Adults Learning Mathematics An International Journal Chief Editor Javier Díez-Palomar Editor Anestine Hector-Mason Guest Editor Graham Griffiths Volume 9(2) November 2014 ISSN 1744-1803 ALM International Journal, Volume 9(2) Objectives Adults Learning Mathematics – An International Research Forum has been established since 1994 (see www.alm-online.net), with an annual conference and newsletters for members. ALM is an international research forum bringing together researchers and practitioners in adult mathematics/ numeracy teaching and learning in order to promote the learning of mathematics by adults. Since 2000, ALM has been a Company Limited by Guarantee (No.3901346) and a National and Overseas Worldwide Charity under English and Welsh Law (No.1079462). Through the annual ALM conference proceedings and the work of individual members an enormous contribution has been made to making available theoretical and practical research in a field, which remains under- researched and under-theorised. Since 2005 ALM also provides an international journal. Adults Learning Mathematics – An International Journal is an international refereed journal that aims to provide a forum for the online publication of high quality research on the teaching and learning, knowledge and uses of numeracy/mathematics to adults at all levels in a variety of educational sectors. Submitted papers should normally be of interest to an international readership. Contributions focus on issues in the following areas: Research and theoretical perspectives in the area of adults learning mathematics/numeracy Debate on special issues in the area of adults learning mathematics/numeracy Practice: critical analysis of course materials and tasks, policy developments in curriculum and assessment, or data from large-scale tests, nationally and internationally. The ALM International Journal will be published twice a year. ISSN 1744-1803 © Adults Learning Mathematics – An International Research Forum (2006) Editorial Team: Dr. Javier Díez-Palomar, Universitat de Barcelona, Spain [Chief Editor] Dr. Anestine Hector-Mason, American Institutes for Research, Washington, DC, USA [Editor]. Graham Griffith, Institute of Education, University of London [Guest Editor] Dr. Katherine Safford-Ramus, Saint Peter’s College, Jersey City, New Jersey, USA Dr. Chris Klinger, University of South Australia, Adelaide, Australia Kees Hoogland, APS - National Center for School Improvement, Utrecht, the Netherlands Editorial Board: Prof. Alan Bishop, Monash University, Melbourne, Australia Prof. Marta Civil, University of North Carolina, Chapel Hill, U.S. Prof. Diana Coben, Kings College London, UK Dr. Jeff Evans, Middlesex University, London, UK Dr. Gail FitzSimons, Monash University, Melbourne, Australia Prof. Gelsa Knijnik, Universidade do Vale do Rio dos Sinos, Brazil Prof. John O’Donoghue, University of Limerick, Ireland Prof. Wolfgang Schloeglmann, University of Linz, Austria Prof. Ole Skovsmose, Aalborg University, Denmark Dr. Alison Tomlin, Kings College London, UK Prof. Lieven Verschaffel, University of Leuven, Belgium Prof. John Volmink, Natal University Development Foundation, Durban, South Africa Prof. Tine Wedege, Malmö University, Malmö, Sweden 2 Adults Learning Mathematics – An International Journal ALM International Journal, Volume 9(2), pp. 1-115 Adults Learning Mathematics – An International Journal Special Issue Critical Moments in Adult Mathematics Education In this Volume 9(2) Editorial 4 Graham Griffiths and Anestine Hector-Mason More… or less? Towards a critical pedagogy of adult numeracy 7 Aileen Ackland “I remember the whole board being full of different calculations and trying 22 to make some sense of it.” The influence of significant moments in adult numeracy teachers’ own learning experiences on their teaching practice Carolyn Brooks Beyond questionnaires – Exploring adult education teachers’ mathematical beliefs 35 with pictures and interviews Sonja Beeli-Zimmermann Critical issues in adult numeracy practice – contradictions and strategies 54 David Kaye Numbers talk – words count: Language policy and adult numeracy education in 63 Wales and New Zealand Diana Coben and Barbara Miller-Reilly Accreditation not aggravation 79 Cath Moss and Judith Archer Implications of social practice theory for the development of a numeracy 85 programme for the Gusilay people group in Senegal Elisabeth Gerger Provoking mathematical thinking: Experiences of doing realistic mathematics tasks 97 with adult numeracy teachers Janette Gibney Volume 9(2) – November 2014 3 ALM International Journal, Volume 9(2), pp.4-6 Editorial Graham Griffiths Institute of Education, University of London London, UK [email protected] and Anestine Hector-Mason American Institutes for Research