Pedro Arteaga

Prospective Primary School Teachers’ Perception of Randomness

Subjective perception of randomness has been researched by psychologists and mathematics educators, using a variety of tasks, resulting in a number of different descriptions for the biases that characterize people’s performances. Analysing prospective teachers’ possible biases concerning randomness is highly relevant as new mathematics curricula for compulsory teaching levels are being proposed that incorporate increased study of random phenomena. In this chapter, we present results of assessing perception of randomness in a sample of 208 prospective primary school teachers in Spain. We first compare three pairs of random variables deduced from a classical task in perception of randomness and deduce the mathematical properties these prospective teachers assign to sequences of random experiments. Then, the written reports, where prospective teachers analyse the same variables and explicitly conclude about their own intuitions are also studied. Results show a good perception of the expected value and poor conception of both independence and variation as well as some views of randomness that parallel some naive conceptions on randomness held at different historic periods.

Characterizing Probability Problems Posed in University Entrance Tests in Andalucia

The compulsory university entrance tests in Andalucia (Spain), which traditionally include a probability problem, often determine whether the student is admitted to study in his or her desired university program. Consequently, it is important to ensure that the content of the test is directly related to the content included in the high school curriculum. The aim of this research was to investigate the distribution of the main variables characterizing the probability problems posed in these tests in Andalucia. Specifically, we examined all the problems posed to students in the period 2003–2014 (n = 144 problems). We considered the following variables: type of experiment and sample space considered, type of probability that should be computed, theorems or properties needed to find the solution, format of the data, and context. The results of the analysis reveal the potential difficulty of the problems, as well as the relevance given to conditional probability in the tests, in comparison to other curricular contents.

Statistical Graphs in Spanish Textbooks and Diagnostic Tests for 6–8-Year-Old Children

Statistical graphs are complex semiotic tools requiring different interpretative processes of the graph components, in addition to the entire graph itself. Taking this assumption and hierarchies proposed in previous research as a starting point, in this chapter we analyse the content related to statistical graphs of the Spanish curricula, textbooks and external compulsory tests taken by 6–9-year-old children. We examine the types of graphs presented to the children, the activity demanded, the reading levels required from them, as well as the graph semiotic complexity and the task context. The examples and analysis will help understand the expected progression of children’s learning of statistical graphs.

Inferencia de indicadores de idoneidad didáctica a partir de orientaciones curriculares. Doi:10.5212/PraxEduc.v.7i2.0002

