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

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

Rural development, population aging and gender in Spain: the case of rural women in the autonomous community of Castilla y León

The transformation that rural areas have undergone during the last 30 years constitutes a very important phenomenon in Spain, but it is especially relevant in certain regions such as the Autonomous Community of Castilla y León. The constant process of depopulation, which a great number of villages of that region are suffering, primarily caused by the continuous transfer of labour force from agriculture activities to the industrial sector and, more recently, towards the service sector of urban areas, is provoking the progressive demographic and economic decadence of rural areas. In this context, women played a key role in the process of rural exodus, especially in the case of young women. This trend has created highly aged, male rural populations, with few potential human resources, which are incapable of sustaining and promoting economic and social development in the future. This project attempts to determine to which extent women have been and continue to be the protagonists of the social and economic transformations which have affected rural areas during the last decades. To this aim, we will undertake an analysis by sex of different demographic, economic and social variables at the municipal level, which will show women’s spatial situation, according to rural criteria. We will also undertake a prospective analysis of the population evolution of these rural areas, in order to obtain a probable demographic scenario which rural women will have to face in the future. The specific focus of this study will be the territory of the Autonomous Community of Castilla y León. The results of this analysis will serve as a very useful reference for the public authorities as well as for private agents of this and other Spanish regions whenever they have to design alternative policies and actions regarding the role that rural women play and will play in the economic maintenance and development of rural areas. This is especially true given that, until now, studies which focus on the quantitative analysis of the economic and social situation of rural women have been practically nonexistent.

Integration of didactical knowledge and mathematical content knowledge in pre-service teacher training

We suggest some ideas about how content knowledge and didactical knowledge could be integrated in pre-service secondary mathematics teachers' training. We identify the activities we expect a teacher to perform when planning a lesson and determine the didactical knowledge that she has to put into play in order to do so. We then show the relationship between that didactical knowledge and the corresponding content knowledge

Desarrollo del conocimiento didáctico de futuros profesores de matemáticas. Análisis de los resultados de las producciones utilizadas para las presentaciones

En este documento presentamos el análisis de los resultados obtenidos al codificar y analizar la información contenida en las transparencias utilizadas por los futuros profesores para hacer sus presentaciones en clase. El análisis considera varias dimensiones: la caracterización de los estados de desarrollo del conocimiento didáctico, la descripción de ese desarrollo para los grupos de futuros profesores y el análisis de las discrepancias, de las fases y de las variables

Esquema de análisis de información para la descripción del desarrollo del conocimiento didáctico de futuros profesores de matemáticas

En este documento, describo el procedimiento que utilicé en un estudio sobre el desarrollo del conocimiento didáctico de futuros profesores de matemáticas de secundaria. Con este procedimiento pude caracterizar una sucesión de estados, en términos de atributos de producciones de esos futuros profesores, que permiten describir la evolución en dichas producciones

La formación profesional del obrero como mecanismo de modernización económica e industrial durante la Dictadura de Primo de Rivera (1923-1930)

El objeto del presente trabajo es analizar como la Dictadura de Primo de Rivera, a través de los Reales Decretos del Estatuto de Enseñanza Industrial de 1924 y del Estatuto de Formación Profesional de 1928, pretendió impulsar un proyecto educativo que sirviera para modernizar la economía el país, dentro de una concepción corporativa del Estado. La dictadura primorriverista instrumentalizó la formación profesional técnica-industrial como una política económica y social al servicio del gobierno, ya que era el mecanismo idóneo para formar un capital humano especializado en las técnicas propias de la segunda revolución industrial, capaz de potenciar el progreso industrial del país, pero siempre dentro de las coordenadas ideológicas del Estado. Para poner en marcha este proyecto, no podía obviar la participación privada de la patronal. El problema fue encauzar la presencia de estos intereses particulares dentro de un plan de estudios técnico e industrial, controlado desde los principios reaccionarios y autoritarios del EstadoL'objecte del present treball és analitzar com la Dictadura de Primo de Rivera, a través dels Reials Decrets de l'Estatut d'Ensenyament Industrial de 1924 i de l'Estatut de Formació Professional de 1928, va pretendre impulsar un projecte educatiu que servís per modernitzar l'economia al país, dins d'una concepció corporativa de l'Estat. La dictadura primorriverista instrumentalitzar la formació professional tècnica-industrial com una política econòmica i social al servei del govern, ja que era el mecanisme idoni per formar un capital humà especialitzat en les tècniques pròpies de la segona revolució industrial, capaç de potenciar el progrés industrial del país, però sempre dins de les coordenades ideològiques de l'Estat. Per posar en marxa aquest projecte, no podia obviar la participació privada de la patronal. El problema va ser canalitzar la presència d'aquests interessos particulars dins d'un pla d'estudis tècnic i industrial, controlat des dels principis reaccionaris i autoritaris de l'Estat.This paper studies the vocational training of workers project promoted by the dictatorship of Primo de Rivera through the decrees of the "Estatuto de Enseñanza Industrial" in 1924 and the Estatuto de Formación Profesional in 1928. The project tried to modernize the economy of Spain from the point of view of a corporate State. The dictatorship used the technical and industrial training as part of its economic and social policy to rise human capital able to incorporate the most important features of the second industrial revolution. This policy pretended to speed up industrialization in Spain, yet inspired by the ideological principles of the Regime. In order to implement this project, the participation of entrepreneurs was necessary. The problem was to reconcile in the same project private interests with the reactionary and authoritarian principles of the dictatorship

Learning within communities of practice in preservice secondary school teachers education

We present the main features of a study that explored the learning processes of a group of preservice mathematics teachers in a methods course. We discuss the implications of using the communities of practice perspective in designing and developing teacher training programs