Description
Book SynopsisThis 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 that builds 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.
Table of ContentsForeword
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, TheoreticalMethodological 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
