The role of technology in the study of semiotic representations in mathematics

En este trabajo resumimos algunas reflexiones sobre el papel que pueden desarrollar la tecnología en el estudio de sistemas semióticos de representación, y que constituyen el núcleo para la comprensión de los procesos de construcción del conocimiento matemático de los estudiantes. La cita corresponde con el resumen de una página publicado.

[Conference report] Magic and mathematics: The life and work of John Dee. National Maritime Museum, Greenwich, 13-14 June 2003

Tony Mann provides a report of a two-day meeting "Magic and mathematics: The life and work of John Dee" held from 13-14 June 2003 at the National Maritime Museum, Greenwich.

History of the Continuous Plankton Recorder Database. Proceedings of 'The Colour of Ocean Data' Symposium, Brussels, 25-27 November 2002.

The Continuous Plankton Recorder Survey has operated in the North Atlantic and North Sea since 1931, providing a unitque multi-decadal dataset of plankton abundance. Over the period since 1931 technology has advanced and the system for storing the CPR data has developed considerably. From 1969 an electronic database was developed to store the results of CPR analysis. Since that time the CPR database has undergone a number of changes due to performance related factors such as processor speed and disk capacity as well as economic factors such as the cost of software. These issues have been overcome and the system for storing and retrieving the data has become more user friendly at every development stage.

Short reflections on the history of African communication

This article aims to propose a chronological subdivision in the history of African communication. African communication today is one of the most important axes for implementing development strategies, sustaining education, health, and schooling programmes, and so on. However, many of these programmes fail due to a lack of or ineffective communication between international organisations, local elite and lay people. The reasons for this situation must be found in Africa’s history of communication, which has undergone radical transformations in its different phases. Using the functionalist analysis drawn up by Jakobson, this article proposes a new chronological subdivision of Africa’s history of communication, reflecting on the current contradictions in contemporary communication in Africa.

Understandings of citizenship education in Northern Ireland and the Republic of Ireland: Public discourses among stakeholders in the public and private sectors

Internationally, citizenship education has come to the fore in the past decade. It may be particularly importantwithin the context of societies with a legacy of political conflict, such as Northern Ireland and the Republic of Ireland, where it is being implemented as part of the statutory curriculum. This article explores understandingsof citizenship education among stakeholders in the private and public sectors in Northern Ireland and the Republic of Ireland with the aim to compare these with curricular conceptualizations of citizenship inboth contexts. Semi-structured interviews were conducted in both societies involving non-governmentalorganizations, political parties, trade unions and the police. Results indicated that levels of awareness aboutcitizenship education varied substantially and understandings mainly reflected current theory and curriculumpractice in citizenship. Commonalities emerged as in both societies similar key concepts were identified whiledifferences transpired over issues relating to national identity and political conflict, which may raise questionsfor history and citizenship education in both societies.

Validity of a personal and family history of cataract and cataract surgery in genetic studies.

PURPOSE:

To determine the accuracy of a history of cataract and cataract surgery (self-report and for a sibling), and to determine which demographic, cognitive, and medical factors are predictive of an accurate history.

METHODS:

All participants in the Salisbury Eye Evaluation (SEE) project and their locally resident siblings were questioned about a personal and family history of cataract or cataract surgery. Lens grading at the slit lamp, using standardized photographs and a grading system, was performed for both SEE participants (probands) and their siblings. Cognitive testing and a history of systemic comorbidities were also obtained for all probands.

RESULTS:

Sensitivity of a history of cataract provided on behalf of a sibling was 32%, specificity 98%. The performance was better for a history of cataract surgery: sensitivity 90%, specificity 89%. For self-report of cataract, sensitivity was also low at 55%, with specificity at 77%. Self-report of cataract surgery gave a much better performance: sensitivity 94%, specificity 100%. Different cutoffs in the definition of cataract had little impact. Factors predicting a correct history of cataract included high school or greater education in the proband (odds ratio [OR] = 1.13, 95% confidence interval [CI]1.02-1.25) and younger sibling (but not proband) age (OR = 0.94 for each year of age, 95% CI 0.90-0.99). Gender, race and Mini-Mental Status Examination (MMSE) result were not predictive.

CONCLUSIONS:

Whereas accurate self and family histories for cataract surgery may be obtainable, it is difficult to ascertain cataract status accurately from history alone.

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.

Teachers' professional learning within communities of mathematics-for-teaching practice

Ontario bansho is an emergent mathematics instructional strategy used by teachers working within communities of practice that has been deemed to have a transformational effect on teachers' professional learning of mathematics. This study sought to answer the following question: How does teachers' implementation of Ontario bansho within their communities of practice inform their professional learning process concerning mathematics-for-teaching? Two other key questions also guided the study: What processes support teachers' professional learning of content-for-teaching? What conditions support teachers' professional learning of content-for-teaching? The study followed an interpretive phenomenological approach to collect data using a purposive sampling of teachers as participants. The researcher conducted interviews and followed an interpretive approach to data analysis to investigate how teachers construct meaning and create interpretations through their social interactions. The study developed a model of professional learning made up of 3 processes, informing with resources, engaging with students, and visualizing and schematizing in which the participants engaged and 2 conditions, ownership and community that supported the 3 processes. The 3 processes occur in ways that are complex, recursive, nonpredictable, and contextual. This model provides a framework for facilitators and leaders to plan for effective, content-relevant professional learning by placing teachers, students, and their learning at the heart of professional learning.

