Teaching secondary school mathematics : research and practice for the 21st century

For the last decade or so, educational policy makers and researchers in many countries have been calling for significant changes to the way mathematics is taught in secondary schools. Australian mathematics curriculum documents now promote learning goals that go beyond mastery of a pre-determined body of knowledge and procedures - the traditional emphasis on facts, skills, formulae - to include mathematical reasoning and problem solving, communication, and real world applications. There is also pressure to move away from over-reliance on teacher-centred practices such as exposition and individual seatwork, towards activities that promote learners' involvement in constructing, applying, and evaluating mathematical ideas. Further impetus for reform comes from research recommending that if learners are to develop mathematically powerful forms of thinking and habits of mind, then classrooms should immerse them in the authentic practices of the discipline by supporting a culture of collaboration and sense-making. Teaching Secondary School Mathematics - incorporates recent developments in research and practice and applications to teaching mathematics in Australian secondary schools. Covering such areas as curriculum, pedagogy and assessment; teaching mathematical content; equity and diversity in the classroom; and professional and community engagement, it is an invaluable resource for all practising and pre-service mathematics teachers.

Understanding criminal behaviour: identifying psychological differences between domestically violent offenders and non-offenders

Numerous theories have been formulated in an attempt to explain the psychological differences between violent offenders and non-offenders. Constructs that have emerged as salient in such scholarship include anger expression, social problem solving, locus of control, attitudes toward women, impulsivity and temper. Although a considerable amount of sound research has been conducted into 'violent offending' per se, in general terms, research into family and domestic violence is yet to be as methodologically and theoretically rigorous. In an attempt to link these areas of work, and to identify the risk factors (or 'criminogenic needs') of specific sub-groups of male offenders, this research compared: (I) property offenders, (2) those who had been· 'violent against strangers', (3) those who had been 'violent against intimates' and (4) non-offenders. In an effort to address one of the shortcomings of prior research, potentially confounding variables such as age, education level cultural identity, and socio-economic status were controlled for in an effort to arrive at more meaningful representations of each offender group's specific psychological deficits and abundances. A number of differences were highlighted between the groups, but few of these remained after demographic
covariates were controlled for. This paper details the nature of these differences, while also proposing that future studies adopt a similar methodology.

Learners' perceptions about the relationship between music education and generic skills development : a case study within the Australian higher education sector

A major issue emerging from the research and debate concerning quality in higher education has been an emphasis on the value of the acquisition of generic skills by undergraduate students, as indicators of quality in education. Music educators have long recognised the contribution music makes to the general education of learners. Learning in and through music can present varied and complex means for the acquisition of generic life skills such as: problem solving, decision-making, critical thinking, oral and written communication and teamwork. This paper documents one particular course of action that was implemented within a university undergraduate primary teacher education program, to systematically gauge learner perceptions about generic skill development/enhancement before and after participation in the music component of the core arts education subject.

The graphic calculator as a thinking tool: perspectives from the classroom

For over a decade the graphic calculator has been promoted not only as a computational tool but also as a thinking tool — for example, as an aid to enhance conceptual understanding, as a problem-solving tool and as a means of enabling students to engage in meaningful investigations. However, research studies focusing on these aspects have shown mixed results and have mostly focused on graphs and functions. This paper reports on one aspect of a case study in a year 10 mathematics classroom — the role of the graphic calculator as a thinking tool. Data from observations of nine statistics lessons and interviews with the teacher and five students are analysed from three perspectives: the teacher’s intentions with respect to the use of the graphic calculator as a tool to promote conceptual understanding as opposed to procedural competence; the opportunities afforded during the lessons for student investigation; and students’ views of how the graphic calculator enhanced conceptual understanding. The results provide insights into ways in which students perceive the graphic calculator as promoting conceptual understanding, as well as some of the difficulties encountered in practice in a classroom.

