Modelling mathematical argumentation: the importance of qualification

In recent years several mathematics education researchers have attempted to analyse students’ arguments using a restricted form of Toulmin’s [The Uses of Argument, Cambridge University Press, UK, 1958] argumentation scheme. In this paper we report data from task-based interviews conducted with highly talented postgraduate mathematics students, and argue that a superior categorisation of genuine mathematical argumentation is provided by the use of Toulmin’s full scheme. In particular, we suggest that modal qualifiers play an important and previously unrecognised role in mathematical argumentation, and that one of the goals of instruction should be to develop students’ abilities to appropriately match up warrant-types with modal qualifiers.     

The Development of Adolescents' Emotional Stability and General Self-Concept: The interplay of parents,peers, and gender

Gender differences associated with the development of adolescents' sense of general self-concept (confidence and self-worth) and emotional stability (calmness, freedom from anxiety, and depression) were investigated using a sample of 655 adolescents (mean age 16 years). Relationships with parents were important for males' emotional stability but not females' and so this finding challenges the belief that adolescent males are more concerned with establishing independence from parents than females. The research also challenges the notion that adolescent boys are less interested in close personal peer relationships than girls. Same sex and opposite sex peer relationships were more influential in the formation of adolescents' emotional stability than parental relationships. A reciprocal relationship was revealed between general self-concept and emotional stability. Comparing these results with results obtained on the same students 18 months previously (aged 14.5 years), demonstrates that adolescents increasingly transfer their emotional attachment from parents to peers in a process called individuation.     

Some Simple Analytics of Access and Revenue Targets

If a museum faces a price inelastic demand and twin targets of a minimum number of visits and a minimum revenue, those targets need not be compatible. This paper explores the implications of such targets and shows that their compatibility depends critically on the admission price-elasticity. If the targets are incompatible it may be possible to engineer compatibility by shifting the demand curve. However, if the demand shift (eg resulting from advertising or improving the quality of the visitor experience) requires resourcing and is to be self-financing, it may or may not be possible to bring about compatibility.     

The Public Schools and Organized Football in Britain: Fresh Perspectives on Old Paradigms

Modern football, especially soccer, was the product of a fusion of ideas from both the public schools and wider society. In the period between 1830 and 1859 there were far more football teams outside the public schools than those within it, and while the ideas stemming from public schools were important in terms of the code that was established to regulate the game it was only when they were fused and applied with concepts from the wider society that they gained both effectiveness and popularity. The principal creator of this code was the football club at Sheffield, an organization that was easily the most influential and important in the period prior to 1870.     

The development of a system for supporting the lifelong learner

Given the rapidly changing skills needs of ‘post‐industrial economies’, lifelong learning forms an integral part of government policy within the UK and abroad. However, like the UK, most economies are faced with the problem of how to reach those sections of the community that have traditionally not embraced learning and educational opportunities. In this paper, the development and evaluation of a system designed to address this problem is described. The Lifelong Learning in London for All (L4All) project has investigated the concept of ‘trails’ as a way of organising lifelong learning opportunities. The L4All pilot system combines a set of web services to provide the functionality needed to support this central idea. The development process was outlined, and the findings of an empirical study were used to confirm proof of concept.     

How Can Teaching Aids Improve the Quality of Mathematics Education

The interplay among and connections between objects (structured or unstructured), images, language and symbols that lead to mathematical reasoning and the stating of mathematical propositions of very wide generality is well worth closer study. I believe that the subtle distinction between the way mathematical ideas are constructed from objects and the particular characteristics of the objects is often not clear in many teachers' minds. In the plenary, with the help of colleagues, using practical examples and situations, I would like to explore the distinction between the mathematical ideas that are being discussed in classrooms and the objects that are used in helping with abstractions. The use of interactive technology in the creation of mathematical meanings will form an important part of my colleagues' contributions.     

English Language Teaching in Singapore

This paper describes and analyses the changes and innovations in English language teaching in Singapore from the 1980s to the 1990s. The review includes a brief historical look at changes in the English language syllabuses from the colonial days to the recently launched 2001 syllabus. Trends and practices in English language teaching and learning will be discussed in the context of the various educational initiatives in Singapore. The paper will conclude with some thoughts about the future of ELT in the island state.     

University students’ perceptions of summative assessment: The role of context

We report on a mixed-method study that compared students’ perceptions of summative assessment across two distinct disciplines – education and mathematics, at two research-intensive institutions in the UK. The disciplines chosen represent opposing positions in Biglan’s classification of academic disciplines, as well as having very different assessment practices. Results suggest that these education students prefer to be assessed by methods they perceive to discriminate on the basis of academic abilities. Moreover, they perceive the traditional closed-book examination as inadequate to assess the capabilities which are key to being successful in their subject, which fits some but not all of the general findings in the literature. However, comparing these results with those of an identical study with mathematics students, we find that the perceptions of summative assessment are very different. We account for that difference by suggesting that students’ epistemic beliefs play a role in shaping these perceptions and conclude that, in designing summative assessment in higher education, generalised and centralised forces for change need to be tempered by contextual and disciplinary factors.