Application of bending under tension test to determine the effect of tool radius and the contact pressure on the coefficient of friction in sheet metal forming

To quantify the frictional behaviour in sheet forming operations, several laboratory experiments which simulate the real forming conditions are performed. The Bending Under Tension Test is one such experiment which is often used to represent the frictional flow of sheet material around a die or a punch radius. Different mathematical representations are used to determine the coefficient of friction in the Bending Under Tension Test. In general the change in the strip thickness in passing over the die radius is neglected and the radius of curvature to thickness ratio is assumed to be constant in these equations. However, the effect of roller radius, sheet thickness and the surface pressure are also omitted in some of these equations. This work quantitatively determined the effect of roller radius and the tooling pressure on the coefficient of friction. The Bending Under Tension Test was performed using rollers with different radii and also lubricants with different properties. The tool radii were found to have a direct influence in the contact pressure. The effect of roller radius on friction was considerable and it was observed that there is a clear relationship between the contact pressure and the coefficient of friction.

Potential of technology and a familiar context to enhance students' concept of rate of change

Students' concept image of rate of change may be incomplete or erroneous. This paper reports a pilot study, with secondary school students, which explores the potential of technology (JavaMathWorlds), depicting a familiar context of motion, to develop students' existing schema of informal understandings of rate of change to more formal mathematical representations. Students developed numerous 'models of' rate of change in a motion context which then transferred to serve as a 'model for' rate of change in other contexts.

Relationships between identity and self-representations during adolescence

By drawing from literature on identity development as well as on self-discrepancy, the present study aimed to investigate variations in the magnitude of self-belief discrepancies among adolescents with different levels of identity development. The respondents consisted of 336 male and female adolescents, from 5 private secondary schools, ranging in age from 14 to 18 years (M = 15.98, SD = 0.89). Four levels of identity status (Achieved, Moratorium, Foreclosed, and Diffused identity status) were used as the method of identity classification in this study. Four types of self-discrepancies (Actual/Ideal (own), Actual/Ideal (other), Actual/Ought (own), and Actual/Ought (other) self-discrepancy) were also obtained. Multivariate analyses of variance showed that respondents with different identity statuses significantly varied on the magnitude of self-discrepancy experienced. The Foreclosed and Achieved statuses were found to have lower levels of self-belief discrepancy than the Moratorium and Diffused statuses. However, most of the significant differences among the statuses were for the Actual/Ideal (own) and Actual/Ideal (other) self-discrepancies. These results indicate that identity development is related to the magnitude of self-belief discrepancy. However, further research with more developed instruments is needed to explore this relationship more fully.

Elections and representations in local government: A Victorian case study

This article examines the application of different views of representation in the electoral systems at local government level: interest, corporate and mirror representation. The electoral framework underpins the process of representation, influencing both who are eligible to become voters and how their votes are collected and counted. The paper examines the  interrelationship between representation and the electoral framework in local government in Victoria. We use a historical analysis, and identify a long period of interest representation; a short, relatively recent period of corporate representation; and an attempt to introduce some elements of mirror representation. We conclude by arguing that local electoral reform needs to take into account the multiple meanings of representation.

Mathematical games with the alphabet

John Gough once again makes the ordinary fascinating as he piques our curiosity about the origins of the alphabet and turns the various mathematical properties of letters into bases for games.

Mathematical modelling of the refractive index reconstruction through global optimization

We examine a mathematical model of non-destructive testing of planar waveguides, based on numerical solution of a nonlinear integral equation. Such problem is ill-posed, and the method of Tikhonov regularization is applied. To minimize Tikhonov functional, and find the parameters of the waveguide, we use two new optimization methods: the cutting angle method of global optimization, and the discrete gradient method of nonsmooth local optimization. We examine how the noise in the experimental data influences the solution, and how the regularization parameter has to be chosen. We show that even with significant noise in the data, the numerical solution is of high accuracy, and the method can be used to process real experimental da.ta..

Developing formal mathematical assessment for 4-to-8-year-olds

The assessment of children in their years before school and their first years of school has been, traditionally, informal. Further, assessment of children's mathematical skills at this level has been infrequent compared to social, emotional and physical assessments. However, there are contexts where reliable, valid, standardised data from assessment in mathematics are required. This paper outlines the development of two assessment tools for mathematics that were originally developed for such contexts. Item Response Theory (IRT) analyses enabled the construction of assessment forms that address the range of abilities of 4- to 8-year-old children, and provided the scales used for constructing formative and summative reports of achievement. A description of the development of the assessment tools and the IRT analysis that provides the reporting formats are presented together with some research uses of the tools.

Hops, steps and jumps : mathematical progress in the early years

While curriculum frameworks ale major influences on learning, teachers know that children progress at different rates. Sometimes this is evident within a particular topic. and at other times more obvious across different topics. In this paper. we present the hops, steps, and jumps of numeracy learning of some 3000 Australian children. All were assessed using I Can Do Maths, and their achievements mapped to provide a detailed picture of how children hop, step and jump on their numeracy journey. This mapping provides teachers with infonnation about key hurdles to numeracy learning for Australian children.

Mathematical and pedagogical understanding as situated cognition

One mathematics lesson was planned by two Grade 2 teachers together. TheirSeparate teaching of it was videotaped. and each teacher was interviewed before and after her lesson. The "same" lesson resulted in different sets of worthwhile learning outcomes. In this research report. the notion of situated cognition is used as a tool for analysis of how this divergence seemed to happen. It is agued that the teachers' development and uses of mathematical concepts were mediated by the social situations.

Altered images : the relations between design representations and design practice

As information systems move out of the office into the wider world and are merged with mobile appliances, buildings and even clothing, the representations traditionally used in any one discipline may not be adequate for understanding these new domains. Design representations are ‘ways of seeing and not seeing’. Despite the central role representations play in design, the information systems design community has little understanding of the relation, ideal or actual, between design practice and design representation. This paper reports on an extensive design case study that aims at increasing understanding of the nature and affordances of representations in the design process and argues for the need for information systems as a discipline to open up discussion of the design representations that may be required to effectively design systems that mix traditional IS with disciplines such as industrial design, architecture and fashion design.

An aspect of mathematical understanding: the notion of 'connected knowing'

Much advice about teaching for understanding implies that teacher should help children to develop connections between aspects of their experience, knowledge, and skills. This paper outlines points from the literature about different types of connections and describes relevant points from four case study teachers said and did.