Theory and its role in mathematics education

The increased recognition of the theory in mathematics education is evident in numerous handbooks, journal articles, and other publications. For example, Silver and Herbst (2007) examined ―Theory in Mathematics Education Scholarship‖ in the Second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007) while Cobb (2007) addressed ―Putting Philosophy to Work: Coping with Multiple Theoretical Perspectives‖ in the same handbook. And a central component of both the first and second editions of the Handbook of International Research in Mathematics Education (English, 2002; 2008) was ―advances in theory development.‖ Needless to say, the comprehensive second edition of the Handbook of Educational Psychology (Alexander & Winne, 2006) abounds with analyses of theoretical developments across a variety of disciplines and contexts. Numerous definitions of ―theory‖ appear in the literature (e.g., see Silver & Herbst, in Lester, 2007). It is not our intention to provide a ―one-size-fits-all‖ definition of theory per se as applied to our discipline; rather we consider multiple perspectives on theory and its many roles in improving the teaching and learning of mathematics in varied contexts.

Methodologies for investigating relationships between concept development and the development of problem solving abilities

This paper is the second in a pair that Lesh, English, and Fennewald will be presenting at ICME TSG 19 on Problem Solving in Mathematics Education. The first paper describes three shortcomings of past research on mathematical problem solving. The first shortcoming can be seen in the fact that knowledge has not accumulated – in fact it has atrophied significantly during the past decade. Unsuccessful theories continue to be recycled and embellished. One reason for this is that researchers generally have failed to develop research tools needed to reliably observe, document, and assess the development of concepts and abilities that they claim to be important. The second shortcoming is that existing theories and research have failed to make it clear how concept development (or the development of basic skills) is related to the development of problem solving abilities – especially when attention is shifted beyond word problems found in school to the kind of problems found outside of school, where the requisite skills and even the questions to be asked might not be known in advance. The third shortcoming has to do with inherent weaknesses in observational studies and teaching experiments – and the assumption that a single grand theory should be able to describe all of the conceptual systems, instructional systems, and assessment systems that strongly molded and shaped by the same theoretical perspectives that are being used to develop them. Therefore, this paper will describe theoretical perspectives and methodological tools that are proving to be effective to combat the preceding kinds or shortcomings. We refer to our theoretical framework as models & modeling perspectives (MMP) on problem solving (Lesh & Doerr, 2003), learning, and teaching. One of the main methodologies of MMP is called multi-tier design studies (MTD).

An exploration of knowledge management and intellectual capital in a nonprofit organisation context