Washington, DC, USA [email protected] The 20th International Conference of Adults Learning Mathematics – A Research Forum was held in Caerleon at the University of South Wales. The title of the conference was ‘Critical Moments in Adult mathematics,’ a topic that is sufficiently broad to allow for a range of contributions from researchers and practitioners in adult mathematics. Two volumes of articles were derived from this effort, the first of which was published on ALM-online.net in June, 2014. The articles in this second volume address the title of the conference in a variety of ways, which reinforces the notion of the criticality of the varied mathematical moments that participants and submitters experienced. In the articles for this edition we see an undergirding motif reflecting cases made for an education based on a critical understanding of the world. Some articles reflect on critical moments in the lives of individuals – both teachers and learners, for example; in other articles, readers are made to reflect on the case for policy and practice to be more critically informed. In all cases, it appears very obvious that the authors offer adult numeracy practitioners a number of significant and meaningful ideas that could potentially reshape their thinking about mathematics, if not drive their efforts in advancing mathematical policy, practice, and research. The first article More… or less? Towards a critical pedagogy of adult numeracy by Aileen Ackland argues for a new look at the socio-cultural understanding of mathematics. Ackland posits that in Scotland, like many places across the world, a ‘social practice approach’ is often argued for in the context of mathematical practice, and adult numeracy practitioners are often encouraged to use ‘more context, more activity’, as she puts it. Ackland draws upon studies primarily around the idea of mathematical practice and she presents a strong argument indicating that the corpus she selected, display not only a limited perspective on mathematics in use, but they also form an essentially neo- deficit perspective in terms of approaches to mathematics pedagogy. Contending with these perspectives, Ackland argues for a critical mathematics education that uses real situations derived 4 Adults Learning Mathematics – An International Journal Griffiths & Hector-Mason, Editorial. from the adult learner perspectives. Ackland’s work presents several implications for teacher education. The next article is a contribution from Carolyn Brooks entitled “I remember the whole board being full of different calculations and trying to make some sense of it:” The influence of significant moments in adult numeracy teachers’ own learning experiences on their teaching practice. In the paper Brooks reports on the testimony of personal mathematics histories of two adult numeracy teachers including some critical moments in their personal developments. Brooks compares and contrasts the two experiences and argues that these are intertwined with their teaching practices. In line with the motif of both the conference and the articles in this edition of the journal, Brooks work appears to be an exemplification of Ackland’s notion around using real situations derived from the adult learner perspectives. In the next article, Sonja Beeli-Zimmermann, brings to light some of the similar concerns in both Brook’s and Ackland’s articles, though in her discussion of the issue of ‘beliefs,’ Zimmerman’s article reflects some of the same matters, and perhaps coheres more closely with Brook’s. Zimmerman’s Beyond questionnaires – Exploring adult education teachers’ mathematical beliefs with pictures and interviews is an exploratory investigation of the use of pictures in analysing the beliefs of teachers. The author poses a thought provoking, if not provocative question to participants, namely “Imagine you were an artist and agreed to do the following contract work: What is mathematics? Analyses of the images participants generated from this question involves the use of a scheme, including deductive codes, developed by Rolka and Halverscheid (2011). Like the other articles in this volume, this is also a unique contribution to mathematics in general and specifically to mathematical thinking. In Critical issues in adult numeracy practice – contradictions and strategies, David Kaye reflects on his experience working within the context of professional development in mathematics, and uses selected cases to generate three key areas for investigation. Kaye argues that three significant perspectives: ‘multiple intelligences’, ‘a profound understanding of fundamental mathematics’ and ‘how the mind creates mathematics’ provide a useful framework for practitioners to reflect critically on practice. The approach