This book is about the unique, sophisticated, and rigorous study of mathematics in Latin America developed over centuries of cultural exchange between Europe, North, and South America. More specifically, the book explores the tradition of mathematical modelling, introduced a century ago. This modelling was adapted to assist members of distinct communities to draw information about their own realities through the elaboration of representations, which generate mathematical knowledge that deals with creativity and invention. The book provides empirical evidence that a category of mathematical modelling developed in Latin America assesses the horizontal and reciprocal relations between mathematics (school/non-school contexts) and the real world. These relations provide an epistemological and ontological change, where mathematical knowledge of the others is recognized on a horizontal plane. Further, they oblige mathematics teachers and students to understand as a community of knowledge thatbuilds their own mathematical categories of their environment governed by the reciprocal relationships between academic knowledge and functional knowledge. The dimensions of the relationships make up a frame of reference that guides educational change in mathematics. The book presents an inquiry-based approach of three Latin American modelling programs: ethnomodelling, transversality of knowledge, and reasoned decision-making. Each one, with its respective theoretical and methodological foundations related to ethnomathematics and mathematical modelling, socioepistemology, and the attribution of meaning to learning. Undoubtedly, the three mathematical modelling programs, independently, provide educational gains, each with its levels of specificity and loyal to its philosophical, theoretical, and methodological principles. However, the book places them together, organized by axes, to define a corpus of mathematical knowledge that envisions profound educational change through the development of different approaches of mathematical modelling. The authors of the 18 chapters in this book, who represent the diversity of Latin America, are from eight countries: Argentina, Brazil, Chile, Colombia, Costa Rica, Cuba, Ecuador, Honduras, and Mexico. They were invited to share their ideas, perspectives, and discuss investigations that represent a rich sample of three Latin American perspectives on mathematical modelling.
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PART I.- Introduction.- Chapter 1 Modelling in the life of people: an alternative program for teaching and learning of mathematics.- PART II Ethnomathematics and Ethnomodelling: Empirical Work, Theoretical Methodological Approaches, and Research Questions.- Chapter 2 Conceptualizing positive deviance in ethnomodelling research: creatively insubordinating and responsably subverting mathematics education.- Chapter 3 Ethnomodelling as an alternative to Basic Education: perceptions of members of a research project.- Chapter 4 Ethnomodelling aspects of positionality between local and global knowledge through glocalization: a case of a farmer vendor.- Chapter 5 Ethnomodeling as a pedagogical action in diverse contexts by using dialogical knowledge.- Chapter 6 Ethnomodelling: weaving networks between academic mathematical knowledge and cultural knowledge in the southeastern region of Tocantins.- Chapter 7 Mathematical Analysis of the Ceramic Designs of the Pre-Columbian Cultures of Ecuador through Ethnomodelling with a Sociocultural Approach.- PART III Interdisciplinary Ecosystems: Empirical Work, Theoretical-Methodological Approaches, and Research Questions.- Chapter 8 Analyzing the availability of renewable energy resources in a project in real context: a framework for making sense of learning.- Chapter 9 Descriptive and prescriptive modeling in a math class project: disciplinary concepts participating in the construction of arguments for decision-making.- Chapter 10 Designing and building a mobile support for solar panels: a project for 12-year-old students that required mathematical modelling and more.- Chapter 11 From an epistemological approach to an epistemic one: reference change in the looks of math teachers in real context projects.- PART IV Mathematics and People: Empirical Work, Theoretical-Methodological Approaches, and Research Questions.- Chapter 12 A category of modelling: the uses and learning of mathematical knowledge in different scenarios.- Chapter 13 Modelling and anticipation of graphical behaviors in Industrial Chemical Engineering: the role of transversality of knowledge in learning mathematics.- Chapter 14 Category of modelling and reproduction of behaviours in other disciplines: the teaching of mathematics and engineering.- Chapter 15 The disciplinary identity in initial mathematics teacher training and people´s category of modelling: a valorization of the knowledge of the learner.- Chapter 16 Contemporary learning in the interaction of the human with data, via technology-mediated graphics: the discourse-representation dialogue in mathematics.- Capítulo 17 Modelling of natural phenomena as a source to re-signify mathematical knowledge: some examples.- Part V.- Conclusion The Mathematical Teaching and Learning Process through Mathematical Modelling: Educational Change in Latin America.
