Curriculum innovation in teacher education : exploring conceptions among Tanzanian teacher educators

The focus of the study is to understand curriculum innovation from the perspective of Tanzanian teacher educators. It is argued that the deterioration of quality of education in schools is partly to be attributed to the way in which teachers are educated. Curriculum innovation is considered as an essential strategy for bringing about improvement in teacher education. Therefore, in 2000 a new curriculum was introduced; however, right from the inception the curriculum was criticised by teacher educators. The overall aim of the study is to investigate teacher educators’ conceptions of curriculum innovation. In the theoretical framework the main focus is on discussion about different curriculum approaches for teacher education and innovation. In order to achieve the aim of the study, a phenomenographic approach is employed. This approach is used in order to identify similarities and variation in educators’ conceptions of curriculum innovation. The empirical basis of the study consists of interviews with thirty teacher educators working in eight teachers’ colleges situated in various parts of Tanzania. The findings, in brief, reveal variation in teacher educators’ conceptions of the dominant domains of innovation. Two broad conceptions of teaching with six aspects are identified. Conceptions of educational studies are presented in four broad categories of description with four aspects. Similarly, in methodology subjects two conceptions are described with four aspects. On the integration of subject matter studies and subject methods, two broad conceptions are presented with six aspects. Conceptions of textbook prescription policy are characterised in two broad categories of description with four aspects. With the use of modules two broad conceptions are identified with six aspects. In addition, the study identifies four broad conceptions of future curriculum approaches with eight aspects. Looking across the categories of description, the results indicate that educators cope with innovation individually. Three character types of teacher educators are presented: loyal, creative and critical. Furthermore, four types of phenomena suggesting critical areas about teacher educators’ conceptions of innovation are described: educators’ prior educational background, technical factors, student teachers’ factors and shifting from teaching to learning. On the whole, educators express a number of frame factors in the process of change towards the aim of curriculum innovation. This indicates that the new curriculum (2000) is not implemented as intended by curriculum developers. Constraints to the implementation are presented and discussed in detail. From these findings, two models of educators’ stance towards curriculum innovation are presented and can be used as a framework for planning successful curriculum innovations and analysing practice in teachers’ colleges.

A composição do curriculum vitae entre estudantes de medicina e seus condicionantes

Nesta pesquisa, investigam-se as escolhas de atividades formadoras feitas por estudantes de Medicina e seus motivos, com o fim de apreender a lógica dessas escolhas no contexto institucional em que se apresentam e no contexto social mais amplo das sociedades capitalistas atuais, onde se afirmam novos padrões de autorrealização, conforme as pesquisas de A. Ehrenberg. Assim, não só escutamos os estudantes, como também estivemos atentos às práticas e aos valores vigentes na faculdade estudada e a outros procedimentos indicados pelos entrevistados, entre eles a seleção para a residência médica. Parte-se de dados colhidos por meio de entrevistas semiestruturadas com 12 alunos e mediante um questionário respondido por 156 dos 160 alunos que cursavam o oitavo período da Faculdade de Medicina estudada. A análise dos dados apoia-se em pesquisas similares e em estudos sobre as transformações atuais nos padrões de comportamento dos indivíduos na sociedade.

O Core Curriculum da Unesco como Base para Formação em Bioética

RESUMO A revolução biotecnológica das últimas décadas teve como resultado o desenvolvimento de um poder quase sem limites sobre a vida humana. Tal contexto exige do profissional uma visão globalizada dos problemas éticos e sociais da era contemporânea, alicerçada em sólidas bases filosóficas e legais. Este contexto torna necessária a promoção de novas competências e habilidades relacionadas à vida profissional. Neste sentido, o ensino da Bioética desponta como uma possibilidade de inovação curricular alternativa ao tradicional modelo prescritivo e normativo. Este artigo relata a experiência da Cátedra Unesco de Bioética da Universidade de Brasília com a utilização do Core Curriculum proposto pela Unesco como instrumento didático-pedagógico adequado ao ensino da Bioética. Entre os dilemas pedagógicos enfrentados pela Bioética como disciplina encontram-se: a construção de seus conteúdos, sua estruturação, as concepções teóricas a serem seguidas e seus objetivos. A contextualização e o aperfeiçoamento da estratégia proposta pelo Core Curriculum podem significar importantes instrumentos facilitadores para docentes que buscam organizar práticas didático-pedagógicas inovadoras em Bioética com o intuito de proporcionar resultados efetivos na formação de seus estudantes.

The mathematics of McTaggart's paradox

Mc Taggart's celebrated proof of the unreality of time is a chain of implications whose final step asserts that the A-series (i.e. the classification of events as past, present or future) is intrinsically contradictory. This is widely believed to be the heart of the argument, and it is where most attempted refutations have been addressed; yet, it is also the only part of the proof which may be generalised to other contexts, since none of the notions involved in it is specifically temporal. In fact, as I show in the first part of the paper, McTaggart's refutation of the A-series can be easily interpreted in mathematical terms; subsequently, in order to strengthen my claim, I apply the same framework by analogy to the cases of space, modality, and personal identity. Therefore, either McTaggart's proof as a whole may be extended to each of these notions, or it must embed some distinctly temporal element in one of the steps leading up to the contradiction of the A-series. I conclude by suggesting where this element might lay, and by hinting at what I believe to be the true logical fallacy of the proof.

HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS

Abstract: In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call "Frege's Problem", form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution.

