Daniel Clark Orey

O campo de pesquisa em etnomodelagem: as abordagens êmica, ética e dialética

Neste artigo, oferecemos um conceito alternativo de pesquisa por meio da aquisicao dos conhecimentos emico e etico para a implementacao da etnomodelagem, que tem o objetivo de conectar os aspectos culturais da matematica com os seus aspectos academicos. Nessa perspectiva, a utilizacao das abordagens emica e etica facilita a traducao de situacoes-problema presentes nos sistemas, retirados da realidade de grupos culturais distintos, para a matematica academica. O conhecimento emico e essencial para a compreensao intuitiva e empatica das praticas matematicas desenvolvidas por determinado grupo cultural, enquanto o conhecimento etico e essencial para a comparacao entre essas praticas. Discutimos tambem a abordagem dialetica para a pesquisa em etnomodelagem, que utiliza ambos os conhecimentos emico e etico por meio de um processo dialogico, auxiliando uma compreensao mais completa sobre o conhecimento das praticas matematicas desenvolvidas pelos membros de distintos grupos culturais. Nesse sentido, o conhecimento emico e uma valiosa fonte de inspiracao para a elaboracao de hipoteses eticas. Em tal contexto dialetico, um curriculo matematico baseado na perspectiva da etnomodelagem favorece o desenvolvimento da geracao do conhecimento matematico para garantir a integracao equilibrada do dominio efetivo dos objetivos educacionais, que sao essenciais para o reconhecimento e a utilizacao do conhecimento emico dos alunos.

Ethnomodelling as a Research Lens on Ethnomathematics and Modelling

Mathematics used outside of the school may be considered as a process of modelling rather than a mere process of manipulation of numbers and procedures. The application of ethnomathematical techniques and the tools of modelling allow us to see a different reality and give us a more holistic insight into the kind of mathematics used by specific groups of people. The pedagogical approach that connects the academic to the cultural aspects of mathematics is named ethnomodelling; which is a process of translation and elaboration of problems and questions taken from systems that are part of any given cultural group.

Ethnomodelling as a Methodology for Ethnomathematics

The application of ethnomathematical techniques and tools of modelling allows us to examine systems taken from reality and offers insight into forms of mathematics done in a holistic way. The pedagogical approach that respects a diversity of cultural forms of mathematics is best represented through ethnomodelling, which is a process of translation and elaboration of problems and the questions taken from reality. We would like to broaden the discussion of possibilities for the inclusion of ethnomathematics and associated ethnomodelling perspectives that respect the social diversity of distinct cultural groups with guarantees for the development of understanding different ways of doing mathematics through dialogue and respect.

A modelagem como um ambiente de aprendizagem para a conversão do conhecimento matemático

Modeling investigation as a learning environment for the construction of mathematical knowledge is becoming prevalent in academic environments. This learning environment facilitates a pedagogical structure that promotes the identification and dissemination of both explicit and tacit student knowledge through the study and codification of mathematical ideas, present in systems taken from reality. In this article, we discuss the main features for the conversion of both explicit and tacit mathematical knowledge through the use of modeling as a learning environment.

Social-critical Dimension of Mathematical Modelling

Among innovative teaching methodologies, it is important to highlight the use of the social-critical dimension of mathematical modelling to solve problem situations that afflict contemporary society. Research related to mathematical modelling and the social-critical dimension of this approach has redefined its objectives, and is developing a sense of its own nature and potential of research methods in order to legitimize its pedagogical action. In this regard, it is necessary to discuss the importance of philosophical and theoretical perspectives found in social-critical dimensions of mathematical modelling and its epistemology as well. The importance of a learning environment that helps students to develop their social-critical efficacy is supported by the use of mathematical modelling.

Mathematical Modelling in a Long-Distance Teacher Education in Brazil: Democratizing Mathematics

This chapter describes how a group of mixed ability students used long-distance education technologies to develop mathematical models in relation to their experience with nationwide protests related to sudden and steep rises in transportation costs during June 2013 in Brazil. Mathematical modelling became a teaching methodology that focused on the development of a critical and reflective efficacy engaging students in a contextualized teaching-learning process that allowed them to become involved in the construction of solutions of social significance. Pertinent theories related to critical mathematical modelling in the context of long-distance technologies are outlined. This approach allows for the democratization of higher education in Brazil by democratizing mathematics through the development of the modelling process in virtual learning environments.

State of the Art in Ethnomathematics

Ethnomathematics uses the etymology of three Greek roots, ethno, mathema, and tics. It is a program that incorporates mathematical ideas and procedures practiced by the members of distinct cultural groups, which are identified not only as indigenous societies but as groups of workers, professional classes, and groups of children of a certain age group as well.

History of Mathematics and Culture: Moments and Movements in Brazilian Mathematics Education

This chapter presents moments and movements discussed by the Working Group WG05-History of Mathematics and Culture of the Brazilian Society of Mathematics Education. Considering the proceedings and the books that have resulted from the six editions of the International Seminar of Research, SIPEM, we conducted a survey to map the current research and explore the discussions, drawing conclusions concerning the theoretical and methodological perspectives of the group. In the study, three axes have been characterized: ethnomathematics, history of mathematics, and history of mathematics education. We observed a variety of approaches that can be summarized around the area of multicultural education, the role of history in teaching and teacher education, and the importance of developing historical knowledge about the creation of knowledge, methodologies, and pedagogical practices. Here, the importance of research that incorporates diverse sociocultural methods to produce mathematical and historical knowledge in school mathematics and its pedagogical practices cannot be overstated.

STEM Education in the Brazilian Context: An Ethnomathematical Perspective

Our ethnomathematical curriculum perspective helps students to demonstrate effective mathematical processes as they reason, solve problems, communicate mathematical ideas, chose appropriate representations through the development of mathematical practices, as well as recognize connections between mathematical concepts and the STEM disciplines. Our proposal is based on the trivium curriculum for mathematics by Ubiratan D’Ambrosio and provides communicative, analytical, and technological instruments necessary for a twenty-first-century reality. STEM education for a Junior Secondary school mathematics curriculum in Brazil proposes pedagogical action that deals with problem-solving, modeling, critical judgment, and making sense of mathematical and non-mathematical contexts, which involve distinct ways of thinking, reasoning, and knowing mathematics in practical contexts. This ethnomathematical perspective proposes a transformative pedagogy exposing its power to transform learners into critical and reflective citizens of change within the society.

The Critical-Reflective Dimension of Ethnomodelling

This discussion is related to critical-reflective dimensions of ethnomodelling, which is the creation of indeed the exploration of contexts that develop creativity in students in order to enable them to solve problems they face in their own sociocultural contexts. The critical-reflective dimensions of ethnomodelling allows learners the opportunity to develop a sense of purpose and their own potential by using mathematics to examine and solve problems they themselves choose and deem important. In this chapter, the author also discusses the importance to use both emic and etic approaches in the implementation of ethnomodelling in investigations. Emic approach is essential for an intuitive and empathic understanding of mathematical ideas, procedures, and practices developed by the members of distinct cultural groups while etic approach is important for cross-cultural comparisons that demand standardized categories to facilitate communication. This context enables ethnomodelling to bring cultural elements to the modelling process because it is the study of mathematical phenomena within a culture. If mathematics is considered as a universal language, then the process of the elaboration of an ethnomodel is the act of creating a mathematical poem. Thus, working with learners in assisting them in this creation is the act of ethnomodelling.