Getting skilled for education, training and employment : Indigenous Cultural Knowledges and mainstream knowledges of mathematics

This abstract is a preliminary discussion of the importance of blending of Indigenous cultural knowledges with mainstream knowledges of mathematics for supporting Indigenous young people. This import is emphasised in the documents Preparing the Ground for Partnership (Priest, 2005), The Indigenous Education Strategic Directions 2008–2011 (Department of Education, Training and the Arts, 2007) and the National Goals for Indigenous Education (Department of Education, Employment and Work Relations, 2008). These documents highlight the contextualising of literacy and numeracy to students’ community and culture (see Priest, 2005). Here, Community describes “a culture that is oriented primarily towards the needs of the group. Martin Nakata (2007) describes contextualising to culture as about that which already exists, that is, Torres Strait Islander community, cultural context and home languages (Nakata, 2007, p. 2). Continuing, Ezeife (2002) cites Hollins (1996) in stating that Indigenous people belong to “high-context culture groups” (p. 185). That is, “high-context cultures are characterized by a holistic (top-down) approach to information processing in which meaning is “extracted” from the environment and the situation. Low-context cultures use a linear, sequential building block (bottom-up) approach to information processing in which meaning is constructed” (p.185). In this regard, students who use holistic thought processing are more likely to be disadvantaged in mainstream mathematics classrooms. This is because Westernised mathematics is presented as broken into parts with limited connections made between concepts and with the students’ culture. It potentially conflicts with how they learn. If this is to change the curriculum needs to be made more culture-sensitive and community orientated so that students know and understand what they are learning and for what purposes.

Integrating engineering education in the middle school mathematics curriculum

Many nations are experiencing a decline in the number of graduating engineers, an overall poor preparedness for engineering studies in tertiary institutions, and a lack of diversity in the field. Given the increasing importance of mathematics, science, engineering, and technology in our world, it is imperative that we foster an interest and drive to participate in engineering from an early age. This discuission paper argues for the intergration of engineering education within the elementary and middle school mathematics curricula. In doing so, we offer a definition of engineering education and address its core goals; consider some perceptions of engineering and engineering education held by teachers and students; and offer one approach to promoting engineering education within the elementary and middle school mathematics curriculum, namely through mathematical modeling.

Students’ perceptions of a blended web-based learning environment

The enhanced accessibility, affordability and capability of the Internet has created enormous possibilities in terms of designing, developing and implementing innovative teaching methods in the classroom. As existing pedagogies are revamped and new ones are added, there is a need to assess the effectiveness of these approaches from the students’ perspective. For more than three decades, proven qualitative and quantitative research methods associated with learning environments research have yielded productive results for educators. This article presents the findings of a study in which Getsmart, a teacher-designed website, was blended into science and physics lessons at an Australian high school. Students’ perceptions of this environment were investigated, together with differences in the perceptions of students in junior and senior years of schooling. The article also explores the impact of teachers in such an environment. The investigation undertaken in this study also gave an indication of how effective Getsmart was as a teaching model in such environments.

Integrating Engineering Experiences within the Elementary Mathematics Curriculum

Engineering education for elementary school students is a new and increasingly important domain of research by mathematics, science, technology, and engineering educators. Recent research has raised questions about the context of engineering problems that are meaningful, engaging, and inspiring for young students. In the present study an environmental engineering activity was implemented in two classes of 11-year-old students in Cyprus. The problem required students to use the data to develop a procedure for selecting among alternative countries from which to buy water. Students created a range of models that adequately solved the problem although not all models took into account all of the data provided. The models varied in the number of problem factors taken into consideration and also in the different approaches adopted in dealing with the problem factors. At least two groups of students integrated into their models the environmental aspect of the problem (energy consumption, water pollution) and further refined their models. Results provide evidence that engineering model-eliciting activities can be successfully integrated in the elementary mathematics curriculum. These activities provide rich opportunities for students to deal with engineering contexts and to apply their learning in mathematics and science to solving real-world engineering problems.

