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.

Ways of telling : tacit knowledge transfer for fashion design research

The knowledge and skills of fashion and textiles design have traditionally been transferred through the indenture of an apprentice to a master. This relationship relied heavily on the transfer of explicit methods of design and making but also on the transfer of tacit knowledge, explained by Michael Polanyi as knowledge that cannot be explicitly known. By watching the master and emulating his efforts in the presence of his example, the apprentice unconsciously picks up the rules of the art, including those which are not explicitly known to the master himself (Polanyi, 1962 p.53). However, it has been almost half a century since Michael Polanyi defined the tacit dimension as a state in which “we can know more than we can tell” (Polanyi, 1967 p.4) at a time when the accepted means of ‘telling’ was through academic writing and publishing in hardcopy format. The idea that tacit knowledge transfer involves a one to one relationship between apprentice and master would appear to have dire consequences for a discipline, such as fashion design, where there is no such tradition of academic writing. This paper counters this point of view by providing examples of strategies currently being employed in online environments (principally through ‘craft’) and explains how these methods might prove useful to support tacit knowledge transfer in respect to academic research within the field of fashion design, and in the wider academic community involved in creative practice research. A summary of the implications of these new ideas for contemporary fashion research will conclude the paper.

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.

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.

Knowledge management strategy for the Building Division, Queensland Department of Public Works

This paper describes the background and methodology developed and employed in undertaking research developing a Knowledge Management Strategy for a key construction focused government agency. This paper reviews this methodology and examines a likely Knowledge Management Strategy. Two central objectives structure this Case Study: 1. Identify categories of important information generated by the Building Division, Queensland Department of Public Works in its service delivery to internal and external stake-holders, and 2. Formulate an appropriate and targeted Knowledge Management Strategy to meet the needs of the Queensland Building Capital Works program. The structure of this paper includes: *Description of the Queensland construction industry setting *Review the relevant literature *Design an appropriate research methodology *Analyse results *Formulate conclusions, contributions and implications of the targeted strategy.

Towards a model for the analysis and description of mathematical knowledge and understanding

Mathematics education literature has called for an abandonment of ontological and epistemological ideologies that have often divided theory-based practice. Instead, a consilience of theories has been sought which would leverage the strengths of each learning theory and so positively impact upon contemporary educational practice. This research activity is based upon Popper’s notion of three knowledge worlds which differentiates the knowledge shared in a community from the personal knowledge of the individual, and Bereiter’s characterisation of understanding as the individual’s relationship to tool-like knowledge. Using these notions, a re-conceptualisation of knowledge and understanding and a subsequent re-consideration of learning theories are proposed as a way to address the challenge set by literature. Referred to as the alternative theoretical framework, the proposed theory accounts for the scaffolded transformation of each individual’s unique understanding, whilst acknowledging the existence of a body of domain knowledge shared amongst participants in a scientific community of practice. The alternative theoretical framework is embodied within an operational model that is accompanied by a visual nomenclature with which to describe consensually developed shared knowledge and personal understanding. This research activity has sought to iteratively evaluate this proposed theory through the practical application of the operational model and visual nomenclature to the domain of early-number counting, addition and subtraction. This domain of mathematical knowledge has been comprehensively analysed and described. Through this process, the viability of the proposed theory as a tool with which to discuss and thus improve the knowledge and understanding with the domain of mathematics has been validated. Putting of the proposed theory into practice has lead to the theory’s refinement and the subsequent achievement of a solid theoretical base for the future development of educational tools to support teaching and learning practice, including computer-mediated learning environments. Such future activity, using the proposed theory, will advance contemporary mathematics educational practice by bringing together the strengths of cognitivist, constructivist and post-constructivist learning theories.

Knowledge-based urban development of multimedia super corridor, Malaysia : an overview

In recent years, with the impact of the global knowledge economy, a more comprehensive urban development approach, so called 'knowledge-based urban development', has gained significant popularity. This paper discusses the critical connections among knowledge-based urban development strategies, knowledge-intensive industries and information and communication technology infrastructures. In particular, the research focuses on investigating the application of the knowledge-based urban development concept by discussing one of the South East Asia's large scale knowledge-based urban development manifestations of Malaysia's Multimedia Super Corridor. The paper scrutinises Malaysia's experience in the development and evolution of the Multimedia Super Corridor from the angle of knowledge-based urban development policy implementation, infrastructural implications, and actors involved in its development and management. This paper provides a number of lessons learned from the Multimedia Super Corridor on the orchestration of knowledge-based development that is a necessity for cities seeking successful knowledge city and knowledge economy transformations.

