Mathematics in the Baroque Period in Spain

The 17th century Spain is very advanced culturally and, in certain respects, very refined. Although Spanish culture in the reached an unprecedented peak, mathematics activity in Spain entered a period of decline and did not share in the burst of mathemathical knowledge occurring in other European countries during this century

Didactical knowledge development of pre-service secondary mathematics teachers

We present the results of a study on the didactical knowledge development of pre-service secondary mathematics teachers participating in a methods course. In this course, we expected pre-service teachers to learn and use a series of conceptual and methodological tools that could help them in the design of didactical units. We coded and analyzed the information contained in the transparencies used by the teachers while presenting their solution to a series of tasks proposed in the course. Four stages of didactical knowledge development were identified and characterized. The evolution in teachersÕ performance over time is described based on those stages

The 16th Century mathematics academy: Philip II, Siliceo, Juan de Herrera

During the 16th century, architects, and engineers performed a crucial role in the Spanish monarchy. They were new social agents and leaders combining theoretical and practical knowledge in their professional practice. Engineers and architects connect to scientific culture through the so-called “arts”, which include the military arts, construction, extracting benefits from metals (or metallurgy), and navigation, or nautical science. The scientific renaissance underway in Hispanic society continued during the reign of Philip II (1556-1598). For the first Ame, during this period, the cultivation of scientific-technical knowledge became a State affair, as the rulers recognized the great utility of improving management of the Empire

Meanings of fractions as demonstrated by future primary teachers in the initial phase of teacher education

Fractions are a fundamental content of primary-level education and must therefore be included in the training courses for primary school teachers. Experts argue that deep understanding is required to improve primary school teachers’ knowledge of this mathematical concept (Ball, 1990; Cramer, Post & del Mas, 2002; Newton, 2008). Our study focuses on the part-whole relationship as a crucial foundation in working with fractions. This paper characterizes some of the meanings of this relationship for a group of future primary school teachers

Meaning of the part-whole relation and the concept of fraction for primary teachers

The part-whole relation is complex and raises questions that affect different disciplines. Researchers have proposed different interpretations of the notions of fraction and rational number (e.g., Behr, Lesh, Post & Silver, 1983; Kieren, 1976). We highlight three kinds of relations in the study of rational numbers—the part whole-relation, the part-part relation, and the functional relation—through which we organize the different subconstructs of rational number. We claim that the meaning of fractions should be understood through three components: their mathematical structure, their representations and their senses

Análisis conceptual e investigación en Didáctica de la Matemática

En este capítulo se resalta la importancia del análisis conceptual como herramienta metodológica que permite controlar la complejidad, seleccionar las opciones conceptuales idóneas y disponer del aparato teórico adecuado en una investigación. Se ubica el análisis conceptual dentro del proceso de diseño de una investigación y se presenta un ejemplo de esta herramienta para la noción de modelo. In this chapter we emphasize the conceptual analysis as a methodological instrument which allows in a research to control the complexity, to choose the conceptual suitable options and to lay out a theoretical framework. The conceptual analysis is embedded in the process of designing a research and is presented as an instrument for the notion of a model

Conclusiones del grupo de trabajo 02 números y álgebra del V Congreso Iberoamericano de Educación Matemática CIBEM

Durante los días 18, 19, 21 y 22 de Julio tuvieron lugar las sesiones de discusión y trabajo del Grupo Números y Álgebra. Participaron un total de 54 profesores e investigadores, con una media de asistencia de 35.Se han presentado 10 comunicaciones sobre enseñanza, aprendizaje y comunicación de conceptos numéricos y algebraicos, relacionadas con distintos trabajos que han propuesto estudios sobre números, relaciones y estructuras en el Sistema Educativo. El interés de estos trabajos ha estado enfocado en los diferentes procesos con que se asignan y comparten significados, mediante el uso de diferentes estructuras numéricas y algebraicas

Reivindicación del error en el aprendizaje de las matemáticas

Hace tiempo que quiero poner por escrito algunas reflexiones en torno a la cuestión del error en los procesos de aprendizaje de las matemáticas y a la consideración y tratamiento que el profesor de matemáticas debe dar a tales errores. La ocasión del homenaje al Profesor Gonzalo Sánchez Vázquez me ofrece la oportunidad de concretar estas ideas en un documento, dándoles el tono de diálogo con un amigo con el que se quieren compartir unas preocupaciones y a cuyo juicio se quieren presentar cuestiones de cierta complejidad, cuya aceptación general es controvertida. Este es el tono que quiero dar a este trabajo: traer a reflexión común algunas consideraciones sobre un punto conflictivo en el desempeño profesional de los profesores de matemáticas. Es mi intención profundizar sobre algunas ideas y compartir unas reflexiones, sin eludir, si es necesario, los aspectos polémicos. Entiendo que la autonomía del profesor de matemáticas se ha de basar en un esfuerzo crítico de clarificación conceptual, no exento de conflictividad, pero sostenido por un estilo de honestidad intelectual y un respeto y cordialidad hacia las personas, del que Gonzalo nos ofreció un claro ejemplo. Trataré de seguir esos criterios en estas reflexiones