Mathematics in different settings: plenary panel.

When we think about the title “Mathematics in different settings”, a number of questions arise. For example: • How many mathematics are there – one or many? Is there a mathematics that is “prior to”, or independent of, any setting? • What (who) is it that makes settings “different”? And how does this relate to social differences among people? • What is an appropriate typology of different settings – for research or for curriculum design purposes? Relatedly, we might ask: who decides what is “important”? • What is the nature of relations among policy arrangements, research and educational institutional settings? • How are different settings represented in mathematics teaching and assessment? • What is the relationship of mathematics education researchers to any setting

Teachers and didacticians: key stakeholders in the processes of developing mathematics teaching

This paper sets the scene for a special issue of ZDM-The International Journal on Mathematics Education-by tracing key elements of the fields of teacher and didactician/teacher-educator learning related to the development of opportunities for learners of mathematics in classrooms. It starts from the perspective that joint activity of these two groups (teachers and didacticians), in creation of classroom mathematics, leads to learning for both. We trace development through key areas of research, looking at forms of knowledge of teachers and didacticians in mathematics; ways in which teachers or didacticians in mathematics develop their professional knowledge and skill; and the use of theoretical perspectives relating to studying these areas of development. Reflective practice emerges as a principal goal for effective development and is linked to teachers' and didacticians' engagement with inquiry and research. While neither reflection nor inquiry are developmental panaceas, we see collaborative critical inquiry between teachers and didacticians emerging as a significant force for teaching development. We include a summary of the papers of the special issue which offer a state of the art perspective on developmental practice. © 2014 FIZ Karlsruhe

O lugar das matemáticas na Licenciatura em Matemática: que matemáticas e que práticas formativas?

Este artigo é um ensaio que tem por objetivo problematizar e discutir o lugar da matemática na formação do futuro professor, em cursos de Licenciatura em Matemática. O ensaio é organizado em torno de duas questões básicas: de que matemática estamos falando, quando dizemos que o professor precisa saber bem matemática para ensiná-la? Que práticas formativas podem contribuir para que o futuro professor possa se apropriar dessa matemática fundamental para seu trabalho profissional? Para respondê-las, foram analisadas e problematizadas as diferentes práticas sociais do educador matemático, tentando perceber, nelas, indícios do tipo de saber matemático mobilizado e requerido. A seguir, foram trazidas algumas tentativas históricas de tratar o problema da formação matemática dos professores, tendo por base Felix Klein, Richard Courant e Bento de Jesus Caraça, e algumas pesquisas brasileiras e internacionais que têm como foco de estudo a formação matemática do professor. A partir desses estudos, o artigo destaca a existência, na formação inicial do professor de matemática, de uma quase tricotomia entre formação matemática, formação didático-pedagógica e prática profissional. Para romper com essa tradição tricotômica são sugeridas algumas mudanças em relação à prática e à pesquisa sobre formação de professores tais como: a formação do professor de matemática deve orientar-se pelas diferentes práticas sociais do educador matemático; adotar, na formação inicial, práticas e projetos nos quais os licenciandos possam integrar, fazendo contrastes, problematizações e investigações sobre as relações entre sua formação matemática na licenciatura, sua formação didático-pedagógica relacionada ao conteúdo, e a complexidade das práticas escolares

The sleep EEG spectrum is a sexually dimorphic marker of general intelligence

The shape of the EEG spectrum in sleep relies on genetic and anatomical factors and forms an individual “EEG fingerprint”. Spectral components of EEG were shown to be connected to mental ability both in sleep and wakefulness. EEG sleep spindle correlates of intelligence, however, exhibit a sexual dimorphism, with a more pronounced association to intelligence in females than males. In a sample of 151 healthy individuals, we investigated how intelligence is related to spectral components of full-night sleep EEG, while controlling for the effects of age. A positive linear association between intelligence and REM anterior beta power was found in females but not males. Transient, spindle-like “REM beta tufts” are described in the EEG of healthy subjects, which may reflect the functioning of a recently described cingular-prefrontal emotion and motor regulation network. REM sleep frontal high delta power was a negative correlate of intelligence. NREM alpha and sigma spectral power correlations with intelligence did not unequivocally remain significant after multiple comparisons correction, but exhibited a similar sexual dimorphism. These results suggest that the neural oscillatory correlates of intelligence in sleep are sexually dimorphic, and they are not restricted to either sleep spindles or NREM sleep

Mathematics teaching development as a human practice: identifying and drawing the threads

This article was published in the journal, ZDM Mathematics Education [© FIZ Karlsruhe] and the definitive version is available at: http://dx.doi.org/10.1007/s11858-012-0437-7The didactic triangle links mathematics, teachers and students in a consideration of teaching– learning interactions in mathematics classrooms. This paper focuses on teachers and teaching in the development of fruitful learning experiences for students with mathematics. It recognises primarily that teachers are humans with personal characteristics, subject to a range of influences through the communities of which they are a part, and considers aspects of teachers’ personhood, identity and agency in designing teaching for the benefit of their students. Teaching is seen as a developmental process in which inquiry plays a central role, both in doing mathematics in the classroom and in exploring teaching practice. The teacher-as-inquirer in collaboration with outsider researchers leads to growth of knowledge in teaching through development of identity and agency for both groups. The inclusion of the outsider researcher brings an additional node into the didactic triangle

Mathematics teacher change in a collaborative environment: to what extent and how

This article reports on a study into how collaborative contexts influence the professional development of an early-career primary teacher, Julia. We describe the process of change by which Julia manages to make her planning to teach mathematics more flexible so as to adapt to student difficulties, and we analyse the role that joint reflection plays in promoting this change. In order to understand the how of this influence, we carried out an analysis of the interactions within the group from Julia’s point of view, following a dialogical approach to discourse. We believe that it is in and through the interactions that Julia constructs her interpretation of the opinions, critiques and suggestions expressed. This interpretation conditions the extent of her involvement and moulds the influence of the context on her professional development. The presence of skilled collaborators (Day, 1993) proved decisive in promoting this development