Generalising unitary time evolution

In this third Quantum Interaction (QI) meeting it is time to examine our failures. One of the weakest elements of QI as a field, arises in its continuing lack of models displaying proper evolutionary dynamics. This paper presents an overview of the modern generalised approach to the derivation of time evolution equations in physics, showing how the notion of symmetry is essential to the extraction of operators in quantum theory. The form that symmetry might take in non-physical models is explored, with a number of viable avenues identified.

Report on Innovation Working Group : The Mathematics Education into the 21st Century Project. Dresden, Saxony

This document reports on the Innovations Working Group that met at the 10th International Conference “Models in Developing Mathematics Education” from the 11-17th September 2009 in Dresden, Saxony. It briefly describes the over arching and consistent themes that emerged from the numerous papers presented. The authors and titles of each of the papers presented will be listed in Table 2.

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.

Property Education : an evaluation of how well undergraduate property students are prepared for commencing their careers

The evolution of property education to adapt to the changing business environment requires changes to course content, method of delivery and assessment. Many universities have a special interest in understanding how the students transition in and transition out of the property programs. The impact of the first year student experience is often easier to assess through students’ progression in the course and performance in their intermediate and advanced units. However, the students’ success in transitioning from university student to property professional is often more difficult to determine. In an environment where many property students commence their professional careers while still completing their undergraduate property qualification, a survey of current final year students was undertaken to identify the students’ perception of their level of preparedness for entry into the professional world. This study has also been informed by feedback received from and informal discussions held with industry representative bodies, alumni and senior members of professional organisations. The QUT UD40 Bachelor of Urban Development, Property Economics course has been designed to achieve graduate capabilities in core technical skills and generic professional skills which are required by property professionals. The results of this study were that some units in the program were perceived to provide direct preparation for students commencing their professional careers whilst the impact of other units was less tangible. Valuable feedback received during the study included an assessment of the relevance of many multi-disciplinary units, the appropriateness of the programming of units within the course and the appropriateness of repetition of content during the course. The further research question arises as to how universities can better assist students in the transition to the professional environment when frequently this occurs prior to completion of the property course.

Use of Property Rights Registers for sustainability : a Queensland Case Study

Sustainable natural resource management has been a concern of governments and legislators for the last 20 years. A key aspect of an effective management framework is easy access to information about rights and obligations in land and the natural resources in, on or below the land. Information about legal interests in land is managed through a Torrens register in each Australian State. These registers are primarily focused on the registration of a narrow group of legal interests in the land, and rights or obligations that fall outside of these recognised interests are not capable of registration. Practices have developed however for the recording of property rights in natural resources either on separate registers, with no link to the Torrens register or on a separate register managed by the Registrar of Titles but having no legal effect on the title to the land. This paper will discuss and analyse the various ways in which registers have been used in Queensland to provide access to information about rights in natural resources, and provide examples as to how this approach has impacted on the desire for sustainable management. It will also provide a critique of the Queensland model, and call for reform of the present system.

A holistic approach to the support and engagement of first year students : a retention strategy

Institutions should enact holistic approaches that address students’ personal, social and academic engagement in the early weeks of first year to facilitate retention (Nelson, Kift & Clarke, 2008). This holistic approach is central to the FYE program at Queensland University of Technology (QUT), which was established to maximise learning engagement and hence positively influence the retention of commencing students. The program aims to • engage students in their learning through an intentionally designed and enacted curriculum (Kift, 2008) • facilitate timely access to life and learning support • promote a sense of belonging to the discipline, cohort and profession. The FYE program’s aims are achieved by strategic alliances between academic and professional staff across the institution.

A holistic approach to the support and engagement of first year students : a retention strategy.

Institutions should enact holistic approaches that address students’ personal, social and academic engagement in the early weeks of first year to facilitate retention (Nelson, Kift & Clarke, 2008). This holistic approach is central to the FYE program at Queensland University of Technology (QUT), which was established to maximise learning engagement and hence positively influence the retention of commencing students.

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.

