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]

Re-thinking home economics : from modern to postmodern accounts of pedagogical bodies

Two perceptions of the marginality of home economics are widespread across educational and other contexts. One is that home economics and those who engage in its pedagogy are inevitably marginalised within patriarchal relations in education and culture. This is because home economics is characterised as women's knowledge, for the private domain of the home. The other perception is that only orthodox epistemological frameworks of inquiry should be used to interrogate this state of affairs. These perceptions have prompted leading theorists in the field to call for non-essentialist approaches to research in order to re-think the thinking that has produced this cul-de-sac positioning of home economics as a body of knowledge and a site of teacher practice. This thesis takes up the challenge of working to locate a space outside the frame of modernist research theory and methods, recognising that this shift in epistemology is necessary to unsettle the idea that home economics is inevitably marginalised. The purpose of the study is to reconfigure how we have come to think about home economics teachers and the profession of home economics as a site of cultural practice, in order to think it otherwise (Lather, 1991). This is done by exploring how the culture of home economics is being contested from within. To do so, the thesis uses a 'posthumanist' approach, which rejects the conception of the individual as a unitary and fixed entity, but instead as a subject in process, shaped by desires and language which are not necessarily consciously determined. This posthumanist project focuses attention on pedagogical body subjects as the 'unsaid' of home economics research. It works to transcend the modernist dualism of mind/body, and other binaries central to modernist work, including private/public, male/female,paid/unpaid, and valued/unvalued. In so doing, it refuses the simple margin/centre geometry so characteristic of current perceptions of home economics itself. Three studies make up this work. Studies one and two serve to document the disciplined body of home economics knowledge, the governance of which works towards normalisation of the 'proper' home economics teacher. The analysis of these accounts of home economics teachers by home economics teachers, reveals that home economics teachers are 'skilled' yet they 'suffer' for their profession. Further,home economics knowledge is seen to be complicit in reinforcing the traditional roles of masculinity and femininity, thereby reinforcing heterosexual normativity which is central to patriarchal society. The third study looks to four 'atypical'subjects who defy the category of 'proper' and 'normal' home economics teacher. These 'atypical' bodies are 'skilled' but fiercely reject the label of 'suffering'. The discussion of the studies is a feminist poststructural account, using Russo's (1994) notion of the grotesque body, which is emergent from Bakhtin's (1968) theory of the carnivalesque. It draws on the 'shreds' of home economics pedagogy,scrutinising them for their subversive, transformative potential. In this analysis, the giving and taking of pleasure and fun in the home economics classroom presents moments of surprise and of carnival. Foucault's notion of the construction of the ethical individual shows these 'atypical' bodies to be 'immoderate' yet striving hard to be 'continent' body subjects. This research captures moments of transgression which suggest that transformative moments are already embodied in the pedagogical practices of home economics teachers, and these can be 'seen' when re-looking through postmodemist lenses. Hence, the cultural practices ofhome economics as inevitably marginalised are being contested from within. Until now, home economics as a lived culture has failed to recognise possibilities for reconstructing its own field beyond the confines of modernity. This research is an example of how to think about home economics teachers and the profession as a reconfigured cultural practice. Future research about home economics as a body of knowledge and a site of teacher practice need not retell a simple story of oppression. Using postmodemist epistemologies is one way to provide opportunities for new ways of looking.

Understanding evaluation of learning support in mathematics and statistics

With rapid and continuing growth of learning support initiatives in mathematics and statistics found in many parts of the world, and with the likelihood that this trend will continue, there is a need to ensure that robust and coherent measures are in place to evaluate the effectiveness of these initiatives. The nature of learning support brings challenges for measurement and analysis of its effects. After briefly reviewing the purpose, rationale for, and extent of current provision, this article provides a framework for those working in learning support to think about how their efforts can be evaluated. It provides references and specific examples of how workers in this field are collecting, analysing and reporting their findings. The framework is used to structure evaluation in terms of usage of facilities, resources and services provided, and also in terms of improvements in performance of the students and staff who engage with them. Very recent developments have started to address the effects of learning support on the development of deeper approaches to learning, the affective domain and the development of communities of practice of both learners and teachers. This article intends to be a stimulus to those who work in mathematics and statistics support to gather even richer, more valuable, forms of data. It provides a 'toolkit' for those interested in evaluation of learning support and closes by referring to an on-line resource being developed to archive the growing body of evidence. © 2011 Taylor & Francis.

