Sequential development of algebra knowledge : a cognitive analysis

Learning to operate algebraically is a complex process that is dependent upon extending arithmetic knowledge to the more complex concepts of algebra. Current research has shown a gap between arithmetic and algebraic knowledge and suggests a pre-algebraic level as a step between the two knowledge types. This paper examines arithmetic and algebraic knowledge from a cognitive perspective in an effort to determine what constitutes a pre-algebraic level of understanding. Results of a longitudinal study designed to investigate students' readiness for algebra are presented. Thirty-three students in Grades 7, 8, and 9 participated. A model for the transition from arithmetic to pre-algebra to algebra is proposed and students' understanding of relevant knowledge is discussed.

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.

Decentralised particle filtering for multiple target tracking in wireless sensor networks

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Pedagogy and participation : literacy education for low-literate refugee students of African origin in a western school system

For ESL teachers working with low-literate adolescents the challenge is to provide instruction in basic literacy capabilities while also realising the benefits of interactive and dialogic pedagogies advocated for the students. In this article we look at literacy pedagogy for refugees of African origin in Australian classrooms. We report on an interview study conducted in an intensive English language school for new arrival adolescents and in three regular secondary schools. Brian Street’s ideological model is used. From this perspective, literacy entails not only technical skills, but also social and cultural ways of making meaning that are embedded within relations of power. The findings showed that teachers were strengthening control of instruction to enable mastery of technical capabilities in basic literacy and genre analysis. We suggest that this approach should be supplemented by a critical approach transforming relations of linguistic power that exclude, marginalise and humiliate the study students in the classroom.

Primary students’ interpretation of maps : gesture use and mapping knowledge

Maps are used to represent three-dimensional space and are integral to a range of everyday experiences. They are increasingly used in mathematics, being prominent both in school curricula and as a form of assessing students understanding of mathematics ideas. In order to successfully interpret maps, students need to be able to understand that maps: represent space, have their own perspective and scale, and their own set of symbols and texts. Despite the fact that maps have an increased prevalence in society and school, there is evidence to suggest that students have difficulty interpreting maps. This study investigated 43 primary-aged students’ (aged 9-12 years) verbal and gestural behaviours as they engaged with and solved map tasks. Within a multiliteracies framework that focuses on spatial, visual, linguistic, and gestural elements, the study investigated how students interpret map tasks. Specifically, the study sought to understand students’ skills and approaches used to solving map tasks and the gestural behaviours they utilised as they engaged with map tasks. The investigation was undertaken using the Knowledge Discovery in Data (KDD) design. The design of this study capitalised on existing research data to carry out a more detailed analysis of students’ interpretation of map tasks. Video data from an existing data set was reorganised according to two distinct episodes—Task Solution and Task Explanation—and analysed within the multiliteracies framework. Content Analysis was used with these data and through anticipatory data reduction techniques, patterns of behaviour were identified in relation to each specific map task by looking at task solution, task correctness and gesture use. The findings of this study revealed that students had a relatively sound understanding of general mapping knowledge such as identifying landmarks, using keys, compass points and coordinates. However, their understanding of mathematical concepts pertinent to map tasks including location, direction, and movement were less developed. Successful students were able to interpret the map tasks and apply relevant mathematical understanding to navigate the spatial demands of the map tasks while the unsuccessful students were only able to interpret and understand basic map conventions. In terms of their gesture use, the more difficult the task, the more likely students were to exhibit gestural behaviours to solve the task. The most common form of gestural behaviour was deictic, that is a pointing gesture. Deictic gestures not only aided the students capacity to explain how they solved the map tasks but they were also a tool which assisted them to navigate and monitor their spatial movements when solving the tasks. There were a number of implications for theory, learning and teaching, and test and curriculum design arising from the study. From a theoretical perspective, the findings of the study suggest that gesturing is an important element of multimodal engagement in mapping tasks. In terms of teaching and learning, implications include the need for students to utilise gesturing techniques when first faced with new or novel map tasks. As students become more proficient in solving such tasks, they should be encouraged to move beyond a reliance on such gesture use in order to progress to more sophisticated understandings of map tasks. Additionally, teachers need to provide students with opportunities to interpret and attend to multiple modes of information when interpreting map tasks.

The democratic deficit and school-based management in Australia

Purpose: The paper seeks to apply the theory of the democratic deficit to school-based management with an emphasis on Australia. This theory was developed to examine managerial restructuring of the Australian Public Service in the 1990s. Given similarities between the use of managerial practices in the public service and government schools, the authors draw on recent literature about school-based management in Australia and apply the democratic deficit theory to it. ----- ----- Design/methodology/approach: This paper is conceptual in focus. The authors analyse literature in terms of the three components of the democratic deficit – i.e. the weakening of accountability, the denial of the roles and values of public employees, and the emergence of a “hollow state” – and in relation to the application of this theory to the Australian Public Service.----- ----- Findings: A trend towards the three components of the democratic deficit is evident in Australia although, to date, its emergence has not been as extensive as in the UK. The authors argue that the democratic principles on which public schooling in Australia was founded are being eroded by managerial and market practices.----- ----- Practical implications: These findings provide policy makers and practitioners with another way of examining managerial and market understandings of school-based management and its impact on teachers and on students. It offers suggestions to reorient practices away from those that are exclusively managerial-based towards those that are public-sector based.----- ----- Originality/value: The value of this paper is that it applies the theory of the democratic deficit to current understandings of school-based management.

