Internationally, adult literacy and numeracy are in general recognized as cultural techniques. However, the meaning of the two competences and the means of their development are contested among politicians, education bureaucrats, and researchers. Numeracy is often subsumed under literacy and/or described in isolation from the situational context. Adult numeracy at work is often described unproblematically as the transfer of mathematical knowledges and skills from school to workplace. With reference to Bernstein’s theoretical framework, we claim that adult numeracy in the labour market is a horizontal discourse, in contrast to the vertical discourse of mathematics. This article draws on the findings from an Australian study of numeracy in the context of chemical spraying and handling, utilising a methodology based on activity theory. The main findings are that mathematically straightforward skills become transformed into workplace numeracy competence, when the complexities associated with successful task completion as well as the supportive role of mediating artefacts and the workplace community of practice are taken into account.

In this Commentary I reflect on the work done by the authors of five chapters in relation to technology-related professional development for mathematics teachers across a range of educational levels, undertaken in a variety of contextual settings, and drawing on a wealth of theoretical frameworks to support a diversity of practical approaches to implementation involving teachers, current and prospective, their students, and researchers in ongoing knowledge building and theory development. My reflections will be refracted through the three other major themes of this book which intersect in professional development: (a) technology as a tool for teaching and learning mathematics, (b) communication inside and outside the classroom, and (c) information tools, to inform oneself and to inform others.

Preparing students for their lives beyond schooling appears to be a universal goal of formal education. Much has been done to make mathematics education more “realistic,” but such activities nevertheless generally remain within the institutional norms of education. In this article, we assume that pedagogic relations are also an integral part of working life and draw on Bernstein’s work to address their significant features in this context. However, unlike participation in formal mathematics education, where the discipline is central, workers are likely to be confronted by, and need to reconcile, a range of other valued workplace discourses, both epistemic and social/cultural in nature. How might mathematics education work towards overcoming the hiatus between these two very different institutional settings? This article will argue that the skills of recontextualisation, central to teachers’ work, should be integral to the mathematics education of all future workers. It will consider theoretical perspectives on pedagogic discourse and the consequences of diverse knowledge structures at work, with implications for general and vocational mathematics education.

I have recently received, in close succession, two reviews of the same book Mathematics and the Body: Material Entanglements in the Classroom, by Elizabeth de Freitas and Nathalie Sinclair. Judging from the reviews, this is a book which challenges many of the orthodoxies of mathematics education as it is currently constituted for many academics and practising teachers. It is clear that the book also demanded a great deal of effort on the part of the reviewers to convey their own developing understandings as well as how it might be of interest to the diversity of readers of this journal. One review was submitted by a single author, Francesca Ferrara, who prepared a very careful and thoughtful review of the book, relating it to her research interests and recent readings. Comprising about 3000 words, her submission was of typical length for such reviews. The second review was submitted by a team of doctoral students who worked with Beth Herbel-Eisenmann, their supervisor, to prepare a much longer review essay which also incorporated reflections and questions based on lengthy discussions which were enriched by their diverse theoretical and experiential backgrounds. Both reviews are to be commended, and I encourage readers to submit both single author and collaborative reviews and feel welcome to contact me as the book review editor, particularly if they are contemplating a longer review essay. Educ Stud Math (2015) 90:213 DOI 10.1007/s10649-015-9622-2

In this commentary I will address the notions of work, the need for innovation, and the role of workplace mathematics. I will then provide an overview of some of the complex issues that confront the subfield of vocational mathematics education with consequences for current and future workers, drawing in part on the work of Basil Bernstein. Finally, I will address the question of workplace research and offer some possible directions for future research, as well as implications for policy. Reflections on the articles included in this special issue will frame the discussion.