Even moderate visual impairments degrade drivers’ ability to see pedestrians at night

Purpose: To determine the effect of moderate levels of refractive blur and simulated cataracts on nighttime pedestrian conspicuity in the presence and absence of headlamp glare. Methods: The ability to recognize pedestrians at night was measured in 28 young adults (M=27.6 years) under three visual conditions: normal vision, refractive blur and simulated cataracts; mean acuity was 20/40 or better in all conditions. Pedestrian recognition distances were recorded while participants drove an instrumented vehicle along a closed road course at night. Pedestrians wore one of three clothing conditions and oncoming headlamps were present for 16 participants and absent for 12 participants. Results: Simulated visual impairment and glare significantly reduced the frequency with which drivers recognized pedestrians and the distance at which the drivers first recognized them. Simulated cataracts were significantly more disruptive than blur even though photopic visual acuity levels were matched. With normal vision, drivers responded to pedestrians at 3.6x and 5.5x longer distances on average than for the blur or cataract conditions, respectively. Even in the presence of visual impairment and glare, pedestrians were recognized more often and at longer distances when they wore a “biological motion” reflective clothing configuration than when they wore a reflective vest or black clothing. Conclusions: Drivers’ ability to recognize pedestrians at night is degraded by common visual impairments even when the drivers’ mean visual acuity meets licensing requirements. To maximize drivers’ ability to see pedestrians, drivers should wear their optimum optical correction, and cataract surgery should be performed early enough to avoid potentially dangerous reductions in visual performance.

Exploring antecedent factors in (Queensland) secondary school teachers’ early retirement intentions

Mature-age secondary teachers offer teaching a wealth of knowledge and skills that can contribute greatly to the quality of education. However, as with the greater workforce, there is an increasing trend for mature-age teachers to elect to retire early or to move into other work. Despite studies suggesting that teachers may be negatively affected by stress, there has been no research into the attitudes of mature-age teachers relating to early retirement and whether these or other factors are instrumental in their decision to retire from teaching. There is, however, a broad range of studies, commentary and analyses on ageing and work that can be utilised to develop a powerful analytical framework to identify the factors that can potentially influence the decision to take early retirement. This study examined the antecedent factors which influenced the early retirement decisions in 16 Queensland secondary school teachers. This study examined factors relating to the teachers decision to retire early and explored school and other factors relating to their decision. In addition, differences between urban and rural secondary school teachers were examined. Given the potentially complex nature of teachers. retirement decisions, the study utilised a qualitative approach. The study found that retired secondary teachers are confronted by ageing realities that are not responded to adequately by the education system, and participants expressed a general dissatisfaction with aspects of school management, especially as it related to bullying and non-inclusion in teaching-related decision making. This study also identified organisational issues within Education Queensland which contributed to system failures that affected mature-age teachers that need to be addressed. This study is one of the first studies to explore the factors influencing early retirement decisions in teachers. The implications of these factors on policy for Education Queensland and for workplace policies in general are discussed.

A left realist approach to antifeminist fathers’ rights groups

Despite earlier critiques of left realists’ failure to adequately address feminist concerns, recent left realist theorizing and empirical research have made valuable contributions to the understanding of woman abuse and other forms of gendered violence. Left realism has further potential to contribute to the criminological understanding of woman abuse and its contributing socioeconomic and cultural contexts. This article describes left realists’ early efforts to include gender in analyses of crime. It then summarizes feminist critiques of left realism and reviews the work that has responded to them. Drawing upon two prominent strands of feminist left realist theorizing about violence and gender, the paper proposes a preliminary left realist theory of antifeminist fathers’ rights group activism. It then outlines a provisional research agenda on antifeminist fathers’ rights groups, and proposes short and long term policies and practices to enhance the safety of abused mothers and their children following divorce or separation.

Learning to think spatially : what do students 'see' in numeracy test items?

Learning to think spatially in mathematics involves developing proficiency with graphics. This paper reports on 2 investigations of spatial thinking and graphics. The first investigation explored the importance of graphics as 1 of 3 communication systems (i.e. text, symbols, graphics) used to provide information in numeracy test items. The results showed that graphics were embedded in at least 50 % of test items across 3 year levels. The second investigation examined 11 – 12-year-olds’ performance on 2 mathematical tasks which required substantial interpretation of graphics and spatial thinking. The outcomes revealed that many students lacked proficiency in the basic spatial skills of visual memory and spatial perception and the more advanced skills of spatial orientation and spatial visualisation. This paper concludes with a reaffirmation of the importance of spatial thinking in mathematics and proposes ways to capitalize on graphics in learning to think spatially.

