Construction and modification of the autonomy of school mathematical knowledge in Portugal

During the second half of the nineteenth century and early twentieth century the discipline of secondary mathematics was gradually built in Portugal and certified teachers, textbooks, programs, special teaching techniques emerge. This consolidation process ends with the emergency of school subjects that develop some kind of autonomy as Chervel puts it. This article discusses how the school discipline of mathematics in secondary education in Portugal was set. This process is inseparable from teacher training and so we will observe professional legitimation processes paying special attention to ways in which autonomy has been building and modifying over time

Construcción y modificación de la autonomía del conocimiento matemático escolar en Portugal

During the second half of the nineteenth century and early twentieth century the discipline of secondary mathematics was gradually built in Portugal and certified teachers, textbooks, programs, special teaching techniques emerge. This consolidation process ends with the emergency of school subjects that develop some kind of autonomy as Chervel puts it. This article discusses how the school discipline of mathematics in secondary education in Portugal was set. This process is inseparable from teacher training and so we will observe professional legitimation processes paying special attention to ways in which autonomy has been building and modifying over time.Durante la segunda mitad del siglo XIX y principios del siglo XX la disciplina de las matemáticas en secundaria fue construida gradualmente en Portugal y emergen libros de texto, programas, técnicas de enseñanza especiales y la certificación de maestros. Este proceso de consolidación termina con el surgimiento de disciplinas escolares desarrolladas con algún tipo de autonomía como la planteada por Chervel. Este artículo describe cómo se creó la disciplina escolar de las matemáticas en la educación secundaria en Portugal. Este proceso va unido a la formación docente y, por tanto, se observan procesos de legitimación profesional, prestando especial atención a las formas en que la autonomía se ha estado construyendo y modificando en el tiempo

Construction and modification of the autonomy of school mathematical knowledge in Portugal

During the second half of the nineteenth century and early twentieth century the discipline of secondary mathematics was gradually built in Portugal and certified teachers, textbooks, programs, special teaching techniques emerge. This consolidation process ends with the emergency of school subjects that develop some kind of autonomy as Chervel puts it. This article discusses how the school discipline of mathematics in secondary education in Portugal was set. This process is inseparable from teacher training and so we will observe professional legitimation processes paying special attention to ways in which autonomy has been building and modifying over time. Construcción y modificación de la autonomía del conocimiento matemático escolar en Portugal Durante la segunda mitad del siglo XIX y principios del siglo XX la disciplina de las matemáticas en secundaria fue construida gradualmente en Portugal y emergen libros de texto, programas, técnicas de enseñanza especiales y la certificación de maestros. Este proceso de consolidación termina con el surgimiento de disciplinas escolares desarrolladas con algún tipo de autonomía como la planteada por Chervel. Este artículo describe cómo se creó la disciplina escolar de las matemáticas en la educación secundaria en Portugal. Este proceso va unido a la formación docente y, por tanto, se observan procesos de legitimación profesional, prestando especial atención a las formas en que la autonomía se ha estado construyendo y modificando en el tiempo.Handle: http://hdl.handle.net/10481/39494WOS-ESC

Changing representations and practices in school mathematics: the case of Modern Math in Portugal

The curricular movement known as Modern Mathematics aimed at the transformation of representations and practices in school mathematics. Its study provides us with ways of understanding how these changes came about. The purpose of this paper is to contribute to the understanding of the ways in which representations of school mathematics gradually were influenced by ideas from the Modern Mathematics movement, how these new ideas merged into local educational traditions, and how they were transformed into meaningful practice. This work is centred on the Portuguese context from the middle 1950s to the middle 1960s, and builds on Chervel’s notion of school culture and Gruzinski’s discussion of connected histories.Fundação para a Ciência e Tecnologia(FCT

