Form tutors in the joint teaching of music: perspectives and experiences

In the Portuguese school system, form tutors (FTs) are an intermediate education management structure. The form tutor is responsible for a position of coordination and orientation with a «threefold function»: a relationship with students, relationship with the student’s family and relationship with other class teachers. The joint teaching of music is a part of the educational system in basic education. It is optional and provides musical and instrumental training to students who are interested in taking it. In order to achieve this, there is a system, subject to protocols, between general education schools and schools specializing in teaching music. There is also the position of FT in specialized schools and it also includes a «threefold function». However, these FTs have the additional role of representing music teachers at the class council, which is held at the general education school. Thus, in these cases, both FTs have a fourth joint area, between the music school and the general education school, which makes the relationship between them even more complex. This paper is based on the analysis of empirical data obtained from the testimonies of FTs regarding their representations and experiences in leadership and the coordination of teachers among schools in which there is a joint teaching system. The aim of collecting narratives is to look into some of the main challenges and confrontations related to leadership issues, which we assume to be the focus of those who have the role of form tutor in that specific context.

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.

Online teaching of inflammatory skin pathology by a French-speaking International University Network

INTRODUCTION: Developments in technology, web-based teaching and whole slide imaging have broadened the teaching horizon in anatomic pathology. Creating online learning material including many types of media such as radiologic images, whole slides, videos, clinical and macroscopic photographs, is now accessible to most universities. Unfortunately, a major limiting factor to maintain and update the learning material is the amount of resources needed. In this perspective, a French-national university network was initiated in 2011 to build joint online teaching modules consisting of clinical cases and tests. The network has since expanded internationally to Québec, Switzerland and Ivory Coast. METHOD: One of the first steps of the project was to build a learning module on inflammatory skin pathology for interns and residents in pathology and dermatology. A pathology resident from Québec spent 6 weeks in France and Switzerland to develop the contents and build the module on an e-learning Moodle platform under the supervision of two dermatopathologists. The learning module contains text, interactive clinical cases, tests with feedback, virtual slides, images and clinical photographs. For that module, the virtual slides are decentralized in 2 universities (Bordeaux and Paris 7). Each university is responsible of its own slide scanning, image storage and online display with virtual slide viewers. RESULTS: The module on inflammatory skin pathology includes more than 50 web pages with French original content, tests and clinical cases, links to over 45 virtual images and more than 50 microscopic and clinical photographs. The whole learning module is being revised by four dermatopathologists and two senior pathologists. It will be accessible to interns and residents in the spring of 2014. The experience and knowledge gained from that work will be transferred to the next international resident whose work will be aimed at creating lung and breast pathology learning modules. CONCLUSION: The challenges of sustaining a project of this scope are numerous. The technical aspect of whole-slide imaging and storage needs to be developed by each university or group. The content needs to be regularly updated and its accuracy reviewed by experts in each individual domain. The learning modules also need to be promoted within the academic community to ensure maximal benefit for trainees. A collateral benefit of the project was the establishment of international partnerships between French-speaking universities and pathologists with the common goal of promoting pathology education through the use of multi-media technology including whole slide imaging.

An international university network for online teaching of pathology in Frenchspeaking countries

