Surveying theories and philosophies of mathematics education

Any theory of thinking or teaching or learning rests on an underlying philosophy of knowledge. Mathematics education is situated at the nexus of two fields of inquiry, namely mathematics and education. However, numerous other disciplines interact with these two fields which compound the complexity of developing theories that define mathematics education. We first address the issue of clarifying a philosophy of mathematics education before attempting to answer whether theories of mathematics education are constructible? In doing so we draw on the foundational writings of Lincoln and Guba (1994), in which they clearly posit that any discipline within education, in our case mathematics education, needs to clarify for itself the following questions: (1) What is reality? Or what is the nature of the world around us? (2) How do we go about knowing the world around us? [the methodological question, which presents possibilities to various disciplines to develop methodological paradigms] and, (3) How can we be certain in the “truth” of what we know? [the epistemological question]

Adventures in pedagogy : the trials and tribulations of teaching common law in China

China is now seen as arguably, the next economic giant of the 21st century. From a country closed in the past to the external world, the Chinese market now presents as one of the most lucrative in the world economy. One area that has drawn increasing international interest is education - it has been estimated that by 2020 there will be 25 million excess demands for higher education places that the Chinese tertiary educational system cannot meet. Many overseas institutions have developed programs to cater for this immense potential market. In 2000 the Law Faculty of the University of Technology, Sydney (UTS)introduced a new postgraduate program specifically targeting the Chinese market. This paper is a brief assessment of the program - it examines general issues in the pedagogical delivery of programs in LOTE (Language Other Than English) and the use of 'proxies' in the delivery of LOTE programs. The paper concludes that while the UTS program demonstrates that it is feasible to use proxy lecturers or interpreters in the delivery of programs in LOTE, the exercise entails significant problems that can undermine the integrity of such programs.

Literacy and religion : the textual politics and practice of Seventh-day Adventism

This book explores the interrelation of literacy and religion as practiced by Western Christians in, first, historical contexts and, second, in one contemporary church setting. Using both a case study and a Foucauldian theoretical framework, the book provides a sustained analysis of the reciprocal discursive construction of literacy, religiosity and identity in one Seventh-day Adventist Church community of Northern Australia. Critical linguistic and discourse analytic theory is used to disclose processes of theological (church), familial (home) and educational (school) normalisation of community members into regulated ways of hearing and speaking, reading and writing, being and believing. Detailed analyses of spoken and written texts taken from institutional and local community settings show how textual religion is an exemplary technology of the self, a politics constituted by canonical texts, interpretive norms, textual practices, ritualised events and sociopolitical protocols that, ultimately, are turned in upon the self. The purpose of these analyses is to show how, across denominational difference in belief (tradition) and practice, particular versions of self and society are constructed through economies of truth from text, enabling and constraining what can and cannot be spoken and enacted by believers.

Structural behaviour and design of cold-formed steel beams at elevated temperatures

