The role of fluency in a mathematics item with an embedded graphic: Interpreting a pie chart.

The purpose of this study was to identify the pedagogical knowledge relevant to the successful completion of a pie chart item. This purpose was achieved through the identification of the essential fluencies that 12–13-year-olds required for the successful solution of a pie chart item. Fluency relates to ease of solution and is particularly important in mathematics because it impacts on performance. Although the majority of students were successful on this multiple choice item, there was considerable divergence in the strategies they employed. Approximately two-thirds of the students employed efficient multiplicative strategies, which recognised and capitalised on the pie chart as a proportional representation. In contrast, the remaining one-third of students used a less efficient additive strategy that failed to capitalise on the representation of the pie chart. The results of our investigation of students’ performance on the pie chart item during individual interviews revealed that five distinct fluencies were involved in the solution process: conceptual (understanding the question), linguistic (keywords), retrieval (strategy selection), perceptual (orientation of a segment of the pie chart) and graphical (recognising the pie chart as a proportional representation). In addition, some students exhibited mild disfluencies corresponding to the five fluencies identified above. Three major outcomes emerged from the study. First, a model of knowledge of content and students for pie charts was developed. This model can be used to inform instruction about the pie chart and guide strategic support for students. Second, perceptual and graphical fluency were identified as two aspects of the curriculum, which should receive a greater emphasis in the primary years, due to their importance in interpreting pie charts. Finally, a working definition of fluency in mathematics was derived from students’ responses to the pie chart item.

Social adaptation of children with mild intellectual disability : effects of partial integration within primary school classes

Examined the social adaptation of 32 children in grades 3–6 with mild intellectual disability: 13 Ss were partially integrated into regular primary school classes and 19 Ss were full-time in separate classes. Sociometric status was assessed using best friend and play rating measures. Consistent with previous research, children with intellectual disability were less socially accepted than were a matched group of 32 children with no learning disabilities. Children in partially integrated classes received more play nominations than those in separate classes, but had no greater acceptance as a best friend. On teachers' reports, disabled children had higher levels of inappropriate social behaviours, but there was no significant difference in appropriate behaviours. Self-assessments by integrated children were more negative than those by children in separate classes, and their peer-relationship satisfaction was lower. Ratings by disabled children of their satisfaction with peer relationships were associated with ratings of appropriate social skills by themselves and their teachers, and with self-ratings of negative behaviour. The study confirmed that partial integration can have negative consequences for children with an intellectual disability.

Two Thai teachers' perceptions of cooperative learning

Over the past decade, the need for educational reform in Thailand has become increasingly apparent. The strong tradition of teacher-directed instruction has been the major teaching and learning style in Thai education. Recent policy changes have focused on expanding education opportunities, the implementation of compulsory education and also on more student-centered pedagogies (Carter, 2006). A suggested way of bringing about the changes necessary to improve the standard of education in primary schools and retention rates is to incorporate cooperative learning into Thai primary school classrooms. The action research in this study proceeded in four stages. There were pre-implementation interviews of teachers, teacher preparation, implementation of program, and post-implementation evaluation. This study focused on the two Thai teachers' perceptions about the benefits of cooperative learning and the roles of the teachers in cooperative learning classroom. The study found that the two teachers had constructed different levels of perceptions about the benefits of cooperative learning and the roles of the teacher. These findings indicated that Thai teachers who are relatively inexperienced, lacking in confidence and with little or no experience with group work strategies such as peer tutoring need alternative, less intense professional development programs conducted over a period of a semester than the professional development program implemented in this study. In addition to being conducted over a longer period of time, the findings also indicate that alternative teacher professional programs need to provide additional workshops to improve their understanding of cooperative learning and the teachers' roles.

