Audit of mathematics learning support in Ireland in 2015 – the key findings

In 2015 the Irish Mathematics Learning Support Network (IMLSN) commissioned a comprehensive audit of the extent and nature of mathematics learning support (MLS) provision on the island of Ireland. An online survey was sent to 32 institutions, including universities, institutes of technology, further education and teacher training colleges, and a 97% response rate was achieved. While the headline figure – 84% of institutions that responded to the survey provide MLS – sounds good, deeper analysis reveals that the true state of MLS is not so solid. For example, in 25% of institutions offering MLS, only five hours per week (at most) of physical MLS are available, while in 20% of institutions the service is provided by only one or two staff members. Furthermore, training of tutors is minimal or non-existent in at least half of the institutions offering MLS. The results provide an illuminating picture, however, identifying the true state of MLS in Ireland is beneficial only if it informs developments in the years ahead. This talk will present some of the findings of the survey in more depth along with conclusions and recommendations. Key among these is the need for institutions to recognise MLS as a vital element of mathematics teaching and learning strategy at third level and devote the necessary resources to facilitate the provision of a service which can grow and adapt to meet student requirements.

Humor in mathematics teaching

HUMOR: OUR VIEW FOR MATHEMATICS TEACHING Our assumptions and context. Process humor and be able to produce is clearly a sign of intelligence, revealing, when done well, complex reasoning. Humor has an important social role, assuming as a cognitive experience that as well as creating a sense of well-being, predisposes people to work and can improve the productivity of that work. Mathematics is a discipline in which the reasoning occupies a very prominent place, both as a science as a school area. At the same time, students' interest for mathematics is not always the same and some have initially not very favorable feelings (Toh, 2009; Wanzer, Frymier & Irwin, 2010). Recent curriculum changes to the teaching of mathematics have been, in most countries of the world, showing the need for students to develop skills of critical nature, such as communication, thinking and problem solving along with the acquisition of mathematical knowledge. Also in Portugal, it is claimed the importance of promoting learning that combine the construction of mathematical knowledge with its use, when performing mathematical tasks and communicating mathematical ideas and mathematical reasoning. In the early years of schooling, corresponding to primary education in many countries, the use of texts such as short stories or comics, from which we can develop challenging mathematical tasks, is reported in the literature as having potential to promote learning specified in curricular documents (Wanzer, Frymier., & Irwin, 2010). In particular, some texts focus on mathematical topics in a humorous way and to be understood, students must develop their mathematical competence. The development of mathematical tasks from stories and other humorous presents big challenges to teachers (Flores & Moreno, 2011). Our questions. In this context, we put some questions: Primary teachers use in their classes tasks or situations that present, in a humorous way, mathematical ideas? What resources do they use? Also: How to select, adapt or build texts and tasks which have, in a humorous way, mathematical ideas with didactic potential for education in the early years of schooling? If the resources for this purpose have been produced and if teachers have been sensitized for their use, are they able to integrate them in their classes? Our intentions. This research project seeks to address these questions, focused on: (i ) assessment of teachers’ practices and underlying knowledge, resources available for the use of texts with mathematical ideas presented in a humorous way; (ii) selection, adaptation and construction of mathematical tasks from texts that present, in a humorous way, mathematical ideas with didactic potential in education for the early years of schooling; and ( iii ) integration and use, by primary school teachers, of texts that present , in a humorous way, contexts for the teaching of mathematics. So, the project is organized into three tasks and as a methodological design that combines qualitative elements with quantitative elements, the first one prevailing.

[the Teaching Of Social Sciences In Health: Between Practice And Theory].

The models of teaching social sciences and clinical practice are insufficient for the needs of practical-reflective teaching of social sciences applied to health. The scope of this article is to reflect on the challenges and perspectives of social science education for health professionals. In the 1950s the important movement bringing together social sciences and the field of health began, however weak credentials still prevail. This is due to the low professional status of social scientists in health and the ill-defined position of the social sciences professionals in the health field. It is also due to the scant importance attributed by students to the social sciences, the small number of professionals and the colonization of the social sciences by the biomedical culture in the health field. Thus, the professionals of social sciences applied to health are also faced with the need to build an identity, even after six decades of their presence in the field of health. This is because their ambivalent status has established them as a partial, incomplete and virtual presence, requiring a complex survival strategy in the nebulous area between social sciences and health.

