Discussing mathematical modeling coursein a long distance course

The research related to critical and reflective dimensions of mathematical modeling isseeking identity, definition, and objectives. As well, it is developing a sense of its own nature andpotential for research methods used in order to legitimize pedagogical action. It is necessary to discussthe importance of philosophical and theoretical perspectives found in critically reflective dimensionsof mathematical modeling. As well, the importance of a virtual learning environment that helpsstudents to develop critical-reflective efficiencies has become increasingly important to enable the exploration of theories related to critical mathematical modeling, distance interactions, and transactional distance by using long-distance technologies. These interactions are triggered by lessons placed on platforms, which are virtual learning environments (VLE) and that enable the use a combination of technology, teaching and the learning of specific content. By developing discusión forums and video conferences, professors and tutors are able to analyze interactions enabled by these tools, which contributed to the reflective developmentof the elaboration of mathematical models in the VLE

Humanizing Mathematics through Ethnomodelling

Ethnomathematical techniques and modelling tools allow us to examine systems taken from the real world and offer us insight into forms of mathematics performed in holistic contexts [3]. A pedagogical approach that connects a diversity of cultural forms of mathematics can be implemented by the use of ethnomodelling, a process of translation and elaboration of problems and questions taken from non-academic systems. Here, we offer examples of studies conducted in Brazil and in the United States that explore this pedagogical approach. Our goal is to broaden the discussion of possibilities for ethnomathematics and associated ethnomodelling perspectives that respect the social diversity of distinct cultural group members with guarantees for the development of understanding of the different ways of doing mathematics through dialogue and respect

Ethnomodelling as a glocalization process of mathematical practices through cultural dynamism

Ethnomodelling can be considered as the association between ethnomathematics and mathematical modelling that enables members of distinct cultural groups to perceive a different reality in relation to the nature of mathematical knowledge. It also provides insights into many diverse forms of mathematics developed locally. Thus, ethnomodelling is defined as the study of mathematical phenomena that adds cultural components to the modelling process. The development of this connection is conducted through three cultural approaches: local, global, and glocal, which are used in the conduction of ethnomodelling investigations that aim to work against colonialism in order to value and respect sociocultural diversity of members of distinct cultural groups. Because ethnomodelling seeks to promote the development of understanding of differences through dialogue; it is important to argue for its inclusion as a translational process for systems taken from the reality of the members of diverse cultures. In this article we argue that ethnomodelling creates a firm foundation that allows for the integration of these three cultural approaches in exploring mathematical knowledge developed in distinct cultural groups through cultural dynamism

Conceitos de desvio positivo na ação pedagógica do programa etnomatemática

Um importante dilema em educação matemática é o seu contundente viés contra uma orientação local em seu paradigma de pesquisa. Assim, a busca por metodologias inovadoras como a etnomatemática é necessária para registrar formas históricas de ideias, procedimentos e práticas matemáticas desenvolvidas em contextos culturais diversos. É importante ressaltar que o programa etnomatemática não é uma tentativa de substituir a matemática acadêmica, mas, ao mesmo tempo, é necessário reconhecer a existência de conhecimentos matemáticos locais no currículo de matemática. Nesse contexto, a insubordinação desencadeada pela etnomatemática é criativa, pois evoca um distúrbio que desencadeia uma revisão das regras e regulamentos do currículo matemático. Esse contexto permite que os professores utilizem o desvio positivo para desenvolverem ações para lidar com essas normas. Assim, o desvio positivo envolve um ato intencional de quebrar as regras para servir um bem maior. Esse potencializa crescimento contínuo do debate sobre a natureza da matemática em relação à cultura uma vez que propõe um diálogo entre as abordagens locais e globais para a construção do conhecimento matemático

Reflecting on ethnomathematics as pedagogical action in the mathematics curriculum

The history of research in ethnomathematics has been dominated by the study of the fundamental differences in ways of doing mathematics among various cultures. Understanding these differences allows students and teachers to connect culture and mathematics by providing a transformational and holistic environment in which diversity is seen as good, valuable, and necessary to living in a contemporary world. The use of mathematics in everyday life varies according to each different culture and its needs. Ethnomathematics, which is the study of mathematics within its diverse cultural contexts, is used to express relationships between culture and mathematics. Thus, ethnomathematics is primarily concerned with connections that exist between the symbols, representations, and the imagery used to solve problems. The development of ethnomathematics as a program has challenged traditional concepts of Euro-Western centered mono-representational systems of mathematics transforming it into a multirepresentational system that represents mathematics as human endeavor. Hence, an ethnomathematics-based curriculum is grounded in the incorporation of mathematical ideas and activity that echo a diversity of cultures, particularly, those that experienced oppression or exclusion from society. Ethnomathematics is a pedagogical action that starts with teachers and students who learn to think flexibly about how they use mathematics in everyday and academic contexts

