Formação de professores no programa nacional para a alfabetização na idade certa com uso das TIC: um estudo de caso no ensino fundamental

Dissertação de mestrado em Ciências da Educação (área de especialização em Tecnologia Educativa)

The Philosophical magazine : or Annals of chemistry, mathematics, astronomy, natural history and general science.

2nd ser. : v.9 (1831)

The Philosophical magazine : or Annals of chemistry, mathematics, astronomy, natural history and general science.

2nd ser. : v.3 (1828)

The Philosophical magazine : or Annals of chemistry, mathematics, astronomy, natural history and general science.

2nd ser. : v.4 (1828)

The days of a man, being memories of a naturalist, teacher, and minor prophet of democracy.

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The days of a man, being memories of a naturalist, teacher, and minor prophet of democracy.

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Una Aproximació a la construcció significativa del coneixement matemàtic a l'ESO

This study displays and analyzes the contents of the Mathematics subject in ESO’s second cycle from a constructivist perspective. This analysis has been carried out by contrasting two groups of participants (control group and experimental group). These groups were formed by a sample of 240 students between the ages of 14 and 16 from four different educational centres of the Osona area. Research – Action methodology has been employed, combining quantitative techniques (statistical study with the SPSS package) with qualitative analysis (transcriptions of interviews and discussion group). This study has been carried out after years of classroom observation, reflection and action. The theoretical framework employed is a cognitive one, based on Ausubel’s Significative Learning Theory. Quantitative analysis shows how the researcher’s design improves, on the one hand, the students’ academic motivation and, on the other hand, their comprehensive memory, enabling them to achieve a more significant learning of the subjects’ contents. Furthermore, our analysis shows that the proposed method is more comprehensive than those employed by teachers collaborating with control groups. The main aim of the qualitative analysis is that of identifying the elements which configure the programme and contribute to an improvement of the aspects mentioned above. The key elements here are: co-operation as the basis of group dynamics; the employment, in some cases, of easily handled materials; the type of interaction between teacher and students, where, through open discussion, students are lead by teaching staff towards the course objectives; induction, that is, deducing formulae by initially using examples which are close to the students’ knowledge and experience or taken from everyday life (what we could call “down-top” mathematics). We should add here that the qualitative analysis does not only corroborate the results obtained by quantitative techniques, but also displays an increase of motivation in teaching staff. Teachers did show a positive attitude and welcomed the use and development of these materials in the next academic year. Finally, we discuss possible directions for further research.

On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

New Evidence on Allyn Young’s Style and Influence as a Teacher

This paper publishes the hitherto unpublished correspondence between Allyn Abbott Young’s biographer Charles Blitch and 17 of Young’s former students or associates. Together with related biographical and archival material, the paper shows the way in which this adds to our knowledge of Young’s considerable influence as a teacher upon some of the twentieth century’s greatest economists. The correspondents are as follows: James W Angell, Colin Clark, Arthur H Cole, Lauchlin Currie, Melvin G de Chazeau, Eleanor Lansing Dulles, Howard S Ellis, Frank W Fetter, Earl J Hamilton, Seymour S Harris, Richard S Howey, Nicholas Kaldor, Melvin M Knight

The effects of teacher talk on students’ oral productions

The present study is a brief personal enquiry into the teaching and learning of EFL in the classroom with an orientation to action and personal professional development. It focuses on teacher talk, making special emphasis on questions, as well as on students’ resulting oral productions. The research contains samples of empirical data, which include their interpretations in the light of relevant research literature, and a more personal overall reflection of the teaching practice. Both the analysis and the reflections derive to a large extent from the self-observation paper 1 (SO1) and the Practicum portfolio (PP) developed within the TED Masters Degree practicum stages

Teacher strategies to elicit knowledge from students in the CLIL classroom: the purpose of questions in controlled patterns of teacher-student interaction

This Master Dissertation comprises two parts: a personal reflection and an empirical study. The personal reflection reviews the process of professionalization undergone by its author throughout the Master. The empirical study tackles teacher strategies to elicit knowledge from students in the CLIL classroom and more specifically the purpose of questions in controlled patterns of teacher-student interaction. The theories of relevant authors such as Vigotsky, Mercer and Tsui are used as a framework to analyze the data presented. The analysis shows the different strategies to elicit knowledge used by the teacher and the appropriateness of her questions in the analyzed interaction

The first steps of a secondary school teacher: experiences and studies of a student-teacher

This dissertation aims at fostering the professional development of the EFL teacher. This document compiles two small scale empirical studies carried out during the practicum periods of the TED's course. The first one is based on the role of the teacher's talk in the EFL classroom and the second one focuses on students’ small group talk, analysing the impact of cooperative learning in the EFL classroom by examining students' conversation. The following section gathers the teacher's personal reflections upon the process of professionalization. The paper concludes with a summary of the major findings and further professional improvement proposals

Teacher training in "multicultural" Sweden

This paper builds on the experience of the on-going, mainly ethnographic, research project called Teacher training in’ multicultural’ Sweden. Class, gender and ethnicity. In this multi-disciplinary project a number of scholars conduct research through participant observation in, and through the study and analysis of documents from, a number of teacher training colleges in Sweden. In this paper I will use empirical material gathered from two teacher training colleges to discuss this basic issue. One college is situated in a suburb outside Stockholm and it consciously portrays itself as a college for ‘multicultural’ students who will later teach in ‘multicultural’ suburbs. The other college is situated in a small town and although ‘multiculturalism’ is seen as important in the educational system students with mainly ‘Swedish’ background are recruited. In the first college ‘differences’ are lauded and students are encouraged to ponder upon and develop their ethnic profile. In the second ‘similarities’ are more taken for granted. I will argue, however, that within these colleges ‘differences’ and ’similarities’ are not only discussed but actually created against a backdrop of macro-constraints which are not much scrutinized within these colleges.