Investigating behavioural and computational approaches for defining imprecise regions

People often communicate with reference to informally agreedplaces, such as “the city centre”. However, views of the spatial extent of such areas may vary, resulting in imprecise regions. We compare perceptions of Sheffield’s City Centre from a street survey to extents derived from various web-based sources. Such automated approaches have advantages of speed, cost and repeatability. We show that footprints from web sources are often in concordance with models derived from more labour-intensive methods. Notable exceptions however were found with sources advertising or selling residential property. Agreement between sources was measured by aggregating them to identify locations of consensus

The phenomenology of the mathematics classroom

This paper describes the mathematics classroom from the perspective of social phenomenology. Here the classroom is seen as an environment of signs, comprising things and people, which impinge on the reality of the individual child. The paper introduces a framework through which mathematical work is seen as taking place in the imagined world through the filter of the world in immediate perception. This provides an approach to structuring evolving mathematical understanding. It is suggested that mathematical ideas are contained and shaped by the child's personal phenomenology, which evolves through time. Further, I argue these ideas are never encountered directly but rather are met through a circular hermeneutic process of reconciling expectation with experience. © 1996 Kluwer Academic Publishers

At the intersection between the subject and the political: a contribution to an ongoing discussion

The issue of subjectivity has recently occasioned a lively discussion in this journal opposing socioculturalism and Lacanian psychoanalysis. By confronting Luis Radford’s cultural theory with Jacques Lacan’s psychoanalysis, Tony Brown sought to show the limitations of socioculturalism. This article takes advantage of that discussion to develop a critique of Radford’s theory of objectification, taken as an exemplary sociocultural theorization of the teaching and learning of mathematics. It does so by extending the criticism made by Brown at the level of the subject, namely by showing what is lost in socioculturalism when it reduces the Hegelian notion of dialectics to a relation between constituted entities; but mostly by exploring the possibility opened by contemporary theory to posit the discussion around subjectivity in the political. While socioculturalism assumes the possibility of a synthesis between person and culture thus making education possible, it will be argued that a theory which assumes the impossibility of education is in a better position to, on the one hand, conceptualize the resistance of many towards the learning of mathematics, and on the other hand, to address the ongoing political failure in achieving the desired goal of “mathematics for all”

Radical constructivism—von Glasersfeld

Radical constructivism was defined by von Glasersfeld as a theory of knowing that provides a pragmatic approach to questions about reality, truth, and human understanding. Radical constructivism draws heavily on Jean Piaget’s constructivism, but also on ideas about epistemology, or how we come to acquire knowledge, from British empiricism, Kant’s idealism, and Saussure’s structuralism, among others. Following Piaget, von Glasersfeld argued that we construct our concepts and our understanding of the world, developmentally. Knowledge is categorized by its viability in the domain of experience, rather than by the traditional philosophical position that it is constitutive of Truth, that is, that it corresponds to an objective reality. The two basic principles of radical constructivism are that knowledge is not passively received through the senses but is actively constructed by the cognizing subject, the learner, and that the function of cognition is organization of the experiential world rather than discovery of an independent reality. This chapter gives an overview of the theory underpinning radical constructivism and explores its implications for science education. It also examines critiques of radical constructivism, such as it neglects the social aspect of cognition and that it leads to an anti-realist stance on science teaching and learning