Future directions and perspectives for problem solving research and curriculum development

Since the 1960s, numerous studies on problem solving have revealed the complexity of the domain and the difficulty in translating research findings into practice. The literature suggests that the impact of problem solving research on the mathematics curriculum has been limited. Furthermore, our accumulation of knowledge on the teaching of problem solving is lagging. In this first discussion paper we initially present a sketch of 50 years of research on mathematical problem solving. We then consider some factors that have held back problem solving research over the past decades and offer some directions for how we might advance the field. We stress the urgent need to take into account the nature of problem solving in various arenas of today’s world and to accordingly modernize our perspectives on the teaching and learning of problem solving and of mathematical content through problem solving. Substantive theory development is also long overdue—we show how new perspectives on the development of problem solving expertise can contribute to theory development in guiding the design of worthwhile learning activities. In particular, we explore a models and modeling perspective as an alternative to existing views on problem solving.

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).

Seeing is understanding : the effect of visualisation in understanding programming concepts

How and why visualisations support learning was the subject of this qualitative instrumental collective case study. Five computer programming languages (PHP, Visual Basic, Alice, GameMaker, and RoboLab) supporting differing degrees of visualisation were used as cases to explore the effectiveness of software visualisation to develop fundamental computer programming concepts (sequence, iteration, selection, and modularity). Cognitive theories of visual and auditory processing, cognitive load, and mental models provided a framework in which student cognitive development was tracked and measured by thirty-one 15-17 year old students drawn from a Queensland metropolitan secondary private girls’ school, as active participants in the research. Seventeen findings in three sections increase our understanding of the effects of visualisation on the learning process. The study extended the use of mental model theory to track the learning process, and demonstrated application of student research based metacognitive analysis on individual and peer cognitive development as a means to support research and as an approach to teaching. The findings also forward an explanation for failures in previous software visualisation studies, in particular the study has demonstrated that for the cases examined, where complex concepts are being developed, the mixing of auditory (or text) and visual elements can result in excessive cognitive load and impede learning. This finding provides a framework for selecting the most appropriate instructional programming language based on the cognitive complexity of the concepts under study.

Integrating engineering education within the elementary and middle school mathematics curriculum

Many nations are experiencing a decline in the number of graduating engineers, an overall poor preparedness for engineering studies in tertiary institutions, and a lack of diversity in the field. Given the increasing importance of mathematics, science, engineering, and technology in our world, it is imperative that we foster an interest and drive to participate in engineering from an early age. This discussion paper argues for the integration of engineering education within the elementary and middle school mathematics curricula. In doing so, we offer a definition of engineering education and address its core goals; consider some perceptions of engineering and engineering education held by teachers and students; and offer one approach to promoting engineering education within the elementary and middle school mathematics curriculum, namely through mathematical modeling.

Peace education

There are various understandings of peace education. What might be called maximalist peace education refers to educating students towards personal fulfilment and the creation of a just and co-operative society. What might be called minimalist peace education refers to educating students to avoid war, militarism and arms races. Peace education is only now being formally accepted as an integral part of educational endeavour, and an important part of this acceptance is recognition in international pronouncements and instruments, emphasizing the importance of a culture of peace and the right to peace. In terms of methodology, peace education includes curriculum, structures and process, and personal leadership. This last element is clearly the most challenging of all.

Transfer of learning across the globe : pre-service teachers taking the initiative