Teaching sustainability : vehicle or endpoint?

In 2006, the Faculty of Built Environment and Engineering introduced the first faculty wide unit dedicated to sustainability at any Australian University. BEB200 Introducing Sustainability has semester enrolments of up to 1500 students. Instruments such as lectures, readings, field visits, group projects and structured tutorial activities are used and have evolved over the last five years in response to student and staff feedback and attempts to better engage students. More than seventy staff have taught in the unit, which is in its final offering in this form in 2010. This paper reflects on the experiences of five academics who have played key roles in the development and teaching of this unit over the last five years. They argue that sustainability is a paradigm that allows students to explore other ways of knowing as they engage with issues in a complex world, not an end in itself. From the students’ perspective, grappling with such issues enables them to move towards a context in which they can understand their own discipline and its role in the contradictory and rapidly changing professional world. Insights are offered into how sustainability units may be developed in the future.

Embedding gifted education in preservice teacher education : a collaborative school-university approach

A country’s prosperity relies on the creative potential of its people. Educating gifted students must be a priority for educators and education systems if society is to capitalise on their potential to contribute to an economical and sustainable future. Given the importance of teachers in supporting academic achievement, educating preservice teachers on how to cater for gifted students commences the process as they can foster the implementation of current teaching practices that draw on substantial research into the education of gifted children. This study investigated preservice teachers’ perceptions for teaching gifted students after participating in a school-based intervention with gifted students. The teachers implemented differentiated curriculum activities that catered for the diverse needs of learners. Participants (n=22) were surveyed at the end of the program on their perceptions of how to differentiate the curriculum for meeting the needs of the student. Analysis of the survey indicated these preservice teachers agreed or strongly agreed they had developed skills in curriculum planning (91%) with well-designed activities (96%), and lesson preparation skills (96%). They also claimed they were enthusiastic for teaching (91%) and had understanding of school practices and policies (96%). However, only 46% agreed they had knowledge of syllabus documents with 50% claiming an ability to provide written feedback on the student’s learning. Furthermore, only 64% suggested they had educational language from the syllabus and effective student management strategies. Preservice teachers require direction on how to cater for diversity by building knowledge from direct gifted education experiences. The survey may be used as a diagnostic tool to determine areas for developing education experiences related to the education of the gifted for preservice teachers.

Development of new evaluation methods for qualitative alternatives, using fuzzy calculations

Evaluation, selection and finally decision making are all among important issues, which engineers face in long run of projects. Engineers implement mathematical and nonmathematical methods to make accurate and correct decisions, whenever needed. As extensive as these methods are, effects of any selected method on outputs achieved and decisions made are still suspicious. This is more controversial and challengeable, where evaluation is made among non-quantitative alternatives. In civil engineering and construction management problems, criteria include both quantitative and qualitative ones, such as aesthetic, construction duration, building and operation costs, and environmental considerations. As the result, decision making frequently takes place among non-quantitative alternatives. It should be noted that traditional comparison methods, including clear-cut and inflexible mathematics, have always been criticized. This paper demonstrates a brief review of traditional methods of evaluating alternatives. It also offers a new decision making method using, fuzzy calculations. The main focus of this research is some engineering issues, which have flexible nature and vague borders. Suggested method provides analyzability of evaluation for decision makers. It is also capable to overcome multi criteria and multi-referees problems. In order to ease calculations, a program named DeMA is introduced.

Early childhood teachers' mathematical content knowledge

The process of becoming numerate begins in the early years. According to Vygotskian theory (1978), teachers are More Knowledgeable Others who provide and support learning experiences that influence children’s mathematical learning. This paper reports on research that investigates three early childhood teachers mathematics content knowledge. An exploratory, single case study utilised data collected from interviews, and email correspondence to investigate the teachers’ mathematics content knowledge. The data was reviewed according to three analytical strategies: content analysis, pattern matching, and comparative analysis. Findings indicated there was variation in teachers’ content knowledge across the five mathematical strands and that teachers might not demonstrate the depth of content knowledge that is expected of four year specially trained early years’ teachers. A significant factor that appeared to influence these teachers’ content knowledge was their teaching experience. Therefore, an avenue for future research is the investigation of factors that influence teachers’ content numeracy knowledge.

