Mathematical Modelling and Didactic Moments

Sodré, Gleison de Jesus Marinho

doi:10.17648/acta.scientiae.6543

Cited by 2 publications

(2 citation statements)

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“…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.…”

Section: Future Research Outcomessupporting

confidence: 57%

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

2022

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Background: Several studies in mathematics education show the use of the physical abacus in the activities of teachers in initial graduation, emphasising, in their manipulation, practices with addition or subtraction operations, or yet, which express a direct translation of the numeral to the physical abacus and, vice versa, without, however, explaining part of the complexity involved the social practice of quantifying physical quantities, which even makes possible the structuring of the numeral. Objective: To show that the use of the abacus by teachers in initial training may not ensure the realisation or mastery of the practice of quantifying physical quantities with discrete units. Design: In this sense, a study and research path (SRP) was carried out based on the training of early years teachers. Environment and participants: 25 students in initial training of a degree course at a public educational institution participated in an activity on decimal number system (DNS), but largely positional number system (PNS), proposed based on a problem in an unusual context (for them), they mobilised to face and answer questions. Data collection and analysis: We present an excerpt from the empirical research forwarded by Ferreira (2020) with teachers in initial training. Results: The data observed in the empirical confirms the hypothesis of the existence of a problem regarding the use of the abacus as a possible facilitator in the structuring of non-decimal numbers through the practice of quantifying physical quantities. Conclusions: The results found with the teachers revealed, in addition to the problem of teacher training on what to teach and how to teach numerals, that using the abacus made it difficult, if not hindered, the practice of quantifying physical quantities with discrete units. We also found changes in the quality of the teachers’ relationships with structuring decimal and non-decimal numbers.

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Section: Future Research Outcomessupporting

confidence: 57%

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

2022

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“…In MM, Guerra e Silva (2009) and Sodré (2021) say that the situation and the mathematical model are interdependent and, therefore, it makes no sense to speak in the strict field of mathematical tasks. In this case, they are praxeological organisations with mathematics, those involving mathematical tasks and non-mathematical tasks, for example, the definition of a variable that is not reduced only to numbers, as mathematics considers, as they are endowed with senses and meanings not achieved by the mathematical tasks and, not least, by the complexity of articulations between different types of knowledge for the development of the MM process.…”

Section: Introduction: the Problem Of The Reverse Mathematical Modellingmentioning

confidence: 99%

Reverse Mathematical Modelling

2022

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Background: Research in mathematics education shows that mathematical modelling is a practice that seeks to “translate” problem situations into possible mathematical models without, however, explaining the complexity involved in the reverse formulation, starting from the mathematical model to delimit the type of situation. Objective: To highlight the problem of reverse mathematical modelling, in the sense of a reverse formulation that goes from the mathematical model to the situation. Design: For this, a course of study and research was carried out guided by the investigative cycle of mathematical modelling that is based on theoretical-methodological resources of the anthropological theory of the didactic. Setting and Participants: Pre-service teachers of a teaching degree at a public institution were faced with a problem in an unusual context about the decimal number system and, more broadly, the positional number system. Data collection and analysis: We present an empirical approach based on research carried out by Ferreira (2020) with teachers in initial training. Results: The empirical results observed confirm the hypothesis of the existence of the problem of reverse mathematical modelling, even in the face of normative models, in the sense that they can faithfully describe a real situation. Conclusions: Ultimately, the study of a type of problem in an unusual context, in addition to highlighting the encounter of teachers with different objects of knowledge, revealed the remarkable difficulty in delimiting the type of quantification situation that can be associated with the mathematical model of the number and as stimulate future research on the teaching of reverse mathematical modelling.

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Mathematical Modelling and Didactic Moments

Cited by 2 publications

References 9 publications

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

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

Reverse Mathematical Modelling

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