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.

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.

“A special kind of city knowledge” : innovative clusters, tacit knowledge and the ‘Creative City’

That the cultural industries are highly networked and operate in clusters is now well established. The notion of cluster is linked to the idea of place-based advantage with cultural industries gaining competitive advantage from mobilising the resources of places to compete in global markets. ‘Place’ in the cultural industries is frequently taken to be the city where city is seen as the key resource for cultural industry clusters and a primary point of intervention for cultural industry policy in creative city policy making. In this article I want to look at some of the implications of these moves for both academic research and policy discussion. The reasons for this emphasis on policy relates to some large questions of urban governance and cultural politics surrounding the proactive government of clusters which are raised by recent work on the cultural industries, notably by Alan Scott.

The HRM practices of innovative knowledge-intensive firms

There is little research on HRM practices in knowledge-intensive firms (KIFs), especially in comparison to that conducted in traditional production environments. Whether such HRM practices are appropriate for KIFs, particularly ones that differentiate themselves on their ability to innovate, is the basis of this research. The study investigates the HRM practices being used by four innovative firms: two KIFs and two traditional production companies. The findings suggest that there are some similarities between the HRM practices of the case firms, but there are also important differences. Specifically, the KIFs emphasise use of selection criteria and processes that secure a workforce with a desire for challenging work and the ability to work collaboratively. The KIFs are also more likely to provide a breadth of training and development opportunities for teams and individuals, to make extensive use of performance management systems, and to utilise a range of strategies to encourage and reward innovation.

The internetalisation of information, knowledge and interaction components of the firm’s internationalisation process

Transcending traditional national borders, the Internet is an evolving technology that has opened up many new international market opportunities. However, ambiguity remains, with limited research and understanding of how the Internet influences the firm’s internationalisation process components. As a consequence, there has been a call for further investigation of the phenomenon. Thus, the purpose of this study was to investigate the Internet’s impact on the internationalisation process components, specifically, information availability, information usage, interactive communication and international market growth. Analysis was undertaken using structural equation modelling. Findings highlight the mediating impact of the Internet on information and knowledge transference in the internationalisation process. Contributions of the study test conceptualisations and give statistical validation of interrelationships, while illuminating the Internet’s impact on firm internationalisation.

New modes of governance and the commodification of criminological knowledge

This article explores the influence of new modes of governance on the production of criminological knowledge. In doing so, it examines the rise of discourses on risk and critiques the ways in which academic environments are changing under new managerialist philosophies. The article further explores the increasing 'commodification of criminological knowledge' and analyses its effect on contemporary criminological scholarship. Finally, this article examines the contours of critical criminological scholarship and advocates for a criminology of resistance.

New maps of learning for quality art education : what pre-service teachers should learn and be able to do

It would be a rare thing to visit an early years setting or classroom in Australia that does not display examples of young children’s artworks. This practice serves to give schools a particular ‘look’, but is no guarantee of quality art education. The Australian National Review of Visual Arts Education (NRVE) (2009) has called for changes to visual art education in schools. The planned new National Curriculum includes the arts (music, dance, drama, media and visual arts) as one of the five learning areas. Research shows that it is the classroom teacher that makes the difference, and teacher education has a large part to play in reforms to art education. This paper provides an account of one foundation unit of study (Unit 1) for first year university students enrolled in a 4-year Bachelor degree program who are preparing to teach in the early years (0–8 years). To prepare pre-service teachers to meet the needs of children in the 21st century, Unit 1 blends old and new ways of seeing art, child and pedagogy. Claims for the effectiveness of this model are supported with evidence-based research, conducted over the six years of iterations and ongoing development of Unit 1.