In recent years, practitioners and researchers alike have turned their attention to knowledge management (KM) in order to increase organisational performance (OP). As a result, many different approaches and strategies have been investigated and suggested for how knowledge should be managed to make organisations more effective and efficient. However, most research has been undertaken in the for-profit sector, with only a few studies focusing on the benefits nonprofit organisations might gain by managing knowledge. This study broadly investigates the impact of knowledge management on the organisational performance of nonprofit organisations. Organisational performance can be evaluated through either financial or non-financial measurements. In order to evaluate knowledge management and organisational performance, non-financial measurements are argued to be more suitable given that knowledge is an intangible asset which often cannot be expressed through financial indicators. Non-financial measurement concepts of performance such as the balanced scorecard or the concept of Intellectual Capital (IC) are well accepted and used within the for-profit and nonprofit sectors to evaluate organisational performance. This study utilised the concept of IC as the method to evaluate KM and OP in the context of nonprofit organisations due to the close link between KM and IC: Indeed, KM is concerned with managing the KM processes of creating, storing, sharing and applying knowledge and the organisational KM infrastructure such as organisational culture or organisational structure to support these processes. On the other hand, IC measures the knowledge stocks in different ontological levels: at the individual level (human capital), at the group level (relational capital) and at the organisational level (structural capital). In other words, IC measures the value of the knowledge which has been managed through KM. As KM encompasses the different KM processes and the KM infrastructure facilitating these processes, previous research has investigated the relationship between KM infrastructure and KM processes. Organisational culture, organisational structure and the level of IT support have been identified as the main factors of the KM infrastructure influencing the KM processes of creating, storing, sharing and applying knowledge. Other research has focused on the link between KM and OP or organisational effectiveness. Based on existing literature, a theoretical model was developed to enable the investigation of the relation between KM (encompassing KM infrastructure and KM processes) and IC. The model assumes an association between KM infrastructure and KM processes, as well as an association between KM processes and the various levels of IC (human capital, structural capital and relational capital). As a result, five research questions (RQ) with respect to the various factors of the KM infrastructure as well as with respect to the relationship between KM infrastructure and IC were raised and included into the research model: RQ 1 Do nonprofit organisations which have a Hierarchy culture have a stronger IT support than nonprofit organisations which have an Adhocracy culture? RQ 2 Do nonprofit organisations which have a centralised organisational structure have a stronger IT support than nonprofit organisations which have decentralised organisational structure? RQ 3 Do nonprofit organisations which have a stronger IT support have a higher value of Human Capital than nonprofit organisations which have a less strong IT support? RQ 4 Do nonprofit organisations which have a stronger IT support have a higher value of Structural Capital than nonprofit organisations which have a less strong IT support? RQ 5 Do nonprofit organisations which have a stronger IT support have a higher value of Relational Capital than nonprofit organisations which have a less strong IT support? In order to investigate the research questions, measurements for IC were developed which were linked to the main KM processes. The final KM/IC model contained four items for evaluating human capital, five items for evaluating structural capital and four items for evaluating relational capital. The research questions were investigated through empirical research using a case study approach with the focus on two nonprofit organisations providing trade promotions services through local offices worldwide. Data for the investigation of the assumptions were collected via qualitative as well as quantitative research methods. The qualitative study included interviews with representatives of the two participating organisations as well as in-depth document research. The purpose of the qualitative study was to investigate the factors of the KM infrastructure (organisational culture, organisational structure, IT support) of the organisations and how these factors were related to each other. On the other hand, the quantitative study was carried out through an online-survey amongst staff of the various local offices. The purpose of the quantitative study was to investigate which impact the level of IT support, as the main instrument of the KM infrastructure, had on IC. Overall several key themes were found as a result of the study: • Knowledge Management and Intellectual Capital were complementary with each other, which should be expressed through measurements of IC based on KM processes. • The various factors of the KM infrastructure (organisational culture, organisational structure and level of IT support) are interdependent. • IT was a primary instrument through which the different KM processes (creating, storing, sharing and applying knowledge) were performed. • A high level of IT support was evident when participants reported higher level of IC (human capital, structural capital and relational capital). The study supported previous research in the field of KM and replicated the findings from other case studies in this area. The study also contributed to theory by placing the KM research within the nonprofit context and analysing the linkage between KM and IC. From the managerial perspective, the findings gave clear indications that would allow interested parties, such as nonprofit managers or consultants to understand more about the implications of KM on OP and to use this knowledge for implementing efficient and effective KM strategies within their organisations.

Effective models of employment-based training

Australia needs highly skilled workers to sustain a healthy economy. Current employment-based training models have limitations in meeting the demands for highly skilled labour supply. The research explored current and emerging models of employment-based training to propose more effective models at higher VET qualifications that can maintain a balance between institution and work-based learning.

Imaginary relish and exquisite torture : the elaborated intrusion theory of desire

The authors argue that human desire involves conscious cognition that has strong affective connotation and is potentially involved in the determination of appetitive behavior rather than being epiphenomenal to it. Intrusive thoughts about appetitive targets are triggered automatically by external or physiological cues and by cognitive associates. When intrusions elicit significant pleasure or relief, cognitive elaboration usually ensues. Elaboration competes with concurrent cognitive tasks through retrieval of target related information and its retention in working memory. Sensory images are especially important products of intrusion and elaboration because they simulate the sensory and emotional qualities of target acquisition. Desire images are momentarily rewarding but amplify awareness of somatic and emotional deficits. Effects of desires on behavior are moderated by competing incentives, target availability, and skills. The theory provides a coherent account of existing data and suggests new directions for research and treatment.

Innovative approaches to intervention for problem drinking

Purpose of review: To critique the recent literature on telephone, correspondence-based, and computerized interventions for alcohol problems, which enhance or substitute for practitioner-delivered treatments. Recent findings: There is an unmet need for screening, assessment and intervention for alcohol problems, in part because of the difficulty in accessing such treatment within the current health care system. Research on the efficacy of correspondence or electronic (for example Internet-based) interventions is beginning to emerge. In the period 2003–2004 we identified nine acceptability or feasibility studies of these approaches and seven efficacy trials covering a wide range of settings. These modes of intervention are acceptable to patients and the public, and with careful planning, can be implemented in a variety of settings. Treatment trials demonstrate the efficacy of these interventions in reducing hazardous drinking by university students, in delaying initiation of heavy drinking in children and adolescents, and, intriguingly, in addressing insomnia among recovering alcoholics. Summary: There is strong support among potential users for alcohol interventions that employ telephone assistance, written correspondence, and the Internet. These new technologies offer the prospect of increasing the reach of interventions for problem drinking and being cost- effective alternatives or supplements to face-to-face health service delivery.

