Abstract:Desde la educación matemática, la formación inicial del maestro debe promover la adquisición de competencias en la enseñanza y aprendizaje de las matemáticas, asumiendo adquiridas, al menos en gran parte, las relativas a la disciplina. Este objetivo se ve mermado por las numerosas y graves lagunas en conocimientos puramente matemáticos de los estudiantes para maestro que acceden a ella, que les impide implicarse en razonamientos didácticos específicos. En este artículo describimos las competencias numéricas de… Show more
“…Similar results were provided by [16] in a study with Spanish pre-service primary teachers. The outcomes obtained by [16] and [34] are contrary to those obtained by [6,33,[35][36][37] with Spanish pre-service primary teachers, Spanish secondary school students, and Dutch, Chinese, American, and Flemish primary school students. In the five aforementioned studies, the individuals usually performed a correct computation of the division; however, they were unable to give appropriate results, as they failed to interpret the remainder in the context of the problems.…”
Unlike previous research, this study analyzes the strategies of pre-service early childhood teachers when solving multi-digit division problems and the errors they make. The sample included 104 subjects from a university in Spain. The data analysis was framed under a mixed-method approach, integrating both quantitative and qualitative analyses. The results revealed that the traditional division algorithm was widely used in problems involving integers, but not so frequently applied to problems with decimal numbers. Often, number-based and algebraic strategies were employed as an alternative to the traditional algorithm, as the pre-service teachers did not remember how to compute it. In general, number-based strategies reached more correct solutions than the traditional algorithm, while the algebraic strategies did not usually reach any solution. Incorrect identifications of the mathematical model were normally related to an exchange of the dividend and divisor roles. Most pre-service teachers not only failed to compute the division, but also to interpret the obtained solution in the problem context. The study concludes that, during their schooling, students accessing the Degree in Early Childhood education have not acquired the necessary knowledge and skills to solve multi-digit division problems, and thus the entrance requirements at the university must be rethought.
“…Similar results were provided by [16] in a study with Spanish pre-service primary teachers. The outcomes obtained by [16] and [34] are contrary to those obtained by [6,33,[35][36][37] with Spanish pre-service primary teachers, Spanish secondary school students, and Dutch, Chinese, American, and Flemish primary school students. In the five aforementioned studies, the individuals usually performed a correct computation of the division; however, they were unable to give appropriate results, as they failed to interpret the remainder in the context of the problems.…”
Unlike previous research, this study analyzes the strategies of pre-service early childhood teachers when solving multi-digit division problems and the errors they make. The sample included 104 subjects from a university in Spain. The data analysis was framed under a mixed-method approach, integrating both quantitative and qualitative analyses. The results revealed that the traditional division algorithm was widely used in problems involving integers, but not so frequently applied to problems with decimal numbers. Often, number-based and algebraic strategies were employed as an alternative to the traditional algorithm, as the pre-service teachers did not remember how to compute it. In general, number-based strategies reached more correct solutions than the traditional algorithm, while the algebraic strategies did not usually reach any solution. Incorrect identifications of the mathematical model were normally related to an exchange of the dividend and divisor roles. Most pre-service teachers not only failed to compute the division, but also to interpret the obtained solution in the problem context. The study concludes that, during their schooling, students accessing the Degree in Early Childhood education have not acquired the necessary knowledge and skills to solve multi-digit division problems, and thus the entrance requirements at the university must be rethought.
“…1 introdUCCiÓn: antecedentes y motivación del estudio La investigación actual está poniendo de relieve lo que ya percibíamos como formadores de profesores: la importancia de que los profesores tengan un profundo conocimiento de las matemáticas que enseñan para favorecer un buen aprendizaje matemático de sus estudiantes (e.g., CONTRERAS et al, 2012;HILL;ROWAN;BALL, 2005;MA, 1999). En los últimos treinta años uno de los focos de atención en Educación Matemática ha sido la discusión sobre el conocimiento que puede ser útil para el profesor que enseña matemáticas, que se ha reflejado en diversos modelos de análisis de conocimiento, cada uno de los cuales subraya aspectos particulares de la naturaleza de dicho conocimiento (CARRILLO et al, 2017).…”
