Trailblazers

A recent study in the United Kingdom (Ofsted Report 2008) provides strong evidence that well-organized activities outside the classroom contribute significantly to the quality and depth of children's learning, including their personal, social, and emotional development. Outdoor math trails supply further evidence of such enhanced learning: They are meaningful, stimulating, challenging, and exciting for children. Most important, these trails invite all students, irrespective of their classroom achievement level, to participate successfully in the problem activities and gain a sense of pride in the mathematics they create. Additionally, Math trails empower lifelong learning. Integrating "outside" mathematics with "inside" classroom mathematics can sow the seeds to develop flexible, creative, future-oriented mathematical thinkers and problem solvers. Here, English et al discuss how to design and implement math trails to promote active, meaningful, real-world mathematical learning beyond the classroom walls.

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.

Transition pedagogy : a third generation approach to FYE : a case study of policy and practice for the higher education sector

Current research and practice related to the first year experience (FYE) of commencing higher education students are still mainly piecemeal rather than institution-wide with institutions struggling to achieve cross-institutional integration, coordination and coherence of FYE policy and practice. Drawing on a decade of FYE-related research including an ALTC Senior Fellowship and evidence at a large Australian metropolitan university, this paper explores how one institution has addressed that issue by tracing the evolution and maturation of strategies that ultimately conceptualize FYE as “everybody's business.” It is argued that, when first generation co-curricular and second generation curricular approaches are integrated and implemented through an intentionally designed curriculum by seamless partnerships of academic and professional staff in a whole-of-institution transformation, we have a third generation approach labelled here as transition pedagogy. It is suggested that transition pedagogy provides the optimal vehicle for dealing with the increasingly diverse commencing student cohorts by facilitating a sense of engagement, support and belonging. What is presented here is an example of transition pedagogy in action.

Solving graphics tasks : gender differences in middle-school students

The capacity to solve tasks that contain high concentrations of visual-spatial information, including graphs, maps and diagrams, is becoming increasingly important in educational contexts as well as everyday life. This research examined gender differences in the performance of students solving graphics tasks from the Graphical Languages in Mathematics (GLIM) instrument that included number lines, graphs, maps and diagrams. The participants were 317 Australian students (169 males and 148 females) aged 9 to 12 years. Boys outperformed girls on graphical languages that required the interpretation of information represented on an axis and graphical languages that required movement between two- and three-dimensional representations (generally Map language).

Individual differences in learning from worked examples by senior secondary mathematics students

The primary purpose of this research was to examine individual differences in learning from worked examples. By integrating cognitive style theory and cognitive load theory, it was hypothesised that an interaction existed between individual cognitive style and the structure and presentation of worked examples in their effect upon subsequent student problem solving. In particular, it was hypothesised that Analytic-Verbalisers, Analytic-Imagers, and Wholist-lmagers would perform better on a posttest after learning from structured-pictorial worked examples than after learning from unstructured worked examples. For Analytic-Verbalisers it was reasoned that the cognitive effort required to impose structure on unstructured worked examples would hinder learning. Alternatively, it was expected that Wholist-Verbalisers would display superior performances after learning from unstructured worked examples than after learning from structured-pictorial worked examples. The images of the structured-pictorial format, incongruent with the Wholist-Verbaliser style, would be expected to split attention between the text and the diagrams. The information contained in the images would also be a source of redundancy and not easily ignored in the integrated structured-pictorial format. Despite a number of authors having emphasised the need to include individual differences as a fundamental component of problem solving within domainspecific subjects such as mathematics, few studies have attempted to investigate a relationship between mathematical or science instructional method, cognitive style, and problem solving. Cognitive style theory proposes that the structure and presentation of learning material is likely to affect each of the four cognitive styles differently. No study could be found which has used Riding's (1997) model of cognitive style as a framework for examining the interaction between the structural presentation of worked examples and an individual's cognitive style. 269 Year 12 Mathematics B students from five urban and rural secondary schools in Queensland, Australia participated in the main study. A factorial (three treatments by four cognitive styles) between-subjects multivariate analysis of variance indicated a statistically significant interaction. As the difficulty of the posttest components increased, the empirical evidence supporting the research hypotheses became more pronounced. The rigour of the study's theoretical framework was further tested by the construction of a measure of instructional efficiency, based on an index of cognitive load, and the construction of a measure of problem-solving efficiency, based on problem-solving time. The consistent empirical evidence within this study that learning from worked examples is affected by an interaction of cognitive style and the structure and presentation of the worked examples emphasises the need to consider individual differences among senior secondary mathematics students to enhance educational opportunities. Implications for teaching and learning are discussed and recommendations for further research are outlined.

Struggles Over Difference: Curriculum, texts and pedagogy in the Asia-Pacific

Struggles over Difference addresses education, schools, textbooks, and pedagogies in various countries of the Asia-Pacific, offering critical curriculum studies and policy analyses of national and regional educational systems. These systems face challenges linked to new economic formations, cultural globalization, and emergent regional and international geopolitical instabilities and conflicts. Contributors offer insights on how official knowledge, text, discourse and discipline should be shaped; who should shape it; through which institutional agencies it should be administered: and social and cultural practices through which this should occur.

Assessment for learning as a participative pedagogy

AfL practices observed in case studies in a North Queensland school were analysed from a sociocultural theoretical perspective. AfL practices of feedback, dialogue and peer assessment were viewed as an opportunity for students to learn the social expectations about being an autonomous learner, or central participant within the classroom community of practice. This process of becoming more expert and belonging within the community of practice involved students negotiating identities of participation that included knowing both academic skills and social expectations within the classroom. This paper argues that when AfL practices are viewed as ways of enhancing participation, there is potential for learners to negotiate identities as autonomous learners. AfL practices within the daily classroom interactions and pedagogy that enabled students to develop a shared repertoire, joint enterprise and mutual engagement in the classroom communities of practice are described. The challenges for teachers in shifting their gaze to patterns of participation are also briefly discussed.

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.