Spatial abilities have been found to interact with the design of visualizations in educational materials in different forms: (1) spatial abilities enhanced learning with optimized visual design (ability-as-enhancer) or (2) spatial abilities compensated for suboptimal visual design (ability-as-compensator). A brief review of pertinent studies…

This paper combines recent developments in theories of knowledge (complex dynamic systems), technologies (embodied interactions), and research tools (multimodal data collection and analysis) to offer new insights into how conceptual mathematical understanding can emerge. A complex dynamic system view models mathematics learning in terms of a…

In many schools across the world, students experience mathematical concepts as ideas empty of wisdom and possibility. In this paper the authors analyze a philosophical conversation in which fifth-grade students were caught up in the animacy of the concept of space. Challenging the common view of mathematics as dealing with absolute truths and…

The present study compared Japanese and U.S. preschool children's knowledge of geometric shapes. The main goal was to explore if differences in shape-naming conventions in Japanese and English could explain differences in children's understanding of geometric shapes. In ancient Chinese-based languages (e.g., Japanese), all standard 2D shapes…

Spatial geometry is one of the multi-purpose fields of mathematics and is tightly linked to the development of mathematical and intellectual thinking. Spatial thinking is necessary in various areas of life such as civil engineering, mechanical engineering, interior design, graphic design and other. At present, teaching spatial geometry is mainly…

In mathematics education, students are repeatedly confronted with the tasks of interpreting and relating different representations. In particular, switching between equations and diagrams plays a major role in learning mathematical procedures and solving mathematical problems. In this article, we investigate a rather unexplored topic with…

Mathematics is an essential subject in schools, helping develop cognitive skills such as critical analysis, logical reasoning, and problem-solving. However, academic achievement in mathematics often declines, with some students having difficulty understanding mathematical ideas. Many factors influence mathematics achievement, including students'…

This theoretical article explores the affordances and challenges of Euler diagrams as tools for supporting undergraduate introduction-to-proof students to make sense of, and reason about, logical implications. To theoretically frame students' meaning making with Euler diagrams, we introduce the notion of logico-spatial linked structuring (or…

Background: Disembedding is a crucial spatial thinking skill in visual arts and mathematics education. It is important in creating and analyzing artworks by separating a figure from its background, as well as for solving geometric problems where shapes must be viewed from new perspectives. Drawing upon research in psychology, arts, and mathematics…

3D geometry is an essential concept in mathematics because it relates to real-world experiences and numerous mathematical topics. However, some students still have difficulty understanding this geometry. Therefore, this study aims to identify and describe students' epistemological obstacles to the dimensions of representation, spatial structure,…

The perception of 3D features from 2D representations depend on their number of salient features, recognizable canonical axes, and orientations. Informed by form-perception literature, we proposed a hexagonal prism as an external reference frame to identify positions of elements in relation to each other and the observer when studying Diels-Alder…

This study continues an investigation of how spherical units, compared to cubical units, can facilitate students' units-locating and organizing units in composites. We analyze how Norwegian grade 3 students enumerate 3D arrays with cubical and spherical units. Our results show how spherical units can act as perceptual clues that facilitate…

In the 11th-grade Vietnamese Mathematics Curriculum, students learn about parallel relations between planes in space. This is cognitively challenging for many students. Studies have shown difficulties relating to limited spatial imagination and drawing representations. The teacher's approach also causes difficulties for some students; for example,…

Recent research in numerical cognition has begun to systematically detail the ability of humans and nonhuman animals to perceive the magnitudes of nonsymbolic ratios. These relationally defined analogs to rational numbers offer new potential insights into the nature of human numerical processing. However, research into their similarities with and…

When students see mathematics as an integrated field of study, they make connections, gain a deeper understanding of mathematical concepts, and see mathematics as a whole rather than disconnected, unrelated ideas. Measurement concepts are the perfect "seed to plant" to show how different mathematical strands integrate within other…