Cold-formed steel members are extensively used in the building construction industry, especially in residential, commercial and industrial buildings. In recent times, fire safety has become important in structural design due to increased fire damage to properties and loss of lives. However, past research into the fire performance of cold-formed steel members has been limited, and was confined to compression members. Therefore a research project was undertaken to investigate the structural behaviour of compact cold-formed steel lipped channel beams subject to inelastic local buckling and yielding, and lateral-torsional buckling effects under simulated fire conditions and associated section and member moment capacities. In the first phase of this research, an experimental study based on tensile coupon tests was undertaken to obtain the mechanical properties of elastic modulus and yield strength and the stress-strain relationship of cold-formed steels at uniform ambient and elevated temperatures up to 700oC. The mechanical properties deteriorated with increasing temperature and are likely to reduce the strength of cold-formed beams under fire conditions. Predictive equations were developed for yield strength and elastic modulus reduction factors while a modification was proposed for the stressstrain model at elevated temperatures. These results were used in the numerical modelling phases investigating the section and member moment capacities. The second phase of this research involved the development and validation of two finite element models to simulate the behaviour of compact cold-formed steel lipped channel beams subject to local buckling and yielding, and lateral-torsional buckling effects. Both models were first validated for elastic buckling. Lateral-torsional buckling tests of compact lipped channel beams were conducted at ambient temperature in order to validate the finite element model in predicting the non-linear ultimate strength behaviour. The results from this experimental study did not agree well with those from the developed experimental finite element model due to some unavoidable problems with testing. However, it highlighted the importance of magnitude and direction of initial geometric imperfection as well as the failure direction, and thus led to further enhancement of the finite element model. The finite element model for lateral-torsional buckling was then validated using the available experimental and numerical ultimate moment capacity results from past research. The third phase based on the validated finite element models included detailed parametric studies of section and member moment capacities of compact lipped channel beams at ambient temperature, and provided the basis for similar studies at elevated temperatures. The results showed the existence of inelastic reserve capacity for compact cold-formed steel beams at ambient temperature. However, full plastic capacity was not achieved by the mono-symmetric cold-formed steel beams. Suitable recommendations were made in relation to the accuracy and suitability of current design rules for section moment capacity. Comparison of member capacity results from finite element analyses with current design rules showed that they do not give accurate predictions of lateral-torsional buckling capacities at ambient temperature and hence new design rules were developed. The fourth phase of this research investigated the section and member moment capacities of compact lipped channel beams at uniform elevated temperatures based on detailed parametric studies using the validated finite element models. The results showed the existence of inelastic reserve capacity at elevated temperatures. Suitable recommendations were made in relation to the accuracy and suitability of current design rules for section moment capacity in fire design codes, ambient temperature design codes as well as those proposed by other researchers. The results showed that lateral-torsional buckling capacities are dependent on the ratio of yield strength and elasticity modulus reduction factors and the level of non-linearity in the stress-strain curves at elevated temperatures in addition to the temperature. Current design rules do not include the effects of non-linear stress-strain relationship and therefore their predictions were found to be inaccurate. Therefore a new design rule that uses a nonlinearity factor, which is defined as the ratio of the limit of proportionality to the yield stress at a given temperature, was developed for cold-formed steel beams subject to lateral-torsional buckling at elevated temperatures. This thesis presents the details and results of the experimental and numerical studies conducted in this research including a comparison of results with predictions using available design rules. It also presents the recommendations made regarding the accuracy of current design rules as well as the new developed design rules for coldformed steel beams both at ambient and elevated temperatures.

Identification and specification of relationships as the foundation for service bundling

Service bundling can be regarded as an option for service providers to strengthen their competitive advantages, cope with dynamic market conditions and heterogeneous consumer demand. Despite these positive effects, actual guidance for the identification of service bundles and the act of bundling itself can be regarded as a gap. Previous research has resulted in a conceptualization of a service bundling method relying on a structured service description in order to fill this gap. This method addresses the reasoning about the suitability of services to be part of a bundle based on analyzing existing relationships between services captured by a description language. This paper extends the aforementioned research by presenting an initial set of empirically derived relationships between services in existing bundles that can subsequently be utilized to identify potential new bundles. Additionally, a gap analysis points out to what extent prominent ontologies and service description languages accommodate for the identified relationships.

