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In mathematics education, the Van Hiele model is a theory that describes how students learn geometry. The theory originated in 1957 in the doctoral dissertations of Dina van Hiele-Geldof and Pierre van Hiele (wife and husband) at Utrecht University, in the Netherlands. The Soviets did research on the theory in the 1960s and integrated their ...
Teaching should be appropriate to students' developmental level: Young students should be able to explain the difference between a rectangle and a square, while older students should be able to express more complex reasoning, including simple mathematical proofs. [11] (See van Hiele model.)
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The resulting structure, a model of elliptic geometry, satisfies the axioms of plane geometry except the parallel postulate. With the development of formal logic, Hilbert asked whether it would be possible to prove that an axiom system is consistent by analyzing the structure of possible proofs in the system, and showing through this analysis ...
Mathematics education reform built up momentum in the early 1980s, as educators reacted to the "new math" of the 1960s and 1970s.The work of Piaget and other developmental psychologists had shifted the focus of mathematics educators from mathematics content to how children best learn mathematics. [3]
A geometry is a pregeometry in which the closure of singletons are singletons and the closure of the empty set is the empty set. Independence, bases and dimension [ edit ]
Absolute geometry is a geometry based on an axiom system consisting of all the axioms giving Euclidean geometry except for the parallel postulate or any of its alternatives. [69] The term was introduced by János Bolyai in 1832. [70] It is sometimes referred to as neutral geometry, [71] as it is neutral with respect to the parallel postulate.
Mathematics and Plausible Reasoning is a two-volume book by the mathematician George Pólya describing various methods for being a good guesser of new mathematical results. [ 1 ] [ 2 ] In the Preface to Volume 1 of the book Pólya exhorts all interested students of mathematics thus: "Certainly, let us learn proving, but also let us learn guessing."