A continuing challenge for pre-service teacher education is the learning transfer between the university based components and the practical school based components of their training. It is not clear how easily pre-service teachers can transfer university learnings into ‘in school’ practice. Similarly, it is not clear how easily knowledge learned in the school context can be disembedded from this particular context and understood more generally by the pre-service teacher. This paper examines the effect of a community of practice formed specifically to explore learning transfer via collaboration and professional enquiry, in ‘real time’, across the globe. “Activity Theory” (Engestrom, 1999) provided the theoretical framework through which the cognitive, physical and social processes involved could be understood. For the study, three activity systems formed community of practice network. The first activity system involved pre-service teachers at a large university in Queensland, Australia. The second activity system was introduced by the pre-service teachers and involved Year 12 students and teachers at a private secondary school also in Queensland, Australia. The third activity system involved university staff engineers at a large university in Pennsylvania, USA. The common object among the three activity systems was to explore the principles and applications of nanotechnology. The participants in the two Queensland activity systems, controlled laboratory equipment (a high powered Atomic Force Microscope – CPII) in Pennsylvania, USA, with the aim of investigating surface topography and the properties of nano particles. The pre-service teachers were to develop their remote ‘real time’ experience into school classroom tasks, implement these tasks, and later report their findings to other pre-service teachers in the university activity system. As an extension to the project, the pre-service teachers were invited to co-author papers relating to the project. Data were collected from (a) reflective journals; (b) participant field notes – a pre-service teacher initiative; (c) surveys – a pre-service teacher initiative; (d) lesson reflections and digital recordings – a pre-service teacher initiative; and (e) interviews with participants. The findings are reported in terms of the major themes: boundary crossing, the philosophy of teaching, and professional relationships The findings have implications for teacher education. The researchers feel that deliberate planning for networking between activity systems may well be a solution to the apparent theory/practice gap. Proximity of activity systems need not be a hindering issue.

Biotechnology education : topics of interest to students and teachers

This paper presents the findings of a survey that investigates the biotechnology topics of interest according to students and teachers for inclusion in biology lessons and reports on the similarities and differences in teachers’ and students’ biotechnology topics of interest. The study is of significance as biotechnology has been identified as a key area of technological and economic importance worldwide yet there is scant literature relating to teachers’ and students’ interests concerning biotechnology education topics. 500 students and their 15 teachers completed the survey. Interviews were conducted with 3 teachers and 60 students. Responses indicate there is a mismatch in the interests of students and teachers, and what they perceive as being possible topics for inclusion in biology and biotechnology lessons. Where teachers are provided with the freedom to design and assess their own units of work, this mismatch of interests causes problems. The study found students withdrawing from biology courses in post compulsory settings due to lack of interest, and perceived lack of relevance of the course. It is possible that this lack of agreement on topics of interest is a factor in the world wide decline of enrolments in the sciences.

In Pursuit of Excellence : A Policy Driven Systemic Initiative to Embed Gifted Education

Embedding gifted education practices requires major professional development strategies supported by transparent, credible and enforceable policy. This paper describes an analysis of a state-wide initiative involving the establishment of a series of schools tasked to develop and disseminate gifted education principles. The authors have been involved with this initiative at a number of levels over a ten-year period. Their involvement culminated in a commissioned review of the program. Extensive qualitative data were purposively collected from all stakeholders and the effectiveness of the initiative is examined from a theoretical framework of policy development and excellence. The findings summarised in this proposal, indicate the achievement of excellence at a systemic level was constrained by lack of vision, leadership and commitment to long term achievements of excellence. At a local level evidence exists that excellence can be manifested when there is synchronicity of vision, purpose, decisions, and actions.

Between flagged borders, across gendered lands : the voiceless female space in contemporary representations of Australian beach

International and national representations of the beach perpetuate normative female concepts by maintaining dominant masculine myths, such as that of the heroic lifesaver and tanned sunbaker. Female experiences on the beach are traditionally associated with rhetorics of danger and peril, contrasted to the welcomed and protective gaze of the beach male. Conventional understandings of the gaze promote male surveillance of women, and although some resistance exists, the beach primarily remains a place to observe the female form. This article attempts to explore currents of resistance at the beach through a self-reflexive examination of Schoolies. Although the event is fixed within patriarchal codes and structures, small eddies of resistance exist amongst female participants in light of increasing awareness of masculine hegemony. The Australian beach remains a contested site of multiple constructs of gender and national identity. This article reveals the changing tides of resistance.