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 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.

Although today's mathematical research community takes its international character very much for granted, this ``global nature'' is relatively recent, having evolved over a period of roughly 150 years-from the beginning of the nineteenth century to the middle of the twentieth century. During this time, the practice of mathematics changed from being centered on a collection of disparate national communities to being characterized by an international group of scholars for whom thegoal of mathematical research and cooperation transcended national boundaries. Yet, the development of an international community was far from smooth and involved obstacles such as war, political upheaval, and national rivalries. Until now, this evolution has been largely overlooked by historians andmathematicians alike. This book addresses the issue by bringing together essays by twenty experts in the history of mathematics who have investigated the genesis of today's international mathematical community. This includes not only developments within component national mathematical communities, such as the growth of societies and journals, but also more wide-ranging political, philosophical, linguistic, and pedagogical issues. The resulting volume is essential reading for anyone interestedin the history of modern mathematics. It will be of interest to mathematicians, historians of mathematics, and historians of science in general.

This book includes 18 peer-reviewed papers from nine countries, originally presented in a shorter form at TSG 25 The Role of History of Mathematics in Mathematics Education, as part of ICME-13 during. It also features an introductory chapter, by its co-editors, on the structure and main points of the book with an outline of recent developments in exploring the role of history and epistemology in mathematics education. It serves as a valuable contribution in this domain, by making reports on recent developments in this field available to the international educational community, with a special focus on relevant research results since 2000. The 18 chapters of the book are divided into five interrelated parts that underlie the central issues of research in this domain: 1. Theoretical and conceptual frameworks for integrating history and epistemology in mathematics in mathematics education; 2. Courses and didactical material: Design, implementation and evaluation; 3. Empirical investigations on implementing history and epistemology in mathematics education; 4. Original historical sources in teaching and learning of and about mathematics; 5. History and epistemology of mathematics: Interdisciplinary teaching and sociocultural aspects. This book covers all levels of education, from primary school to tertiary education, with a particular focus on teacher education. Additionally, each chapter refers to and/or is based on empirical research, in order to support, illuminate, clarify and evaluate key issues, main questions, and conjectured theses raised by the authors or in the literature on the basis of historical-epistemological or didactical-cognitive arguments.

Las ciencias y las técnicas han formado parte, desde el principio de la civilización, del desarrollo de la sociedad. Los cambios que han caracterizado las diferentes etapas del pensamiento científico se han producido dentro del marco de determinadas formaciones sociales y en condiciones específicas de producción del conocimiento. En este libro se aborda la manera en que se relacionan ciencia y sociedad: las formas de valorización social de las investigaciones, el sistema de trabajo en el interior de los laboratorios, las razones ideológicas de las teorías científicas, los mecanismos de financiación de la indagaciones científicas, las luchas jerárquicas entre los sabios y académicos, etc. Un conjunto de problemas que están más que nunca implicados en nuestros grandes problemas sociales. La explosión de las nanotecnologías, la controversia sobre los OGM, el cambio climático, etc., tantas temáticas cuya comprensión y control implican también conocer mejor las dinámicas sociales que forman parte de la producción de conocimientos y de las innovaciones. La presente obra, refundición de Sociología de las ciencias, publicada en 1995, muestra un planteamiento completo de todos estos problemas, con numerosos ejemplos y una muy amplia documentación. Presenta las diferentes formas de articulación ciencia/sociedad (emergencia de las ciencias, dinámica de innovación y democracia técnica) y los principales mecanismos sociales que hacen vivir a las ciencias (instituciones, organizaciones, intercambios entre investigadores, elaboración de contenidos, etc.). Este libro permite aprehender tanto la cultura material y cognitiva de un laboratorio como el funcionamiento del mercado de empleo científico. Más allá de la referencia a los grandes autores, corrientes de pensamiento y debates, ayuda a comprender mejor qué la sociedad y aquellas personas que tiene el poder decisorio fuerzan el desarrollo de las ciencias y de las técnicas, y qué los artesanos de estas últimas imponen a cambio sus lógicas propias. Habla así sobre la sociología de "la sociedad de los conocimientos”.