Introduction: Building online courses is a highly time consuming task for teachers of a single university. Universities working alone create high-quality courses but often cannot cover all pathological fields. Moreover this often leads to duplication of contents among universities, representing a big waste of teacher time and energy. We initiated in 2011 a French university network for building mutualized online teaching pathology cases, and this network has been extended in 2012 to Quebec and Switzerland. Method: Twenty French universities (see & for details), University Laval in Quebec and University of Lausanne in Switzerland are associated to this project. One e-learning Moodle platform (http://moodle.sorbonne-paris-cite.fr/) contains texts with URL pointing toward virtual slides that are decentralized in several universities. Each university has the responsibility of its own slide scanning, slide storage and online display with virtual slide viewers. The Moodle website is hosted by PRES Sorbonne Paris Cité, and financial supports for hardware have been obtained from UNF3S (http://www.unf3s.org/) and from PRES Sorbonne Paris Cité. Financial support for international fellowships has been obtained from CFQCU (http://www.cfqcu.org/). Results: The Moodle interface has been explained to pathology teachers using web-based conferences with screen sharing. The teachers added then contents such as clinical cases, selfevaluations and other media organized in several sections by student levels and pathological fields. Contents can be used as online learning or online preparation of subsequent courses in classrooms. In autumn 2013, one resident from Quebec spent 6 weeks in France and Switzerland and created original contents in inflammatory skin pathology. These contents are currently being validated by senior teachers and will be opened to pathology residents in spring 2014. All contents of the website can be accessed for free. Most contents just require anonymous connection but some specific fields, especially those containing pictures obtained from patients who agreed for a teaching use only, require personal identification of the students. Also, students have to register to access Moodle tests. All contents are written in French but one case has been translated into English to illustrate this communication (http://moodle.sorbonne-pariscite.fr/mod/page/view.php?id=261) (use "login as a guest"). The Moodle test module allows many types of shared questions, making it easy to create personalized tests. Contents that are opened to students have been validated by an editorial committee composed of colleagues from the participating institutions. Conclusions: Future developments include other international fellowships, the next one being scheduled for one French resident from May to October 2014 in Quebec, with a study program centered on lung and breast pathology. It must be kept in mind that these e-learning programs highly depend on teachers' time, not only at these early steps but also later to update the contents. We believe that funding resident fellowships for developing online pathological teaching contents is a win-win situation, highly beneficial for the resident who will improve his knowledge and way of thinking, highly beneficial for the teachers who will less worry about access rights or image formats, and finally highly beneficial for the students who will get courses fully adapted to their practice.

Online teaching of inflammatory skin pathology by a French-speaking International University Network.

INTRODUCTION: Developments in technology, web-based teaching and whole slide imaging have broadened the teaching horizon in anatomic pathology. Creating online learning material including many types of media such as radiologic images, whole slides, videos, clinical and macroscopic photographs, is now accessible to most universities. Unfortunately, a major limiting factor to maintain and update the learning material is the amount of resources needed. In this perspective, a French-national university network was initiated in 2011 to build joint online teaching modules consisting of clinical cases and tests. The network has since expanded internationally to Québec, Switzerland and Ivory Coast. METHOD: One of the first steps of the project was to build a learning module on inflammatory skin pathology for interns and residents in pathology and dermatology. A pathology resident from Québec spent 6 weeks in France and Switzerland to develop the contents and build the module on an e-learning Moodle platform under the supervision of two dermatopathologists. The learning module contains text, interactive clinical cases, tests with feedback, virtual slides, images and clinical photographs. For that module, the virtual slides are decentralized in 2 universities (Bordeaux and Paris 7). Each university is responsible of its own slide scanning, image storage and online display with virtual slide viewers. RESULTS: The module on inflammatory skin pathology includes more than 50 web pages with French original content, tests and clinical cases, links to over 45 virtual images and more than 50 microscopic and clinical photographs. The whole learning module is being revised by four dermatopathologists and two senior pathologists. It will be accessible to interns and residents in the spring of 2014. The experience and knowledge gained from that work will be transferred to the next international resident whose work will be aimed at creating lung and breast pathology learning modules. CONCLUSION: The challenges of sustaining a project of this scope are numerous. The technical aspect of whole-slide imaging and storage needs to be developed by each university or group. The content needs to be regularly updated and its accuracy reviewed by experts in each individual domain. The learning modules also need to be promoted within the academic community to ensure maximal benefit for trainees. A collateral benefit of the project was the establishment of international partnerships between French-speaking universities and pathologists with the common goal of promoting pathology education through the use of multi-media technology including whole slide imaging.

