Seeking big ideas in algebra: the evolution of a task

In this paper we describe a strand of activities for teachers of mathematics that we used with two cohorts of participants in a professional development program called Revitalizing Algebra (REAL). We first discuss our goals and describe the participants, and then we describe the construction and selection of the tasks followed by teacher responses. Finally, we reflect on different iterations of the tasks, their impact on the teachers’ thinking and practice, and the role of school and department culture in the process of change.     

Challenging teacher beliefs about student engagement in mathematics

This study explored the beliefs about student engagement in mathematics of three Year 5 and 6 teachers, focusing on the shifts that occurred during a 10-week intervention. Data obtained from teacher surveys, interviews, video-recorded workshop observations and artefacts from teachers’ classrooms reveal variations in their reactions to the professional learning experiences. Teacher responses were mediated by personal and contextual elements including teacher efficacy beliefs, teacher confidence in mathematics and their conceptions of student engagement. Theories of teacher conceptual change are used to account for variations to teacher beliefs.     

LEARNING TO BE IN PUBLIC SPACES: IN FROM THE MARGINS WITH DANCERS, SCULPTORS, PAINTERS AND MUSICIANS

ABSTRACT:  This article reports research in three Nottingham schools, concerned with (1) 'The school as fertile ground: how the ethos of a school enables everyone in it to benefit from the presence of artists in class'; (2) 'Children on the edge: how the arts reach those children who otherwise exclude themselves from class activities, for any reason' and (3) 'Children's voices and choices: how even very young children can learn to express their wishes, and then have them realised through arts projects'. The research methodology was rooted in two modes of inquiry, philosophical investigation and action research. The article draws on this research to argue that arts-based work in school has helped disadvantaged and/or disaffected children to engage in activities (both arts-based and others), and to be able to lay the groundwork for exercising voice and agency as they did so. If social justice is to flourish there is a need for particular kinds of public spaces and a need to create conditions such that children can learn to participate in those spaces, whether or not they are comfortable with the usual settings for 'rational argument' or 'deliberative democracy'. It is suggested that arts-based education, in some forms, is one good way of creating these conditions.     

On a theory of instruction: Why different forms of instruction result in similar knowledge

Why can instructional processes having widely different topographies—such as teaching through a demonstration (modeling), teaching through verbal explanation, and teaching by simply providing an occasion for the child's direct contingent experience—all result in the development of the same or similar knowledge? A recent series of experiments that examined the role of instruction in the intellectual development of young children provides evidence for the equivalence of different forms of instruction and leads to the postulation of a set of invariant processes of information exchange that underlies the surface characteristics of various forms of instruction.     

Leadership for inclusion: a comparison of international practices

The issue of inclusion is high on the educational reform agenda in many countries. Set within the context of the United Nations organisation's push for ‘Education for All’, the aim is to find ways of increasing the participation and learning of pupils who are vulnerable to marginalisation within existing educational arrangements ( World Education Forum, 2000 ). In the United States, inclusive education is generally thought of as an approach to serving children with disabilities within general education settings. Internationally, however, it is sometimes seen more broadly as a reform that supports and welcomes diversity among all learners ( Ainscow, 1999 ). The research reported in this paper adopts this broadened formulation. It presumes that the aim of inclusive education is to eliminate social exclusion and that is a consequence of attitudes and responses to diversity in race, social class, ethnicity, religion, gender and ability ( Vitello & Mithaug, 1998 ). Children with disabilities and others seen as having special educational needs are part of this agenda. The paper focuses specifically on the implications of these developments for leadership roles in schools. In particular, it uses evidence from case studies of leadership practice in three countries to address the question, what types of leadership practice foster inclusion in schools? The paper provides a theoretical framework that throws light on what is involved in such practices and presents illustrative examples. The aim is to provide an analysis that will be of direct relevance to practitioners, whilst at the same time adding to theory. The examples of leadership that are examined were found in schools in England, Portugal, and the United States that serve culturally and linguistically diverse groups of children, including significant numbers from low‐income families. In each of the schools, children with disabilities and others categorised as having special educational needs are taught in general education classrooms alongside their peers.