In this introductory article, I argue why this special issue focuses on the question of how the mathematical knowledge required at work can be characterised and developed in vocational education and workplace training. After some words on the importance of this subfield of mathematics education and the need to rethink metaphors of learning in this area, I summarise the structure of the special issue and highlight a few main points raised in the various contributions.Keywords Boundary crossing . Metaphors of learning . Transition . Webbing . Webs of reasons .
Workplace mathematicsIt seems impossible to analyze education -in schooling, craft apprenticeship, or any other form -without considering its relations with the world for which it ostensibly prepares people. (Lave, 1988, p. xiii) This opening sentence of Lave's (1988) seminal book on cognition in practice underlines the importance of studying relations between knowledge taught in education, on the one hand, and knowledge used in daily life or workplace settings, on the other. Though she writes "it seems impossible to analyze education… without considering" such relations, studying these relations and strengthening them prove to be hard. The vast majority of studies in mathematics education deal with students and their teachers in general education as a relatively closed system, and a small minority of studies deal with workplace mathematics with little consideration of its relation to school mathematics. Much less is known about transitional settings such as vocational education where students develop mathematical knowledge required in occupations or professions and learn to use it in practice. In this special issue, we bring together the latest insights in this area.What we know from earlier research is mostly presented as a stark contrast between school mathematics and "street mathematics" (Nunes, Schliemann, & Carraher, 1993). This research (including Lave's) has led to a fundamental critique of framing transitions of knowledge Educ Stud Math (2014) 86:151-156 DOI 10.1007 A. Bakker (*) Freudenthal Institute for Science and Mathematics Education, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands e-mail: a.bakker4@uu.nl learned at school to knowledge applied in daily life or at work as a matter of transfer. It has also contributed to the development of situated approaches (Brown, Collins, & Duguid, 1989;Greeno, 1998) and sociocultural theories (e.g., Lave & Wenger, 1991). It became clear, as Tuomi-Gröhn and Engeström (2003) argued, that more sophisticated conceptions of transfer are required when we want to understand the boundary crossing between school and real-life settings such as work.This special issue focuses on vocational education and workplace training, which could be seen as a transitional stage between cognition in captivity and cognition in the wild (Hutchins, 1995). In this domain of vocational education and workplace training, the nature of mathematics as generally applicable and abstract is confronted with p...