Sharing and reuse of web developers experience

Development of commercial web systems is laborious, lengthy and costly. This is partly due to the fact that the methods of their development can hardly cope with the complexity of provided services. Such services may need to be distributed and collaborative, require sophisticated software architecture, be rich in form, content and interactivity, and have a wide range of potentially casual users. While web development methodologies are slowly emerging from research methodologies, their adoption is far from wide-spread. To improve this situation, the authors propose an approach based on the observed practices of professional web developers, who openly share and reuse their web development experience, while guarding their development workproducts. To this end, we suggest to enhance web development methods, by collecting problem-solving experience of web developers, packaging it into a reusable form, and providing a navigable decision structure assisting developers in identifying proven expert solutions suitable for a given problem context.

Employer requirements of economics graduates and the implications for undergraduate economics programs

In recent years there has been considerable debate about the general decline in the number of students undertaking bachelor degrees and majors in economics. The discussion has stemmed mainly from a supply-side perspective of the economics education market. The goal of this paper is to add another dimension to the debate and report the results of a survey of employers of economics graduates. Drawing on the extensive customer services literature it is argued that a market oriented, or demand-side analysis is also an important component in redressing low student enrolments and retention. A first step in adopting a market oriented approach is to determine the skills required of the economics graduates entering the jobs market. With the support of The Economics Society of Au~tralia, twenty-nine public and private sector employers were surveyed in 2002. The aim of the survey was to establish the demand for economics graduates with bachelor and honours degrees, the skills and knowledge required of these graduates, and the performance of such graduates. The study found that economic knowledge and skill were important to employers. However, the skills rated most important by employers were the more general or 'generic' skills of clear writing, data analysis, interpersonal skills and a practical problem-solving orientation. While graduates generally performed satisfactorily in relation to the economic skills required by employers, this was not the case for generic skills. The result of the survey findings have some significant implications for the content and teaching of undergraduate economics programs. This paper outlines these implications and also discusses areas for future research It is argued that such research should aim to utilize both the demand and supplyside perspectives with the development of more precise definitions and measurement of the economic skills required by the various stakeholders in the economics education market.

Teaching for life : generic capabilities that link university learning with workplace learning

Business schools are under increasing pressure to enhance the learning capability and employability of graduates. Business professional institutes and employer organizations are demanding more than the technical knowledge and skills required to perform discipline/professional specific tasks. They want graduates who can demonstrate capabilities in communication, teamwork, risk taking, decision making, problem solving, critical thinking, analytical reasoning, visioning and innovation, leadership, ethical practices, appreciation of diversity, and a commitment to social justice. Evidence in literature and reports (Karpin, 1995; Kirby, 2000; Commonwealth of Australia, 2002; Nelson, 2002) and in test data (McCowan & Richardson, 1998; Employer Survey, 1998; DETYA, 2000) shows that the employability gap7 is closed when graduates possess these generic capabilities. What is important, however, is the increasing research showing that the strategies used to develop generic capabilities lead to improved learning, both in university courses and in the workplace.

Simulation to practice: developing nursing skills in mental health: an Australian perspective

A variety of developments in nursing education in Australia including some innovative and exciting models, educational enterprises between education and industry, and evidence of developing strengths in research and professional alliances on a national level have been discussed recently. This paper presents Simulation to Practice as an example of an educational program that can maximise skill mastery for nurses in mental health fields as practised by Deakin University in Victoria, Australia. The program is multimodal and is under-pinned by a problem-solving approach and has an online presentation. The extension of nursing skills through this approach encourages nurses to take theoretical skills to practice during these scenarios which help student nurses to gain experience through simulated real life characters. These sessions, while challenging at the time, were highly valued by students and seen as a beneficial part of their learning as a beginning nurse and often instrumental in moving comprehensively trained students into mental health careers.

