Years 2 to 6 students' ability to generalise : models, representations and theory for teaching and learning

Over the last three years, in our Early Algebra Thinking Project, we have been studying Years 3 to 5 students’ ability to generalise in a variety of situations, namely, compensation principles in computation, the balance principle in equivalence and equations, change and inverse change rules with function machines, and pattern rules with growing patterns. In these studies, we have attempted to involve a variety of models and representations and to build students’ abilities to switch between them (in line with the theories of Dreyfus, 1991, and Duval, 1999). The results have shown the negative effect of closure on generalisation in symbolic representations, the predominance of single variance generalisation over covariant generalisation in tabular representations, and the reduced ability to readily identify commonalities and relationships in enactive and iconic representations. This chapter uses the results to explore the interrelation between generalisation and verbal and visual comprehension of context. The studies evidence the importance of understanding and communicating aspects of representational forms which allowed commonalities to be seen across or between representations. Finally the chapter explores the implications of the studies for a theory that describes a growth in integration of models and representations that leads to generalisation.

Is the association between temperature and mortality modified by age, gender and socio-economic status?

Background: A number of studies have examined the relationship between high ambient temperature and mortality. Recently, concern has arisen about whether this relationship is modified by socio-demographic factors. However, data for this type of study is relatively scarce in subtropical/tropical regions where people are well accustomed to warm temperatures. Objective: To investigate whether the relationship between daily mean temperature and daily all-cause mortality is modified by age, gender and socio-economic status (SES) in Brisbane, Australia. Methods: We obtained daily mean temperature and all-cause mortality data for Brisbane, Australia during 1996–2004. A generalised additive model was fitted to assess the percentage increase in all deaths with every one degree increment above the threshold temperature. Different age, gender and SES groups were included in the model as categorical variables and their modification effects were estimated separately. Results: A total of 53,316 non-external deaths were included during the study period. There was a clear increasing trend in the harmful effect of high temperature on mortality with age. The effect estimate among women was more than 20 times that among men. We did not find an SES effect on the percent increase associated with temperature. Conclusions: The effects of high temperature on all deaths were modified by age and gender but not by SES in Brisbane, Australia.

Talkin' up sport and gender : Three Australian Aboriginal women speak

This paper presents the perspectives from three Aboriginal women on body image, sport and physical activity within Australian contemporary society. It draws on a range of literature along with artworks from visual artist Pamela Croft.

Gender and political leadership : moving beyond stereotypes

This short paper suggests that the categories of ‘transformational’ and ‘transactional’ leadership styles ( see Burns 1972) may provide analytical purchase on the question of whether current women leaders have radically different styles and approaches to the earlier second wave feminist generation. The two cases chosen for this paper are the senior women in the Labor and Liberal Parties – Julia Gillard and Julie Bishop. The evidence – explored below – indicates there are strong transactional qualities to both women leaders.

Age and gender differences in ambulance utilisation in Queensland

Introduction Queensland has the highest ambulance utilisation (150 per 1000 population) in Australia and growing 4.4% annually. However, the impact of gender and age on utilisation is unknown. Methods & Materials Data on ambulance utilisation from Queensland Ambulance Service for the period 2002-2009 were analysed. Results Between 2002 and 2009, the number of ambulance patients per 1000 population increased overall by 17% (females) and 18% (males). The utilisation rate remained highest among the elderly but grew differently across age groups. For females, the rates were 55% (0-14yo), 73% (15-29yo), 38% (30-44yo), 22% (45-59yo), -9% (60-74yo) and -6% (75,+ yo); for males they were 48%, 59%, 38%, 17%, -13% and -2% respectively. Within the same age groups and period, the population adjusted number of males per 100 females (M:F ratio) changed from 134 to 128 (-5% growth), 98 to 91 (-8%), 101 to 100 (-0.4%), 115 to 111 (-3%), 114 to 108 (-5%) and 106 to 111 (4%). Conclusion Understanding the impact of patients’ demographic profiles on service utilisation and broader effects on the emergency health system is imperative for policy-making, demand management, designing public health campaigns and health promotions. Gender and age characteristics of ambulance users in Queensland appear to be changing most noticeably in the youngest and oldest groups. Physical and mental health, attitudinal, lifestyle, parenting, financial and socio-cultural reasons may account for these trends, but little evidence exists. A theoretical framework will be discussed to contextualise the findings.

Cognitive processes and strategies employed by children to learn spatial representations

Children often have difficulties in learning spatial representations. This study investigated the effect of four different instructional formats on learning outcomes and strategies used when dealing with spatial tasks such as assembly procedures. It was hypothesised that instructional material that imposed least extraneous cognitive load would facilitate enhanced learning. Forty secondary students were presented with four types of instruction; orthographic drawing, isometric drawing, physical model and, isometric and physical model together. The findings provide evidence to suggest that working from physical models caused least extraneous cognitive load compared to the isometric and orthographic groups. The model group took less time, had more correctly completed models, required fewer extra looks, spent less time studying the instruction and made fewer errors. Problem decomposition, forward working and attending to information in the foreground of the graphical representation strategies were analysed.

Processing load and the use of concrete representations and strategies for solving linear equations

This paper is a report of students' responses to instruction which was based on the use of concrete representations to solve linear equations. The sample consisted of 21 Grade 8 students from a middle-class suburban state secondary school with a reputation for high academic standards and innovative mathematics teaching. The students were interviewed before and after instruction. Interviews and classroom interactions were observed and videotaped. A qualitative analysis of the responses revealed that students did not use the materials in solving problems. The increased processing load caused by concrete representations is hypothesised as a reason.