Cognitive models for the concept of angle

Tese de doutoramento em FilosofiaThe instructional models taught in class were similar to the students' models. The teachers addressed angle as a basic-level category, discussed its submodels, clarified the boundaries, and established cognitive reference points. They gradually increased the use of complex metaphors and of several models. The study enriched the characterization of the first two levels of van Hiele theory and demonstrated the value of categorization theory in understanding how our comprehension of mathematics is rooted in basic human attributes pertaining to the material and social conditions of human life. The embodiment of mathematical ideas by the material world, including our bodies, needs greater emphasis in all facets of mathematics education

A reforma da Matemática Moderna em contextos Ibero-Americanos

José Manuel Matos e Wagner Rodrigues Valente (Editores) © UIED, Unidade de Investigação, Educação e Desenvolvimento 1ª edição: Outubro de 2010 Tiragem: 200 exemplares ISBN: 978-989-691-033-4 Depósito legal: 317563/10 UIED | Colecção Educação e Desenvolvimento Faculdade de Ciência e Tecnologia da Universidade Nova de Lisboa Campus da Caparica 2829-516 Caparica, Portugal Tel.: +351 212948383 e-mail: [email protected] A UIED é uma Unidade de Investigação financiada pela Fundação para a Ciência e a Tecnologia.A reforma da Matemática Moderna em contextos ibero-americanos é um livro que recolhe estudos da autoria de especialistas da América Latina e da Península Ibérica. Trata-se de um dos resultados do projecto A Matemática Moderna nas escolas do Brasil e de Portugal: Estudos históricos comparativos financiado pela Fundação para a Ciência e a Tecnologia portuguesa e pela Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) brasileira. José Manuel Matos e Wagner Rodrigues Valente Editores UIE

Evaluación del currículo de matemáticas modernas

This article intends to understand the degree in which expectations about the modern mathematics reform were fulfilled. Focusing on the Portuguese case, we probed four quantitative studies developed by governmental institutions at the time of the reform, usually intended to evaluate its implementation at several grade levels. Re-appreciated in modern times, these studies provided us with insights about the reform. More specifically, following Gimeno’s distinction among several curricular levels, the contemporary inspection of those studies allowed us to have an insight of the curriculum presented to teachers, the curriculum modelled by them, and the attained curriculum at the time of the reform.Este artículo pretende comprender el grado en que se cumplieron las expectativas sobre la reforma matemática moderna. Centrándonos en el caso portugués, examinamos cuatro estudios cuantitativos desarrollados por instituciones gubernamentales en el momento de la reforma, generalmente destinados a evaluar su implementación en varios niveles de grado. Reconocidos en los tiempos modernos, estos estudios nos proporcionaron ideas sobre la reforma. Más específicamente, siguiendo la distinción de Gimeno entre varios niveles curriculares, la investigación contemporánea de esos estudios nos permitió tener una idea del currículum presentado a los maestros, el currículo modelado por ellos y el currículo alcanzado en el momento de la reforma

Highlighting links between Geology, index properties and mechanical behaviour at the beginning of a first course in Soil Mechanics

The paper reports the experience of the authors teaching Soil Mechanics to undergraduate students. The focus is on the first three or four weeks of the semester. The practice consists of establishing, for the main soil archetypes (sedimentary sands and clays and residual soils), a strong relationship between: i) geological conditions prevailing during soil formation and thereafter; ii) soil physical-identification parameters; iii) basic trends of mechanical soil behaviour. The purpose is to explain - through simple mental models - how to interpret the basic physical and geological characterisation of the soil, in order to anticipate the main difficulties for a given (simple) project. These difficulties may include insufficient bearing capacity, very large and delayed settlements (soft clay), large settlements under seismic loading (loose sands), etc. In light of these difficulties, some solutions (just the main idea) are discussed (soil reinforcement, acceleration of settlements, vibro compaction, deep foundations instead of shallow foundations, etc.). The experience of transmitting this perspective is that these early classes enable: i) a better apprehension of the subsequent truly mechanical chapters; ii) a proper evaluation by the students of the technical and practical relevance of the subjects; iii) a strong motivation for the study of the discipline