A Brazilian Original Pedagogical Approach To The Teaching Of Neurology.

The two-arm Clinical Decisions/Diagnostic Workshop (CD/DW) approach to undergraduate medical education has been successfully used in Brazil. Present the CD/DW approach to the teaching of stroke, with the results of its pre-experimental application and of a comparative study with the traditional lecture-case discussion approach. Application of two questionnaires (opinion and Knowledge-Attitudes-Perceptions-KAP) to investigate the non-inferiority of the CD/DW approach. The method was well accepted by teachers and students alike, the main drawback being the necessarily long time for its completion by the students, a feature that may better cater for different educational needs. The comparative test showed the CD/DW approach to lead to slightly higher cognitive acquisition as opposed to the traditional method, clearly showing its non-inferiority status. The CD/DW approach seems to be another option for teaching neurology in undergraduate medical education, with the bonus of respecting each learner`s time.

Transition From Glass To Digital Slide Microscopy In The Teaching Of Oral Pathology In A Brazilian Dental School.

Several medical and dental schools have described their experience in the transition from conventional to digital microscopy in the teaching of general pathology and histology disciplines; however, this transitional process has scarcely been reported in the teaching of oral pathology. Therefore, the objective of the current study is to report the transition from conventional glass slide to virtual microscopy in oral pathology teaching, a unique experience in Latin America. An Aperio ScanScope® scanner was used to digitalize histological slides used in practical lectures of oral pathology. The challenges and benefits observed by the group of Professors from the Piracicaba Dental School (Brazil) are described and a questionnaire to evaluate the students' compliance to this new methodology was applied. An improvement in the classes was described by the Professors who mainly dealt with questions related to pathological changes instead of technical problems; also, a higher interaction with the students was described. The simplicity of the software used and the high quality of the virtual slides, requiring a smaller time to identify microscopic structures, were considered important for a better teaching process. Virtual microscopy used to teach oral pathology represents a useful educational methodology, with an excellent compliance of the dental students.

Proposal for the teaching of the chemical control of supragingival biofilm

The mechanical control of supragingival biofilm is accepted as one of the most important measures to treat and prevent dental caries and periodontal diseases. Nevertheless, maintaining dental surfaces biofilm-free is not an easy task. In this regard, chemical agents, mainly in the form of mouthwashes, have been studied to help overcome the difficulties involved in the mechanical control of biofilm. The aim of this paper was to discuss proposals for the teaching of supragingival chemical control (SCC) in order to improve dentists' knowledge regarding this clinical issue. Firstly, the literature regarding the efficacy of antiseptics is presented, clearly showing that chemical agents are clinically effective in the reduction of biofilm and gingival inflammation when used as adjuvant agents to mechanical control. Thus, it is suggested that the content related to SCC be included in the curricular grid of dental schools. Secondly, some essential topics are recommended to be included in the teaching of SCC as follows: skills and competencies expected of a graduate dentist regarding SCC; how to include this content in the curricular grid; teaching-learning tools and techniques to be employed; and program content.

Undergraduate teaching of ideal and real fluid flows: The value of real-world experimental projects

