Constructing a consensus problem space from extensive qualitative data for an ill-structured real-life problem and expressing the result to a broader audience is challenging. To effectively communicate a complex problem space, visualization of that problem space must elucidate inter-causal relationships among the problem variables. In this…

Tentativeness is often framed as a deficit, synonymous with timidity or a lack of confidence. In this article, I situate the notion of tentativeness in an enactivist framework and describe its role as both a strategy and affordance in a spatial visualization exercise. Drawing on insights from mathematics education and ecological psychology, I…

The article uses dynamic visualizations in Excel to examine a variety of ways in which students can attain a much greater depth of understanding of optimization problems in introductory calculus. The topics discussed include a variety of common optimization problems that appear in virtually every calculus textbook that can all be enhanced…

Visual scaffolding, a type of scaffolding provided in a visual format, is considered to have potential in web-based learning environments as it naturally includes tacit information, highlights the critical features of tasks and promotes learning through the spatial organization of tasks. However, systematic approaches to visual scaffolding design…

Visualising positive and negative numbers on a number line is helpful for exploring problems involving operations with positive and negative numbers. This is because number lines lend themselves to exploring problems involving continuous linear contexts such as travelling distances and temperature. Teachers in a professional development program…

An augmented reality (AR) application and an activity worksheet have been developed to support students in visualizing the concepts involved when solving [superscript 1]H NMR problems. This instructional resource was designed to encourage conceptual problem-solving and prevent memorization by eliminating the use of chemical shift tables. It uses…

The last 15 years have witnessed a quiet revolution in the understanding of spatial skills, and the authors are finding that these all-important science, technology, engineering, and math (STEM) competencies are rooted in spatial knowledge. Spatial skills are the tools use to visualize and navigate the world. Spatial skills allows people to…

While data analysis and the related skills of data management and data visualization are important skills for undergraduates in the field of political science, the process of learning these skills can also be used to develop critical thinking, encourage active and collaborative learning, and to apply knowledge gained in the classroom. Drawing on…

The higher education system of the Republic of Kazakhstan emphasizes the need for the development of institutional science, including the field of information technology, with a priority on fundamental research. Professional training of future computer science teachers requires them to know the range of tasks related to computer graphics, and the…

Launching a problem is critical in a problem-based lesson. We investigated teachers' perspectives on the use of a problem that was analogous to the one provided during a launch. Our goal was to identify teachers' underlying assumptions regarding what should constitute a launch as elements of the "practical rationality of mathematics…

Computer-supported collaboration by spatially distributed group members still involves interaction problems within the group. This article presents an empirical study investigating the question of whether computer-supported collaborative problem solving by spatially distributed group members can be fostered by evoking knowledge and information…

Research (Fish, 2004) suggests that everybody should be taught how to freehand sketch and utilise it as a tool for supporting the visualising instinct. A fundamental shift in philosophy of the technology education system in Ireland towards design driven subjects brought with it a need to develop practising teacher's technological capabilities.…

This paper documents the development of the Geometric Spatial Assessment. We detail the development of this instrument which was designed to identify middle school students' strategies and advancement in understanding of four geometric concept domains (geometric spatial visualization, spatial projection, cardinal directions, and periodic patterns)…

The purpose of this study was to determine whether or not the use of solid modeling software increases participants' success in solving a specified technical problem and how visualization affects their ability to solve a technical problem. Specifically, the study sought to determine if (a) students' visualization skills affect their problem…

A random sample of middle school special education teachers from various classroom settings completed a survey asking them about what instructional practices and materials they used to teach students with disabilities how to solve word problems, how much time they allocated to problem solving instruction, and what type of problems they gave their…