Indices and Implications of Emotional Underarousal for Persons with a History of Head Trauma

We examined the role of altered emotional functioning across the spectrum of injury severity (mild head injury [MHI], moderate/severe traumatic brain injury [TBI]), its implications for social behaviours, and the effect of modifying arousal and its relation to cognitive performance. In the first study (N = 230), students with self-reported MHI endorsed engaging in socially unacceptable and erratic behaviours significantly more often than did those with no MHI. We did not find significant differences between the groups in the measure of emotional intelligence (EI); however, for students who reported a MHI, scores on the EI measure significantly predicted reports of socially unacceptable behaviours such that lower scores predicted poorer social functioning, accounting for approximately 20% of the variance. Also, the experience of postconcussive symptoms was found to be significantly greater for students with MHI relative to their peers. In the second study (N = 85), we further examined emotional underarousal in terms of physiological (i.e., electrodermal activation [EDA]) and self-reported responsivity to emotionally-evocative picture stimuli. Although the valence ratings of the stimuli did not differ between students with and without MHI as we had expected, we found evidence of reduced and/or indiscriminate emotional responding to the stimuli for those with MHI which mimics that observed in other studies for persons with moderate/severe TBI. We also found that emotional underarousal followed a gradient of injury severity despite reporting a pattern of experiencing more life stressors. In the third study (N = 81), we replicated our findings of emotional underarousal for those with head trauma and also uniquely explored neuroendocrine aspects (salivary cortisol; cortisol awakening response [CAR]) and autonomic indices (EDA) of emotional dysregulation in terms of stress responsivity across the spectrum of injury severity (MHI [n = 32], moderate/severe TBI [n = 9], and age and education matched controls [n = 40]). Although the manipulation was effective in modifying arousal state in terms of autonomic and self-reported indices, we did not support our hypothesis that increased arousal would be related to improved performance on cognitive measures for those with prior injury. To our knowledge, this is the only study to examine the CAR with this population. Repeated measure analysis revealed that, upon awakening, students with no reported head trauma illustrated the typical CAR increase 45 minutes after waking, whereas, students who had a history of either mild head trauma or moderate/severe TBI demonstrated a blunted CAR. Thus, across the three studies we have provided evidence of emotional underarousal, its potential implications for social interactions, and also have identified potentially useful indices of dysregulated stress responsivity regardless of injury severity.

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.

Understanding the past to imagine the future : the history of industrial design practice in Alberta

La pratique du design industriel dans la province canadienne de l’Alberta est en pleine croissance. Ses activités sont principalement concentrées à Edmonton et à Calgary, qui sont les plus grandes villes de la province. On y trouve des studios de design de renom, des communautés de design complexes et des programmes universitaires de design bien établis. Cependant, la pratique du design industriel albertaine est sous-développée en comparaison avec celle du reste du Canada et il y a peu de recherches et de documentation sur le design industriel en Alberta. Dans ce projet de mémoire, la pratique du design industriel en Alberta a été explorée depuis une approche historique. Pour pallier le manque de documentation, la collecte de données a été faite par une recherche qualitative, des entretiens narratifs et une recherche quantitative statistique. Une base d’information historique sur le design industriel albertain a été établie puis située par rapport au développement de la pratique du design industriel ailleurs au Canada. Les facteurs, événements et tendances dans l’histoire de la pratique du design industriel en Alberta ont été identifiés. De plus, le développement de la pratique du design industriel de l’Alberta a été comparé à celui du Québec et de l’Ontario. Les retombées de cette étude indiquent que la pratique du design industriel en Alberta présente quatre domaines de spécialisations distincts se développant depuis les années 1980. La pratique du design industriel en Alberta est sous-développée en comparaison à celui du Québec et de l’Ontario, mais elle peut devenir plus compétitive, au niveau canadien, avec plus de soutien gouvernemental, de meilleures relations avec l’industrie manufacturière et les institutions académiques, une communauté de design plus unifiée et en portant une plus grande attention aux domaines les plus prometteurs de l’industrie. Ces informations supportent une meilleure compréhension de la pratique du design industriel en Alberta et pourront informer les praticiens, enseignants et administrateurs du domaine du design industriel dans la province. Finalement, le mémoire servira de base à d’autres projets de recherche sur les changements potentiels dans la pratique du design industriel en Alberta et l’étude du design canadien et des industries de design régionales.

Mathematical modelling in mathematics education and instruction

This paper aims at giving a concise survey of the present state-of-the-art of mathematical modelling in mathematics education and instruction. It will consist of four parts. In part 1, some basic concepts relevant to the topic will be clarified and, in particular, mathematical modelling will be defined in a broad, comprehensive sense. Part 2 will review arguments for the inclusion of modelling in mathematics teaching at schools and universities, and identify certain schools of thought within mathematics education. Part 3 will describe the role of modelling in present mathematics curricula and in everyday teaching practice. Some obstacles for mathematical modelling in the classroom will be analysed, as well as the opportunities and risks of computer usage. In part 4, selected materials and resources for teaching mathematical modelling, developed in the last few years in America, Australia and Europe, will be presented. The examples will demonstrate many promising directions of development.