Middle school social sciences : exploring teachers’ conceptions of essential knowledge

This study examines teachers’ conceptions of essential knowledge in the humanities and social sciences, commonly referred to as "social education", in the middle years of schooling. Social education has long been a highly contested area of the curriculum in Australia. In Queensland, social education comprises the integrated learning area of Studies of Society and Environment (SOSE). However, the new Australian Curriculum marks a return to discipline-based study of history and geography. This phenomenographic study addresses a perceived lack of understanding in the current research literature in Australia of the nature of middle school teachers’ professional knowledge for teaching the social sciences. Teachers are conceptualised in this study as curriculum makers in the classroom and, as such, their conceptions of essential knowledge are significant. Shulman’s (1986, 1987) theory of teachers’ knowledge forms the theoretical foundation of the study, which is contextualised in Federal and State education policies and the literature on the middle phase of schooling. Transcripts of interviews conducted with a group of thirty-one Queensland middle school teachers of SOSE were subjected to phenomenographic analysis, revealing seven qualitatively different categories of description. Essential aspects of knowledge for social education emerging from the study were: (1) discipline-based knowledge; (2) curriculum knowledge; (3) knowledge derived from teaching experience; (4) knowledge of middle years learners; (5) knowledge of integration; (6) knowledge of current affairs; and (7) knowledge invested in teacher identity. The three dimensions of variation that linked and differentiated the categories were: (1) content; (2) inquiry learning; and (3) teacher autonomy. These findings are presented as an outcome space where the categories are grouped as knowledge of the learning area, knowledge of contexts and knowledge of self as teacher. The results of the study suggest that social education teachers’ identity and knowledge of self are critical aspects of their knowledge as curriculum makers. The results illustrate that the professional and personal domains intersect, extending Shulman’s (1986, 1987) original theorisation of teachers’ knowledge into the personal arena. Further, middle years teachers’ conceptions of essential knowledge reveal a practice-based theorisation of knowledge for social education that fits the goals of middle schooling. The research concludes that attention to teacher identity in teacher education and in-service professional development has considerable potential to grow teachers’ knowledge in the social sciences and enhance their capacity for school-based curriculum leadership.

Design of a knowledge base to teach programming

Programming is a subject that many beginning students find difficult. This paper describes a knowledge base designed for the purpose of analyzing programs written in the PHP web development language. The aim is to use this knowledge base in an Intelligent Tutoring System that will provide effective feedback to students. The main focus of this research is that a programming exercise can have many correct solutions. This paper presents an overview of how the proposed knowledge base can be utilized to accept different solutions to a given exercise

The applicability of aesthetic knowledge in organizational decision making processes

We argue that aesthetic knowledge, which is a form of tacit knowledge of beauty and related concepts, is an important, yet under-researched, topic in the study of organizational decision making processes. The significance of aesthetic knowledge for decision making processes is derived from its universal application by humans to commonplace practices; its use as the basis of decision criteria in complex situations to which the effective application of logic and reason is difficult; and its role both in assisting cognition in general and in enabling the choice of solutions generated from rational decision making processes. Despite its importance, the empirical research examining the application of aesthetic knowledge in organizational decision making processes is limited. Further detailed study of aesthetic knowledge in the context of organizational decision making processes is required to extend the recent movement in the field aimed at examining the role that extrarational, human-centered factors play in organizational decisions.

A world map of knowledge in the making : Wikipedia's Inter-Language Linkage as a dependency explorer of global knowledge accumulation

Analysis of Wikipedia's inter-language links provides insight into a new mechanism of knowledge sharing and linking worldwide.

Larger or broader : performance implications of size and diversity of the knowledge worker's egocentric network. [更多或更广：知识员工个人中心网络大小和 多样性对绩效的影响]

Management scholars and practitioners emphasize the importance of the size and diversity of a knowledge worker's social network. Constraints on knowledge workers’ time and energy suggest that more is not always better. Further, why and how larger networks contribute to valuable outcomes deserves further understanding. In this study, we offer hypotheses to shed insight on the question of the diminishing returns of large networks and the specific form of network diversity that may contribute to innovative performance among knowledge workers. We tested our hypotheses using data collected from 93 R&D engineers in a Sino-German automobile electronics company located in China. Study findings identified an inflection point, confirming our hypothesis that the size of the knowledge worker's egocentric network has an inverted U-shaped effect on job performance. We further demonstrate that network dispersion richness (the number of cohorts that the focal employee has connections to) rather than network dispersion evenness (equal distribution of ties across the cohorts) has more influence on the knowledge worker's job performance. Additionally, we found that the curvilinear effect of network size is fully mediated by network dispersion richness. Implications for future research on social networks in China and Western contexts are discussed.