Ten basic factors to identify suitable subcontractors for construction projects

With unpredictable workloads and a need for a multitude of specialized skills, many main contractors rely heavily on subcontracting to reduce their risks (Bresnen et al., 1985; Beardsworth et al., 1988). This is especially the case In Hong Kong, where the average direct labour content accounts for only around 1% of the total contract sum (Lai, 1987). Extensive usage of subcontracting is also reported in many other countries, including the UK (Gray and Flanagan, 1989) and Japan (Bennett et al., 1987). In addition, and depending upon the scale and complexity of works, it is not uncommon for subcontractors to further sublet their works to lower tier(s) subcontractors. Richter and Mitchell (1982) argued that main contractors can obtain a higher profit margin by reducing their performance costs by subcontracting work to those who have the necessary resources to perform the work more efficiently and economically. Subcontracting is also used strategically to allow firms to employ a minimum work force under fluctuating demand (Usdiken and Sözen, 1985). Through subcontracting, the risks of main contractors are also reduced, as errors in estimating or additional costs caused by delays or extra labour requirements can be absorbed by the subcontractors involved (Woon and Ofori, 2000). Despite these benefits, the quality of work can suffer when incapable or inexperienced subcontractors are employed. Additional problems also exist in the form of bid shopping, unclear accountability, and high fragmentation (Palaneeswaran et al., 2002). A recent CIB TG 23 International Conference, October 2003, Hong Kong report produced by the Hong Kong Construction Industry Review Committee (CIRC) points to development of a framework to help distinguish between capable and incapable subcontractors (Tang, 2001). This paper describes research aims at identifying and prioritising criteria for use in such a framework.

Experimental arts practice incorporating motion capture

My practice-led research explores and maps workflows for generating experimental creative work involving inertia based motion capture technology. Motion capture has often been used as a way to bridge animation and dance resulting in abstracted visuals outcomes. In early works this process was largely done by rotoscoping, reference footage and mechanical forms of motion capture. With the evolution of technology, optical and inertial forms of motion capture are now more accessible and able to accurately capture a larger range of complex movements. Made by Motion is a collaboration between digital artist Paul Van Opdenbosch and performer and choreographer Elise May; a series of studies on captured motion data used to generate experimental visual forms that reverberate in space and time. The project investigates the invisible forces generated by and influencing the movement of a dancer. Along with how the forces can be captured and applied to generating visual outcomes that surpass simple data visualisation, projecting the intent of the performer’s movements. The source or ‘seed’ comes from using an Xsens MVN – Inertial Motion Capture system to capture spontaneous dance movements, with the visual generation conducted through a customised dynamics simulation. In my presentation I will be displaying and discussing a selected creative works from the project along with the process and considerations behind the work.

Rich and purposeful mathematical knowledge of mothers and children in a Torres Strait Islander community

This paper focuses on a pilot study that explored the situated mathematical knowledge of mothers and children in one Torres Strait Islander community in Australia. The community encouraged parental involvement in their children’s learning and schooling. The study explored parents’ understandings of mathematics and how their children came to learn about it on the island. A funds of knowledge approach was used in the study. This approach is based on the premise that people are competent and have knowledge that has been historically and culturally accumulated into a body of knowledge and skills essential for their functioning and well-being (Moll, 1992). The participants, three adults and one child are featured in this paper. Three separate events are described with epiphanic or illuminative moments analysed to ascertain the features that enabled an understanding of the nature of the mathematical events. The study found that Indigenous ways of knowing of mathematics were deeply embedded in rich cultural practices that were tied to the community. This finding has implications for teachers of children in the early years. Where school mathematics is often presented as disembodied and isolated facts with children seeing little relevance, learning a different perspective of mathematics that is tied to the resources and practices of children’s lives and facilitated through social relationships, may go a long way to improving the engagement of children and their parents in learning and schooling.

Are we there yet? A step closer to theorizing information systems success

The need for native Information Systems (IS) theories has been discussed by several prominent scholars. Contributing to their conjectural discussion, this research moves towards theorizing IS success as a native theory for the discipline. Despite being one of the most cited scholarly works to-date, IS success of DeLone and McLean (1992) has been criticized by some for lacking focus on the theoretical approach. Following theory development frameworks, this study improves the theoretical standing of IS success by minimizing interaction and inconsistency. The empirical investigation of theorizing IS success includes 1396 respondents, gathered through six surveys and a case study. The respondents represent 70 organisations, multiple Information Systems, and both private and public sector organizations.

