Early childhood teachers' mathematical content knowledge

The process of becoming numerate begins in the early years. According to Vygotskian theory (1978), teachers are More Knowledgeable Others who provide and support learning experiences that influence children’s mathematical learning. This paper reports on research that investigates three early childhood teachers mathematics content knowledge. An exploratory, single case study utilised data collected from interviews, and email correspondence to investigate the teachers’ mathematics content knowledge. The data was reviewed according to three analytical strategies: content analysis, pattern matching, and comparative analysis. Findings indicated there was variation in teachers’ content knowledge across the five mathematical strands and that teachers might not demonstrate the depth of content knowledge that is expected of four year specially trained early years’ teachers. A significant factor that appeared to influence these teachers’ content knowledge was their teaching experience. Therefore, an avenue for future research is the investigation of factors that influence teachers’ content numeracy knowledge.

Challenges of tracking topical discussion networks online

Attempts to map online networks, representing relationships between people and sites, have covered sites including Facebook, Twitter, and blogs. However, the predominant approach of static network visualization, treating months of data as a single case rather than depicting changes over time or between topics, remains a flawed process. As different events and themes provoke varying interactions and conversations, it is proposed that case-by-case analysis would aid studies of online social networks by further examining the dynamics of links and information flows. This study uses hyperlink analysis of a population of French political blogs to compare connections between sites from January to August 2009. Themes discussed in this period were identified for subsequent analysis of topic-oriented networks. By comparing static blogrolls with topical citations within posts, this research addresses challenges and methods in mapping online networks, providing new information on temporal aspects of linking behaviors and information flows within these systems.

A mathematical model of chlamydial infection incorporating movement of chlamydial particles

We present a spatiotemporal mathematical model of chlamydial infection, host immune response and spatial movement of infectious particles. The re- sulting partial differential equations model both the dynamics of the infection and changes in infection profile observed spatially along the length of the host genital tract. This model advances previous chlamydia modelling by incorporating spatial change, which we also demonstrate to be essential when the timescale for movement of infectious particles is equal to, or shorter than, the developmental cycle timescale. Numerical solutions and model analysis are carried out, and we present a hypothesis regarding the potential for treatment and prevention of infection by increasing chlamydial particle motility.

Towards a model for the analysis and description of mathematical knowledge and understanding

Mathematics education literature has called for an abandonment of ontological and epistemological ideologies that have often divided theory-based practice. Instead, a consilience of theories has been sought which would leverage the strengths of each learning theory and so positively impact upon contemporary educational practice. This research activity is based upon Popper’s notion of three knowledge worlds which differentiates the knowledge shared in a community from the personal knowledge of the individual, and Bereiter’s characterisation of understanding as the individual’s relationship to tool-like knowledge. Using these notions, a re-conceptualisation of knowledge and understanding and a subsequent re-consideration of learning theories are proposed as a way to address the challenge set by literature. Referred to as the alternative theoretical framework, the proposed theory accounts for the scaffolded transformation of each individual’s unique understanding, whilst acknowledging the existence of a body of domain knowledge shared amongst participants in a scientific community of practice. The alternative theoretical framework is embodied within an operational model that is accompanied by a visual nomenclature with which to describe consensually developed shared knowledge and personal understanding. This research activity has sought to iteratively evaluate this proposed theory through the practical application of the operational model and visual nomenclature to the domain of early-number counting, addition and subtraction. This domain of mathematical knowledge has been comprehensively analysed and described. Through this process, the viability of the proposed theory as a tool with which to discuss and thus improve the knowledge and understanding with the domain of mathematics has been validated. Putting of the proposed theory into practice has lead to the theory’s refinement and the subsequent achievement of a solid theoretical base for the future development of educational tools to support teaching and learning practice, including computer-mediated learning environments. Such future activity, using the proposed theory, will advance contemporary mathematics educational practice by bringing together the strengths of cognitivist, constructivist and post-constructivist learning theories.

A discussion of Fashion Victims: Various responses to the report by War on Want, Critical Perspectives on International Business, Vol. 3 Iss: 2, pp.170 - 185

Purpose – The purpose of this paper is to present a selection of responses to the report Fashion Victims, published by War on Want in December 2006. It offers a range of viewpoints presented by members of the Editorial Advisory Board of CPOIB. These are presented in chronological order of submission. There is some cross-reference by contributors to the work of others, but no attempt is made to present a unified argument. Design/methodology/approach – Presents the full contributions of involved participants, without mediation or editorial change. Findings – A number of different perspectives are presented on the central issue that is summarised by the opening heading in War on Want’s report – “How cheap is too cheap?” It is seen that the answer to this question is very much dependent upon the standpoint of the respondent. Originality/value – In presenting this form of commentary, members of the CPOIB Editorial Board seek to stimulate debate about an issue of concern to contemporary society, without resort to the time delay and mediating processes of peer-review normally attached to academic writing. It is hoped that this discussion will provoke further contributions and a widening of the debate. Keywords Corporate social responsibility, Multinational companies, Conditions of employment, Trade unions