This study describes the pedagogical impact of real-world experimental projects undertaken as part of an advanced undergraduate Fluid Mechanics subject at an Australian university. The projects have been organised to complement traditional lectures and introduce students to the challenges of professional design, physical modelling, data collection and analysis. The physical model studies combine experimental, analytical and numerical work in order to develop students’ abilities to tackle real-world problems. A first study illustrates the differences between ideal and real fluid flow force predictions based upon model tests of buildings in a large size wind tunnel used for research and professional testing. A second study introduces the complexity arising from unsteady non-uniform wave loading on a sheltered pile. The teaching initiative is supported by feedback from undergraduate students. The pedagogy of the course and projects is discussed with reference to experiential, project-based and collaborative learning. The practical work complements traditional lectures and tutorials, and provides opportunities which cannot be learnt in the classroom, real or virtual. Student feedback demonstrates a strong interest for the project phases of the course. This was associated with greater motivation for the course, leading in turn to lower failure rates. In terms of learning outcomes, the primary aim is to enable students to deliver a professional report as the final product, where physical model data are compared to ideal-fluid flow calculations and real-fluid flow analyses. Thus the students are exposed to a professional design approach involving a high level of expertise in fluid mechanics, with sufficient academic guidance to achieve carefully defined learning goals, while retaining sufficient flexibility for students to construct there own learning goals. The overall pedagogy is a blend of problem-based and project-based learning, which reflects academic research and professional practice. The assessment is a mix of peer-assessed oral presentations and written reports that aims to maximise student reflection and development. Student feedback indicated a strong motivation for courses that include a well-designed project component.

Teaching of medical ethics: Implications for an integrated curriculum

This paper reports on an investigation into the teaching of medical ethics and related areas in the medical undergraduate course at the University of Queensland. The project was designed in the context of a major curriculum change to replace the current 6 year course by an integrated, problem-based, 4 year graduate medical course, which began in 1997. A survey of clinical students, observations of clinical teaching sessions, and interviews with clinical teachers were conducted. Data obtained have contributed to curriculum development and will provide a baseline for comparison and evaluation of the graduate course in this field. A view of integrated ethics teaching is advanced in the light of the data obtained.

The teaching of History meets its past: memories of teaching staff during the civil-military dictatorship

The civil-military dictatorship, which took power in 1964, influenced the daily activities of schools and teachers. Many transformations occurred during this period, including the new legislation enacted under Law 5692/71 and changes which occurred due to the vigilance which teachers felt when working. The memories analyzed here of teachers from public schools in Sao Paulo show different perceptions of this surveillance, involving various forms of acceptance or resistance. The purpose of this article is to show that although there was no direct repression of schools, unlike in the universities, teachers at the elementary school also felt constrained and this can be seen in their educational practices and teaching concepts.

Historical and dialectical perspectives on the teaching of Aboriginal and Torres Strait Islander musics in the Australian education system

Indigenous studies (also referred to as Aboriginal and Torres Strait Islander studies) has a double identity in the Australian education system, consisting of the education of Indigenous students and education of all students about Aboriginal and Torres Strait Islander cultures and histories. Through explanations of the history of the inclusion of Aboriginal and Torres Strait Islander musics in Australian music education, this article critiques ways in which these musics have been positioned in relation to a number of agendas. These include definitions of Aboriginal and Torres Strait Islander musics as types of Australian music, as ethnomusicological objects, as examples of postcolonial discourse, and as empowerment for Indigenous students. The site of discussion is the work of the Australian Society for Music Education, as representative of trends in Australian school-based music education, and the Centre for Aboriginal Studies in Music at the University of Adelaide, as an example of a tertiary music program for Indigenous students.

Mathematical education and interdisciplinarity : promoting public awareness of mathematics in the Azores

Mathematical literacy in Portugal is very unsatisfactory in what concerns international standards. Even more disturbingly, the Azores archipelago ranks as one of the worst regions of Portugal in this respect. We reason that the popularisation of Mathematics through interactive exhibitions and activities can contribute actively to disseminate mathematical knowledge, increase awareness of the importance of Mathematics in today’s world and change its negative perception by the majority of the citizens. Although a significant investment has been undertaken by the local regional government in creating several science centres for the popularisation of Science, there is no centre for the popularisation of Mathematics. We present our first steps towards bringing Mathematics to unconventional settings by means of hands-on activities. We describe in some detail three activities. One activity has to do with applying trigonometry to measure distances in Astronomy, which can also be applied to Earth objects. Another activity concerns the presence of numerical patterns in the Azorean flora. The third activity explores geometrical patterns in the Azorean cultural heritage. It is our understanding that the implementation of these and other easy-to-follow and challenging activities will contribute to the awareness of the importance and beauty of Mathematics.

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.