Work Experience and VET: Insights from the Connective Typology and the Recontextualisation Model

The chapter compares two models of work experience – connective typology of work experience and recontextualisation of knowledge model – and uses the term work experience to refer to the way that young people enrolled in both school- and apprenticeship-based VET learn to relate their experience of education as represented by the acquisition of domain knowledge and their experience of work as represented by occupational values, skill and knowledge to one another. The common link between the two models is that they accept the existence of a mediated relationship between education and work. The former explores this relationship from a boundary-crossing perspective, focusing on learners’ movement between education and work, and identifies the outcomes associated with different models of work experience. The latter focuses on the interplay between the manifestation of knowledge in the contexts of education and work and learners’ movement within and between both contexts. It differs from the connective typology, because it takes account of the mediated nature of the contexts of education and work as well as the process of learning through work experience. The chapter concludes by using the concept of recontextualisation to highlight how digital and mobile technologies could serve as resources to facilitate learning through work experience in school- and apprenticeship-based VET

Boundary objects and boundary crossing for numeracy teaching

In this paper, we share analysis of an episode of a pre-service teacher’s handling of a map artefact within his practicum teaching of ‘Mathematical Literacy’ in South Africa. Mathematical Literacy, as a post-compulsory phase subject in the South African curriculum, shares many of the aims of numeracy as described in the international literature— including approaches based on the inclusion of real life contexts and a trajectory geared towards work, life and citizenship. Our attention in this paper is focused specifically on artefacts at the boundary of mathematical and contextual activities. We use analysis of the empirical handling of artefacts cast as ‘boundary objects’ to argue the need for ‘boundary crossing’ between mathematical and contextual activities as a critical feature of numeracy teaching. We pay particular attention to the differing conventions and extents of applicability of rules associated with boundary artefacts when working with mathematical or contextual perspectives. Our findings suggest the need to consider boundary objects more seriously within numeracy teacher education, with specific attention to the ways in which they are configured on both sides of the boundary in order to deal effectively with explanations and interactions in classrooms aiming to promote numeracy

Inferentialism as an alternative to socioconstructivism in mathematics education

The purpose of this article is to draw the attention of mathematics education researchers to a relatively new semantic theory called inferentialism, as developed by the philosopher Robert Brandom. Inferentialism is a semantic theory which explains concept formation in terms of the inferences individuals make in the context of an intersubjective practice of acknowledging, attributing, and challenging one another’s commitments. The article argues that inferentialism can help to overcome certain problems that have plagued the various forms of constructivism, and socioconstructivism in particular. Despite the range of socioconstructivist positions on offer, there is reason to think that versions of these problems will continue to haunt socioconstructivism. The problems are that socioconstructivists (i) have not come to a satisfactory resolution of the social-individual dichotomy, (ii) are still threatened by relativism, and (iii) have been vague in their characterization of what construction is. We first present these problems; then we introduce inferentialism, and finally we show how inferentialism can help to overcome the problems. We argue that inferentialism (i) contains a powerful conception of norms that can overcome the social-individual dichotomy, (ii) draws attention to the reality that constrains our inferences, and (iii) develops a clearer conception of learning in terms of the mastering of webs of reasons. Inferentialism therefore represents a powerful alternative theoretical framework to socioconstructivism

The French Didactic Tradition in Mathematics

This chapter presents the French didactic tradition. It first describes theemergence and development of this tradition according to four key features (role ofmathematics and mathematicians, role of theories, role of design of teaching andlearning environments, and role of empirical research), and illustrates it through two case studies respectively devoted to research carried out within this traditionon algebra and on line symmetry-reflection. It then questions the influence of thistradition through the contributions of four researchers from Germany, Italy, Mexicoand Tunisia, before ending with a short epilogue

Supporting Key Aspects of Practice in Making Mathematics Explicit in Science Lessons

STEM integration has often been recommended as a way to support students to develop 21st Century skills needed to function in the complex modern world. In order for students to experience integration, however, their teachers need support in designing, developing and implementing integrated curricular instruction, which is often at odds with a very subject-focused educational system. This paper reports on the second year of a research study conducted with five secondary science and mathematics teachers, concerned with supporting them to teach explicitly the mathematics components within science lessons, mediated via technology. It outlines how the teachers collaborated with the support of science and mathematics education researchers within a community of practice, named a Teaching and Learning Network (TLN). The network was intended to promote and enhance teacher capacity for the interdisciplinary teaching of mathematics in science in the face of various contextual and other obstacles observed in the first year of the study. This study found that the opportunity to work in a Teaching and Learning Network supported the teachers’ ownership of the design of the integrated learning unit, enhanced their content knowledge of the mathematics, their use of the data logging technology and their understanding of an inquiry based pedagogical approach. Participation in the TLN provided teachers with the mechanism to cross the boundaries of the subject disciplines, and thereby promoted change in their attitudes, professional knowledge and to some extent, practice