Humans appear to intuitively grasp definitions foundational to formal geometry, like definitions that describe points as infinitely small and lines as infinitely long. Nevertheless, previous studies exploring human's intuitive natural geometry have consistently focused on geometric principles in planar Euclidean contexts and thus may not…

Euclidean geometry has formed the foundation of architecture, science, and technology for millennia, yet the development of human's intuitive reasoning about Euclidean geometry is not well understood. The present study explores the cognitive processes and representations that support the development of humans' intuitive reasoning about Euclidean…

The study examined differences in students' conceptual and procedural knowledge of angles among two grades and gender. Participants were 382 sixth and 376 seventh graders from a metropolitan city in Turkey. Turkish students' conceptual and procedural knowledge of angles declined from sixth to seventh grade. Gender differences were found for…

The purpose of this study was to investigate kindergartners' geometric (shape, area and symmetry) and spatial (spatial orientation and spatial visualization) thinking skills, in the context of gender and age. Whether kindergartners' geometric and spatial thinking skills vary by their age or gender was questioned. A total of 73 kindergartners (40…

Four- to 10-year-old children (n = 50) participated in a 2D search task that included geometry (with- and without lines) and feature conditions. During each of 27 trials, participants watched as a cartoon character hid behind one of three landmarks arranged in a triangle on a computer screen. During feature condition trials, participants could use…

The aim of this study was to examine if there is a difference in the performance on non-linear problems regarding age, gender, and solving situation, and whether the multiple-choice answer format influences students' thinking. A total of 112 students, aged 15-16 and 18-19, were asked to solve problems for which solutions based on proportionality…

Geometry, e.g., the shape of the environment, can be used by numerous animal species to orientate, but data concerning the mouse are lacking. We addressed the question of whether mice are capable of using geometry for navigating. To test whether aging could affect searching strategies, we compared adult (3- to 5-mo old) and aged (20- to 21-mo old)…

This article examines students' development of levels of understanding for measurement by describing the coordination of geometric reasoning with measurement and numerical strategies. In analyzing the reasoning and argumentation of 38 Grade 2 through Grade 10 students on linear measure tasks, we found support for the application and elaboration of…

A four-year longitudinal study of concept attainment and uses of concepts, as specified by the Conceptual Learning and Development Model, is described. Data collected during the first two years were based upon the assessment of the concept, equilateral triangle. The assessment battery was administered to 351 children (grades K, 3, 6, and 9) in…

A total of 100 3- and 5-year-old children were trained and assessed individually on the concept of equilateral triangle at three levels of attainment: concrete, identity, and classificatory. Five training conditions existed: (1) visual inspection; (2) visual inspection and verbal orienting instruction; (3) visual inspection, free haptic activity,…