Leadership construction : an exploratory case study of two exemplary female principals in urban primary schools in mainland China

Worldwide, education systems have undergone unprecedented change due to a variety of economic, social, and political forces (Limerick, Cunnington & Crowther, 2002). The People’s Republic of China (PRC) is no exception. Continuous educational reform at primary and secondary levels in Mainland China has created new challenges and accountabilities for school principals. The important role of principals in primary and secondary schools has been acknowledged in both policy documents and the broader literature (Central Committee of the Chinese Communist Party, 1985; F. Chen, 2005; Chu, 2003; W. Huang, 2005; T. Wang, 2003). Yet, most of the literature on primary and secondary school principals in Mainland China is prescriptive in nature, identifying from the perspectives of researchers and academics what principals should do and how they should enact leadership. Lacking in this research is an awareness of the daily practices and lived experiences of principals. Furthermore, within the small body of writing on primary and secondary school principals in Mainland China, gender is seldom given any attention. To date, only a small number of empirical studies have focused on female principals as a specific category of research (Zen, 2004; Zhong, 2004). This study aimed to explore the professional lives of two female exemplary school principals in urban primary schools in Mainland China. A qualitative exploratory case study was used. Semi-structured interviews with each individual female principal, with six teachers in each of the school sites and with the superintendent of each principal were conducted. Field observations and document analysis were also undertaken to obtain multiple insights about their leadership practices. The conceptual framework was based largely on the theory of Gronn (1999) and incorporated five core leadership practices (vision building, ethical considerations, teaching and learning, power utilisation, and dealing with risks and challenges) taken from the wider literature. The key findings of this study were twofold. Firstly, while the five leadership practices were evident in the leadership of the two principals, this study identified some subtle differences in the way they approached each of them. Secondly, contextual factors such as Chinese traditional culture, the contemporary societal context, and the school organisational context, in addition to the biographical experiences of each principal were significant factors in shaping the way in which they exercised their leadership practices in the schools.

A Conceptualisation of Courseware Development Process in Malaysian Educational Context

Multimedia-based learning has been accepted as an effective learning tool and has broadly prevailed in various types of education around the world. The Malaysian ministry of education has also adopted this information communication technology (ICT) as the means of an education reformation project called, ‘Smart School’ since 1998, aiming to improve all Malaysian Primary and Secondary students’ learning ability, attitudes, achievement, and further enhance teachers’ teaching performance. As a result, Malaysian Ministry of Education has distributed a number of interactive courseware of the key learning domains such as Mathematics, Science, Bahasa Melayu (Malay language), and English. According to recent reports by Malaysian Ministry of Education (MOE), however, the courseware has not been effectively used in schools, and many researchers point out there are vital issues concerning the interface and interaction design. Within this context, this paper presumes that one of the main reasons could derive from a structural aspect of the course development process that is devaluing or ignoring the importance of interface and interaction design. Therefore, it is imperative to conceptualise the courseware development process in terms of creating interactive and quality learning experiences through defining the stakeholders’ needs in terms of better learning and teaching. Within this context, this paper reviews the current development process and proposes a new concept called the interactive communication component which enables courseware developers to embed interactive and quality learning experiences into their courseware development process. The key objective is to provide opportunities to discuss the courseware development process from the different stakeholders’ perspectives of the educational courseware in a Malaysian context.

Leading learning within a PLC : implementing new mathematics content

This paper does two things. Firstly, it examines the literature that coalesces around theoretical models of teacher professional development (PD) within a professional learning community (PLC). Secondly, these models are used to analyse support provided to two year 3 teachers, while implementing the draft Queensland mathematics syllabus. The findings from this study suggest that the development of this small PLC extended the teachers’ Zone of Enactment which in turn led to teacher action and reflection. This was demonstrated by the teachers leading their own learning as well as that of their students.

Is the world their oyster? The global imagination of pre-service teachers

This paper reports on a qualitative interview study with eleven pre-service primary teachers in Queensland about their career plans exploring whether and how a global imagination motivates this next generation of teachers. The study is framed within sociological theory of globalisation, with regard to the growing possibilities for international mobility for work purposes, and the new life circumstances which make this imaginable. Teaching as a profession has changed and teachers are no longer as entangled with specific systems or geographical locations anymore. International recruitment campaigns are shown to pursue these pre-service teachers during their university preparation. The analysis of the interview data reveals the kind of impact these possibilities make on how pre-service teachers imagine their career, and what other considerations enhance or limit their global imagination. The findings are used to reflect on the highly localised governance of pre-service teacher preparation and the limited state-bound imaginaries to which these pre-service teachers are unnecessarily confined in their preparation.

