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Direct linkHart, Yuval; Mahadevan, L.; Dillon, Moira R. – Cognitive Science, 2022
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…
Descriptors: Geometry, Cognitive Processes, Thinking Skills, Geometric Concepts
Download full textCandace Walkington; Mitchell J. Nathan; Min Wang; Kelsey Schenck – Grantee Submission, 2022
Theories of grounded and embodied cognition offer a range of accounts of how reasoning and body-based processes are related to each other. To advance theories of grounded and embodied cognition, we explore the "cognitive relevance" of particular body states to associated math concepts. We test competing models of action-cognition…
Descriptors: Thinking Skills, Mathematics Skills, Cognitive Processes, Models
Candace Walkington; Mitchell J. Nathan; Min Wang; Kelsey Schenck – Cognitive Science, 2022
Theories of grounded and embodied cognition offer a range of accounts of how reasoning and body-based processes are related to each other. To advance theories of grounded and embodied cognition, we explore the "cognitive relevance" of particular body states to associated math concepts. We test competing models of action-cognition…
Descriptors: Thinking Skills, Mathematics Skills, Cognitive Processes, Models
Mariotti, Maria Alessandra; Pedemonte, Bettina – ZDM: The International Journal on Mathematics Education, 2019
The cognitive relationship between intuition and proof is complex and often students struggle when they need to find mathematical justifications to explain what appears as self-evident. In this paper, we address this complexity in the specific case of open geometrical problems that ask for a conjecture and its proof. We analyze four meaningful…
Descriptors: Mathematical Logic, Mathematics Instruction, Teaching Methods, Intuition
Gómez-Chacón, Inés Ma; Kuzniak, Alain – International Journal of Science and Mathematics Education, 2015
The main goal of this research was to assess the effect of a dynamic environment on relationships between the three geneses (figural, instrumental, and discursive) of Spaces for Geometric Work. More specifically, it was to determine whether the interactive geometry program GeoGebra could play a specific role in the geometric work of future…
Descriptors: Correlation, Geometry, Mathematics Instruction, Educational Technology
Sriraman, Bharath – Journal for the Education of the Gifted, 2004
High school students normally encounter the study and use of formal proof in the context of Euclidean geometry. Professional mathematicians typically use an informal trial-and-error approach to a problem, guided by intuition, to arrive at the truth of an idea. Formal proof is pursued only after mathematicians are intuitively convinced about the…
Descriptors: Grade 9, Intuition, Academically Gifted, Geometry
Peer reviewedAvital, Shmuel; Barbeau, Edward J. – For the Learning of Mathematics, 1991
Presents 13 examples in which the intuitive approach to solve the problem is often misleading. Presents analysis of these problems for five different sources of misleading intuitive generators: lack of analysis, unbalanced perception, improper analogy, improper generalization, and misuse of symmetry. (MDH)
Descriptors: Cognitive Development, Cognitive Processes, Generalization, Geometric Concepts