Que historia, para qual cidadania? O ensino de historia na educacao basica no Mexico No Mexico a reflexao acerca dos vinculos entre a historia como disciplina escolar e os processos sociais de construcao de cidadania, requer conceber este objeto de estudo como apenas uma parte de um processo muito mais complexo que o vincula tanto a educacao civica e etica, como as praticas cotidianas conformadoras de uma certa cultura escolar. E necessario situar historicamente as origens e formas de funcionamento de cada uma dessas facetas, assim como a maneira em que entre elas se reforcam em suas pretensoes formativas. Somente desse modo e possivel reconhecer os fins, utilidades e limites do ensino de historia tal qual e concebido hoje em dia, assim como sua impossibilidade de assumir como objetivos educativos a construcao de nocoes democraticas referidas a uma concepcao moderna de cidadania. Palavras-chave: Cidadania. Historia e seu ensino. Formacao para a democracia. Resumen En Mexico la reflexion acerca de los vinculos entre la historia como disciplina escolar y los procesos sociales de construccion de ciudadania, requiere concebir este objeto de estudio como solo una parte de un proceso mucho mas complejo que lo vincula tanto a la educacion civica y etica, como a las practicas cotidianas conformadoras de una cierta cultura escolar. Es necesario ubicar historicamente los origenes y formas de funcionamiento de cada una de esas facetas, asi como la manera en que entre ellas se refuerzan en sus afanes formativos. Solo de esa forma es posible reconocer los fines, utilidades y limites de la ensenanza de la historia tal cual es concebida hoy en dia, asi como su imposibilidad de asumir como objetivos educativos la construccion de nociones democraticas referidas a una concepcion moderna de ciudadania. Palabras claves: Ciudadania. Historia y su ensenanza. Formacion para la democracia. Abstract Which history, to which citizens? History teaching in basic education in Mexico In Mexico, a reflection on the links between History as a school subject and the processes of social construction of citizenship requires conceiving the object of study as only part of a much more complex process that binds it both to civic education and ethics, and to everyday forming practices of a certain school culture. It is necessary to historically locate the sources and forms of operation of each of these facets as well as the way they reinforce their training claims.Only in this way it is possible to recognize purposes, uses and limits of teaching History as it is conceived today, as well as its inability to take as an educational goalthe building of democratic notions related to a modern conception of citizenship. Keywords: Citizenship. History and its teaching. Training for democracy.Resumen En este trabajo se evaluan algunos elementos del conocimiento matematico comun y especializado del contenido y del conocimiento del contenido y los estudiantes en relacion con la probabilidad elemental en una muestra de profesores en formacion. El conocimiento comun del contenido se evalua a partir de las soluciones de 157 profesores en formacion a tres problemas. Una vez discutidas con los participantes estas soluciones, se analizan dos componentes del conocimiento de 81 de ellos, trabajando en pequenos grupos: (a) El conocimiento especializado del contenido se evalua a partir de los contenidos matematicos identificados en los problemas; (b) el conocimiento del contenido y los estudiantes a partir de la identificacion y justificacion de respuestas de alumnos de educacion primaria. Aunque en la evaluacion inicial se observo un bajo razonamiento probabilistico, en la segunda los participantes son capaces de identificar y explicar las respuestas incorrectas de los alumnos. Palabras clave: Conocimiento Matematico para la Ensenanza. Probabilidad. Educacion Primaria. Abstract Normal 0 21 false false false PT-BR X-NONE X-NONE MicrosoftInternetExplorer4 Prospective primary school teachers’ mathematical knowledge for teaching probability: an exploratory study This study assesses some elements of common and specialized mathematical knowledge and of knowledge of content and students in relation to elementary probability from a sample of prospective primary school teachers. Common knowledge of content is assessed from the individual solution of 157 prospective teachers to three problems. Once the solution to these problems was discussed with the participants, two additional components of these teachers’ mathematical knowledge for teaching were analyzed based on small group work developed by 81 participants: (1) To assess specialized knowledge of content we asked participants to identify the tasks mathematical content; (b) to assess their knowledge of content and students we asked them to identify and justify correct and incorrect answers to the problems given by primary school children. While in the initial assessment we observed a poor probabilistic reasoning, in the second part they were able to identify and explain incorrect answers given by students. Keywords: Mathematical Knowledge for Teaching. Probability. Primary School. Resumo Normal 0 21 false false false PT-BR X-NONE X-NONE MicrosoftInternetExplorer4 Conhecimento m atematico de p rofessores dos anos iniciais do Ensino Fundamental em formacao para o ensino de probabilidade : u m estudo exploratorio Neste trabalho foi realizada uma avaliacao de alguns elementos do conhecimento matematico comum e especializado e do conhecimento do conteudo e os alunos sobre a probabilidade elementar de professores do ensino primario em formacao. O conhecimento comum do conteudo e avaliado a partir das solucoes de 157 professores em formacao a tres problemas. Uma vez que os participantes discutiram com estas solucoes , analisamos dois componentes do conhecimento matematico para o ensino de 81 desses alunos , trabalhando em pequenos grupos: a) O conhecimento especializado do conteudo e avaliado com base no conteudo matematico dos problemas identificados , ( b) o conhecimento do conteudo e os alunos sao avaliados com base na identificacao e justificacao das respostas de alunos do ensino fundamental . Enquanto na avaliacao inicial mostrou um raciocinio probabilistico pobre, na segunda, os participantes sao capazes de identificar e explicar as respostas incorretas dos alunos. Palavras-chave: Conhecimento matematico para o ensino. Probabilidade. Ensino Fundamental.1024x768 Este artigo visa enfatizar a necessidade, que um Programa de Pos-Graduacao em Educacao pode ter, de produzir conhecimentos, a partir de um esforco continuado de abertura a totalidade da experiencia humana, nao se fechando em posicoes epistemologicas reducionistas dessa experiencia. O artigo pontua, tambem, que a formacao de estudiosos e de profissionais da educacao tem, como tarefa principal, a consolidacao do habito intelectual de sensibilidade e de criatividade diante de qualquer manifestacao da vida humana, tal como aflora nos varios processos culturais, na diversidade e na complexidade de cada um deles, na concreticidade das praticas sociais que os engendram. Palavras-chave: Educacao. Experiencia. Significado. Abstract Meaning of knowledge production in Postgraduate studies and its communication with social practices This paper highlights the need, which a Postgraduate Programme in Education may have, of producing knowledge from a continuous effort of integral human experience openness, not closing itself to narrow epistemological positions of that experience. This paper also enphasizes that the education of scholars and education professionals has as main task the consolidation of the intellectual habit of being creative and sensitive towards any manifestation of human life, just as it emerges in various cultural processes, in the diversity and complexity of each one of them and in the reality of social practices that give birth to them. Keywords: Education. Experience. Meaning. Resumen Significados de la produccion del conocimiento en el Posgrado y en sus interlocuciones con la practica social El articulo tiene como objetivo enfatizar la necesidad, que un Programa de Posgrado en Educacion puede tener, de producir conocimientos, empezando por um esfuerzo continuado de apertura a la totalidad de la experiencia humana, sin cerrarse en posiciones epistemologicas reduccionistas acerca de esa experiencia. Enfatizar tambien que la formacion de estudiosos y profesionales de la educacion tiene, como tarea principal, la consolidacion del habito intelectual de la sensibilidad y de la creatividad, delante de cualquier manifestacion de vida humana, tal como emerge en sus varios procesos culturales; en la diversidad y complejidad de cada uno de ellos; em la concrecion de las practicas sociales que los engendran. Palabras clave: Educacion. Experiencia. Significado.