An ethnomathematical perspective of STEM education in a glocalized world

An Ethnomathematics-based curriculum helps students demonstrate consistent mathematical processes as they reason, solve problems, communicate ideas, and choose appropriate representations through the development of daily mathematical practices. As well, it recognizes connections with Science, Technology, Engineering, and Mathematics (STEM) disciplines. Our pedagogical work, in relation to STEM Education, is based on the trivium curriculum for mathematics and ethnomodelling, which provides communicative, analytical, material, and technological tools to the development of emic, etic, and dialogic approaches that are necessary for the elaboration of the school curricula. STEM education facilitates pedagogical action that connects ethnomathematics; mathematical modelling, problem-solving, critical judgment, and making sense of mathematical and non-mathematical environments, which involves distinct ways of thinking, reasoning, and developing mathematical knowledge in distinct sociocultural contexts. The ethnomathematical perspective for STEM education proposed here provides a transformative pedagogy that exposes its power to transform students into critical and reflective citizens in order to enable them to transform society in a glocalized world

A theoretical discussion to reveal the principles of culturally relevant education in an etnomathematical perspective

The implementation of Culturally Relevant Education helps to develop student intellectual, social, and political learning by using their cultural referents to acquire knowledge. It uses prior experiences of minority students to make learning more relevant and effective in order to strengthen their connectedness with school. Culturally relevant schools contextualize instruction and schooling practices while maintaining academic rigor. In these schools, school leaders, teachers, and staff members are able to recognize and build upon the strengths of students by applying instructional strategies that are culturally relevant. Culturally relevant leadership is grounded in the belief that minority students are able to excel in academic endeavors. Thus, it is necessary to enable the implementation of culturally relevant pedagogy into school curricula, which is designed to fit together school culture with students’ cultural backgrounds to help them to conceptualize knowledge. There is a need to examine the embeddedness of culture mathematics, which takes on the cultural nature of knowledge production into the mathematics curriculum. Ethnomathematics and culturally relevant pedagogy-based approaches to mathematics curriculum are intended to make mathematical content relevant to students. The objective of this theoretical article is to discuss the principles of culturally relevant education according to an ethnomathematical perspective

Applying Ethnomodelling to Explore Glocal Mathematical Knowledge Systems

Background: Ethnomodelling methods examine how members of distinct cultural groups have come to develop local mathematical knowledge. However, what may indeed be less evident is how mathematical thinking can be part of the way in which researchers and educators attempt to make sense of the underlying cultural frameworks within which mathematical ideas, procedures, and practices are embedded. Objectives: The main objective of this theoretical article is to present arguments that link mathematics and culture in order to develop an effective understanding of the development of dialogical mathematical knowledge. Design: The theoretical and methodological concepts of this qualitative study are supported by the assumptions of ethnomodelling that adds an important cultural perspective to the modelling process through the development of an extensive literature review on this topic. Results: We present arguments to show that the linking of mathematics and culture is appropriate and necessary for an effective understanding of the development of dialogical mathematical knowledge, which aims at providing a holistic understanding of human knowledge. This means that cognition is a process that is not only embodied and situated, as well as distributed because the members of distinct cultural groups create, process, accumulate, and diffuse mathematical information conjointly. Conclusions: We discuss the role of ethnomodelling in order to develop an understanding the connection between ethnomathematics and modelling. In this context, we present concepts related to the use of both local (emic), global (etic) approaches by applying the glocal (dialogical) approach found in ethnomodelling research

Book Review: Reckonings: Numerals, Cognition, and History by Stephen Chrisomalis

This review of Reckonings shares our thoughts on the diverse insights presented by Stephen Chrisomalis’s version of the history of numerical notation. Chrisomalis suggests that members of distinct cultural groups write numbers as an active choice in accordance with their own sociocultural contexts, which reflect the influences of historical, cognitive, social, economic, political, environmental, and cultural factors. This book integrates comparative, cognitive, and evolutionary understandings on numerical cognition with historical and linguistic evidence on the use and transformation of numeral systems through the historical advancement of numeracy. Chrisomalis offers an interesting historical perspective on numbers that builds upon three main themes: numerals, cognition, and history. Reckonings can inspire us to view the concept and constructs of numeracy through a historical and sociocultural lens