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.

Genome-wide association study identifies a variant in HDAC9 associated with large vessel ischemic stroke

Genetic factors have been implicated in stroke risk, but few replicated associations have been reported. We conducted a genome-wide association study (GWAS) for ischemic stroke and its subtypes in 3,548 affected individuals and 5,972 controls, all of European ancestry. Replication of potential signals was performed in 5,859 affected individuals and 6,281 controls. We replicated previous associations for cardioembolic stroke near PITX2 and ZFHX3 and for large vessel stroke at a 9p21 locus. We identified a new association for large vessel stroke within HDAC9 (encoding histone deacetylase 9) on chromosome 7p21.1 (including further replication in an additional 735 affected individuals and 28,583 controls) (rs11984041; combined P = 1.87 × 10 -11; odds ratio (OR) = 1.42, 95% confidence interval (CI) = 1.28-1.57). All four loci exhibited evidence for heterogeneity of effect across the stroke subtypes, with some and possibly all affecting risk for only one subtype. This suggests distinct genetic architectures for different stroke subtypes.

A "Candidate-Interactome" Aggregate Analysis of Genome-Wide Association Data in Multiple Sclerosis

Though difficult, the study of gene-environment interactions in multifactorial diseases is crucial for interpreting the relevance of non-heritable factors and prevents from overlooking genetic associations with small but measurable effects. We propose a "candidate interactome" (i.e. a group of genes whose products are known to physically interact with environmental factors that may be relevant for disease pathogenesis) analysis of genome-wide association data in multiple sclerosis. We looked for statistical enrichment of associations among interactomes that, at the current state of knowledge, may be representative of gene-environment interactions of potential, uncertain or unlikely relevance for multiple sclerosis pathogenesis: Epstein-Barr virus, human immunodeficiency virus, hepatitis B virus, hepatitis C virus, cytomegalovirus, HHV8-Kaposi sarcoma, H1N1-influenza, JC virus, human innate immunity interactome for type I interferon, autoimmune regulator, vitamin D receptor, aryl hydrocarbon receptor and a panel of proteins targeted by 70 innate immune-modulating viral open reading frames from 30 viral species. Interactomes were either obtained from the literature or were manually curated. The P values of all single nucleotide polymorphism mapping to a given interactome were obtained from the last genome-wide association study of the International Multiple Sclerosis Genetics Consortium & the Wellcome Trust Case Control Consortium, 2. The interaction between genotype and Epstein Barr virus emerges as relevant for multiple sclerosis etiology. However, in line with recent data on the coexistence of common and unique strategies used by viruses to perturb the human molecular system, also other viruses have a similar potential, though probably less relevant in epidemiological terms. © 2013 Mechelli et al.

The correlation between reading and mathematics ability at age twelve has a substantial genetic component

Dissecting how genetic and environmental influences impact on learning is helpful for maximizing numeracy and literacy. Here we show, using twin and genome-wide analysis, that there is a substantial genetic component to children’s ability in reading and mathematics, and estimate that around one half of the observed correlation in these traits is due to shared genetic effects (so-called Generalist Genes). Thus, our results highlight the potential role of the learning environment in contributing to differences in a child’s cognitive abilities at age twelve.

Genome-wide association study of intraocular pressure identifies the GLCCI1/ICA1 region as a glaucoma susceptibility locus

To discover quantitative trait loci for intraocular pressure, amajor risk factor for glaucoma and the only modifiable one,weperformed agenome-wide association studyonadiscoverycohort of2175individualsfromSydney, Australia. We found a novel association between intraocular pressure and a common variant at 7p21 near to GLCCI1 and ICA1. The findings in this region were confirmed through two UK replication cohorts totalling 4866 individuals (rs59072263, Pcombined = 1.10 × 10-8). A copy of the G allele at this SNP is associated with an increase in mean IOP of 0.45 mmHg (95%CI = 0.30-0.61 mmHg). These results lend support to the implication of vesicle trafficking and glucocorticoid inducibility pathways in the determination of intraocular pressure and in the pathogenesis of primary open-angle glaucoma.

Genome-wide association analysis identifies 13 new risk loci for schizophrenia

Schizophrenia is an idiopathic mental disorder with a heritable component and a substantial public health impact. We conducted a multi-stage genome-wide association study (GWAS) for schizophrenia beginning with a Swedish national sample (5,001 cases and 6,243 controls) followed by meta-Analysis with previous schizophrenia GWAS (8,832 cases and 12,067 controls) and finally by replication of SNPs in 168 genomic regions in independent samples (7,413 cases, 19,762 controls and 581 parent-offspring trios). We identified 22 loci associated at genome-wide significance; 13 of these are new, and 1 was previously implicated in bipolar disorder. Examination of candidate genes at these loci suggests the involvement of neuronal calcium signaling. We estimate that 8,300 independent, mostly common SNPs (95% credible interval of 6,300-10,200 SNPs) contribute to risk for schizophrenia and that these collectively account for at least 32% of the variance in liability. Common genetic variation has an important role in the etiology of schizophrenia, and larger studies will allow more detailed understanding of this disorder.