Modelling and execution of asset management process via workflow automation

An Asset Management (AM) life-cycle constitutes a set of processes that align with the development, operation and maintenance of assets, in order to meet the desired requirements and objectives of the stake holders of the business. The scope of AM is often broad within an organization due to the interactions between its internal elements such as human resources, finance, technology, engineering operation, information technology and management, as well as external elements such as governance and environment. Due to the complexity of the AM processes, it has been proposed that in order to optimize asset management activities, process modelling initiatives should be adopted. Although organisations adopt AM principles and carry out AM initiatives, most do not document or model their AM processes, let alone enacting their processes (semi-) automatically using a computer-supported system. There is currently a lack of knowledge describing how to model AM processes through a methodical and suitable manner so that the processes are streamlines and optimized and are ready for deployment in a computerised way. This research aims to overcome this deficiency by developing an approach that will aid organisations in constructing AM process models quickly and systematically whilst using the most appropriate techniques, such as workflow technology. Currently, there is a wealth of information within the individual domains of AM and workflow. Both fields are gaining significant popularity in many industries thus fuelling the need for research in exploring the possible benefits of their cross-disciplinary applications. This research is thus inspired to investigate these two domains to exploit the application of workflow to modelling and execution of AM processes. Specifically, it will investigate appropriate methodologies in applying workflow techniques to AM frameworks. One of the benefits of applying workflow models to AM processes is to adapt and enable both ad-hoc and evolutionary changes over time. In addition, this can automate an AM process as well as to support the coordination and collaboration of people that are involved in carrying out the process. A workflow management system (WFMS) can be used to support the design and enactment (i.e. execution) of processes and cope with changes that occur to the process during the enactment. So far few literatures can be found in documenting a systematic approach to modelling the characteristics of AM processes. In order to obtain a workflow model for AM processes commonalities and differences between different AM processes need to be identified. This is the fundamental step in developing a conscientious workflow model for AM processes. Therefore, the first stage of this research focuses on identifying the characteristics of AM processes, especially AM decision making processes. The second stage is to review a number of contemporary workflow techniques and choose a suitable technique for application to AM decision making processes. The third stage is to develop an intermediate ameliorated AM decision process definition that improves the current process description and is ready for modelling using the workflow language selected in the previous stage. All these lead to the fourth stage where a workflow model for an AM decision making process is developed. The process model is then deployed (semi-) automatically in a state-of-the-art WFMS demonstrating the benefits of applying workflow technology to the domain of AM. Given that the information in the AM decision making process is captured at an abstract level within the scope of this work, the deployed process model can be used as an executable guideline for carrying out an AM decision process in practice. Moreover, it can be used as a vanilla system that, once being incorporated with rich information from a specific AM decision making process (e.g. in the case of a building construction or a power plant maintenance), is able to support the automation of such a process in a more elaborated way.