Achieving effective supervision

Supervision probably does have benefits both for the maintenance and improvement of clinical skills and for job satisfaction, but the data are very thin and almost non-existent in the area of alcohol and other drugs ser vices. Because of the potential complexity of objectives and roles in super vision, a structured agreement appears to be an important part of the effective supervision relationship. Because sessions can degenerate easily into unstructured socialization, agendas and session objectives may also be important. While a working alliance based on mutual respect and trust is an essential base for the supervision relationship, procedures for direct observation of clinical skills, demonstration of new procedures and skills practice with detailed feedback appear critical to super vision’s impact on practice. To ensure effective supervision, there needs not only to be a minimum of personnel and resources, but also a compatibility with the values and procedures of management and staff, access to supervision training and consultation and sufficient incentives to ensure it continues.

Critical Systems Theory: A Political Economy of Language, Thought, and Technology

An emergent form of political economy, facilitated by information and communication technologies (ICTs), is widely propagated as the apotheosis of unmitigated social, economic, and technological progress. Meanwhile, throughout the world, social degradation and economic inequality are increasing logarithmically. Valued categories of thought are, axiomatically, the basic commodities of the “knowledge economy”. Language is its means of exchange. This paper proposes a sociolinguistic method with which to critically engage the hyperbole of the “Information Age”. The method is grounded in a systemic social theory that synthesises aspects of autopoiesis and Marxist political economy. A trade policy statement is analysed to exemplify the sociolinguistically created aberrations that are today most often construed as social and political determinants.

Choreographing research : supervising the dancing thesis

The dancing doctorate is an interrogative endeavour which can but nurture the art form and forge a beneficial dynamism between those who seek and those who assess the emerging knowledges of dance’. (Vincs, 2009) From 2006-2008 three dance academics from Perth, Brisbane and Melbourne undertook a research project entitled Dancing between Diversity and Consistency: Refining Assessment in Postgraduate Degrees in Dance, funded by the ALTC Priority Projects Program. Although assessment rather than supervision was the primary focus of this research, interviews with 40 examiner/supervisors, 7 research deans and 32 candidates across Australia and across the creative arts, primarily in dance, provide an insight into what might be considered best practice in preparing students for higher research degrees, and the challenges that embodied and experiential knowledges present for supervision. The study also gained the industry perspectives of dance professionals in a series of national forums in 5 cities, based around the value of higher degrees in dance. The qualitative data gathered from these two primary sources was coded and analysed using the NVivo system. Further perspectives were drawn from international consultant and dance researcher Susan Melrose, as well as recent publications in the field. Dance is a young addition to academia and consequently there tends to be a close liaison between the academy and the industry, with a relational fluidity that is both beneficial and problematic. This partially explains why dance research higher degrees are predominantly practice-led (or multi-modal, referring to those theses where practice comprises the substantial examinable component). As a physical, embodied art form, dance engages with the contested territory of legitimising alternative forms of knowledge that do not sit comfortably with accepted norms of research. In supporting research students engaged with dance practice, supervisors traverse the tricky terrain of balancing university academic requirements with studies that are emergent, not only in the practice and attendant theory but in their methodologies and open-ended outcomes; and in an art form in which originality and new knowledge also arises from collaborative creative processes. Formal supervisor accreditation through training is now mandatory in most Australian universities, but it tends to be generic and not address supervisory specificity. This paper offers the kind of alternative proposed by Edwards (2002) that improving postgraduate supervision will be effective if supervisors are empowered to generate their own standards and share best practice; in this case, in ways appropriate to the needs of their discipline and alternative modes of thesis presentation. In order to frame the qualities and processes conducive to this goal, this paper will draw on both the experiences of interviewees and on philosophical premises which underpin the research findings of our study. These include the ongoing challenge of dissolving the binary oppositions of theory and practice, especially in creative arts practice where theory resides in and emerges from the doing as much as in articulating reflection about the doing through what Melrose (2003) terms ‘mixed mode disciplinary practices’. In guiding practitioners through research higher degrees, how do supervisors deal with not only different forms of knowledge but indeed differing modes of knowledge? How can they navigate tensions that occur between the ‘incompatible competencies’ (Candlin, 2000) of the ‘spectating’ academic experts with their ‘irrepressible drive ... to inscribe, interpret, and hence to practise temporal closure’, and practitioner experts who create emergent works of ‘residual unfinishedness’ (Melrose 2006) which are not only embodied but ephemeral, as in the case of live performance?

