Hans Freudenthal proposed the Principle of Reinvention for curriculum development in 1973 and explained it through mathematization, using the levels of geometry as an example. He later rejected the distinction between vertical and horizontal mathematization proposed at his institute and redefined mathematization in relation to the “world of living” in 1991. To broaden mathematization into a theory applicable to the world of living and to areas beyond geometry, Isoda proposed the Theory of Representation in 1989 and again in 2015. In this lecture, mathematization is redefined as the process of reorganizing the world of mathematical representations. The discussion draws on several examples, including the Curriculum Framework for Mathematics Education in Southeast Asia,2nd edition in 2024, by Isoda and collaborators, school textbooks such as Gakkotosho and Sumo Primero, and historical sources such as Newton’s fluxions in Colson-1734, to show the significance of representation in comparison with Realistic Mathematics Education. Additional examples, including multiplication and equations in works by Isoda and Olfos, illustrate how intuition changes through the reorganization of representations. Route finding in Pascal’s Triangle by Isoda and collaborators in 2024, and the Tower of Hanoi in a forthcoming work by Isoda, are also examined to show how different worlds of representation support recursive thinking.<\/p>\n
Masami Isoda, University of Tsukuba, Japan<\/p>\n
(With the Support of Yuriko Yamamoto Baldin, University of San Carlos, Brazil)<\/p>\n
———<\/p>\n
Matematizaci\u00f3n y teor\u00eda de la representaci\u00f3n como bases para el desarrollo curricular<\/p>\n
Hans Freudenthal propuso el Principio de Reinvenci\u00f3n para el desarrollo curricular en 1973 y lo explic\u00f3 mediante la matematizaci\u00f3n, utilizando como ejemplo los niveles de la geometr\u00eda. Posteriormente, en 1991, rechaz\u00f3 la distinci\u00f3n entre matematizaci\u00f3n vertical y horizontal propuesta en su instituto y redefini\u00f3 la matematizaci\u00f3n en relaci\u00f3n con el “mundo de la vida”. Para ampliar la matematizaci\u00f3n a una teor\u00eda aplicable al mundo de la vida y a \u00e1reas m\u00e1s all\u00e1 de la geometr\u00eda, Isoda propuso, en 1989 y de nuevo en 2015, la Teor\u00eda de la Representaci\u00f3n. En esta conferencia, la matematizaci\u00f3n se redefine como el proceso de reorganizar el mundo de las representaciones matem\u00e1ticas. La discusi\u00f3n se basa en varios ejemplos, incluyendo el Marco Curricular para la Educaci\u00f3n Matem\u00e1tica en el Sudeste Asi\u00e1tico, 2\u00aa edici\u00f3n en 2024, de Isoda y colaboradores, libros de texto escolares como Gakkotosho y Sumo Primero, y fuentes hist\u00f3ricas como las fluxiones de Newton en Colson-1734, para mostrar la importancia de la representaci\u00f3n en comparaci\u00f3n con la Educaci\u00f3n Matem\u00e1tica Realista. Ejemplos adicionales, incluidos la multiplicaci\u00f3n y las ecuaciones en las obras de Isoda y Olfos, ilustran c\u00f3mo cambia la intuici\u00f3n mediante la reorganizaci\u00f3n de las representaciones. Tambi\u00e9n se examinan la b\u00fasqueda de rutas en El Tri\u00e1ngulo de Pascal por Isoda y colaboradores en 2024, y la Torre de Han\u00f3i en una obra siguiente de Isoda, para mostrar c\u00f3mo diferentes mundos de representaci\u00f3n apoyan el pensamiento recursivo.<\/p>\n
Masami Isoda, Universidad de Tsukuba, Jap\u00f3n<\/p>\n
Con el apoyo de Yuriko Yamamoto Baldin, Universidad de San Carlos, Brasil<\/p>\n
<\/p>\n
<\/p>\n
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