MATLAB toolboxes : robotics and vision for students and teachers

In this column, Dr. Peter Corke of CSIRO, Australia, gives us a description of MATLAB Toolboxes he has developed. He has been passionately developing tools to enable students and teachers to better understand the theoretical concepts behind classical robotics and computer vision through easy and intuitive simulation and visualization. The results of this labor of love have been packaged as MATLAB Toolboxes: the Robotics Toolbox and the Vision Toolbox. –Daniela Rus, RAS Education Cochair

Students as decoders of graphics in mathematics

This paper reports on students’ ability to decode mathematical graphics. The findings were: (a) some items showed an insignificant improvement over time; (b) success involves identifying critical perceptual elements in the graphic and incorporating these elements into a solution strategy; and (c) the optimal strategy capitalises on how information is encoded in the graphic. Implications include a need for teachers to be proactive in supporting students’ to develop their graphical knowledge and an awareness that knowledge varies substantially across students.

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.

Inquiry-based science in a primary classroom : professional development impacting practice

The critical factor in determining students' interest and motivation to learn science is the quality of the teaching. However, science typically receives very little time in primary classrooms, with teachers often lacking the confidence to engage in inquiry-based learning because they do not have a sound understanding of science or its associated pedagogical approaches. Developing teacher knowledge in this area is a major challenge. Addressing these concerns with didactic "stand and deliver" modes of Professional Development (PD) has been shown to have little relevance or effectiveness, yet is still the predominant approach used by schools and education authorities. In response to that issue, the constructivist-inspired Primary Connections professional learning program applies contemporary theory relating to the characteristics of effective primary science teaching, the changes required for teachers to use those pedagogies, and professional learning strategies that facilitate such change. This study investigated the nature of teachers' engagement with the various elements of the program. Summative assessments of such PD programs have been undertaken previously, however there was an identified need for a detailed view of the changes in teachers' beliefs and practices during the intervention. This research was a case study of a Primary Connections implementation. PD workshops were presented to a primary school staff, then two teachers were observed as they worked in tandem to implement related curriculum units with their Year 4/5 classes over a six-month period. Data including interviews, classroom observations and written artefacts were analysed to identify common themes and develop a set of assertions related to how teachers changed their beliefs and practices for teaching science. When teachers implement Primary Connections, their students "are more frequently curious in science and more frequently learn interesting things in science" (Hackling & Prain, 2008). This study has found that teachers who observe such changes in their students consequently change their beliefs and practices about teaching science. They enhance science learning by promoting student autonomy through open-ended inquiries, and they and their students enhance their scientific literacy by jointly constructing investigations and explaining their findings. The findings have implications for teachers and for designers of PD programs. Assertions related to teaching science within a pedagogical framework consistent with the Primary Connections model are that: (1) promoting student autonomy enhances science learning; (2) student autonomy presents perceived threats to teachers but these are counteracted by enhanced student engagement and learning; (3) the structured constructivism of Primary Connections resources provides appropriate scaffolding for teachers and students to transition from didactic to inquiry-based learning modes; and (4) authentic science investigations promote understanding of scientific literacy and the "nature of science". The key messages for designers of PD programs are that: (1) effective programs model the pedagogies being promoted; (2) teachers benefit from taking the role of student and engaging in the proposed learning experiences; (3) related curriculum resources foster long-term engagement with new concepts and strategies; (4) change in beliefs and practices occurs after teachers implement the program or strategy and see positive outcomes in their students; and (5) implementing this study's PD model is efficient in terms of resources. Identified topics for further investigation relate to the role of assessment in providing evidence to support change in teachers' beliefs and practices, and of teacher reflection in making such change more sustainable.