Abstract

GUTIERREZ, Ángel  and  JAIME, Adela. Reflections on the Teaching of Geometry in Primary and Secondary Schools. Rev. Fac. Cienc. Tecnol. [online]. 2012, n.32, pp.55-70. ISSN 0121-3814.

In this paper we introduce some important educational models relevant to the teaching and learning of Geometry in every educational level, from kindergarten to university. First, we describe the Van Hiele model, that currently is the most effective framework to organize the teaching of Geometry in any educational level. We will focus on one of its components, namely the phases of learning that proposes teachers a way to organize the contents of the lessons of Mathematics. Next, we will pay attention to the Vinner model of learning of mathematical concepts having strong graphical support. This model is more specific than the Van Hiele model, although they are fully compatible. The Vinner model describes the learning of concepts with graphical support based on the distinction among concept images and concept definitions, showing the role examples and counterexamples may play in students' understanding and learning. Lastly, we will raise the need for teachers to take into consideration graphical representations, both physical and mental, used in teaching and learning Geometry. I will describe the main components of the images, processes and abilities of visualization present when working with geometric elements.

Keywords : Mathematics education; Geometry education; Van Hiele; model of Vinner; visualization.

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