Montserrat Prat

Conocimiento conceptual y procedimental en matemáticas

espanolLa investigacion en relacion al conocimiento conceptual y al conocimiento procedimental en matematicas ha sido tema de interes y foco de debate a lo largo de los anos. En la literatura se encuentran discusiones que abordan desde que debe desarrollarse en mayor medida en la escuela, si las habilidades o los procedimientos; hasta propuestas acerca de como deben estudiarse las interacciones entre ambos tipos de conocimiento. Este trabajo analiza la situacion actual del campo a traves de la revision de las caracterizaciones mas relevantes presentes en la literatura para ambos tipos de conocimiento, las razones que originaron cambios de enfoque en las investigaciones, las problematicas actuales y las lineas abiertas de investigacion. A su vez, se aporta un cuadro-resumen de los estudios mas relevantes segun cada tipo de conocimiento, poniendo el foco en el dominio matematico al que pertenecen. Las investigaciones consultadas sugieren que inicialmente los estudios sobre el conocimiento conceptual y procedimental se centraron en ninos, extendiendose posteriormente su estudio a adolescentes, adultos jovenes y estudiantes para maestro. En un primer momento, las investigaciones sobre estos tipos de conocimiento se centraron esencialmente en los dominios de conteo, adicion con uno y varios digitos, fracciones y razonamiento proporcional; intentado en la mayoria de los casos, determinar el orden de adquisicion de los conceptos versus habilidades. Con el trascurso de los anos el interes por estos dos tipos de conocimiento se ha acrecentado, y su estudio se ha extendido hacia otros dominios matematicos, como por ejemplo, las ecuaciones, principios de adicion y la substraccion, multiplicacion y division. No obstante, se observa en este trabajo, que tras decadas de investigacion no existe un consenso acerca de como definir y medir el conocimiento conceptual y procedimental con un grado suficiente de validez. EnglishInvestigations related to the conceptual and procedural knowledge in mathematics have been an object of interest and focus of debate throughout the years. In the literature is possible to find discussions that address from which should be further developed in school, if the skills or procedures; up to proposals about how to study interactions between both types of knowledge. This paper analyses the current situation in the field by reviewing the most relevant characterizations in the literature for both types of knowledge, the reasons that led to changes in research focus, the current problems and the open lines of research. In turn, contributes with a summary table of the most significant studies in the literature of each type of knowledge on focus on the mathematical domain to which they belong. The consulted research suggests that initially the studies about conceptual and procedural knowledge focused on children, and being later extended on adolescents, young adults and pre-service teachers. Initially, research on types of knowledge mainly focused on the counting domains, single-digit addition, multi-digit addition, fractions and proportional reasoning; trying in most cases, determine the acquisition order of the concepts versus skills. Over the years the interest in these two types of knowledge has increased, and its study has been extended to other mathematical domains, such as equations, principles of addition and subtraction, multiplication and division. Nevertheless, it is observed in this work that after decades of research there is no consensus about how to define and measure the conceptual and procedural knowledge with an adequate validity level.Investigations related to the conceptual and procedural knowledge in mathematics have been an object of interest and focus of debate throughout the years. In the literature is possible to find discussions that address from which should be further developed in school, if the skills or procedures; up to proposals about how to study interactions between both types of knowledge. This paper analyses the current situation in the field by reviewing the most relevant characterizations in the literature for both types of knowledge, the reasons that led to changes in research focus, the current problems and the open lines of research. In turn, contributes with a summary table of the most significant studies in the literature of each type of knowledge on focus on the mathematical domain to which they belong. The consulted research suggests that initially the studies about conceptual and procedural knowledge focused on children, and being later extended on adolescents, young adults and pre-service teachers. Initially, research on types of knowledge mainly focused on the counting domains, single-digit addition, multi-digit addition, fractions and proportional reasoning; trying in most cases, determine the acquisition order of the concepts versus skills. Over the years the interest in these two types of knowledge has increased, and its study has been extended to other mathematical domains, such as equations, principles of addition and subtraction, multiplication and division. Nevertheless, it is observed in this work that after decades of research there is no consensus about how to define and measure the conceptual and procedural knowledge with an adequate validity level. Castro, A., Prat, M., Gorgorió, N. CONOCIMIENTO CONCEPTUAL Y PROCEDIMENTAL EN MATEMÁTICAS: SU EVOLUCIÓN TRAS DÉCADAS DE INVESTIGACIÓN Revista de Educación, 374. Octubre-Diciembre 2016, pp. 43-68 Recibido: 14-07-2015 Aceptado: 04-06-2016 44

Pre-Service Teachers’ Representations of School Mathematics and Immigrant Children1

Catalonia (capital city Barcelona), located in the north-eastern part of the Iberian Peninsula, is one of the 17 autonomous communities into which the Spanish state is organized. It has two official languages, Catalan and Castilian (Spanish). Because language is one of the defining features of Catalan culture and identity, it is the official language of instruction, even though Spanish is often used as well.