representation of the problem. Instead, we mean a sketch for the solution of the problem. In this paper a new approach to solving physics problems, based on decomposing the problem into with and without gravity, is…

A new visual representation for insight problems permits 22 new quantitative measures; which leads to a detailed diagnosis of a person's (or team's) creative weaknesses; which then leads to prescribing targeted, effective counter-techniques for each weakness. Currently, only two measures are consistently used for insight problem solving: the…

Integrating different perspectives is a sophisticated strategy for developing constructive interactions in collaborative problem solving. However, cognitive aspects such as individuals' knowledge and bias often obscure group consensus and produce conflict. This study investigated collaborative problem solving, focusing on a group member…

This paper uses the lens of a calculus student to examine different solutions to a weekly puzzler from the radio show "Car Talk," hosted by Tom and Ray Magliozzi. The puzzler describes an automobile that is traveling 75 miles per hour and is 75 miles from its destination. The trip is completed by traveling 1 mile at 75 miles per hour, 1…

In more and more countries, the goal of mathematics education is to develop students' mathematical competence beyond procedural and conceptual knowledge. Thus, students need to engage in a rich variety of tasks comprising competencies such as communication, reasoning and problem-solving. In addition, assessment tasks should be constructed to…

Educators often hear about the need for students to be more creative, more free-thinking, and more exploratory throughout projects and class assignments. This article will highlight the importance of creating and implementing an open-classroom environment where students are confident in their ability to ask questions and capable of exploring a…

Current understanding of the development of quantity representations is based primarily on performance in the number-line task. We posit that the data from number-line tasks reflect the observer's underlying representation of quantity, together with the cognitive strategies and skills required to equate line length and quantity. Here, we specify a…

The increasing interest in cultivating the entrepreneurial mindset among engineering students necessitates a shared language around what this looks like in terms of attitudes and behaviors, and frameworks provide this. A framework was developed to characterize the entrepreneurial mindset in light of the Kern Family Foundation's 3C's: curiosity,…

This study aimed to enhance understanding of team creativity by investigating the type of team mental models that team members develop during their work on a creative problem solving task. We hypothesized that teams that develop dissimilar team mental models, compared to similar and complementary team mental models, will achieve a higher…

Accounts of practice within the action learning literature tend to omit the more mundane session-to-session details of the inner-workings of the action learning set. As well as concentrating on the problem, individuals in all sets spend some of their time in unproductive interpersonal exchanges. These exchanges may be considered trivialities and…

Metacognition is linked to academic achievement and personal development, especially as it relates to leadership education. The current study investigated the impact of a course in metacognition. Two hundred and fifty one undergraduates were surveyed for metacognitive ability using the Metacognitive Awareness Inventory (MAI) and Metacognitive…

Comprehending a mathematical modelling task is a central prerequisite for the following modelling process. In this study, we investigated the roles that the language proficiency of the students and the linguistic wording of the task play for the comprehension and the successful solving of mathematical modelling tasks. Five mathematical tasks with…

The aim of this study is to explore feedback practices and how such actions of assessment emerge from embodied participation in classroom interactions between teachers and students. Using video recordings of teacher and student interactions in hairdressing education, I look at how feedback practices within creative subject content are produced…