Reflections, successes and pitfalls of coordinating online discussion forums in a foreign language

The advent of e-learning has seen the adaptation and use of a plethora of educational techniques. Of these, online discussion forums have met with success and been used widely in both undergraduate and postgraduate education. The authors of this paper, having previously used online discussion forums in the postgraduate arena with success, adopted this approach for the design and subsequent delivery of a learning and teaching subject. This learning and teaching subject, however, was part of an international collaboration and designed for nurse academics in another country – Vietnam. With the nursing curriculum in Vietnam currently moving to adopt a competency based approach, two learning and teaching subjects were designed by an Australian university for Vietnamese nurse academics. Subject materials constituted a DVD which arrived by post and access to an online platform. Assessment for the subject included (but was not limited to) mandatory participation in online discussion with the other nurse academics enrolled in the subject. The purpose behind the online discussion was to generate discourse between the Vietnamese nurse academics located across Vietnam. Consequently the online discussions occurred in both Vietnamese and English; the Australian academic moderating the discussion did so in Australia with a Vietnamese translator. For the Australian University delivering this subject the difference between this and past online discussions were twofold: delivery was in a foreign language; and the teaching experience of the Vietnamese nurse teachers was mixed and frequently very limited. This paper will provide a discussion addressing the design of an online learning environment for foreign correspondents, the resources and translation required to maximise the success of the online discussion, the lessons learnt and consequent changes made, as well as the rationale of delivering complex content in a foreign language. While specifically addressing the first iteration of the first learning module designed, this paper will also address subsequent changes made for the second iteration of the first module and comment on their success. While a translator is clearly a key component of success, the elements of simplicity and clarity in hand with supportive online moderation must not be overlooked.

Neural network learning:theoretical foundations

This important work describes recent theoretical advances in the study of artificial neural networks. It explores probabilistic models of supervised learning problems, and addresses the key statistical and computational questions. Chapters survey research on pattern classification with binary-output networks, including a discussion of the relevance of the Vapnik Chervonenkis dimension, and of estimates of the dimension for several neural network models. In addition, Anthony and Bartlett develop a model of classification by real-output networks, and demonstrate the usefulness of classification with a "large margin." The authors explain the role of scale-sensitive versions of the Vapnik Chervonenkis dimension in large margin classification, and in real prediction. Key chapters also discuss the computational complexity of neural network learning, describing a variety of hardness results, and outlining two efficient, constructive learning algorithms. The book is self-contained and accessible to researchers and graduate students in computer science, engineering, and mathematics

Open problems in the security of learning

Machine learning has become a valuable tool for detecting and preventing malicious activity. However, as more applications employ machine learning techniques in adversarial decision-making situations, increasingly powerful attacks become possible against machine learning systems. In this paper, we present three broad research directions towards the end of developing truly secure learning. First, we suggest that finding bounds on adversarial influence is important to understand the limits of what an attacker can and cannot do to a learning system. Second, we investigate the value of adversarial capabilities-the success of an attack depends largely on what types of information and influence the attacker has. Finally, we propose directions in technologies for secure learning and suggest lines of investigation into secure techniques for learning in adversarial environments. We intend this paper to foster discussion about the security of machine learning, and we believe that the research directions we propose represent the most important directions to pursue in the quest for secure learning.

The African Institute for Mathematical Sciences

Its mission is to promote Mathematics and Science in Africa and to provide a focal point for Mathematics university training in Africa. It offers scholarships for up to 50 students to come and study for a period of nine months. Of the 50 students, about 15 positions are reserved for females. In the 2006/2007 intake there were over 250 applicants. The students are housed and fed and their return travel from their home town is fully funded. Lecturers also stay at AIMS and share their meals with the students, so that a rapport quickly develops. The students are away from their families and friends for nine months and are absolutely committed to the discipline of Mathematics. When they first arrive, some of them have little ability in English but since all tuition is in English they quickly learn. Some find the transitions difficult but they all support one another and at the end of their time their English skills are very good. The students do a series of subjects that last for about three weeks each, consisting of 30 contact hours, as well as a thesis/project. Each course has a number of assignments associated with it and these get evaluated. AIMS has seven or eight teaching assistants who help with the tutorials, marking, advice, and who are a vital component of AIMS.