Conflicto, colaboración y consenso en la enseñanza de las ciencias sociales = Conflict, collaboration and consensus in the teaching of the Social sciences

This article suggests the study of the key concept of conflict as a means of implementing a critical and communicativecurriculum based on the study of relevant social themes. To this end we put forward the principal characteristics of thecritical/communicative curriculum. We offer a didactic proposal about conflict and explain the results of its application intwo Secondary Education classrooms

Un análisis optimista de la educación matemática en la formación de maestros de educación infantil = An optimistic analysis of mathematics education in training pre-school teachers

This article offers a panorama of mathematics training for future teachers at pre-school level in Spain. With this goal in mind, this article is structured infour sections: where we come from, where we are, where we’re going and where we want to go. It offers, in short, a brief analysis that shows the efforts made to ensure there is sufficient academic and scientific rigour in teachers’ studies at pre-school in general and students’ mathematics education in particular. Together with a description of the progress made in recent years, it also raises some questions for all those involved in training future teachers for this educational stage

Laboratory projects using inquiry-based learning: an application to a practical inorganic course

This paper reports how laboratory projects (LP) coupled to inquiry-based learning (IBL) were implemented in a practical inorganic chemistry course. Several coordination compounds have been successfully synthesised by students according to the proposed topics by the LP-IBL junction, and the chemistry of a number of metals has been studied. Qualitative data were collected from written reports, oral presentations, lab-notebook reviews and personal discussions with the students through an experimental course with undergraduate second-year students at the Universidad Nacional de Colombia during the last 5 years. Positive skills production was observed by combining LP and IBL. Conceptual, practical, interpretational, constructional (questions, explanations, hypotheses), communicational, environmental and application abilities were revealed by the students throughout the experimental course.

The use of explicit algorithms and episodic context to teach subtraction to students with learning problems in mathematics /

This research attempted to address the question of the role of explicit algorithms and episodic contexts in the acquisition of computational procedures for regrouping in subtraction. Three groups of students having difficulty learning to subtract with regrouping were taught procedures for doing so through either an explicit algorithm, an episodic content or an examples approach. It was hypothesized that the use of an explicit algorithm represented in a flow chart format would facilitate the acquisition and retention of specific procedural steps relative to the other two conditions. On the other hand, the use of paragraph stories to create episodic content was expected to facilitate the retrieval of algorithms, particularly in a mixed presentation format. The subjects were tested on similar, near, and far transfer questions over a four-day period. Near and far transfer algorithms were also introduced on Day Two. The results suggested that both explicit and episodic context facilitate performance on questions requiring subtraction with regrouping. However, the differential effects of these two approaches on near and far transfer questions were not as easy to identify. Explicit algorithms may facilitate the acquisition of specific procedural steps while at the same time inhibiting the application of such steps to transfer questions. Similarly, the value of episodic context in cuing the retrieval of an algorithm may be limited by the ability of a subject to identify and classify a new question as an exemplar of a particular episodically deflned problem type or category. The implications of these findings in relation to the procedures employed in the teaching of Mathematics to students with learning problems are discussed in detail.

Investigating Formative Assessment: Exploring the Impact on the Self-Efficacy and Motivation of Mathematics Students

This is a study of the implementation and impact of formative assessment strategies on the motivation and self-efficacy of secondary school mathematics students. An explanatory sequential mixed methods design was implemented where quantitative and qualitative data were collected and analyzed sequentially in 2 different phases. The first phase involved quantitative data from student questionnaires and the second phase involved qualitative data from individual student and teacher interviews. The findings of the study suggest that formative assessment is implemented in practice in diverse ways and is a process where the strategies are interconnected. Teachers experience difficulty in incorporating peer and self-assessment and perceive a need for exemplars. Key factors described as influencing implementation include teaching philosophies, interpretation of ministry documents, teachers’ experiences, leadership in administration and department, teacher collaboration, misconceptions of teachers, and student understanding of formative assessment. Findings suggest that overall, formative assessment positively impacts student motivation and self-efficacy, because feedback is provided which offers encouragement and recognition by highlighting the progress that has been made and what steps need to be taken to improve. However, students are impacted differently with some considerations including how students perceive mistakes and if they fear judgement. Additionally, the impact of formative assessment is influenced by the connection between self-efficacy and motivation, namely how well a student is doing is a source of both concepts.

