Resumen: Este trabajo es una respuesta al artículo (Godino, 2023), y supone una continuación de un diálogo entre diferentes enfoques en didáctica de las matemáticas iniciado en (Gascón y Nicolás, 2017). Aquí abordamos en profundidad la siguiente cuestión: ¿pueden ser los juicios de valor presentados como resultados de la investigación científica? Para ello, vinculamos esta pregunta con una clásica tesis de Max Weber, y analizamos algunas tesis supuestamente incompatibles con la tesis de Weber. A continuación, argumentamos a favor del carácter no normativo de la ciencia didáctica, y criticamos el papel que se asigna a los criterios de idoneidad didáctica en el Enfoque Ontosemiótico. Terminamos contraponiendo los límites de la ciencia (en particular, la didáctica) con su enorme poder transformador (en particular, de la práctica docente).

Abstract: This work is an answer to the paper (Godino, 2023), and it contributes to a dialogue between different approaches in mathematics education started with (Gascón y Nicolás, 2017). Here we address in depth the following question: can value judgement be presented as results of scientific research? For this, we link this question with a classical thesis by Max Weber, and we analyse some theses allegedly incompatible with that of Weber. Next, we defend the non-normative character of didactics as a scientific activity, and we question the role attributed to the didactic suitability criteria of the Ontosemiotic Approach. Finally, we contrast the limits of science (in particular, didactics) with the great transformative power (in particular, of the teaching practice).

Abstract: Our starting point is the thesis, perhaps already widely accepted, according to which the epistemological model of mathematics prevailing in a didactic institution strongly affects the teaching in that institution. One of the aims of this work is to enlighten and to generalize this thesis. We will suggest that, rather than just the epistemological model, a complete explanation of teaching practices taking place in a certain institution should also take into account what we call didactic paradigms. At the same time, if we enlarge the notion of theory in didactics by means of the idea of praxeology of research in didactics, it becomes clear that a didactic paradigm is something that can also live or be assumed by such a praxeology of research in didactics, and that affects the kind of research problems considered therein. Therefore, for two theories in didactics to stablish a connection, it is required to make explicit the didactic paradigm assumed by each one.

Resumen: La tesis que tomamos aquí como punto de partida, puede formular-se brevemente como sigue: el modelo epistemológico de las matemáticas vigente en una institución didáctica condiciona fuertemente las prácticas docentes que es posible desarrollar en la misma. Uno de los objetivos de este trabajo consiste en clarificar y generalizar esta tesis, mostrando que, más allá del modelo epistemológico subyacente, son los paradigmas didácticos los que permiten explicar las prácticas docentes que la institución lleva a cabo. Paralelamente, al ampliar la noción de teoría didáctica mediante la de praxeología de investigación didáctica, se pone de manifiesto la incidencia del paradigma didáctico que una comunidad científica asume sobre el tipo de problemas de investigación que privilegia y, en última instancia, la importancia del contraste entre paradigmas para profundizar el diálogo entre teorías didácticas.

Nesta investigação estudamos um fenômeno didático complexo que se manifesta na desconexão dos conteúdos matemáticos que constituem o programa oficial do ensino secundário/médio e que está fortemente relacionado com a rigidez e a atomização da Matemática escolar. Para tal estudo utilizamos as ferramentas teóricas e metodológicas que nos proporciona a Teoria Antropológica do Didático (TAD) cujo objeto primário de investigação é a análise da atividade matemática escolar institucional. Assim, realizamos estudos exploratórios nos manuais escolares de Matemática do ensino secundário de Portugal e da Espanha, contrastando e comprovando cinco conjeturas relacionadas, por exemplo, com a ausência de questionamento e justificação das técnicas utilizadas. Concluimos que nestes países as praxeologias matemáticas apresentam-se desarticuladas, rígidas,e, consequentemente, surgem isoladas atividades de modelagem matemática nas instituições escolares.

In this research, we studied a complex didactic phenomenon manifested on the disconnection of mathematical contents that constitute the official program of secondary education and that relates strongly to the rigidity and atomization of school mathematics. For this study, we used the theoretical and methodological tools that the Anthropological Theory of Didactic (ATD) provides us, which primary object of research is the analysis of the institutional school mathematics activity. Thus, we carry out exploratory studies in mathematics textbooks in Portugal and Spain secondary education, contrasting and proving five conjectures related, for example, with the absence of questioning and justification of the used techniques. We conclude that in these countries, the mathematical praxeologies are often disjointed, rigid and, consequently, there are isolated activities of mathematical modelling in educational institutions.