Investigating functional thinking in the elementary classroom : foundations of early algebraic reasoning

This paper examines the development of student functional thinking during a teaching experiment that was conducted in two classrooms with a total of 45 children whose average age was nine years and six months. The teaching comprised four lessons taught by a researcher, with a second researcher and classroom teacher acting as participant observers. These lessons were designed to enable students to build mental representations in order to explore the use of function tables by focusing on the relationship between input and output numbers with the intention of extracting the algebraic nature of the arithmetic involved. All lessons were videotaped. The results indicate that elementary students are not only capable of developing functional thinking but also of communicating their thinking both verbally and symbolically.

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.

Theories of Mathematics Education : Seeking New Frontiers

This inaugural book in the new series Advances in Mathematics Education is the most up to date, comprehensive and avant garde treatment of Theories of Mathematics Education which use two highly acclaimed ZDM special issues on theories of mathematics education (issue 6/2005 and issue 1/2006), as a point of departure. Historically grounded in the Theories of Mathematics Education (TME group) revived by the book editors at the 29th Annual PME meeting in Melbourne and using the unique style of preface-chapter-commentary, this volume consist of contributions from leading thinkers in mathematics education who have worked on theory building. This book is as much summative and synthetic as well as forward-looking by highlighting theories from psychology, philosophy and social sciences that continue to influence theory building. In addition a significant portion of the book includes newer developments in areas within mathematics education such as complexity theory, neurosciences, modeling, critical theory, feminist theory, social justice theory and networking theories. The 19 parts, 17 prefaces and 23 commentaries synergize the efforts of over 50 contributing authors scattered across the globe that are active in the ongoing work on theory development in mathematics education.

Surveying theories and philosophies of mathematics education

Any theory of thinking or teaching or learning rests on an underlying philosophy of knowledge. Mathematics education is situated at the nexus of two fields of inquiry, namely mathematics and education. However, numerous other disciplines interact with these two fields which compound the complexity of developing theories that define mathematics education. We first address the issue of clarifying a philosophy of mathematics education before attempting to answer whether theories of mathematics education are constructible? In doing so we draw on the foundational writings of Lincoln and Guba (1994), in which they clearly posit that any discipline within education, in our case mathematics education, needs to clarify for itself the following questions: (1) What is reality? Or what is the nature of the world around us? (2) How do we go about knowing the world around us? [the methodological question, which presents possibilities to various disciplines to develop methodological paradigms] and, (3) How can we be certain in the “truth” of what we know? [the epistemological question]

Foundations of technology development, innovation and competitiveness in the globalised knowledge economy

With the growth of high-technology industries and knowledge intensive services, the pursuit of industrial competitiveness has progressed from a broad concern with the processes of industrialisation to a more focused analysis of the factors explaining cross-national variation in the level of participation in knowledge industries. From an examination of cross-national data, the paper develops the proposition that particular elements of the domestic science, technology and industry infrastructure—such as the stock of knowledge and competence in the economy, the capacity for learning and generation of new ideas and the capacity to commercialise new ideas—vary cross-nationally and are related to the level of participation of a nation in knowledge intensive activities. Existing understandings of the role of the state in promoting industrial competitiveness might be expanded to incorporate an analysis of the contribution of the state through the building of competencies in science, technology and industry. Keywords: Knowledge; economy; comparative public policy; innovation; science and technology policy

Students' perceptions of the relevance of mathematics in engineering

In this paper, we report on the findings of an exploratory study into the experience of students as they learn first year engineering mathematics. Here we define engineering as the application of mathematics and sciences to the building and design of projects for the use of society (Kirschenman and Brenner 2010)d. Qualitative and quantitative data on students' views of the relevance of their mathematics study to their engineering studies and future careers in engineering was collected. The students described using a range of mathematics techniques (mathematics skills developed, mathematics concepts applied to engineering and skills developed relevant for engineering) for various usages (as a subject of study, a tool for other subjects or a tool for real world problems). We found a number of themes relating to the design of mathematics engineering curriculum emerged from the data. These included the relevance of mathematics within different engineering majors, the relevance of mathematics to future studies, the relevance of learning mathematical rigour, and the effectiveness of problem solving tasks in conveying the relevance of mathematics more effectively than other forms of assessment. We make recommendations for the design of engineering mathematics curriculum based on our findings.

