Experiencing flow while teaching and learning in individual tuition settings

Conferência anual da ISME

Effective teaching and optimal experiences: possible link

ISME, Thessaloniki, 2012

Reasoning and proof in classroom (9th grade)

This paper is research oriented and pretends to contribute toward giving empirical evidence about how students develop their reasoning and how they achieved to a proof construction in school context. Its main theme is epistemology. It describes the way in which four students in 9th Grade explored a task related with the discovery of symmetry axes in various geometric figures. The proof constructed by students had essentially an explaining function and it was related with the symmetry axes of regular polygons. The teacher’s role in meaning negotiation of the proof and its need is described through illustrative episodes. The paper presents part of a study which purpose is to analyse the nature of mathematical proof in classroom, its role and the nature of the relationship between the construction of a proof and the social interactions. Assuming a social perspective, attention is focussed on the social construction of knowledge and on the structuring resources that shape mathematical experience. The study’s methodology has an interpretative nature. One outcome of the study discussed here is that students develop first a practical understanding with no awareness of the reasons founding mathematical statements and after a theoretical one leading them to a proof elaboration.

As Guerras Mundiais e as mutações na teoria social da comunicação e dos media

Se a guerra é a continuação da política por outros meios, então certamente que nela a comunicação, em sentido lato, esteve sempre presente e desempenhou um papel chave. As guerras não implicam apenas a violência, mas também a persuasão, a contrainformação, o convencimento e o combate ideológico. Nas guerras modernas, os media têm sido um elemento fundamental para mobilizar nações moldadas por dinâmicas de desenraizamento e desterritorialização com vista a um esforço conjunto de apoio popular à ação bélica do Estado. Este artigo incide nas transformações que a própria teoria e investigação em comunicação e media sofreram no período entre as duas Guerras Mundiais do século XX. Trata-se de um contexto histórico decisivo para compreender como a institucionalização do campo da comunicação num país central como os EUA ocorreu em condições sociais e políticas que contribuíram para o seu perfil epistemológico, posições teóricas e para a configuração do poder no próprio sistema científico universitário, cujas repercussões continuam a fazer-se sentir de diversas e complexas formas.

A didactic sequence of elementary geometric optics Informed by history and philosophy of science

The concepts and instruments required for the teaching and learning of geometric optics are introduced in the didactic processwithout a proper didactic transposition. This claim is secured by the ample evidence of both wide- and deep-rooted alternative concepts on the topic. Didactic transposition is a theory that comes from a reflection on the teaching and learning process in mathematics but has been used in other disciplinary fields. It will be used in this work in order to clear up the main obstacles in the teachinglearning process of geometric optics. We proceed to argue that since Newton’s approach to optics, in his Book I of Opticks, is independent of the corpuscular or undulatory nature of light, it is the most suitable for a constructivist learning environment. However, Newton’s theory must be subject to a proper didactic transposition to help overcome the referred alternative concepts. Then is described our didactic transposition in order to create knowledge to be taught using a dialogical process between students’ previous knowledge, history of optics and the desired outcomes on geometrical optics in an elementary pre-service teacher training course. Finally, we use the scheme-facet structure of knowledge both to analyse and discuss our results as well as to illuminate shortcomings that must be addressed in our next stage of the inquiry.