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Hacia la transformación de la clase de matemáticas.
Esta investigación sobre el profesor de matemáticas y su acción en clase, responde a un esfuerzo conjunto entre grupos de investigación de Colombia, España, Ecuador y Panamá. Visibiliza aportes de investigación desde distintas perspectivas teóricas y metodológicas. Los focos desarrollados consideran al profesor como aprendiz, en un proceso continuo de mejoramiento de sus prácticas, muestra posibilidades para dinamizar las clases de matemáticas y propiciar el aprendizaje permanente del profesor. Señala resultados que destacan las rutinas de clase con exposición magistral de contenidos, presentación de ejercicios guía y realización de otros similares por los alumnos; identifica...
La incorporación de la conjetura y el contraejemplo
Es bien sabido que en el aprendizaje de la Matematica, estan involucrados varios fenomenos de indole compleja que se presentan en todos los niveles educativos. Uno de tales fenomenos didacticos vertebrales, es el que se refiere a la estructuracion de un pensamiento matematico en los estudiantes. Es entonces pertinente plantear la pregunta: La incorporacion del uso del contraejemplo y la conjetura posibilita que los estudiantes transiten de un pensamiento ingenuo a un pensamiento matematico? Este trabajo analiza desde una perspectiva epistemologica y cognitiva, el papel que juega la incorporacion de estos recursos cuando se pretende instalar algunos de los conceptos fundamentales de la Matematica escolar, asi como la resolucion de problemas.
Mathematical Thinking and Problem Solving
In the early 1980s there was virtually no serious communication among the various groups that contribute to mathematics education -- mathematicians, mathematics educators, classroom teachers, and cognitive scientists. Members of these groups came from different traditions, had different perspectives, and rarely gathered in the same place to discuss issues of common interest. Part of the problem was that there was no common ground for the discussions -- given the disparate traditions and perspectives. As one way of addressing this problem, the Sloan Foundation funded two conferences in the mid-1980s, bringing together members of the different communities in a ground clearing effort, designed ...
Measuring Professional Competence for the Teaching of Mathematical Modelling
This open access book presents a structural model and an associated test instrument designed to provide a detailed analysis of professional competences for teaching mathematical modelling. The conceptualisation is based on the COACTIV model, which describes aspects, areas and facets of professional competences of teachers. The manual provides an overview of the essential teaching skills in application-related contexts and offers the tools needed to capture these aspects. It discusses the objectives and application areas of the instrument, as well as the development of the test. In addition, it describes the implementation and evaluates the quality and results of the structural equation analy...
Navigating Problem-based Learning
This complete guide to problem-based learning (PBL) in medicine and health professions explains the aims and essential elements of PBL and provides keys for successfully working in small groups.
Learning How to Teach Mathematical Modeling in School and Teacher Education
This timely resource fills a gap in existing literature on mathematical modeling by presenting both theory- and evidence-based ideas for its teaching and learning. The book outlines four key professional competencies that must be developed in order to effectively and appropriately teach mathematical modeling, and in so doing it seeks to reduce the discrepancies between educational policy and educational research versus everyday teaching practice. Among the key competencies covered are: Theoretical competency for practical work. Task competency for instructional flexibility. Instructional competency for effective and quality lessons. Diagnostic competency for assessment and grading. Learning How to Teach Mathematical Modeling in School and Teacher Education is relevant to practicing and future mathematics teachers at all levels, as well as teacher educators, mathematics education researchers, and undergraduate and graduate mathematics students interested in research based methods for teaching mathematical modeling.
Mathematical Modelling Education in East and West
This book documents ongoing research and theorizing in the sub-field of mathematics education devoted to the teaching and learning of mathematical modelling and applications. Mathematical modelling provides a way of conceiving and resolving problems in people’s everyday lives as well as sophisticated new problems for society at large. Mathematical tradition in China that emphasizes algorithm and computation has now seen a renaissance in mathematical modelling and applications where China has made significant progress with its economy, science and technology. In recent decades, teaching and learning of mathematical modelling as well as contests in mathematical modelling have been flourishin...
The Argument of Mathematics
Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics.
Matematicas III
Esta obra forma parte de una serie de cinco libros elaborados para cubrir de manera específica los planes de estudio de los cursos de matemáticas a nivel superior: cálculo diferencial, cálculo integral, cálculo vectorial, álgebra lineal y ecuaciones diferenciales. Se trata de un libro de texto pedagógico, matemáticamente formal y accesible.