Flexural behaviour and design of the new built-up LiteSteel beams

LiteSteel Beam (LSB) is a new cold-formed steel beam produced by OneSteel Australian Tube Mills. The new beam is effectively a channel section with two rectangular hollow flanges and a slender web, and is manufactured using a combined cold-forming and electric resistance welding process. OneSteel Australian Tube Mills is promoting the use of LSBs as flexural members in a range of applications, such as floor bearers. When LSBs are used as back to back built-up sections, they are likely to improve their moment capacity and thus extend their applications further. However, the structural behaviour of built-up beams is not well understood. Many steel design codes include guidelines for connecting two channels to form a built-up I-section including the required longitudinal spacing of connections. But these rules were found to be inadequate in some applications. Currently the safe spans of builtup beams are determined based on twice the moment capacity of a single section. Research has shown that these guidelines are conservative. Therefore large scale lateral buckling tests and advanced numerical analyses were undertaken to investigate the flexural behaviour of back to back LSBs connected by fasteners (bolts) at various longitudinal spacings under uniform moment conditions. In this research an experimental investigation was first undertaken to study the flexural behaviour of back to back LSBs including its buckling characteristics. This experimental study included tensile coupon tests, initial geometric imperfection measurements and lateral buckling tests. The initial geometric imperfection measurements taken on several back to back LSB specimens showed that the back to back bolting process is not likely to alter the imperfections, and the measured imperfections are well below the fabrication tolerance limits. Twelve large scale lateral buckling tests were conducted to investigate the behaviour of back to back built-up LSBs with various longitudinal fastener spacings under uniform moment conditions. Tests also included two single LSB specimens. Test results showed that the back to back LSBs gave higher moment capacities in comparison with single LSBs, and the fastener spacing influenced the ultimate moment capacities. As the fastener spacing was reduced the ultimate moment capacities of back to back LSBs increased. Finite element models of back to back LSBs with varying fastener spacings were then developed to conduct a detailed parametric study on the flexural behaviour of back to back built-up LSBs. Two finite element models were developed, namely experimental and ideal finite element models. The models included the complex contact behaviour between LSB web elements and intermittently fastened bolted connections along the web elements. They were validated by comparing their results with experimental results and numerical results obtained from an established buckling analysis program called THIN-WALL. These comparisons showed that the developed models could accurately predict both the elastic lateral distortional buckling moments and the non-linear ultimate moment capacities of back to back LSBs. Therefore the ideal finite element models incorporating ideal simply supported boundary conditions and uniform moment conditions were used in a detailed parametric study on the flexural behaviour of back to back LSB members. In the detailed parametric study, both elastic buckling and nonlinear analyses of back to back LSBs were conducted for 13 LSB sections with varying spans and fastener spacings. Finite element analysis results confirmed that the current design rules in AS/NZS 4600 (SA, 2005) are very conservative while the new design rules developed by Anapayan and Mahendran (2009a) for single LSB members were also found to be conservative. Thus new member capacity design rules were developed for back to back LSB members as a function of non-dimensional member slenderness. New empirical equations were also developed to aid in the calculation of elastic lateral distortional buckling moments of intermittently fastened back to back LSBs. Design guidelines were developed for the maximum fastener spacing of back to back LSBs in order to optimise the use of fasteners. A closer fastener spacing of span/6 was recommended for intermediate spans and some long spans where the influence of fastener spacing was found to be high. In the last phase of this research, a detailed investigation was conducted to investigate the potential use of different types of connections and stiffeners in improving the flexural strength of back to back LSB members. It was found that using transverse web stiffeners was the most cost-effective and simple strengthening method. It is recommended that web stiffeners are used at the supports and every third points within the span, and their thickness is in the range of 3 to 5 mm depending on the size of LSB section. The use of web stiffeners eliminated most of the lateral distortional buckling effects and hence improved the ultimate moment capacities. A suitable design equation was developed to calculate the elastic lateral buckling moments of back to back LSBs with the above recommended web stiffener configuration while the same design rules developed for unstiffened back to back LSBs were recommended to calculate the ultimate moment capacities.

