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).

Channel blurring and consumer expectations : evidence in Chile

An important trend in Chilean retailing industry is the increase in channel blurring. This investigation attempts to identify the relevant store attributes for different retail formats (grocery, department store, drug store, and home improvement). Do consumer store attribute saliency vary for different retail formats? Interviews identified twelve salient store attributes for the different retail formats. Survey results showed differences in store attribute saliencies for consumers when shopping at different formats. Seven of the twelve variables showed significant differences across formats. However, two attributes were relatively important for all four retail formats: product quality and responsiveness of employees.

Informational city

Many cities worldwide face the prospect of major transformation as the world moves towards a global information order. In this new era, urban economies are being radically altered by dynamic processes of economic and spatial restructuring. The result is the creation of ‘informational cities’ or its new and more popular name, ‘knowledge cities’. For the last two centuries, social production had been primarily understood and shaped by neo-classical economic thought that recognized only three factors of production: land, labor and capital. Knowledge, education, and intellectual capacity were secondary, if not incidental, factors. Human capital was assumed to be either embedded in labor or just one of numerous categories of capital. In the last decades, it has become apparent that knowledge is sufficiently important to deserve recognition as a fourth factor of production. Knowledge and information and the social and technological settings for their production and communication are now seen as keys to development and economic prosperity. The rise of knowledge-based opportunity has, in many cases, been accompanied by a concomitant decline in traditional industrial activity. The replacement of physical commodity production by more abstract forms of production (e.g. information, ideas, and knowledge) has, however paradoxically, reinforced the importance of central places and led to the formation of knowledge cities. Knowledge is produced, marketed and exchanged mainly in cities. Therefore, knowledge cities aim to assist decision-makers in making their cities compatible with the knowledge economy and thus able to compete with other cities. Knowledge cities enable their citizens to foster knowledge creation, knowledge exchange and innovation. They also encourage the continuous creation, sharing, evaluation, renewal and update of knowledge. To compete nationally and internationally, cities need knowledge infrastructures (e.g. universities, research and development institutes); a concentration of well-educated people; technological, mainly electronic, infrastructure; and connections to the global economy (e.g. international companies and finance institutions for trade and investment). Moreover, they must possess the people and things necessary for the production of knowledge and, as importantly, function as breeding grounds for talent and innovation. The economy of a knowledge city creates high value-added products using research, technology, and brainpower. Private and the public sectors value knowledge, spend money on its discovery and dissemination and, ultimately, harness it to create goods and services. Although many cities call themselves knowledge cities, currently, only a few cities around the world (e.g., Barcelona, Delft, Dublin, Montreal, Munich, and Stockholm) have earned that label. Many other cities aspire to the status of knowledge city through urban development programs that target knowledge-based urban development. Examples include Copenhagen, Dubai, Manchester, Melbourne, Monterrey, Singapore, and Shanghai. Knowledge-Based Urban Development To date, the development of most knowledge cities has proceeded organically as a dependent and derivative effect of global market forces. Urban and regional planning has responded slowly, and sometimes not at all, to the challenges and the opportunities of the knowledge city. That is changing, however. Knowledge-based urban development potentially brings both economic prosperity and a sustainable socio-spatial order. Its goal is to produce and circulate abstract work. The globalization of the world in the last decades of the twentieth century was a dialectical process. On one hand, as the tyranny of distance was eroded, economic networks of production and consumption were constituted at a global scale. At the same time, spatial proximity remained as important as ever, if not more so, for knowledge-based urban development. Mediated by information and communication technology, personal contact, and the medium of tacit knowledge, organizational and institutional interactions are still closely associated with spatial proximity. The clustering of knowledge production is essential for fostering innovation and wealth creation. The social benefits of knowledge-based urban development extend beyond aggregate economic growth. On the one hand is the possibility of a particularly resilient form of urban development secured in a network of connections anchored at local, national, and global coordinates. On the other hand, quality of place and life, defined by the level of public service (e.g. health and education) and by the conservation and development of the cultural, aesthetic and ecological values give cities their character and attract or repel the creative class of knowledge workers, is a prerequisite for successful knowledge-based urban development. The goal is a secure economy in a human setting: in short, smart growth or sustainable urban development.

Knowledge-based development of cities : a myth or reality?

Urban development in the 21st decade of the 21st century has faced many challenges ranging from rapid to shrinking urbanisation, from emerging knowledge economy to global division of labour and from globalisation to climate change. Along with with these challenges new concepts, such as essentialism, environmentalism and dematerialism, are emerged and started to influence the way urban development plans are prepared and visions for the development of cities are made. Beyond this, scholars, practitioners and decision-makers have also started to discuss the need for an new urban planning and development approach in order to achieve a development that is sustainable and knowledge-based. Limited successful examples of alternative planning and development approaches showcased potentials of moving towards a new plan-making mindset in the era of knowledge economy. This paper presents a new urban planning and development approach that is taking application ground in many parts of the globe, namely knowledge-based urban development. After providing the theoretical foundation and conceptual framework of knowledge-based urban development the paper discusses whether knowledge-based development of cities is a myth or a reality.

Flexible process graph : a prologue

Businesses document their operational processes as process models. The common practice is to represent process models as directed graphs. The nodes of a process graph represent activities and directed edges constitute activity ordering constraints. A flexible process graph modeling approach proposes to generalize process graph structure to a hypergraph. Obtained process structure aims at formalization of ad-hoc process control flow. In this paper we discuss aspects relevant to concurrent execution of process activities in a collaborative manner organized as a flexible process graph. We provide a real world flexible process scenario to illustrate the approach.