Contributions of knowledge-based foundations of universities in knowledge city formation : a Malaysian case study

Purpose – In the 21st Century, as knowledge, technology and education are widely accepted to play key roles in the local economic development, the importance of making space and place for knowledge production is, therefore, on the rise resulting many city administrations and urban policy-makers worldwide restructuring their cities to become highly competitive and creative. Consequently, this has led to a new type of city form, knowledge city, and a new approach in their development, knowledge-based urban development. In this context, knowledge-based foundations of universities are regarded as one of the key elements for knowledge-based urban development and knowledge city formation due to their ability to provide a strong platform for knowledge generation, marketing and transfer. This paper aims to investigate the role and importance of universities and their knowledge-based foundations in the context of developing countries, particularly in Malaysia, in building prosperous knowledge cities of the era of the knowledge economy. Design/Methodology/Approach – The main methodological techniques employed in this research includes: a thorough review of the literature on the role of universities in spatial and socio-economic development of cities; a best practice analysis and policy review of urban and regional development policies targeting to use of university clusters in leveraging knowledge-based development, and; a case study in Malaysia with a review of various policy documents and strategic plans of the local universities and local and state authorities, interviews with key actors, and a trend analysis of local socio-economic and spatial changes. Originality/Value – This paper reports the findings of a pioneering research on examining the role and impact of universities and their knowledge-based foundations, in the context of Malaysia, in building knowledge cities of the era of the knowledge economy. By undertaking a case study investigation in Bandar Seri Iskandar, which is a newly emerging Malaysian knowledge city, located in Perak, Malaysia, the paper sheds light on an important issue of the 21st Century of how universities contribute to the knowledge-based development of cities. Practical Implications – Universities with their rich knowledge-based foundations are increasingly being recognised as knowledge hubs, exercising a strong influence in the intellectual vitality of the city where they are embedded. This paper reveals that universities, in joint action with business and society at large, are necessary prerequisites for constructing and maintaining knowledge societies and, therefore, building prosperous knowledge cities. In light of the literature and case findings, the paper sheds light on the contribution of knowledge-based foundations of universities in knowledge city formation and provides generic recommendations for cities and regions seeking knowledge city transformation.

Foundations of International Climate Law : Objectives, principles and methods

This chapter explores the objectives, principle and methods of climate law. The United Nations Framework Convention on Climate Change (UNFCCC) lays the foundations of the international regime by setting out its ultimate objectives in Article 2, the key principles in Article 3, and the methods of the regime in Article 4. The ultimate objective of the regime – to avoid dangerous anthropogenic interference – is examined and assessments of the Intergovernmental Panel on Climate Change (IPCC) are considered when seeking to understand the definition of this concept. The international environmental principles of: state sovereignty and responsibility, preventative action, cooperation, sustainable development, precaution, polluter pays and common but differentiated responsibility are then examined and their incorporation within the international climate regime instruments evaluated. This is followed by an examination of the methods used by the mitigation and adaptation regimes in seeking to achieve the objective of the UNFCCC. Methods of the mitigation regime include: domestic implementation of policies, setting of standards and targets and allocation of rights, use of flexibility mechanisms, and reporting. While it is noted that methods of the adaptation regime are still evolving, the latter includes measures such as impact assessments, national adaptation plans and the provision of funding.

Assessing the potential of mathematics textbooks to promote deep learning

Curriculum documents for mathematics emphasise the importance of promoting depth of knowledge rather than shallow coverage of the curriculum. In this paper, we report on a study that explored the analysis of junior secondary mathematics textbooks to assess their potential to assist in teaching and learning aimed at building and applying deep mathematical knowledge. The method of analysis involved the establishment of a set of specific curriculum goals and associated indicators, based on research into the teaching and learning of a particular field within the mathematics curriculum, namely proportion and proportional reasoning. Topic selection was due to its pervasive nature throughout the school mathematics curriculum at this level. As a result of this study, it was found that the five textbook series examined provided limited support for the development of multiplicative structures required for proportional reasoning, and hence would not serve well the development of deep learning of mathematics. The study demonstrated a method that could be applied to the analysis of junior secondary mathematics in many parts of the world.