Flexural behaviour and design of hollow flange steel beams

The LiteSteel Beam (LSB) is a new hollow flange channel section developed by OneSteel Australian Tube Mills using a patented Dual Electric Resistance Welding technique. The LSB has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. It is commonly used as rafters, floor joists and bearers and roof beams in residential, industrial and commercial buildings. It is on average 40% lighter than traditional hot-rolled steel beams of equivalent performance. The LSB flexural members are subjected to a relatively new Lateral Distortional Buckling mode, which reduces the member moment capacity. Unlike the commonly observed lateral torsional buckling of steel beams, lateral distortional buckling of LSBs is characterised by simultaneous lateral deflection, twist and web distortion. Current member moment capacity design rules for lateral distortional buckling in AS/NZS 4600 (SA, 2005) do not include the effect of section geometry of hollow flange beams although its effect is considered to be important. Therefore detailed experimental and finite element analyses (FEA) were carried out to investigate the lateral distortional buckling behaviour of LSBs including the effect of section geometry. The results showed that the current design rules in AS/NZS 4600 (SA, 2005) are over-conservative in the inelastic lateral buckling region. New improved design rules were therefore developed for LSBs based on both FEA and experimental results. A geometrical parameter (K) defined as the ratio of the flange torsional rigidity to the major axis flexural rigidity of the web (GJf/EIxweb) was identified as the critical parameter affecting the lateral distortional buckling of hollow flange beams. The effect of section geometry was then included in the new design rules using the new parameter (K). The new design rule developed by including this parameter was found to be accurate in calculating the member moment capacities of not only LSBs, but also other types of hollow flange steel beams such as Hollow Flange Beams (HFBs), Monosymmetric Hollow Flange Beams (MHFBs) and Rectangular Hollow Flange Beams (RHFBs). The inelastic reserve bending capacity of LSBs has not been investigated yet although the section moment capacity tests of LSBs in the past revealed that inelastic reserve bending capacity is present in LSBs. However, the Australian and American cold-formed steel design codes limit them to the first yield moment. Therefore both experimental and FEA were carried out to investigate the section moment capacity behaviour of LSBs. A comparison of the section moment capacity results from FEA, experiments and current cold-formed steel design codes showed that compact and non-compact LSB sections classified based on AS 4100 (SA, 1998) have some inelastic reserve capacity while slender LSBs do not have any inelastic reserve capacity beyond their first yield moment. It was found that Shifferaw and Schafer’s (2008) proposed equations and Eurocode 3 Part 1.3 (ECS, 2006) design equations can be used to include the inelastic bending capacities of compact and non-compact LSBs in design. As a simple design approach, the section moment capacity of compact LSB sections can be taken as 1.10 times their first yield moment while it is the first yield moment for non-compact sections. For slender LSB sections, current cold-formed steel codes can be used to predict their section moment capacities. It was believed that the use of transverse web stiffeners could improve the lateral distortional buckling moment capacities of LSBs. However, currently there are no design equations to predict the elastic lateral distortional buckling and member moment capacities of LSBs with web stiffeners under uniform moment conditions. Therefore, a detailed study was conducted using FEA to simulate both experimental and ideal conditions of LSB flexural members. It was shown that the use of 3 to 5 mm steel plate stiffeners welded or screwed to the inner faces of the top and bottom flanges of LSBs at third span points and supports provided an optimum web stiffener arrangement. Suitable design rules were developed to calculate the improved elastic buckling and ultimate moment capacities of LSBs with these optimum web stiffeners. A design rule using the geometrical parameter K was also developed to improve the accuracy of ultimate moment capacity predictions. This thesis presents the details and results of the experimental and numerical studies of the section and member moment capacities of LSBs conducted in this research. It includes the recommendations made regarding the accuracy of current design rules as well as the new design rules for lateral distortional buckling. The new design rules include the effects of section geometry of hollow flange steel beams. This thesis also developed a method of using web stiffeners to reduce the lateral distortional buckling effects, and associated design rules to calculate the improved moment capacities.

Contextualising the teaching and learning of measurement within Torres Strait Islander schools

A one year mathematics project that focused on measurement was conducted with six Torres Strait Islander schools and communities. Its key focus was to contextualise the teaching and learning of measurement within the students’ culture, communities and home languages. There were six teachers and two teacher aides who participated in the project. This paper reports on the findings from the teachers’ and teacher aides’ survey questionnaire used in the first Professional Development session to identify: a) teachers’ experience of teaching in Torres Strait Islands, b) teachers’ beliefs about effective ways to teach Torres Strait Islander students, and c) contexualising measurement within Torres Strait Islander culture, Communities and home languages. A wide range of differing levels of knowledge and understanding about how to contextualise measurement to support student learning were identified and analysed. For example, an Indigenous teacher claimed that mathematics and the environment are relational, that is, they are not discrete and in isolation from one another, rather they interconnect with mathematical ideas emerging from the environment of the Torres Strait Communities.

Multicultural education, global studies and studies of Asia

Like other nations, Australia has experienced significant change in the past few decades as its society has become increasingly diverse. The new cultures and traditions that result from ethnic and religious diversity have both enriched Australian society and presented it with some challenges. Other challenges have resulted from increased globalisation. For example, the economic fallout from the recent global financial crisis indicates that global issues can impact across a range of levels, from multinational corporations and nation-states to local sites and individual livelihoods. Some suggest that Australia fared better than other nations during this economic crisis because of its export trade with China. Although this is disputed by economists, it highlights another facet of change that is impacting on Australian society and this relates to Australia’s growing engagement with the nations of Asia. There is increasing awareness in education systems that if young people are to achieve their potential as future citizens they need to be able to negotiate the cultural, social, political and economic ties that connect them to the global and regional community through work, leisure and citizenship. Multicultural education, global studies and studies of Asia play a particular part in helping young people to: • appreciate cultural diversity within and beyond their own nation • imagine with some accuracy how others view their world • participate in shaping a better future. This chapter explores the origins, distinctions and common features of each approach.