Resumen: En este trabajo reflexionamos sobre el conocimiento profesional del profesor de Educación Infantil en relación con la resta. La atención al conocimiento deseable de este profesional es relativamente reciente, existiendo escasos estudios que aborden este tema. Partimos de la consideración de que este conocimiento es especializado; diferente al del profesor de Primaria o Secundaria; y su caracterización debe realizarse desde un enfoque centrado en la propia matemática. Esto nos lleva a considerar el modelo del Conocimiento Especializado del Profesor de Matemáticas (Mathematics Teachers’ Specialised Knowledge, MTSK) como herramienta teórica y analítica idónea para ofrecer una propuesta de elementos de conocimiento especializado que, a la luz de nuestra experiencia docente e investigadora, consideramos que deseables para este profesional en relación con la resta, incluyendo aspectos de conocimiento del contenido (Mathematical Knowledge, MK) y de conocimiento didáctico del contenido (Pedagogical Content Knowledge, PCK). La reflexión sobre esta propuesta nos lleva a destacar tres elementos principales que parecen caracterizadores de la naturaleza de este conocimiento: su densidad y cohesión, la profundidad de los conocimientos matemáticos implicados y su repercusión para construir un adecuado PCK; y la relevancia del conocimiento de las fases que los niños siguen en su proceso de comprensión del número. Se aportan sugerencias para la formación inicial y continua de estos profesionales.Palabras clave: Conocimiento especializado del profesor de matemáticas. MTSK. Profesor de Educación Infantil. Resta. Conocimiento matemático del contenido y conocimiento didáctico del contenido.KINDERGARTEN TEACHERS’ SPECIALISED KNOWLEDGE ON SUBTRACTION Abstract: In this paper we reflect upon the early childhood teachers’ professional knowledge in relation to subtraction. Paying attention to this professional desirable knowledge is relatively recent, and thus there are few studies that address it. We assume as a starting point the consideration that this knowledge is specialized; differs from that of primary or secondary teachers’; and its characterization must be carried out from an approach centered on mathematics itself. This leads us to consider the model of Mathematics Teachers’ Specialised Knowledge (MTSK) as a suitable theoretical and analytical tool to offer a proposal of specialized knowledge elements that, in light of our teaching and research experience, we considered desirable for the work of teaching of these professionals in relation to subtraction. In this proposal we include aspects of Mathematical Knowledge (MK) and of Pedagogical Content knowledge (PCK). In the proposal we highlight three main elements that seem to characterize the nature of this knowledge: its density and cohesion; the depth of the mathematical knowledge involved and its impact to build an adequate PCK; and the relevance of knowledge of the phases that children follow in their process of understanding the number. Some recommendations for early years teachers’ education are provided.Keywords: Mathematics Teachers’ Specialised Knowledge. MTSK. Early childhood teacher. Subtraction. Mathematical knowledge. Pedagogical content knowledge.CONHECIMENTO ESPECIALIZADO DO PROFESSOR DA EDUCAÇÃO INFANTIL NO ÂMBITO DO TEMA DA SUBTRAÇÃO Resumo: Neste trabalho, refletimos sobre o conhecimento profissional do professor de Educação Infantil em relação à subtração. Considerar como foco de atenção o conhecimento desejável destes professores é algo relativamente recente, existindo poucos estudos que abordam esta questão. Partimos da consideração de que esse conhecimento é especializado; diferente do conhecimento do professor das etapas escolares seguintes; e sua caracterização deve ser realizada a partir de uma abordagem centrada na própria matemática. Nesse sentido consideramos a conceitualização do Mathematics Teachers’ Specialized Knowledge (MTSK) como uma ferramenta teórica e analítica para conceitualizar uma proposta de elementos constituintes do conhecimento especializado ideal do professor no âmbito que, à luz de nossa experiência de ensino e pesquisa, consideramos desejável para este profissional em relação à subtração. Nesta proposta incluímos aspectos do conhecimento do conteúdo e do conhecimento pedagógico do conteúdo (PCK). Nesta proposta destacamos três elementos principais que parecem caracterizar a natureza desse conhecimento: sua densidade e coesão; a profundidade do conhecimento matemático envolvido e seu impacto para construir um PCK adequado; e a relevância do conhecimento do professor das fases que as crianças seguem no seu processo de compreensão do número em etapas educativas posteriores. São fornecidas sugestões para a formação inicial e contínua de professores.Palavras chave: Conhecimento Especializado em Professores de Matemática. MTSK. Professor de Educação Infantil. Subtração. Conhecimento matemático do conteúdo e conhecimento pedagógico do conteúdo.
“…Estas definiciones muestran que el sentido numérico implica tener conocimiento de los contenidos numéricos, junto con otras habilidades matemáticas que permitan usarlo de manera útil y adecuada en determinadas situaciones cotidianas o tareas matemáticas. En trabajos recientes se ha identificado esta visión del sentido numérico con la competencia numérica (Contreras et al, 2012), concepto que abarca aspectos más amplios que los incluidos en las distintas definiciones de sentido numérico utilizadas hasta el momento en la literatura sobre este tópico.…”
Section: Caracterización Del Sentido Numéricounclassified
Resumen • Se presentan resultados de una investigación sobre el sentido numérico de un grupo de estudiantes universitarios del Grado en Matemáticas en España. El objetivo de la investigación es estudiar el uso de estrategias asociadas al sentido numérico que manifiestan estos estudiantes. Los resultados muestran que, a pesar de la alta formación matemática de estos alumnos, manifiestan bajo éxito en las respuestas a determinadas cuestiones numéricas, cuando se les pide resolverlas siguiendo métodos no tradicionales de cálculo.
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