Political Education in Plural Societies: Using the Anti-Bias Approach to Challenge Oppression in Bombay and Berlin

This study addresses the effectivity of the Anti-Bias approach and training methodology as a pedagogical political strategy to challenge oppression among student groups in the cities of Bombay and Berlin. The Anti-Bias trainings conducted within the framework of this study also become the medium through which the perpetuation of oppressive structures by students within and outside the school is investigated. Empirical data from predominantly qualitative investigations in four secondary schools, two each in Bombay and Berlin, is studied and analysed on the basis of theoretical understandings of prejudice, discrimination and identity. This study builds on insights offered by previous research on prejudices and evaluations of anti-bias and diversity interventions, where the lack of sufficient research and thorough evaluations testing impact has been identified (Levy Paluck, 2006). The theoretical framework suggests that prejudices and discriminatory practices are learnt and performed by individuals over the years by way of pre-existing discourses, and that behaviour and practices can be unlearnt through a multi-step process. It proposes that the discursive practices of students contribute to the constitution of their viable selves and in the constitution of ‘others’. Drawing on this framework, the study demonstrates how student-subjects in Bombay and Berlin perpetuate oppressive discourses by performing their identities and performing identities onto ‘others’. Such performative constitution opens up the agency of the individual, disclosing the shifting and dynamic nature of identities. The Anti-Bias approach is posited as an alternative to oppressive discourses and a vehicle that encourages and assists the agency of individuals. The theoretical framework, which brings together a psychological approach to prejudice, a structural approach to discrimination and a poststructural approach to identity, facilitates the analysis of the perpetuation of dominant discourses by the students, as well as how they negotiate their way through familiar norms and discourses. Group discussions and interviews a year after the respective trainings serve to evaluate the agency of the students and the extent to which the training impacted on their perceptions, attitudes and behavioural practices. The study reveals the recurrence of the themes race, religion, gender and sexuality in the representational practices of the students groups in Berlin and Bombay. It demonstrates how students in this study not only perform, but also negotiate and resist oppressive structures. Of particular importance is the role of the school: When schools offer no spaces for discussion, debate and action on contemporary social issues, learning can neither be put into practice nor take on a positive, transformative form. In such cases, agency and resistance is limited and interventionist actions yield little. This study reports the potential of the Anti-Bias approach and training as a tool of political education and action in education. It demonstrates that a single training can initiate change but sustaining change requires long-term strategies and on-going actions. Taking a poststructural perspective, it makes concrete suggestions to adapt and alter the Anti-Bias approach and the implementation of Anti-Bias trainings.

Efficient data mining based on formal concept analysis

Formal Concept Analysis is an unsupervised learning technique for conceptual clustering. We introduce the notion of iceberg concept lattices and show their use in Knowledge Discovery in Databases (KDD). Iceberg lattices are designed for analyzing very large databases. In particular they serve as a condensed representation of frequent patterns as known from association rule mining. In order to show the interplay between Formal Concept Analysis and association rule mining, we discuss the algorithm TITANIC. We show that iceberg concept lattices are a starting point for computing condensed sets of association rules without loss of information, and are a visualization method for the resulting rules.

Conceptual knowledge processing with formal concept analysis and ontologies

Among many other knowledge representations formalisms, Ontologies and Formal Concept Analysis (FCA) aim at modeling ‘concepts’. We discuss how these two formalisms may complement another from an application point of view. In particular, we will see how FCA can be used to support Ontology Engineering, and how ontologies can be exploited in FCA applications. The interplay of FCA and ontologies is studied along the life cycle of an ontology: (i) FCA can support the building of the ontology as a learning technique. (ii) The established ontology can be analyzed and navigated by using techniques of FCA. (iii) Last but not least, the ontology may be used to improve an FCA application.

On Solutions of Holonomic Divided-Difference Equations on Non-Uniform Lattices

The main aim of this paper is the development of suitable bases (replacing the power basis x^n (n\in\IN_\le 0) which enable the direct series representation of orthogonal polynomial systems on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of this type, the first of which allows to write solutions of arbitrary divided-difference equations in terms of series representations extending results given in [16] for the q-case. Furthermore it enables the representation of the Stieltjes function which can be used to prove the equivalence between the Pearson equation for a given linear functional and the Riccati equation for the formal Stieltjes function. If the Askey-Wilson polynomials are written in terms of this basis, however, the coefficients turn out to be not q-hypergeometric. Therefore, we present a second basis, which shares several relevant properties with the first one. This basis enables to generate the defining representation of the Askey-Wilson polynomials directly from their divided-difference equation. For this purpose the divided-difference equation must be rewritten in terms of suitable divided-difference operators developed in [5], see also [6].

Characterization theorem for classical orthogonal polynomials on non-uniform lattices: The functional approach

Using the functional approach, we state and prove a characterization theorem for classical orthogonal polynomials on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable) including the Askey-Wilson polynomials. This theorem proves the equivalence between seven characterization properties, namely the Pearson equation for the linear functional, the second-order divided-difference equation, the orthogonality of the derivatives, the Rodrigues formula, two types of structure relations,and the Riccati equation for the formal Stieltjes function.