Common variants in the HLA-DRB1-HLA-DQA1 HLA class II region are associated with susceptibility to visceral leishmaniasis

To identify susceptibility loci for visceral leishmaniasis, we undertook genome-wide association studies in two populations: 989 cases and 1,089 controls from India and 357 cases in 308 Brazilian families (1,970 individuals). The HLA-DRB1-HLA-DQA1 locus was the only region to show strong evidence of association in both populations. Replication at this region was undertaken in a second Indian population comprising 941 cases and 990 controls, and combined analysis across the three cohorts for rs9271858 at this locus showed P combined = 2.76 × 10 -17 and odds ratio (OR) = 1.41, 95% confidence interval (CI) = 1.30-1.52. A conditional analysis provided evidence for multiple associations within the HLA-DRB1-HLA-DQA1 region, and a model in which risk differed between three groups of haplotypes better explained the signal and was significant in the Indian discovery and replication cohorts. In conclusion, the HLA-DRB1-HLA-DQA1 HLA class II region contributes to visceral leishmaniasis susceptibility in India and Brazil, suggesting shared genetic risk factors for visceral leishmaniasis that cross the epidemiological divides of geography and parasite species. © 2013 Nature America, Inc. All rights reserved.

Identification of 15 new psoriasis susceptibility loci highlights the role of innate immunity

To gain further insight into the genetic architecture of psoriasis, we conducted a meta-analysis of 3 genome-wide association studies (GWAS) and 2 independent data sets genotyped on the Immunochip, including 10,588 cases and 22,806 controls. We identified 15 new susceptibility loci, increasing to 36 the number associated with psoriasis in European individuals. We also identified, using conditional analyses, five independent signals within previously known loci. The newly identified loci shared with other autoimmune diseases include candidate genes with roles in regulating T-cell function (such as RUNX3, TAGAP and STAT3). Notably, they included candidate genes whose products are involved in innate host defense, including interferon-mediated antiviral responses (DDX58), macrophage activation (ZC3H12C) and nuclear factor (NF)-κB signaling (CARD14 and CARM1). These results portend a better understanding of shared and distinctive genetic determinants of immune-mediated inflammatory disorders and emphasize the importance of the skin in innate and acquired host defense. © 2012 Nature America, Inc. All rights reserved.

Common variants at the MHC locus and at chromosome 16q24.1 predispose to Barrett's Esophagus

Barrett's esophagus is an increasingly common disease that is strongly associated with reflux of stomach acid and usually a hiatus hernia, and it strongly predisposes to esophageal adenocarcinoma (EAC), a tumor with a very poor prognosis. We report the first genome-wide association study on Barrett's esophagus, comprising 1,852 UK cases and 5,172 UK controls in the discovery stage and 5,986 cases and 12,825 controls in the replication stage. Variants at two loci were associated with disease risk: chromosome 6p21, rs9257809 (P combined = 4.09 × 10-9; odds ratio (OR) = 1.21, 95% confidence interval (CI) =1.13-1.28), within the major histocompatibility complex locus, and chromosome 16q24, rs9936833 (P combined = 2.74 × 10-10; OR = 1.14, 95% CI = 1.10-1.19), for which the closest protein-coding gene is FOXF1, which is implicated in esophageal development and structure. We found evidence that many common variants of small effect contribute to genetic susceptibility to Barrett's esophagus and that SNP alleles predisposing to obesity also increase risk for Barrett's esophagus. © 2012 Nature America, Inc. All rights reserved.

Using genome-Wwide complex trait analysis to quantify 'missing heritability' in Parkinson's disease

Genome-wide association studies (GWASs) have been successful at identifying single-nucleotide polymorphisms (SNPs) highly associated with common traits; however, a great deal of the heritable variation associated with common traits remains unaccounted for within the genome. Genome-wide complex trait analysis (GCTA) is a statistical method that applies a linear mixed model to estimate phenotypic variance of complex traits explained by genome-wide SNPs, including those not associated with the trait in a GWAS. We applied GCTA to 8 cohorts containing 7096 case and 19 455 control individuals of European ancestry in order to examine the missing heritability present in Parkinson's disease (PD). We meta-analyzed our initial results to produce robust heritability estimates for PD types across cohorts. Our results identify 27% (95% CI 17-38, P = 8.08E - 08) phenotypic variance associated with all types of PD, 15% (95% CI -0.2 to 33, P = 0.09) phenotypic variance associated with early-onset PD and 31% (95% CI 17-44, P = 1.34E - 05) phenotypic variance associated with late-onset PD. This is a substantial increase from the genetic variance identified by top GWAS hits alone (between 3 and 5%) and indicates there are substantially more risk loci to be identified. Our results suggest that although GWASs are a useful tool in identifying the most common variants associated with complex disease, a great deal of common variants of small effect remain to be discovered. © Published by Oxford University Press 2012.