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Ítem Comparative study of van-Hiele model and theory of Pirie and Kieren. Two alternatives for understanding mathematical concepts(POLICIA NAC COLOMBIA, 2017-10-01) Londono Cano, Rene Alejandro; Jaramillo Lopez, Carlos Mario; Esteban Duarte, Pedro Vicente; Londono Cano, Rene Alejandro; Jaramillo Lopez, Carlos Mario; Esteban Duarte, Pedro Vicente; Universidad EAFIT. Departamento de Ciencias; Educación Matemática e Historia (EAFIT – U de A)This paper is a result of theoretical character, derived from a doctoral study in the frame of Mathematics Education, and its proposal is to describe important similarities and differences between the model of van-Hiele and Pirie and Kieren theory, and which have been theoretical frameworks of some educational experiences for understanding mathematical concepts. Initially, some backgrounds are considered in context itself, and after to be compared through descriptions and the respective nomenclature that each postulated level exhibits and so for characterizing them in order to achieve the respective conclusions. So, it is about to highlight some elements to argue the relevance of some theoretical framework or another one, according to any research purposes considered within the framework of the understanding of mathematical concepts.Ítem Distance-Virtual Education: Development and Characteristics in Mathematics Courses(FUNDACION UNIV CATOLICA NORTE, 2016-05-01) Sucerquia Vega, Edison Alberto; Londono Cano, Rene Alejandro; Jaramillo Lopez, Carlos Mario; de Carvalho Borba, Marcelo; Sucerquia Vega, Edison Alberto; Londono Cano, Rene Alejandro; Jaramillo Lopez, Carlos Mario; de Carvalho Borba, Marcelo; Universidad EAFIT. Departamento de Ciencias; Educación Matemática e Historia (EAFIT – U de A)The distance-virtual learning is a field that permanently transforms itself and allows the creation of new educational programs in different fields of knowledge and educational levels. In this sense currently is conducted a research called ``Interaction Processes for Producing Mathematical Knowledge in a Student Group with Media in Virtual Distance Learning'', aimed at educating a PhD student and contributing to this field with theoretical and methodological perspectives in Mathematical Education in the context of the program of virtual education called Ude@,through a study of qualitative-approach cases. This article deals with some analysis, reflections and significant characteristics of the teaching-learning processes of mathematics in this type of virtual environments, through the proposal of strategies that identify those interaction processes that allow producing mathematical knowledge in virtual-distance-education courses.