Critical reading of science-based news reports: Establishing a knowledge skills and attitudes framework

A recognised aim of science education is to promote critical engagement with science in the media. Evidence would suggest that this is challenging for both teachers and pupils and that at science education does not yet adequately prepare young people for this task. Furthermore, in the absence of clear guidance as to what this means and how this may be achieved it is difficult for teachers to develop approaches and resources that address the matter and that systematically promote such critical engagement within their teaching programmes. Twenty-six individuals with recognised expertise or interest in science in the media, drawn from a range of disciplines and areas of practice, constituted a specialist panel in this study. The question this research sought to answer was ‘what are the elements of knowledge, skill and attitude which underpin critical reading of science based news reports’? During in-depth individual interviews the panel were asked to explore what they considered to be essential elements of knowledge, skills and attitude which people need to enable them to respond critically to news reports with a science component. Analysis of the data revealed fourteen fundamental elements which together contribute to an individual’s capacity to engage critically with science-based news. These are classified in five categories ‘knowledge of science’, ‘knowledge of writing and language’, ‘knowledge about news, newspapers and journalism’, ‘skills’ and ‘attitudes’. Illustrative profiles of each category along with indicators of critical engagement are presented. The implications for curriculum planning and pedagogy are considered.

Architecture as Pedagogy: Alive and Kicking

This workshop draws on an emerging collaborative body of research by Lovett, Morrow and McClean that aims to understand architecture and its processes as a form of pedagogical practice: a civic pedagogy.

Architectural education can be valued not only as a process that delivers architecture-specific skills and knowledges, but also as a process that transforms people into critically active contributors to society. We are keen to examine how and where those skills are developed in architectural education and trace their existence and/or application within practice. We intend to examine whether some architectural and spatial practices are intrinsically pedagogical in their nature and how the level of involvement of clients, users and communities can mimic the project-based learning of architectural education – in particularly in the context of ‘live project learning’

1. This workshop begins with a brief discussion paper from Morrow that sets out the arguments behind why and how architecture can be understood as pedagogy. It will do so by presenting firstly the relationship between architectural practice and pedagogy, drawing out both contemporary and historical examples of architecture and architects acting pedagogically. It will also consider some other forms of creative practice that explicitly frame themselves pedagogically, and focus on participatory approaches in architectural practice that overlap with inclusive and live pedagogies, concluding with a draft and tentative abstracted pedagogical framework for architectural practice.

2. Lovett will examine practices of architectural operation that have a pedagogical approach, or which recognise within themselves an educational subtext/current. He is most interested in a 'liveness' beyond the 'Architectural Education' of university institutions. The presentation will question the scope for both spatial empowerment / agency and a greater understanding and awareness of the value of good design when operating as architects with participant-clients younger than 18, older than 25 or across varied parts of society. Positing that the learning might be greatest when there are no prescribed 'Learning Outcomes' and that such work might depend on risk-taking and playfulness, the presentation will be a curated showcase drawing on his own ongoing work.

Both brief presentations will inform the basis of the workshop’s discussion which hopes to draw on participants views and expereinces to enrich the research process. The intention is that the overall workshop will lead to a call for contributors and respondents to a forthcoming publication on ‘Architecture as Pedagogy’.

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.

Exploring the impact of a hands-on intervention on grade 7 girls and their feelings about self, mathematics, science, technology and related careers

Forty-five 12- and 13-year-old females attending Grade 7 in North York, Ontario were randomly selected from a group of 100 females who had volunteered to participate in a oneday hands-on workshop called It's Your Choice at Seneca College. The goals of this intervention were to broaden the career horizons of these students and to help them realize the need to continue mathematics and science through high school in order to keep occupational options unlimited. The young women were given a pre- and post-attitude survey to provide background information. In the month following participation in the workshop the students were interviewed in small groups (S students per group) to discover their perceptions of the impact of the workshop. The interviews revealed that participants felt that after the workshop their feelings of self-confidence increased, specifically with respect to working with their hands. Participants felt more aware of the usefulness and importance of the study of mathematics, science and technology, They also felt that It's Your Choice increased their interest in careers in these domains and helped them to see that these careers are viable choices for females. The interviews also revealed that many of the participants felt that in this society their roles and their choices were influenced and probably limited by the fact that they are female.

Some aspects of history of Indian mathematics in 18th and early 19th century

This thesis is an attempt to throw light on the works of some Indian Mathematicians who wrote in Arabic or persian In the Introductory Chapter on outline of general history of Mathematics during the eighteenth Bnd nineteenth century has been sketched. During that period there were two streams of Mathematical activity. On one side many eminent scholers, who wrote in Sanskrit, .he l d the field as before without being much influenced by other sources. On the other side there were scholars whose writings were based on Arabic and Persian text but who occasionally drew upon other sources also.

Applications and modelling in mathematics teaching

The aim of this paper is a comprehensive presentation of some important basic and general aspects of the topic applications and modelling, with emphasis on the secondary school level. Owing to the review character of this paper, some overlap with the survey paper Blum and Niss (1989) for ICME-6 in Budapest is inevitable. The paper will consist of three parts. In part 1, I shall try to clarify some basic concepts and remind the reader of a few application and modelling examples suitable for teaching. In part 2, I shall formulate some general aims for mathematics instruction and, on that basis, summarise the most important arguments for and against applications and modelling in mathematics teaching. Finally, in part 3, I shall discuss some relevant instructional aspects resulting from the considerations in part 2.

Digitisation, representation, and formalisation - Digital libraries of mathematics

One of the main tasks of the mathematical knowledge management community must surely be to enhance access to mathematics on digital systems. In this paper we present a spectrum of approaches to solving the various problems inherent in this task, arguing that a variety of approaches is both necessary and useful. The main ideas presented are about the differences between digitised mathematics, digitally represented mathematics and formalised mathematics. Each has its part to play in managing mathematical information in a connected world. Digitised material is that which is embodied in a computer file, accessible and displayable locally or globally. Represented material is digital material in which there is some structure (usually syntactic in nature) which maps to the mathematics contained in the digitised information. Formalised material is that in which both the syntax and semantics of the represented material, is automatically accessible. Given the range of mathematical information to which access is desired, and the limited resources available for managing that information, we must ensure that these resources are applied to digitise, form representations of or formalise, existing and new mathematical information in such a way as to extract the most benefit from the least expenditure of resources. We also analyse some of the various social and legal issues which surround the practical tasks.