The MaPS project: mapping teacher conceptions of musical development

The chapter starts from the premise that an historically- and institutionally-formed orientation to music education at primary level in European countries privileges a nineteenth century Western European music aesthetic, with its focus on formal characteristics such as melody and rhythm. While there is a move towards a multi-faceted understanding of musical ability, a discrete intelligence and willingness to accept musical styles or 'open-earedness', there remains a paucity of documented evidence of this in research at primary school level. To date there has been no study undertaken which has the potential to provide policy makers and practitioners with insights into the degree of homogeneity or universality in conceptions of musical ability within this educational sector. Against this background, a study was set up to explore the following research questions: 1. What conceptions of musical ability do primary teachers hold a) of themselves and; b) of their pupils? 2. To what extent are these conceptions informed by Western classical practices? A mixed methods approach was used which included survey questionnaire and semi-structured interview. Questionnaires have been sent to all classroom teachers in a random sample of primary schools in the South East of England. This was followed up with a series of semi-structured interviews with a sub-sample of respondents. The main ideas are concerned with the attitudes, beliefs and working theories held by teachers in contemporary primary school settings. By mapping the extent to which a knowledge base for teaching can be resistant to change in schools, we can problematise primary schools as sites for diversity and migration of cultural ideas. Alongside this, we can use the findings from the study undertaken in an English context as a starting point for further investigation into conceptions of music, musical ability and assessment held by practitioners in a variety of primary school contexts elsewhere in Europe; our emphasis here will be on the development of shared understanding in terms of policies and practices in music education. Within this broader framework, our study can have a significant impact internationally, with potential to inform future policy making, curriculum planning and practice.

Mutual dependency grid for stakeholder mapping: a component-based approach to supply chain participant analysis

Stakeholder analysis plays a critical role in business analysis. However, the majority of the stakeholder identification and analysis methods focus on the activities and processes and ignore the artefacts being processed by human beings. By focusing on the outputs of the organisation, an artefact-centric view helps create a network of artefacts, and a component-based structure of the organisation and its supply chain participants. Since the relationship is based on the components, i.e. after the stakeholders are identified, the interdependency between stakeholders and the focal organisation can be measured. Each stakeholder is associated with two types of dependency, namely the stakeholder’s dependency on the focal organisation and the focal organisation’s dependency on the stakeholder. We identify three factors for each type of dependency and propose the equations that calculate the dependency indexes. Once both types of the dependency indexes are calculated, each stakeholder can be placed and categorised into one of the four groups, namely critical stakeholder, mutual benefits stakeholder, replaceable stakeholder, and easy care stakeholder. The mutual dependency grid and the dependency gap analysis, which further investigates the priority of each stakeholder by calculating the weighted dependency gap between the focal organisation and the stakeholder, subsequently help the focal organisation to better understand its stakeholders and manage its stakeholder relationships.

Genome-wide association mapping to candidate polymorphism resolution in the unsequenced barley genome

Although commonplace in human disease genetics, genome-wide association (GWA) studies have only relatively recently been applied to plants. Using 32 phenotypes in the inbreeding crop barley, we report GWA mapping of 15 morphological traits across ∼500 cultivars genotyped with 1,536 SNPs. In contrast to the majority of human GWA studies, we observe high levels of linkage disequilibrium within and between chromosomes. Despite this, GWA analysis readily detected common alleles of high penetrance. To investigate the potential of combining GWA mapping with comparative analysis to resolve traits to candidate polymorphism level in unsequenced genomes, we fine-mapped a selected phenotype (anthocyanin pigmentation) within a 140-kb interval containing three genes. Of these, resequencing the putative anthocyanin pathway gene HvbHLH1 identified a deletion resulting in a premature stop codon upstream of the basic helix-loop-helix domain, which was diagnostic for lack of anthocyanin in our association and biparental mapping populations. The methodology described here is transferable to species with limited genomic resources, providing a paradigm for reducing the threshold of map-based cloning in unsequenced crops.

Association mapping of partitioning loci in barley

Background: Association mapping, initially developed in human disease genetics, is now being applied to plant species. The model species Arabidopsis provided some of the first examples of association mapping in plants, identifying previously cloned flowering time genes, despite high population sub-structure. More recently, association genetics has been applied to barley, where breeding activity has resulted in a high degree of population sub-structure. A major genotypic division within barley is that between winter- and spring-sown varieties, which differ in their requirement for vernalization to promote subsequent flowering. To date, all attempts to validate association genetics in barley by identifying major flowering time loci that control vernalization requirement (VRN-H1 and VRN-H2) have failed. Here, we validate the use of association genetics in barley by identifying VRN-H1 and VRN-H2, despite their prominent role in determining population sub-structure. Results: By taking barley as a typical inbreeding crop, and seasonal growth habit as a major partitioning phenotype, we develop an association mapping approach which successfully identifies VRN-H1 and VRN-H2, the underlying loci largely responsible for this agronomic division. We find a combination of Structured Association followed by Genomic Control to correct for population structure and inflation of the test statistic, resolved significant associations only with VRN-H1 and the VRN-H2 candidate genes, as well as two genes closely linked to VRN-H1 (HvCSFs1 and HvPHYC). Conclusion: We show that, after employing appropriate statistical methods to correct for population sub-structure, the genome-wide partitioning effect of allelic status at VRN-H1 and VRN-H2 does not result in the high levels of spurious association expected to occur in highly structured samples. Furthermore, we demonstrate that both VRN-H1 and the candidate VRN-H2 genes can be identified using association mapping. Discrimination between intragenic VRN-H1 markers was achieved, indicating that candidate causative polymorphisms may be discerned and prioritised within a larger set of positive associations. This proof of concept study demonstrates the feasibility of association mapping in barley, even within highly structured populations. A major advantage of this method is that it does not require large numbers of genome-wide markers, and is therefore suitable for fine mapping and candidate gene evaluation, especially in species for which large numbers of genetic markers are either unavailable or too costly.

Numerical conformal mapping and mesh generation for polygonal and multiply-connected regions

Details are given of a boundary-fitted mesh generation method for use in modelling free surface flow and water quality. A numerical method has been developed for generating conformal meshes for curvilinear polygonal and multiply-connected regions. The method is based on the Cauchy-Riemann conditions for the analytic function and is able to map a curvilinear polygonal region directly onto a regular polygonal region, with horizontal and vertical sides. A set of equations have been derived for determining the lengths of these sides and the least-squares method has been used in solving the equations. Several numerical examples are presented to illustrate the method.

Evaluation of a boundary integral representation for the conformal mapping of the unit disk onto a simply-connected domain

A representation of the conformal mapping g of the interior or exterior of the unit circle onto a simply-connected domain Ω as a boundary integral in terms ofƒ|∂Ω is obtained, whereƒ :=g -l. A product integration scheme for the approximation of the boundary integral is described and analysed. An ill-conditioning problem related to the domain geometry is discussed. Numerical examples confirm the conclusions of this discussion and support the analysis of the quadrature scheme.