O Ciclo Investigativo De Modelagem Matemática: Uma Transposição Didática Escolar

Abstract

O objetivo deste texto é analisar o alcance empírico do ciclo investigativo de modelagem matemática reconstruído para o estudo de problemas em contextos concretos. Para isso, foi utilizado esse ciclo construído, à luz de recursos teórico-metodológicos da teoria antropológica do didático, por pressupor que esse dispositivo didático criou condições, nem todas é claro, no sentido da transposição didática institucional para o enfrentamento do problema docente da modelagem matemática sobre como ensiná-la e, com isso, minimizar a invisibilidade dos saberes, matemáticos e não matemáticos. Resultados obtidos a partir da análise empírica com alunos do ensino médio revelam potencialidades do ciclo investigativo para aquisições de novos saberes, bem como se encaminha futura investigação.

Mathematical Modelling and Didactic Moments

“…Although research on the MM teaching by Borromeo Ferri ( 2006), Blum and Borromeo Ferri (2009), Perrenet and Zwaneveld (2012), Blum (2015), Greefrath and Vorhölter (2016), Vorhölter, Greefrath, Borromeo Ferri, Leiß and Schukajlow (2019), and Barquero and Jessen (2020), among others, highlight almost dominantly the didactic technique of MM cycles to minimise the complexity existing in the MM process, it is necessary to consider that this technique of cycles from the perspective of the anthropological theory of didactics, from now on ATD, is likely to be questioned, as highlighted by García, Gascón, Ruiz Higueras, andBosch (2006), Bosch, García, Gascón, andRuiz Higueras (2006), Sodré and Guerra (2018), Sodré (2019), and Sodré and Oliveira (2021), but instead of criticising it, providing it with solid theoretical frameworks that allow better understanding and, if possible, making it more accessible to the teaching and learning of MM.…”

“…In this line of thought, Sodré and Guerra (2018) and Sodré (2019) proposed the Investigative Cycle of Mathematical Modelling, hereinafter ICMM, "as a methodology for the development and analysis of mathematical models of situations in concrete contexts" (Sodré & Guerra, 2018, p. 253), which should "always be understood as relative and provisional, open to 1 Text fragment: Como podemos ensinar modelagem? 2 Text fragment: Un punto de partida bastante común en las líneas de investigación es lo que Gascón (2011) denomina el problema docente de la modelización matemática.…”

“…The ICMM (Sodré & Guerra, 2018;Sodré, 2019;Sodré & Oliveira, 2021) paraphrased from the three genres of genuine tasks of mathematical activity announced by Chevallard, Bosch, and Gáscon (2001): using known mathematics, learning (and teaching) mathematics, and creating new mathematics, should be forwarded sequentially by the study director or the class teacher, as guided by the following genres of tasks reconstructed from Sodré (2019): G1: Use socially legitimate mathematical models for situations in social contexts to answer questions about them, highlighting the associative relationship between situations in contexts and mathematical models; G2: Study a mathematical model in the face of different situations and contexts, and study a situation in a concrete context in the face of different mathematical models; G3: Create a mathematical model associated with a new situation from the study of situations and their associated mathematical models, considering the analogies or homologies between these situations and the new situation.…”

“…However, our assumptions based on Sodré and Guerra (2018), Sodré (2019) and Sodré, and Oliveira (2021), although following elements of the ATD, depart from the perspective of MM as a praxeological organisation of increasing complexity, considering that "school MM activities are not limited 4 Text fragment: Un hecho característico, y diferenciador de las investigaciones desde la TAD sobre los procesos de modelización matemática, es el papel del modelo epistemológico de referencia del ámbito a enseñar. Este modelo es una reconstrucción explícita y alternativa (a la organización del saber escolar) del saber a enseñar.…”

Teacher Training and the use of the Abacus in the Practice of Quantifying Physical Quantities

“…Hence, it somehow ratifies what Chevallard (2005) highlights about the distance between knowledge and social practice, in this case, the knowledge of the technique τ2 (the practice of quantification of discrete units), since knowledge about practices can constitute the specific knowledge of the social practice of quantification, but such an assertion cannot be guaranteed, since implicit or non-mathematical knowings give sense and meaning to social practice, as Sodré (2021) notes. Thus, considering the empirical results found, we motivate other researchers to carry out future research, including facing some problems that emerged, especially in mathematical modelling (Sodré & Guerra, 2018;Sodré, 2021) for the study of normative mathematical models, such as a numeral as a mathematical model that "governs" real-world situations.…”