Rich probabilistic representations for bearing only decentralised data fusion

The aim of this paper is to demonstrate the validity of using Gaussian mixture models (GMM) for representing probabilistic distributions in a decentralised data fusion (DDF) framework. GMMs are a powerful and compact stochastic representation allowing efficient communication of feature properties in large scale decentralised sensor networks. It will be shown that GMMs provide a basis for analytical solutions to the update and prediction operations for general Bayesian filtering. Furthermore, a variant on the Covariance Intersect algorithm for Gaussian mixtures will be presented ensuring a conservative update for the fusion of correlated information between two nodes in the network. In addition, purely visual sensory data will be used to show that decentralised data fusion and tracking of non-Gaussian states observed by multiple autonomous vehicles is feasible.

Analysing queer student media using a combined queer theoretical and media studies approach

Australian queer (GLBTIQ) university student media is an important site of cultural and political self-representation. These groups exist within university student unions and the unions provide them with space, financial support and resources. Community media is a significant site for the development of queer identity, community and a key part of queer politics. This paper reviews my research into queer community media which is grounded in a Queer Theoretical perspective of identity performativity. Cover argues that Queer Theoretical approaches that study media products fail to consider the material contexts which contribute to their construction. I use an ethnographic approach combined with discourse analysis in order to reveal queer student activists’ media representations of queer, and the production contexts which shape them. My research contributes to queer media scholarship by using a methodology to address the gap that Cover identifies.

The impact of gender diversity on performance in services and manufacturing organizations

We present three competing predictions of the organizational gender diversity-performance relationship: a positive linear prediction, a negative linear prediction, and an inverted U-shaped curvilinear prediction. The paper also proposes a moderating effect of industry type (services vs. manufacturing). The predictions were tested using archival quantitative data with a longitudinal design. The results show partial support for the positive linear and inverted U-shaped curvilinear predictions as well as for the proposed moderating effect of industry type. The results help reconcile the inconsistent findings of past research. The findings also show that industry context can strengthen or weaken gender diversity effects.

Workforce gender diversity: Is it a source of competitive advantage?

Research on workforce diversity at the organisational level gained momentum in the 1990s, because of the growing trend in HR research to link HR practices with organisational performance. The new parallel wave of research focused on the business case for diversity, in which diversity was linked to organisational performance. However, the results of these studies, mainly focusing on linear diversity-performance relationships, have been inconsistent. Based on contrasting theories, this paper proposes three competing predictions of the gender diversity-performance relationship at the organisational level: a positive linear relationship derived from the resource-based view of the firm, a negative linear relationship derived from self-categorisation and social identity theories, and a U-shaped curvilinear relationship derived from the integration of the resource-based view of the firm with self-categorisation and social identity theories. The U-shaped relationship accounts for the inconsistent findings in past research, because different proportions of men and women produce different social dynamics that have different effects on organisational performance. Further, the proposed U-shaped relationship can have different slopes in the manufacturing and services industries. The paper contributes to the field of diversity by strengthening its weak theoretical foundations and by highlighting the industry differences.

The organisational gender diversity-performance link : does industry type matter?

Research on workforce diversity gained momentum in the 1990s. However, empirical findings to date on the link between gender diversity and performance have been inconsistent. Based on contrasting theories, this paper proposes a positive linear and a negative linear prediction of the gender diversity-performance relationship. The paper also proposes that industry type (services vs. manufacturing) moderates the gender diversity-performance relationship such that the relationship will be positive in service organisations and negative in manufacturing organisations. The results show partial support for the positive linear gender diversity-performance relationship and for the moderating effect of industry type. The study contributes to the field of diversity by showing that workforce gender diversity can have a different impact on organisational performance in different industries.

Trans digital storytelling : everyday activism, mutable identity and the problem of visibility

Mainstream representations of trans people typically run the gamut from victim to mentally ill and are almost always articulated by non-trans voices. The era of user-generated digital content and participatory culture has heralded unprecedented opportunities for trans people who wish to speak their own stories in public spaces. Digital Storytelling, as an easy accessible autobiographic audio-visual form, offers scope to play with multi-dimensional and ambiguous representations of identity that contest mainstream assumptions of what it is to be ‘male’ or ‘female’. Also, unlike mainstream media forms, online and viral distribution of Digital Stories offer potential to reach a wide range of audiences, which is appealing to activist oriented storytellers who wish to confront social prejudices. However, with these newfound possibilities come concerns regarding visibility and privacy, especially for storytellers who are all too aware of the risks of being ‘out’ as trans. This paper explores these issues from the perspective of three trans storytellers, with reference to the Digital Stories they have created and shared online and on DVD. These examplars are contextualised with some popular and scholarly perspectives on trans representation, in particular embodied and performed identity. It is contended that trans Digital Stories, while appearing in some ways to be quite conventional, actually challenge common notions of gender identity in ways that are both radical and transformative.

Doing justice : young people’s representations of the Murray-Darling Basin

The business of helping children to grow up as ‘custodians’, or ‘future managers’ of the Murray-Darling Basin is not simple, and that single sources of information and ways of seeing the environment are not enough. Children (and adults) need to be able to relate individually, emotionally and aesthetically to their places if they are to learn to love them. However, they also need access to a variety of ways of thinking and seeing those same places if they are to be able to take action to sustain them – action that inevitably involves forms of communication with their fellow citizens. This chapter documents the writing and art program Special Forever, with its focus on communications, as an important intervention into promoting eco-social sustainability.

Gender influences on the work-related stress-coping process

The increasing incidence of occupational stress is recognized as a global phenomenon that is having a detrimental impact on both individuals and organizations. This study aims to identify whether men and women adopt different stress and coping processes when subjected to stress in a work context. A total of 258 workers of various professions (males = 106, females = 152) participated in the study. Results indicated that men and women differ in their stress and coping processes, forming two very distinct groups and adopting specific process models when encountering a stressful situation at work. Limitations and implications from this study are discussed.