Values in mathematics education are those deep, affective qualities which education aims to foster through the school subject of mathematics and are a crucial component of the classroom affective environment. As a result of demands that students become more economically oriented and globally conscious, mathematics educators are being challenged as to which values should be developed through mathematics education. The concern is that, although values teaching and learning inevitably happen in all mathematics classrooms, they appear to be mostly implicit. Thus, it is likely that teachers have only limited understanding of what values are being taught and encouraged. The new questions asked include: (a) What are teachers' understandings of their own intended and implemented values? (b) To what extent can mathematics teachers gain control over their own values teaching? and (c) Is it possible to increase the possibilities for more effective mathematics teaching through values education of teachers and teachers in training? In order to begin to answer these questions, the authors theorize values teaching in mathematics. In this paper the authors analyze three interrelated sources of values which permeate mathematics classrooms: general educational, mathematical, and specifically mathematics educational. The authors also analyze the various influences on teachers' values with regard to explicit and implicit values teaching through an adaptation of Billett's (1998) framework for the genesis of social knowledge. (Contains 64 references.) (Author/ASK) Reproductions supplied by EDRS are the best that can be made from the original document. Values in Mathematics Education: Making Values Teaching Explicit in the Mathematics Classroom by Alan Bishop Gail FitzSimons Wee Tiong Seah Philip Clarkson PERMISSION TO REPRODUCE AND DISSEMINATE THIS MATERIAL HAS BEEN GRANTED BY TO THE EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) 1 U.S. DEPARTMENT OF EDUCATION Office of Educational Research and Improvement EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) received document has been reproduced as r i from the person or organization originating it. Minor changes have been made to improve reproduction quality. Points of view or opinions stated in this document do not necessarily represent official OERI position or policy. 2 BEST COPY AVAILABLE F 2. Values, and Some Theoretical Perspectives T Culture is "an organised system of values which are transmitted to its members both formally and informally" (McConatha & Schnell, 1995, p. 81). It is reasonable, then, to postulate that despite the rather similar, canonical form of school mathematics being taught in different educational systems around the world today, its nature and content in any one culture .) http://www.aare.edu.au/99pap/bis99188.htm ) 3 Monday, May 14, 2001 Values in mathematics education: Making values teaching explicit in the mathematics classroom Page: 1 BIS99188 Values in Mathematics Education: Making Values Teaching Explicit in the Mathematics Classroom. ED Alan Bishop, Gail Fitz Simons, Wee Tiong Seah, Faculty of Education, Monash University, Melbourne, Australia Philip Clarkson, Faculty of Education, Australian Catholic University, Melbourne, Australia. sub-theme: Teachers and Learners: New Questions theme: Mathematics Education Abstract Values in mathematics education are the deep affective qualities which education aims to foster through the school subject of mathematics and are a crucial component of the classroom affective environment. As a result of demands that students become more economically oriented and globally conscious, mathematics educators are being challenged about which values should be developed through mathematics education. Our concern is that, although values teaching and learning inevitably happen in all mathematics classrooms, they appear to be mostly implicit. Thus it is likely that teachers have only limited understanding of what values are being taught and encouraged. The new questions we are asking are: (a) What are teachers' understandings of their own intended and implemented values? (b) To what extent can mathematics teachers gain control over their own values teaching? (c) Is it possible to increase the possibilities for more effective mathematics teaching through values education of teachers, and of teachers in training? In order to begin to answer these questions we need to theorise values teaching in mathematics. In this paper we will analyse three interrelated sources of values which permeate mathematics classrooms: general educational, mathematical, and specifically mathematics educational. We will also analyse the various influences on teachers' values with respect to explicit and implicit values teaching through an adaptation of Billett's (1998) framework for the genesis of social knowledge.

For a variety of historical, cultural, social, and/or economic reasons adults may experience the need to continue their mathematics education in some form. The concept of lifelong learning, posited by Dewey in 1916, has been widely recognised since the 1970s. However, this concept is contested and there are many perspectives which may be in tension or even contradiction according to the lens adopted. The chapter will review some of these perspectives because the dominant one will affect the educational strategies and outcomes.The concept of adult numeracy - which arose in Britain in the 1950s - is becoming increasingly common and is also contested, as is the terminology (e.g., quantitative literacy). Drawing on the work of Bernstein, I will distinguish between mathematics and numeracy as the choice made can also have educational implications, although I have elsewhere argued for a convergence.For mathematics in particular, the concept of transfer is a vexed issue. It is commonly assumed that what is learned in the formal classroom or other learning site will automatically be recognised and applied unproblematically in the very different situation of the workplace. Curriculum and pedagogy for adult numeracy and vocational mathematics need to take cognisance of this and other important issues to avoid the situation of merely replicating the kinds of 'school' mathematics that many people, young and old, have been failed by and continue to avoid engaging with.In today's world, technology is playing an increasingly important role in educational situations, in the workplace, and at home. Technology plays a dual role in the teaching and learning of mathematics/numeracy for adults. Technology, electronic and othenvise, offers a medium to enhance learning in the form of tools such as rulers and compasses as well as software programs. Technology in the form of calculators of various kinds or computer applications, such as spreadsheets or statistics programs can act as aids to overcome the limitations of human memory or to support the exploration of new ideas by experimentation or simulation. However, these need to be made objects of learning in their own right before they can support higher level thinking. Electronic technologies offer increasingly sophisticated means of communication, in education and at work or society at large.