Primary students’ spatial visualization and spatial orientation : an evidence base for instruction

This paper reports on the performance of 58 11 to 12-year-olds on a spatial visualization task and a spatial orientation task. The students completed these tasks and explained their thinking during individual interviews. The qualitative data were analysed to inform pedagogical content knowledge for spatial activities. The study revealed that “matching” or “matching and eliminating” were the typical strategies that students employed on these spatial tasks. However, errors in making associations between parts of the same or different shapes were noted. Students also experienced general difficulties with visual memory and language use to explain their thinking. The students’ specific difficulties in spatial visualization related to obscured items, the perspective used, and the placement and orientation of shapes.

Gender effects in orientation on primary students’ performance on items rich in graphics

This study investigated the longitudinal performance of 378 students who completed mathematics items rich in graphics. Specifically, this study explored student performance across axis (e.g., numbers lines), opposed-position (e.g., line and column graphs) and circular (e.g., pie charts) items over a three-year period (ages 9-11 years). The results of the study revealed significant performance differences in the favour of boys on graphics items that were represented in horizontal and vertical displays. There were no gender differences on items that were represented in a circular manner.

Theory and its role in mathematics education

The increased recognition of the theory in mathematics education is evident in numerous handbooks, journal articles, and other publications. For example, Silver and Herbst (2007) examined ―Theory in Mathematics Education Scholarship‖ in the Second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007) while Cobb (2007) addressed ―Putting Philosophy to Work: Coping with Multiple Theoretical Perspectives‖ in the same handbook. And a central component of both the first and second editions of the Handbook of International Research in Mathematics Education (English, 2002; 2008) was ―advances in theory development.‖ Needless to say, the comprehensive second edition of the Handbook of Educational Psychology (Alexander & Winne, 2006) abounds with analyses of theoretical developments across a variety of disciplines and contexts. Numerous definitions of ―theory‖ appear in the literature (e.g., see Silver & Herbst, in Lester, 2007). It is not our intention to provide a ―one-size-fits-all‖ definition of theory per se as applied to our discipline; rather we consider multiple perspectives on theory and its many roles in improving the teaching and learning of mathematics in varied contexts.

Undressing Kellerman, Uncovering Broadhurst : the modern woman and "un-Australia"

This article explores the contributions of two unique Australian women, Annette Kellerman and Florence Broadhurst, to global fashion and aesthetics through subverting and challenging female gender roles of the early twentieth century. These two women are brought together here as a means of highlighting their markedly contrasting social tactics: undressing versus layering. Kellerman's body became an instrument in her quest for global fame, engaging in daring public "undress" in swimming and diving performances around the world that served to show case her innovative swimwear design. In contrast, Broadhurst, through repeated reconstructions of her persona and constant relayering of identities, concocted versions of herself in order to pass through Shanghai, London, and Sydney societies. Their lives exist as binaristic parallels, expressing contrasting values of un-Australianness - the disavowal of national identity; and Australianness - the promotion of national identity. Both Kellerman and Broadhurst tested the limits of body, dress and national identity as vehicles for global recognition. The recent interest in their historical roles is evidenced in the films "The original Mermaid"( 2004) and "Unfolding Florence" (2005) in addition to numerous books and journal articles. Despite this resurgent public recognition of their lives and achievements, scholarly analysis of their legacies in the fields of fashion and design are still relatively neglected. This article explores their contributions to celebrity and modernity, fashion and gender as modern un-Australian women.

Reunitising hundredths: prototypic and nonprototypic representations

This paper reports on a study in which 29 Year 6 students (selected from the top 30% of 176 Year 6 students) were individually interviewed to explore their ability to reunitise hundredths as tenths (Behr, Harel, Post & Lesh, 1992) when represented by prototypic (PRO) and nonprototypic (NPRO) models. The results showed that 55.2% of the students were able to unitise both models and that reunitising was more successful with the PRO model. The interviews revealed that many of these students had incomplete, fragmented or non-existent structural knowledge of the reunitising process and often relied on syntactic clues to complete the tasks. The implication for teaching is that instruction should not be limited to PRO representations of the part/whole notion of fraction and that the basic structures (equal parts, link between name and number of equal parts) of the part/whole notion needs to be revisited often.

Fractions, reunitisation and the number-line representation

Centre for Mathematics and Science Education, QUT, Brisbane, Australia This paper reports on a study in which Years 6 and 10 students were individually interviewed to determine their ability to unitise and reunitise number lines used to represent mixed numbers and improper fractions. Only 16.7% of the students (all Year 6) were successful on all three tasks and, in general, Year 6 students outperformed Year 8 students. The interviews revealed that the remaining students had incomplete, fragmented or non-existent structural knowledge of mixed numbers and improper fractions, and were unable to unitise or reunitise number lines. The implication for teaching is that instruction should focus on providing students with a variety of fraction representations in order to develop rich and flexible schema for all fraction types (mixed numbers, and proper and improper fractions).

Understanding parental physical activity : meanings, habits, and social role influence

Objectives: The research aimed to explore parents’ understandings of physical activity (PA), patterns of PA-related behaviour, and how constructions of social role expectations might influence their PA behaviour. Design and Method: Using a qualitative descriptive design and adopting a social constructionism approach to broaden interpretations of parents’ understandings, 40 adults (21 mothers, 19 fathers; aged 23 to 49 years) living in South East Queensland, Australia participated in semi-structured individual and group interviews. The interviews were analysed using thematic analysis. Results: Parents had clear understandings of what constitutes PA and engaged in various activities which were integrated with or independent of the children. Being active with children, however, was not always constructed favourably in which many parents described the difficulties of being active with their children. All individuals experienced changes in their PA behaviours after having children. For most, a decline in PA level, intensity, and structure was experienced; however, some did experience parenthood as a time to be active. A level of acceptance for the lack of activity performed was also expressed as were feelings of resentment and envy for those who maintained previous activity habits. Parenting and partner roles were considered most influential on PA-related behaviour and were constructed in ways that had both positive and negative influences on activity performance. Parents, however, were empowered to construct strategies to resolve conflicts between social role performance and being active. Conclusion: Results show that parents experience unique difficulties that intervention work should consider when designing programs aimed at increasing parental PA.

The body literate: Discourse and inscription in early literacy

The collection will cover all the major fields of discourse studies: including, grammar, stylistics, conversation analysis, narrative analysis, argumentation, psychology of comprehension, ethnography of speaking, and media. It will include classic articles, work from the top scholars in the field, and reflect all the significant debates.

Promoting student understanding through complex learning

The world’s increasing complexity, competitiveness, interconnectivity, and dependence on technology generate new challenges for nations and individuals that cannot be met by “continuing education as usual” (The National Academies, 2009). With the proliferation of complex systems have come new technologies for communication, collaboration, and conceptualization. These technologies have led to significant changes in the forms of mathematical thinking that are required beyond the classroom. This paper argues for the need to incorporate future-oriented understandings and competencies within the mathematics curriculum, through intellectually stimulating activities that draw upon multidisciplinary content and contexts. The paper also argues for greater recognition of children’s learning potential, as increasingly complex learners capable of dealing with cognitively demanding tasks.