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Dr. Milton Rosa earned a Masters’ degree in 2001 and a Doctorate degree in 2010 both in Education from California State University in Sacramento. He also earned a post-doctorate degree in Education from Universidade de São Paulo and his studies focuses on ethnomodelling research, which is the connection between ethnomathematics and mathematical modelling. He has published papers and articles in national and international journals, chapter books, and books in Portuguese, Spanish, and English. He joined conferences and symposia in international and national levels with contributions of plenaries, round tables, communications, and posters. He also has supervised numerous master theses in the area of Mathematics Education. In 2010, Dr. Rosa was awarded the Dr. Carlos J. Vallejo Memorial Award, in the area of Multicultural and Multiethnic Education (MME), in the Special Interest Group (SIG) in the American Education Research Association (AERA) for his contributions in the area of cultural diversity in Mathematics Education.
Dr. Francisco Cordero, Ph D, is a Senior Researcher in the Department of Educational Mathematics of the Center for Research and Advanced Studies (CINVESTAV) and Coordinator of the Higher Education Area. He earned his Ph D in Mathematics Education at CINVESTAV and postdoc at Purdue University, Indiana, United States. Dr Cordero’s research topics are the socio-epistemology theory of educational mathematics, categories of the use of mathematical knowledge of people, mathematical modelling and transversality of knowledge, training and professionalization of the teacher in mathematics and the socialization of the science. He is a member of the National System of Researchers (SNI), the Mexican Academy of Sciences (AMC) and the Latin American Committee for Educational Mathematics (Clame). He has trained researchers for several generations: he has supervised a little more than 62 master’s theses and 22 doctoral theses. He has published a hundred articles in prestigious magazines, as well as twenty books and chapters in prestigious publishing houses. Due to his academic leadership, he has given a hundred conferences at universities in different countries: Argentina, Brazil, Colombia, Chile, Cuba, Guatemala, Honduras, Mexico, Panama, Dominican Republic, Uruguay, United States, Spain, France, and Turkey.
Dr. Daniel Clark Orey, Ph.D. is Professor Emeritus of Mathematics and Multicultural Education at California State University, Sacramento where he served from 1987 to January 2011. Dr. Orey graduated from Oregon State University in 1978 and taught in Oregon and in Guatemala. He earned his Ph.D. in Curriculum and Instruction in Multicultural Education at the University of New Mexico in 1988. His masters work took him to Patzun, Chimaltenango in Guatemala where he did field research with Logo, computers and Mayan children. In 1998, at the invitation of Professor Ubiratan D’Ambrosio, Dr. Orey served as a Fulbright Scholar at the Pontifícia Universidade Católica de Campinas in Brasil, which he conducted research in classrooms and taught courses in ethnomathematics and mathematical modeling. In 2007, Dr. Orey served as Senior Fulbright Specialist in Kathmandu University, Nepal, giving lectures on topics related to mathematics education and teaching on Ethnomathematics and Modelling. He is currently professor of mathematics education in the Departamento de Educação Matemática and in the Master’ Degree Program in Mathematics Education at the Universidade Federal de Ouro Preto, Brasil.
Pablo Carranza carried out master’s and doctorate studies in Mathematics Didactics at Denis Diderot University in France. He has worked as a mathematics teacher in rural, urban, public and private schools. He is currently a research professor at the National University of Rio Negro. There he conducts research on projects in real context as a framework for learning disciplinary concepts. In this context, he directs both research and extension projects aimed at real problems in the community.
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