The usefulness of a science degree : the "lost voices" of science trained professionals

This paper reports a study of science graduates who are employed in positions outside their discipline specialisation. The research was designed to uncover the reasons for them choosing to study science at university, the competencies they utilise in their work and their lives, and how these relate to their undergraduate education in science. The study is seen as important in that already about one-half of science graduates are in such positions and it is argued that there is a need in scientific and technologically based societies to have a greater representation of such people in decision-making positions in government and industry. The directions for the science degree that can be drawn from the data gathered are congruent with those arising from other relevant studies. That is, attention should be paid to widely used skills, such as communication and problem-solving, and to developing an understanding of science within its social and ethical context. An argument is mounted for considering the way the science degree is presented to potential students and to the general public.

The impact of the financial costs of multiple sclerosis on quality of life

This study examined the financial costs of multiple sclerosis (MS) and the impact of financial strain on the subjective quality of life of people with MS and their families. Due to the lack of research in this area, a qualitative research design was employed. Interviews were conducted with 16 health professionals, 26 people with MS, and 11 family members of people who had MS. Adjusting to actual or threatened loss of income caused financial stress. These financial struggles led to a lower quality of life among respondents. Problem solving, coping, and positive reappraisal helped people to adjust to financial changes. Professionals focused on increased funding for services, whereas people with MS focused on improved income support. These findings highlight the need for professionals to consider the financial strain associated with this disease and the impact of this strain on the quality of life of individuals with MS and their families.

CHC students online : responses to course organisation

Previous research by the authors has shown that Confucian Heritage Students participating in online problem solving discussions show a high degree of message postings that are related to the organization of the course of study, rather than to its contents and intellectual challenges. The authors argue that this is consistent with the more broadly based research outcomes relating to the achieving strategy that is quite typically exhibited among CHC students. This interview based study explores the perceptions of CHC students as they engage with collaborative learning online, and shows that the concerns relate to matters to do with assessment, with the reliability and timeliness of group member inputs, and the possibilities of plagiarism.

Working and learning in vocational education and training in the knowledge era : final report of the professional development for the future project

This Report summarises the outcomes of the phases of the Professional
Development for the Future Project and presents the implications of this research for professional development of staff in Vocational Education and Training (VET), as they become knowledge workers.

These shifts are occurring within the knowledge era. Distinguishing features of this era are summarised into four broad areas:
- the importance and value placed on knowledge in organisations
- the time span of discretion
- the complexity of relationships, and
- the ubiquitous nature of information and communication technology.

It is within this context that work is currently performed, and understanding this context provides the foundation for considering new capabilities required in the knowledge era.
Key capabilities required of knowledge workers to work effectively in the
knowledge era were drawn together from an analysis of the theoretical literature and the results of interviews with knowledge workers. The core capabilities identified include:
- adaptive problem solving – becoming designers as well as problem -
solvers
- rapid knowledge gathering and sharing with others
- discriminating between relevant and irrelevant information, and
- understanding and working effectively with the organisation’s culture.

Knowledge era characteristics and knowledge worker capabilities have been mapped to each other illustrating conceptual linkages between these two areas.

Professional development themes drawn from interviews with knowledge
workers are presented. While global trends in knowledge work have been well documented, the impact of these trends on the capabilities of workers, and the ways in which knowledge workers develop these capabilities is less well understood. Their learning methods challenge our current thinking in relation to the ways in which workers acquire skills and knowledge. Some of the professional development methods include seeking exposure to new ideas from a wide variety of sources, embracing intense learning opportunities, and using relationships to increase knowledge.

‘Thought pieces’ (see p17 ff) commissioned for this Project, as well as
subsequent interviews with the authors, provided further insights into the
professional development of knowledge workers. The implications of these insights are an extension of earlier themes and emphasise:
- the emergent nature of knowledge work
- the importance of relationships that facilitate knowledge sharing
- coherent conversations and dialogue
- collaborative work and generosity.

A key insight is the shift from thinking about knowledge work in terms of
borrowed knowledge to an emphasis on generated knowledge within a context.