Colin Marsh (2010) Becoming a Teacher : Knowledge, Skills and Issues. 5th edition, Frenchs Forrest : Pearson Education Australia, 459 pages. [Book Review]

In the preface to the fifth edition of Becoming a Teacher, Colin Marsh reminds us that teachers need to have passion, energy and a commitment to enhance students’ learning. This most recent edition certainly provides examples of the author’s wide ranging knowledge and depth of insights that reflect his own commitment to inspirational and dedicated teaching practice. The fifth edition shares those characteristics which made previous editions so worthwhile. Most notable is the subtle but significant dual theme of Marsh’s narrative. That is, first, teaching is a vehicle for increasing the life opportunities of students, and second, teaching is profession that requires continual commitment and critical reflection. These are very important messages for any course that develops teaching methodology. Becoming a Teacher continues to be structured in five readable sections, however the 2010 edition has some exciting new features that warrant the attention of teacher educators and their pre-service students.

Knowledge integration within Japanese firms : the Fujitsu way

The paper analyses knowledge integration processes at Fujitsu from a multi-level and systemic perspective. The focus is on team-building capability, capturing and utilising individual tacit knowledge, and communication networks for integrating dispersed specialist knowledge required in the development of new products and services. The analysis shows how knowledge integration is performed by Fujitsu at different layers of the company.

Indigenous knowledge and effective parent / school partnerships : insights and issues from 4 school case studies

Towards the last decade of the last millennium, Indigenous knowledge has been central to scholarly debates relating to decolonising knowledge on a global level. Much of these debates were advanced by Indigenous scholars in colonised countries particularly Australia, New Zealand, Canada and the United States. Indigenous scholars argue for the location of Indigenous knowledge as the epistemological standpoint (Battiste, Bell and Findlay, 2002; Kai’a, 2005; Nakata 2002, 2007) for intellectual engagements and methodology for resisting colonial constructions of the colonised other (Rigney, 1997; Smith, 1999, 2005). However, the challenge to engage Indigenous knowledge to inform research and educational processes, in many respects, is still a contested debate in western-oriented universities and institutions of higher education. The place of Indigenous knowledge in Australian secondary and primary schools remains vague, while efforts to embed Indigenous perspectives in the curriculum continue to be made by both government and private educational providers. Educational funding for Indigenous education continues to operate from a ‘deficiency’ model, whereby educational outcomes are often measured against set criteria, reflecting a pass/fail structure, than a more comprehensive investigation of educational outcomes and quality of learning experiences. Teacher knowledge, effective parental and community engagement into students’ learning and students’ experiences of schooling continue to be secondary to students’ final results. This paper presents preliminary findings of Parent School Partnership Initiative (PSPI) project conducted by the Oodgeroo Unit at the Queensland University of Technology in partnerships with the Aboriginal and Torres Strait Islander Education Focus Group for the Caboolture Shire, in South East Queensland. The state government sponsored initiative was to examine factors that promote and enhance parent/school engagement with their students’ schooling, and to contribute to Aboriginal and Torres Strait Islander students’ learning and completion of secondary schooling within the participating schools in a more holistic way. We present four school case studies and discuss some of the early findings. We conclude by arguing the importance of the recognition of Indigenous knowledge and its place in enhancing parent – schools partnerships.

Managing specialised knowledge in technopreneurial firms : the Australian experience

Technology-oriented young firms play an important role for innovation and commercialisation of new ideas. These firms are often founded by engineers, scientists or academics who posses great scientific/technological knowledge, but limited know-how in other aspects of managing a business including knowledge management. Successful managing and integrating their specialised knowledge is of particular importance when it comes to developing a new product or process. This article therefore focuses on the particularities of the knowledge management process in technopreneurial firms. Using a qualitative investigation from a sample of Australian SMEs, a number of key observations are derived which show the challenges of managing knowledge and how important knowledge management is as a management tool for R&D and innovation process in technology-oriented SMEs. Findings suggest that knowledge management and integration processes in these firms are very much project focused and mainly based on ad hoc and informal processes and not embedded within the overall organisational routines.

Discussions on conceptual knowledge and the use of blogs

In both Australia and Norway and through a number of Technology projects conducted since 2007, the authors – together and with other collaborators - have attempted to create positive learning environments supported by Web 2.0 communication tools. Through protected public sites and the oz-Teachernet [http://www.otn.edu.au], we have consistently chosen to use blogs to support the social construction of knowledge, that is, to allow students the opportunity to discuss, share and collaborate on their classroom activities and engagement with Technology artefacts and processes. Through comparisons with findings from a small-scale project in Norway and a large-scale project in Australia, this paper will argue for the potential of discussion through blogs but recommend that the purposeful use of scientific language in student communication will not occur without teacher intervention and scaffolding.