Experiencing flow while teaching and learning in individual tuition settings

Conferência anual da ISME

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.

Fundamentos didatológicos para a construção de unidades curriculares integradas

Neste trabalho, com base na análise de diferentes formas de conceber e entender a integração didática na perspetiva curricular portuguesa e da consideração do trinómio didático - globalização da aprendizagem / motivação / ensino e aprendizagem integrados nos primeiros anos de escolaridade –, propomos, do ponto de vista científico - didático, uma reflexão sobre os princípios e fundamentos da sequenciação didática e da construção de unidades didáticas integradoras, com o objetivo de dar contributos significativos para que, desde a formação de professores, se possam criar bases teórico-práticas de definição de percursos de ensino e aprendizagem com potencial efetivo de integração nas dimensões epistemológica e curricular.

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.

Learning and Knowledge in the Context of Absorptive Capacity

Develop a new model of Absorptive Capacity taking into account two variables namely Learning and knowledge to explain how companies transform information into knowledge

Effective teaching and optimal experiences: possible link

ISME, Thessaloniki, 2012

The public performance : impact to music learning in conservatoire tradition

Paper presented at the Conference “The Reflective Conservatoire – 2nd International Conference: Building Connections”. Guildhall School of Music and Drama and Barbican Conference Centre, London. 28 February – 3 March 2009