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J. J. Bissell – International Journal of Mathematical Education in Science and Technology, 2025
The small angle approximation sin[theta approximately theta] is central to all treatments of the simple pendulum as a harmonic oscillator and is typically asserted as a result that follows from calculus. Here, however, we show that the geometry of the pendulum "itself" offers a route to understanding the origin of the small angle…
Descriptors: Motion, Geometry, Scientific Concepts, Mathematics
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Kaur, Harpreet – International Journal of Mathematical Education in Science and Technology, 2020
This paper examines the effect of the use of dynamic geometry environments on young children's (ages 5-6, kindergarten/grade 1) thinking about angle. It provides a detailed description of introductory sessions of a geometry unit about angle, during which children worked in a whole classroom setting in which they could interact directly with…
Descriptors: Educational Technology, Technology Uses in Education, Computer Software, Geometry
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Dolores-Flores, Crisólogo; Rivera-López, Martha Iris; García-García, Javier – International Journal of Mathematical Education in Science and Technology, 2019
This paper reports the results of a research exploring the mathematical connections of pre-university students while they solving tasks which involving rates of change. We assume mathematical connections as a cognitive process through which a person finds real relationships between two or more ideas, concepts, definitions, theorems, procedures,…
Descriptors: Mathematics Instruction, Mathematical Concepts, Foreign Countries, Arithmetic
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Ponce Campuzano, Juan Carlos; Matthews, Kelly E.; Adams, Peter – International Journal of Mathematical Education in Science and Technology, 2018
In this paper, we report on an experimental activity for discussing the concepts of speed, instantaneous speed and acceleration, generally introduced in first year university courses of calculus or physics. Rather than developing the ideas of calculus and using them to explain these basic concepts for the study of motion, we led 82 first year…
Descriptors: Mathematics, History, College Freshmen, College Science
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Junius, Premalatha – International Journal of Mathematical Education in Science and Technology, 2008
The focus of the article is on the complex cognitive process involved in learning the concept of "straightness" in Non-Euclidean geometry. Learning new material is viewed through a conflict resolution framework, as a student questions familiar assumptions understood in Euclidean geometry. A case study reveals how mathematization of the straight…
Descriptors: Cognitive Processes, Geometry, Mathematics Instruction, Case Studies