Mutis y la introducción del método analítico en Colombia

Abstract

En este trabajo se estudian las distintas modalidades de enseñanza del método analítico por José Celestino Mutis (1732-1808) en la cátedra de matemáticas del Colegio del Rosario de Bogotá durante la segunda mitad del siglo XVIII. Como marco de referencia para apreciar mejor las ransformaciones de esta enseñanza, se empezará por recordar algunas de las características históricas y filosóficas más importantes de la distinción cartesiana entre análisis y síntesis en el pensamiento matemático. Mutis empieza introduciendo el enfoque logicista del Discurso del Método de Wolff. Luego explica las reglas cartesianas del análisis y la síntesis, para lo cual traduce fragmentos de los Comentarios a la geometría de Descartes de Rabuel. También presenta las ideas de Newton sobre el método analítico, tanto en la modalidad experimental de la Óptica como en la perspectiva físico-matemática de los Principia. Se analizará el esfuerzo que pudo haber significado la comprensión de este cambio de perspectiva en el proceso de lectura y traducción de los Principia por parte de Mutis. Enseguida se muestra que al centrarse la enseñanza en los Elementos de Matemáticas de Bails —como consecuencia de la reforma del plan de estudios de la cátedra promovida por Mutis—, se termina adoptando la modalidad operatoria del análisis como aplicación del álgebra a la geometría. Finalmente se muestra que la introducción del texto de Bails conllevó una transformación de fondo en el enfoque epistemológico, cognitivo y pedagógico de la enseñanza por el método analítico en la cátedra del Rosario, comparada con los Elementa Matheseos Universae de Wolff en su etapa fundacional.

Strengthening of the water resource management seedbed by implementing project-based learning

“…In the research process developed, quantitative methodologies based on project-based learning are used, a tool that allows students to generate research projects with a social focus, thinking of sustainable and practical solutions for the benefited community, this is where the student's freedom enters in the generation of proposals or alternative solutions to a problem determined by them or by the teacher in order to strengthen academic and professional training processes, It is then clear for the students the plurality of possibilities of work by not having a single project to develop and have the possibility of proposing activities of their interest and generate a taste for research in order to obtain the best results, this idea of work has led the seedbed to generate projects developed and implemented in municipalities of Cundinamarca such as Pacho, Zipaquirá, Nemocón, Tocancipá, Sutatausa and Ubaté, municipalities of origin of the students and that see opportunities for improvement in specific areas of work where it allows them to strengthen human and social relations by interacting with communities under study taking into account the human-centered design (IDEO.org, 2015) this is the tool with which students generate a project with the ideal of satisfying the manifest needs of a community and adapts to the culture and customs depending on the region. Therefore, the work developed with the seedbed has a framework of topics in which students can choose related topics or break them down in a more specific way, in general, the topics selected by them can be grouped into 2 groups: It is here where students apply theoretical knowledge of subjects such as hydraulics, hydrology, aqueducts and treatment plants in a real space in order to generate alternatives for the use of rainwater for resource optimization purposes (Rios & Rios, 2018); (Castillo & Pantoja, 2018) properly distributing the use of drinking water, reducing such consumption by using rainwater for non-drinking uses in homes or even proposing alternatives for water treatability (Romero, 2002); (Arboleda, 2000) with the idea of improving its quality for agricultural purposes, livestock or even for human consumption always taking into account the current regulations (Ministerio de Vivienda Ciudad y Territorio, 2017), the sustainable construction of systems by reducing the amount of material or even generating proposals with recycled materials (C. A. Pérez Rodríguez, 2020b) where constructive alternatives developed by the students of the seedbed are presented from a common idea which contrast with prefabricated systems (PAVCO, 2014). This process arises from the manifest need of the community of the San Jorge hamlet in the municipality of Zipaquirá, where social leaders approach the regional center to seek advice from the civil engineering program and the seedbed in order to propose a possible solution to surface discharges of gray and black water due to the absence of a total sewage system but to the management given by septic tanks, this generates problems identified by (C. A. Pérez Rodríguez, 2020a) by evidencing discharges into bodies of water and surface that generate landscape deterioration which do not comply with current regulations (Ministry of Environment and Sustainable Development, 2015), students see in this process not only the generation of the design of the sewage system but the possibility of treatment of domestic and commercial wastewater in order to reduce its impact on nearby bodies of water and even ...…”

Relaciones entre historia de las matemáticas y formación de ingenieros

“…In the second half of the eighteenth century and the beginning of the nineteenth, the influence of Benito Bails's texts on teachers (of mathematical analysis such as José Celestino Mutis) is highlighted by Professor Luis Carlos Arboleda: Mutis favored the "transformations in the local thought of the analytical method by using the mathematical treatises such as Bails's Elements of Mathematics, with an epistemological, cognitive and pedagogical approach different from a traditional course such as Wolff's" [34]. In Bails's textbooks, the FTC don't appear explicit as a theorem, but one can find the integration methods and the calculation of plane areas [35].…”

Prehistoria del Observatorio Astronómico Nacional. Registros meteorológicos y astronómicos de José Celestino Mutis y Francisco José de Caldas entre 1772 y 1802

“…48(186):178-194, enero-marzo de 2024. doi: https://doi.org/10.18257/raccefyn.2524 Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales Diversos autores han estudiado la formación en astronomía adquirida por Mutis a mediados del siglo XVIII en Cádiz (Arboleda, 1986;Quevedo, 1985;González de Posada, 2009;Molina, 2020). Uno de ellos argumenta que el gaditano accedió a una formación newtoniana y astronómica básica como consecuencia de su participación libre en las sesiones de la "Asamblea amistosa literaria" establecida por Jorge Juan en 1755 (Molina, 2020).…”