Data from focus groups of the Project provide further insights for knowledge worker professional development. These augment the perspectives of the earlier data analysis but also add greater emphasis to:
- the clear and direct relationship between professional development and
work and career aspirations of knowledge workers,
- the relationship of professional development to the organisational
mission, and
- the issues of managing and leading knowledge workers and their
development.

As part of this analysis the defining features of organisational life in VET were reviewed in relation to effective professional development of knowledge workers.

The final section of the Report revisits the core dimensions of the Project.
Concise commentaries on working and learning in the knowledge era,
professional development in the knowledge era, and leadership and
management in the knowledge era are presented.

The Report concludes with a discussion of the enablers of professional
development for knowledge workers in VET. This discussion is introduced by a re-statement of the VET sector’s positioning in the knowledge era and the consequences of this for VET managers an d staff in terms of complexity, uncertainty and diminished prospects for accurate predictiveness. The enablers comprised:
- integration of information technology into socio -technical systems
- greater understanding of the organisation from within
- connecting staff to the organisation’s fundamental identity
- connecting to the work and career trajectories of workers
- establishing work structures which integrate the use of professional
development resources with knowledge work
- providing workers with the autonomy to design their own professional
development activities
- building professional development into the iterative nature of knowledge
work, and
- creating organisational contexts that value intuitive thinking and working.

Professional development needs to be thou ght of in a much broader context in the knowledge era. What each VET staff member knows and shares will become increasingly central to their work, and in that sense all VET workers require capabilities for knowledge work. This report accurately describes t he VET context, the capabilities required, and the organisational enablers that will promote ‘knowing’ and thus embed a new style of professional development within VET.

The graphic calculator as a thinking tool : perspectives from the classroom

For over a decade, the graphic calculator has been promoted not only as a computational tool, but also as a thinking tool - for example, as an aid to enhance conceptual understanding, as a problem-solving tool and as a means of enabling students to engage in meaningful investigations. However, research studies focusing on these aspects have shown mixed results and have mostly focused on graphs and functions.

This paper reports on one aspect of a case study in a year 10 mathematics classroom - the role of the graphic calculator as a thinking tool. Data from observations of nine statistics lessons and interviews with the teacher and five students, are analysed from three perspective's: the teacher's intentions with respect to the use of the graphic calculator as a tool to promote conceptual understanding as opposed to procedural competence; the opportunities afforded during the lessons for student investigation; and students' views of how the graphic calculator enhanced conceptual understanding.

The results provide insights into ways in which students perceive the graphic calculator as promoting conceptual understanding, as well as some of the difficulties encountered in practice in a classroom where the teacher clearly intends to use the graphic calculator as a thinking tool.

Towards a framework for exploring children's analytical thinking and creativity in technology

Technology education provides children with opportunities to be creative as they engage in problem solving and make products that address human needs. When thinking creatively, children generate new ideas through remote associations and brainstorming and this type of thinking is enhanced when attention is allowed to wander in a relaxed and uncompetitive environment. Research shows that the two mental states (generative and nongenerative/analytical) cannot exist simultaneously (Howard-Jones 2002). It follows that at some point in the technological process a child’s generative mental state needs to give way to a nongenerative, analytical state so that the child can focus on analysing information. This research project aims to investigate the impact of analytical thinking on creativity in the context of technology education in young children.

The problem of failing to provide culturally and linguistically appropriate healthcare

Analysing health policy explores Australian health policy using a novel, problem-orientated approach. It shows the problem-solving techniques that are used when developing policy and demonstrates the skills of analysis and decision making.Introductory chapters explain the problem-orientated approach to health policy development and introduce the policy making process. Case studies then explore developments in health policy in both priority and topical areas. Chapters illustrate how policy-makers respond to perennial and emerging policy problems and demonstrate problem-solving approaches to the conception, development and implementation of health policy.