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…

Lockwood has argued that taking a set-oriented perspective is critical for successful combinatorial enumeration. To date, however, the research literature has not yet captured the cognitive processes involved in taking such a perspective. In this theoretical paper, we elaborate the constructs of spatial structuring and spatial-numerical linked…

Measurement concepts such as volume and surface area provide rich contexts for real-world applications of number processes. Despite their importance, many students and prospective teachers show superficial understanding of measurement concepts. A lack of spatial reasoning and integration of geometric knowledge in problem solving situations may be…

Spatial thinking permeates much of our lives and is an asset when solving problems involving well-structured visual information or imagining solutions in physical or digital space. However, an estimated three million US school children have spatial talents that go unrecognized because of the tools commonly used for identification of academic…

Spatial thinking permeates much of our lives and is an asset when solving problems involving well-structured visual information or imagining solutions in physical or digital space. However, an estimated three million US school children have spatial talents that go unrecognized because of the tools commonly used for identification of academic…

Research has demonstrated strong relations between spatial skill and mathematics across ages and in both typical and atypical populations, suggesting that a significant proportion of variance in mathematics performance can be explained by variance in spatial skill. Why do these relations exist and how do they develop? Studies of dimensionality in…

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…

As algebra teachers, the authors explore the following question in this article: "How can algebra 1, algebra 2, and precalculus teachers support students to develop algebraic reasoning and understanding of structure that can serve them in day-to-day algebraic computation?" The article shows how the algebraic identity "(a +…

Organic chemistry education is one of the youngest research areas among all chemistry related research efforts, and its published scholarly work has become vibrant and diverse over the last 15 years. Research on problem-solving behavior, students' use of the arrow-pushing formalism, the investigation of students' conceptual knowledge and…

A group theory course for chemists was taught entirely with process oriented guided inquiry learning (POGIL) to facilitate alternative strategies for learning. Students completed a test of one aspect of visuospatial aptitude to determine their individual approaches to solving spatial tasks, and were sorted into groups for analysis on the basis of…

The article provides a review of recent research on human performance on the traveling salesman problem (TSP) and related combinatorial optimization problems. We discuss what combinatorial optimization problems are, why they are important, and why they may be of interest to cognitive scientists. We next describe the main characteristics of human…

A question posed by a teacher can often serve as an effective and engaging way to start a class. Sometimes, however, interesting questions arise from comments made by students. The investigation presented in this article arose from a student's very simple question: "Is there a perfect rectangle for folding origami?" The initial investigation was…

Using a means-means-ends problem-solving task, this study examined whether 16-month-old walking infants (N = 28) took into account the width of a bridge as a means for crossing a precipice and the location of a handrail as a means for augmenting balance on a narrow bridge. Infants were encouraged to cross from one platform to another over narrow…

Spatial ability tasks appear on many intelligence and aptitude tests. Although the construct validity of spatial ability tests has often been studied through traditional correlational methods, such as factor analysis, less is known about the cognitive processes involved in solving test items. This study examines the cognitive processes involved in…

The authors' primary aim was to investigate a potential causal relationship between spatial ability and math ability. To do so, they used a pretest-training-posttest experimental design in which children received short-term spatial training and were tested on problem solving in math. They focused on first and second graders because earlier studies…