New media pathways : navigating the links between home, school and the workplace

The terms ‘literacy’ and ‘technology’ remain highly contentious within the field of education. What is meant by ‘literacy’ and the methods used to measure it vary quite markedly in educational and historical contexts across the world. Similarly, while there is a shared concern to research the potential impact of new information and communication technologies (ICTs) on patterns of teaching and learning, there are major discrepancies about which aspects and uses of these technologies should be incorporated into formal learning environments and how this can be accomplished. While government policy makers tend to regard ICTs in relation to ideas of ‘smartness’, efficiency, and the ‘knowledge’ (or ‘new’) economy, educators and educational researchers promote them as offering new tools for learning and critical thinking and the development of new literacies and socio-cultural identities. This clearly has ramifications for the ways literacy is taught and conceptualised throughout the years of schooling, K-12. Outside school, meanwhile, students engage with ICTs on another level entirely, as tools for the maintenance of social networks, for leisure, and for learning and participating in the cultures of their peers. Whatever the differences in perspective, it remains the case that a society’s dominant understandings about literacy and technology will have significant implications for the development of school curriculum.

School-based strategies to address cyber bullying

Bullying and victimisation among school age children is recognised as a major public health problem. The Australian Covert Bullying Prevalence Study (ACBPS) reports that just over one quarter (27%) of school students aged 8 to 14 years were bullied and 9% bullied others on a frequent basis (every few weeks or more often) (Cross et al., 2009). Bullying is associated with a host of detrimental effects, including loneliness (Nansel, Overpeck, Pilla, & Ruan, 2001), low self‐esteem (Jankauskiene, Kardelis, Sukys, & Kardeliene, 2008; Salmivalli, Kaukiainen, Kaistaniemi, & Lagerspetz, 1999), anxiety, depression (Kaltiala‐Heino, Rimpela, Rantanen, & Rimpela, 2000), suicide ideation (Kaltiala‐Heino, Rimpela, Marttunen, Rimpela, & Rantanen, 1999), impaired academic achievement (Nansel et al., 2001), and poorer physical health (Wolke, Woods, Bloomfield, & Karstadt, 2001).

Towards a classification of criterion referenced assessment models in mathematics courses : student and academic perspectives

We present the findings of a study into the implementation of explicitly criterion- referenced assessment in undergraduate courses in mathematics. We discuss students' concepts of criterion referencing and also the various interpretations that this concept has among mathematics educators. Our primary goal was to move towards a classification of criterion referencing models in quantitative courses. A secondary goal was to investigate whether explicitly presenting assessment criteria to students was useful to them and guided them in responding to assessment tasks. The data and feedback from students indicates that while students found the criteria easy to understand and useful in informing them as to how they would be graded, it did not alter the way the actually approached the assessment activity.

Waist circumference cut-off values for the prediction of cardiovascular risk factors clustering in Chinese school-aged children : a cross-sectional study

Background: Waist circumference has been identified as a valuable predictor of cardiovascular risk in children. The development of waist circumference percentiles and cut-offs for various ethnic groups are necessary because of differences in body composition. The purpose of this study was to develop waist circumference percentiles for Chinese children and to explore optimal waist circumference cut-off values for predicting cardiovascular risk factors clustering in this population.----- ----- Methods: Height, weight, and waist circumference were measured in 5529 children (2830 boys and 2699 girls) aged 6-12 years randomly selected from southern and northern China. Blood pressure, fasting triglycerides, low-density lipoprotein cholesterol, high-density lipoprotein cholesterol, and glucose were obtained in a subsample (n = 1845). Smoothed percentile curves were produced using the LMS method. Receiver-operating characteristic analysis was used to derive the optimal age- and gender-specific waist circumference thresholds for predicting the clustering of cardiovascular risk factors.----- ----- Results: Gender-specific waist circumference percentiles were constructed. The waist circumference thresholds were at the 90th and 84th percentiles for Chinese boys and girls respectively, with sensitivity and specificity ranging from 67% to 83%. The odds ratio of a clustering of cardiovascular risk factors among boys and girls with a higher value than cut-off points was 10.349 (95% confidence interval 4.466 to 23.979) and 8.084 (95% confidence interval 3.147 to 20.767) compared with their counterparts.----- ----- Conclusions: Percentile curves for waist circumference of Chinese children are provided. The cut-off point for waist circumference to predict cardiovascular risk factors clustering is at the 90th and 84th percentiles for Chinese boys and girls, respectively.

Industry school partnerships : real world learning through the Gateway Schools Projects

In the last decade, a gradual but significant shift in education has taken place. Schools have transformed from hermetically sealed, impermeable bureaucracies to dynamic and flexible organisations characterised by openness to local communities and connectedness to global issues and cultures. They are also more responsive to the aspirations of students and parents. A central feature of what Christian Maroy (2009) has described as the post bureaucratic era of education has been the relationships formed between schools and other organisations through formalised partnerships. Partnerships have been a significant feature of schooling in Queensland since the 1980s when schools developed Vocational Education Programs (VET) providing alternative pathways from schooling to post school training or employment. However, partnerships that have emerged in recent times have been more structured in their organisation and more targeted in terms of the outcomes they aim to achieve. Examples here have included Queensland’s District Youth Achievement plans that linked schools, business, industry bodies, training organisations and community groups to improve transition outcomes, particularly for young people at risk in their transitions from school to post-school life.