Analysis of applications and of conceptions for an application-oriented mathematics instruction

In connection with the (revived) demand for considering applications in the teaching of mathematics, various schemata or lists of criteria have been developed since the end of the sixties, which set up requirements about closeness to the real world or about the type of mathematics being used, and which have made it possible to analyze the available applications in their light. After having stated the problem (in section 1), we present (in section 2) a sketch of some of the best known of these and of some earlier schemata, although we are not aiming for a complete picture. Then (in section 3) we distinguish among different dimensions.in the analysis of applications. With this as a basis, we develop (in section 4) our own suggestion for categorizing types of applications and conceptions for an application-oriented mathematics instruction. Then (in section 5) we illustrate our schemata by some examples of performed evaluations. Finally (in section 6), we present some preliminary first results of the analysis of teaching conceptions.

Using drama techniques for the teaching of early years science : a case study

This paper investigates the effect of drama techniques when employed to facilitate teaching and learning early years science. The focus is a lesson intervention designed for a group of children aged between four and five years old. A number of different drama techniques, such as teacher in role, hot seating and miming, were employed for the teaching of the water cycle. The techniques were implemented based on their nature and on what they can offer to young children considering their previous experiences. Before the beginning of the intervention, six children were randomly selected from the whole class, who were interviewed, aiming to identify their initial ideas in regards to the water cycle. The same children were interviewed after the end of the intervention in an attempt to identify the ways in which their initial ideas were changed. The results appear to be promising in terms of facilitating children’s scientific understanding and show an improvement in the children’s use of vocabulary in relation to the specific topic.

Virtualization for cost-effective teaching of assembly language programming

A virtual system that emulates an ARM-based processor machine has been created to replace a traditional hardware-based system for teaching assembly language. The proposed virtual system integrates, in a single environment, all the development tools necessary to deliver introductory or advanced courses on modern assembly language programming. The virtual system runs a Linux operating system in either a graphical or console mode on a Windows or Linux host machine. No software licenses or extra hardware are required to use the virtual system, thus students are free to carry their own ARM emulator with them on a USB memory stick. Institutions adopting this, or a similar virtual system, can also benefit by reducing capital investment in hardware-based development kits and enable distance learning courses.

The Use of Vocabulary in an Eighth Grade Mathematics Classroom: Improving Usage of Mathematics Vocabulary in Oral and Written Communication

In this action research study of my mathematics classroom of eighth grade students, I investigated the use of mathematics vocabulary by focusing on improving the usage of this vocabulary in both oral and written communication. I discovered oral communication tended to show more improvements compared to written communication done by the same group of students. As a result of this research, I plan to continue to focus my teaching on the use of mathematics vocabulary in an effort to help my students gain a greater understanding of the daily use of that vocabulary.

CLIL materials in Secondary Education: focusing on the language of instruction in the subject area of Mathematics

[EN]Applying a CLIL methodological approach marks a shift in emphasis from language learning based on linguistic form and grammatical progression to a more ‘language acquisition’ one which takes account language functions. In this article we will study the elements of the “language of instruction” of the area of Maths in Secondary Education, by focusing on the analysis of the communicative functions, and the lexical and the cultural items present in the textbook in use. Our aim is to present the CLIL teacher with the linguistic and didactic implications that he or she should take into consideration when implementing the bilingual syllabuses with their students. In order to do that, we will present our conclusions emphasizing the need for coordination in different content areas, linguistic and communicative contents, between the foreign language teacher and the CLIL subject one.