The effectiveness of short-term literacy skills intervention on children at risk of reading and writing difficulties in Tanzania : a study of grade one children with dynamic assessment approach

The aim of the study was to create and evaluate an intervention programme for Tanzanian children from a low-income area who are at risk of reading and writing difficulties. The learning difficulties, including reading and writing difficulties, are likely to be behind many of the common school problems in Tanzania, but they are not well understood, and research is needed. The design of the study included an identification and intervention phase with follow-up. A group based dynamic assessment approach was used in identifying children at risk of difficulties in reading and writing. The same approach was used in the intervention. The study was a randomized experiment with one experimental and two control groups. For the experimental and the control groups, a total of 96 (46 girls and 50 boys) children from grade one were screened out of 301 children from two schools in a low income urban area of Dar-es-Salaam. One third of the children, the experimental group, participated in an intensive training programme in literacy skills for five weeks, six hours per week, aimed at promoting reading and writing ability, while the children in the control groups had a mathematics and art programme. Follow-up was performed five months after the intervention. The intervention programme and the tests were based on the Zambian BASAT (Basic Skill Assessment Tool, Ketonen & Mulenga, 2003), but the content was drawn from the Kiswahili school curriculum in Tanzania. The main components of the training and testing programme were the same, only differing in content. The training process was different from traditional training in Tanzanian schools in that principles of teaching and training in dynamic assessment were followed. Feedback was the cornerstone of the training and the focus was on supporting the children in exploring knowledge and strategies in performing the tasks. The experimental group improved significantly more (p = .000) than the control groups during the intervention from pre-test to follow-up (repeated measures ANOVA). No differences between the control groups were noticed. The effect was significant on all the measures: phonological awareness, reading skills, writing skills and overall literacy skills. A transfer effect on school marks in Kiswahili and English was found. Following a discussion of the results, suggestions for further research and adaptation of the programme are presented.

Conceptions of mathematics teacher education : thoughts among teacher educators in Tanzania

This study addresses the question of teacher educators’ conceptions of mathematics teacher education (MTE) in teacher colleges in Tanzania, and their thoughts on how to further develop it. The tension between exponents of content as opposed to pedagogy has continued to cause challenging conceptual differences, which also influences what teacher educators conceive as desirable in the development of this domain. This tension is connected to the dissatisfaction of parents and teachers with the failure of school mathematics. From this point of view, the overall aim was to identify and describe teacher educators’ various conceptions of MTE. Inspired by the debate among teacher educators about what the balance should be between subject matter and pedagogical knowledge, it was important to look at the theoretical faces of MTE. The theoretical background involved the review of what is visible in MTE, what is yet to be known and the challenges within the practice. This task revealed meanings, perspectives in MTE, professional development and assessment. To do this, two questions were asked, to which no clear solutions satisfactorily existed. The questions to guide the investigation were, firstly, what are teacher educators’ conceptions of MTE, and secondly, what are teacher educators’ thoughts on the development of MTE? The two questions led to the choice of phenomenography as the methodological approach. Against the guiding questions, 27 mathematics teacher educators were interviewed in relation to the first question, while 32 responded to an open-ended questionnaire regarding question two. The interview statements as well as the questionnaire responses were coded and analysed (classified). The process of classification generated patterns of qualitatively different ways of seeing MTE. The results indicate that MTE is conceived as a process of learning through investigation, fostering inspiration, an approach to learning with an emphasis on problem solving, and a focus on pedagogical knowledge and skills in the process of teaching and learning. In addition, the teaching and learning of mathematics is seen as subject didactics with a focus on subject matter and as an organized integration of subject matter, pedagogical knowledge and some school practice; and also as academic content knowledge in which assessment is inherent. The respondents also saw the need to build learner-educator relationships. Finally, they emphasized taking advantage of teacher educators’ neighbourhood learning groups, networking and collaboration as sustainable knowledge and skills sharing strategies in professional development. Regarding desirable development, teacher educators’ thoughts emphasised enhancing pedagogical knowledge and subject matter, and to be determined by them as opposed to conventional top-down seminars and workshops. This study has revealed various conceptions and thoughts about MTE based on teacher educators´ diverse history of professional development in mathematics. It has been reasonably substantiated that some teacher educators teach school mathematics in the name of MTE, hardly distinguishing between the role and purpose of the two in developing a mathematics teacher. What teacher educators conceive as MTE and what they do regarding the education of teachers of mathematics revealed variations in terms of seeing the phenomenon of interest. Within limits, desirable thoughts shed light on solutions to phobias, and in the same way low self-esteem and stigmatization call for the building of teacher educator-student teacher relationships.

Mathematics inspired by Darwin. Adaptive dynamics of dispersal and cooperation

In 1859, Charles Darwin published his theory of evolution by natural selection, the process occurring based on fitness benefits and fitness costs at the individual level. Traditionally, evolution has been investigated by biologists, but it has induced mathematical approaches, too. For example, adaptive dynamics has proven to be a very applicable framework to the purpose. Its core concept is the invasion fitness, the sign of which tells whether a mutant phenotype can invade the prevalent phenotype. In this thesis, four real-world applications on evolutionary questions are provided. Inspiration for the first two studies arose from a cold-adapted species, American pika. First, it is studied how the global climate change may affect the evolution of dispersal and viability of pika metapopulations. Based on the results gained here, it is shown that the evolution of dispersal can result in extinction and indeed, evolution of dispersalshould be incorporated into the viability analysis of species living in fragmented habitats. The second study is focused on the evolution of densitydependent dispersal in metapopulations with small habitat patches. It resulted a very surprising unintuitive evolutionary phenomenon, how a non-monotone density-dependent dispersal may evolve. Cooperation is surprisingly common in many levels of life, despite of its obvious vulnerability to selfish cheating. This motivated two applications. First, it is shown that density-dependent cooperative investment can evolve to have a qualitatively different, monotone or non-monotone, form depending on modelling details. The last study investigates the evolution of investing into two public-goods resources. The results suggest one general path by which labour division can arise via evolutionary branching. In addition to applications, two novel methodological derivations of fitness measures in structured metapopulations are given.