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.

Introducing Engineering Education in the Middle School

This paper first describes a new three-year, longitudinal project that is implementing engineering education in three middle schools in Australia (grade levels 7-9). This important domain is untapped in Australia. Hence, as a starting point, we conducted a context analysis to help situate engineering education in a school system. We report on this analysis with respect to findings from one of two literature-based surveys that gathered middle-school student responses in mathematics (n=172) and science (n=166) towards understanding their dispositions for engineering education. ANOVA indicated gender differences for 3 out of 23 items in both mathematics and science. In addition, the majority of students agreed or strongly agreed with 17 of the 23 survey items, however, there were some differences between mathematics and science. We conclude the paper with some recommendations for establishing engineering education in schools, including the development of partnerships among engineering and education faculties, school systems, and industry to develop contemporary engineering resources to support school-level mathematics, science, and technology.

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).

How well are Australian children doing in the first year of school?

Background: The transition to school is a sensitive period for children in relation to school success. In the early school years, children need to develop positive attitudes to school and have experiences that promote academic, behavioural and social competence. When children begin school there are higher expectations of responsibility and independence and in the year one class, there are more explicit academic goals for literacy and numeracy and more formal instruction. Most importantly, children’s early attitudes to learning and learning styles have an impact on later educational outcomes. Method: Data were drawn from The Longitudinal Study of Australian Children (LSAC). LSAC is a cross-sequential cohort study funded by the Australian Government. In these analyses, Wave 2 (2006) data for 2499 children in the Kindergarten Cohort were used. Children, at Wave 2, were in the first year of formal school. They had a mean age of 6.9 years (SD= 0.26). Measures included a 6-item measure of Approaches to Learning (task persistence, independence) and the Academic Rating Scales for language and literacy and mathematical thinking. Teachers rated their relationships with children on the short form of the STRS. Results: Girls were rated by their teachers as doing better than boys on Language and literacy, Approaches to learning; and they had a better relationship with their teacher. Children from an Aboriginal or Torres Strait Island (ATSI) background were rated as doing less well on Language and Literacy and Mathematical thinking and on their Approaches to learning. Children from high Socio Economic Position families are doing better on teacher rated Language and Literacy, Mathematical thinking, Approaches to learning and they had a better relationship with their teacher. Conclusions: Findings highlight the importance of key demographic variables in understanding children’s early school success.

Public awareness of ‘green’ residential property – an empirical survey based on data from New Zealand and Germany

Over the last few years more stringent environmental laws (e.g. the German “Energie¬ein-sparverordnung ENEV” - Energy Performance of Buildings Directive) and soaring energy prices has increased the need for the real estate industry to react and participate in overall energy reduction through efficient house construction and design, as well as upgrading the existing housing stock to be more energy efficient. Therefore the Property Economics Group at Queensland University of Technology in Australia and Nuertingen-Geislingen University in Germany are carrying out research in relation to sustainable housing construction and public awareness of “green” residential property. Part of this research is to gain an understanding of the level of knowledge and importance of these issues to the house buyer and to determine the importance of sustainable housing to the general public. The paper compares data from two different empirical studies; one of studies analyzes the situation in New Zealand, the other is focused on Germany.

Communicating ecologically positive development

It is difficult to present a paradigm shift from resource efficient to ecologically sustainable design, when many students have not yet thought about what sustainability is, let alone what it implies for the design of the built environment ‘Positive Development’ requires students to think beyond green building to something that does not yet exist. The concept of ecologically positive development suggests a product, building, system or urban area that leaves the ecological base and public estate better off than if no development had occurred. For some years now, I have experimented with communicating this paradigm shift in design to students and professionals ‐ with mixed results. This paper discusses some of the challenges, failures and successes in shifting design studio work from environmentally‐sensitive to eco-positive. The framework underlying this exploration is action research. Conclusions about the success of the strategies used for overcoming perceptual barriers to new typologies of architecture are drawn from recent student feedback. The talk will show examples of student projects that attempt eco-positive development projects.