Shaping the 'at-risk' youth : risk, governmentality and the Finn Report

The category of the `at-risk youth' currently underpins a good deal of youth policy, and in particular, education policy. Primarily, the category is centred around a range of programmes associated with the need for state intervention, intervention which largely occurs `at a distance' within domains such as the school and the family. While it is argued that in some ways, the `at-risk youth' simply replaces older characterisations used in the policing of the young, it will also be argued that the preventative policies associated with `risk' are constituted in terms of factors rather than individuals; that prevention is no longer primarily based upon personal expertise, but rather upon the gathering and collation of statistical knowledge which identifies `risks' within given populations; and that `risk' permits a greater number of young people to be brought into the field of regulatory strategies. Importantly, the category of the `at-risk youth' underpins crucial sections of policy documents such as the Finn Report (into credentialling/ education and vocational competency). In this case, youth is deemed to be `at-risk' of not making the transition to adulthood successfully. It will be argued that not only is the Finn Report significant in the administrative and cultural shaping of the category of `youth', but also by employing the notion of `risk', the Report puts in place yet another element of an effective network of governmental intelligibility covering the young. Finally, it will be argued that young women, as a specific example of a `risk' group (vis-a-vis obtaining certain types of employment), require particular forms of intervention, primarily through changing the vocational aspirations of their parents.

Re-assessing streetkids : a critique of subculture theory

Focusing on the notion of street kids, the paper suggests that youth be viewed in an alternative way to the subculture theory associated with the Center for Contemporary Cultural Studies in Birmingham (CCCS). It is argued that not only is subculture theory an unsuitable mechanism for understanding homeless youth but also, and more importantly, is itself fundamentally problematic. It is suggested that the work of Michel Foucault necessitates a reevaluation of the domain assumptions underlying subculture theory and offers in its place a model that relocates street kids, and youth itself, as artifacts of a network of governmental strategies.

Education research and youth subculture theory

Recent theoretical developments (particularly those involving the work of Michel Foucault) have challenged the foundations upon which subcultural analysis is built. It is not the intention of this paper to take issue with the underpinning neo-Marxist assumptions concerning hegemony, consciousness and culture. Rather, the intention is simply to problematise the use of subculture theory in terms of its totalising, normalising and dichotomising nature.

Shaping the at-risk youth

The category of the `at-risk' youth currently underpins a good deal of youth policy. Primarily, it centres around a range of programs associated with the need for state intervention. The `at-risk' youth tenuously appears at the intersection of a variety of knowledges/problematisations, such as vocational guidance, youth welfare, family management, and so on. Whilst it is argued that in some ways, the `at-risk' youth simply replaces older characterisations used in the policing of the young, it will also be argued that the preventative policies associated with `risk' are constituted in terms of factors rather than individuals, that prevention is no longer primarily based upon personal expertise, but rather upon the gathering and collation of statistical knowledge which identifies `risks' within given populations, and that `risk' legitimates unlimited governmental intervention. Importantly, the category of the `at-risk' youth underpins crucial sections of policy documents such as the Finn Report (into credentialling/education and vocational competency). In this case, youth is deemed to be `at-risk' of not making the transition to adulthood successfully. It will be argued that not only is the Finn Report significant in the administrative and cultural shaping of the category of `youth', but also by employing the notion of `risk', the Report puts in place yet another element of an effective network of governmental intelligibility covering the young. Finally, it will be argued that young women, as a specific an example of a `risk' group (vis-a-vis obtaining certain types of employment), require particular forms of intervention, primarily through changing the vocational aspirations of their parents.

Promoting creativity in education : from policy to practice : an Australian perspective

In the 21st century, our global community is changing to increasingly value creativity and innovation as driving forces in our lives. This paper will investigate how educators need to move beyond the rhetoric to effective practices for teaching and fostering creativity. First, it will describe the nature of creativity at different levels, with a focus on personal and everyday creativity. It will then provide a brief snapshot of creativity in education through the lens of new policies and initiatives in Queensland, Australia. Next it will review two significant areas related to enriching and enhancing students’ creative engagement and production: 1) influential social and environmental factors; and 2) creative self-efficacy. Finally, this paper will propose that to effectively promote student creativity in schools, we need to not only emphasise policy, but also focus on establishing a shared discourse about the nature of creativity, and researching and implementing effective practices for supporting and fostering creativity. This paper has implications for educational policy, practice and teacher training that are applicable internationally.