Contours in Motion

My practice-led research explores and maps workflows for generating experimental creative work involving inertia based motion capture technology. Motion capture has often been used as a way to bridge animation and dance resulting in abstracted visuals outcomes. In early works this process was largely done by rotoscoping, reference footage and mechanical forms of motion capture. With the evolution of technology, optical and inertial forms of motion capture are now more accessible and able to accurately capture a larger range of complex movements. The creative work titled “Contours in Motion” was the first in a series of studies on captured motion data used to generating experimental visual forms that reverberate in space and time. With the source or ‘seed’ comes from using an Xsens MVN - Inertial Motion Capture system to capture spontaneous dance movements, with the visual generation conducted through a customised dynamics simulation. The aim of the creative work was to diverge way from a standard practice of using particle system and/or a simple re-targeting of the motion data to drive a 3d character as a means to produce abstracted visual forms. To facilitate this divergence a virtual dynamic object was tether to a selection of data points from a captured performance. The proprieties of the dynamic object were then adjusted to balance the influences from the human movement data with the influence of computer based randomization. The resulting outcome was a visual form that surpassed simple data visualization to project the intent of the performer’s movements into a visual shape itself. The reported outcomes from this investigation have contributed to a larger study on the use of motion capture in the generative arts, furthering the understanding of and generating theories on practice.

Successful outcomes in vocational education and training courses and mathematics: how pedagogy and expectations influence achievement

This paper reports on a four year Australian Research Council funded Linkage Project titled Skilling Indigenous Queensland, conducted in regional areas of Queensland, Australia from 2009 to 2013. The project sought to investigate Vocational Education and Training (VET) and teaching, Indigenous learners’ needs, employer culture and expectations and community culture and expectations to identify best practice in numeracy teaching for Indigenous VET learners. Specifically it focused on ways to enhance the teaching and learning of courses and the associated mathematics in such courses to benefit learners and increase their future opportunities of employment. To date thirty - nine teachers/trainers/teacher aides and two hundred and thirty - one students consented to participate in the project. Nine VET courses offered in schools and Technical and Further Education Institutes (TAFE) were nominated to be the focus on the study. This paper focuses on student questionnaire responses and interview responses from teachers/trainers one high school principal and five students as a result of these processes, the findings indicated that VET course teachers work hard to adopt contextualising strategies to their teaching; however this process is not always straight forward because of the perceptions of how mathematics has been taught and learned by trainers and teachers. Further teachers, trainers and students have high expectations of one another with the view to successful outcomes from the courses.

Secure coprocessor-based private information retrieval without periodical preprocessing

Early works on Private Information Retrieval (PIR) focused on minimizing the necessary communication overhead. They seemed to achieve this goal but at the expense of query response time. To mitigate this weakness, protocols with secure coprocessors were introduced. They achieve optimal communication complexity and better online processing complexity. Unfortunately, all secure coprocessor-based PIR protocols require heavy periodical preprocessing. In this paper, we propose a new protocol, which is free from the periodical preprocessing while offering the optimal communication complexity and almost optimal online processing complexity. The proposed protocol is proven to be secure.

An intervention to discourage Australian mothers from unnecessarily exposing their babies to the sun for therapeutic reasons

Parents play a key role in children’s sun-protective behaviour, with good sun-protective habits established early tending to be sustained. We designed a maternity hospital-based educational intervention to reduce myths that could result in mothers intentionally sunning their babies. Interviews were conducted with two cross-sections of healthy post-partum inpatients in the maternity ward of a large regional public hospital. The first group (n¼106) was recruited before the commencement of educational in-services for maternity nursing staff; the second group (n¼203) was interviewed after the last staff in-service session. More pre-intervention than post-intervention women reported they would expose their baby to sunlight to: treat suspected jaundice (28.8% vs. 13.3%; p<0.001) or help their baby’s skin adapt to sunlight (10.5% vs. 2.5%; p¼0.003). Fewer post-intervention women indicated they would sun themselves to treat breastfeeding-associated sore/cracked nipples (7.6% vs. 2%; p¼0.026). This educational intervention should be used to educate parents, health professionals and students