Vygotskian approaches in human development in the information era

The paper explores the opportunities and challenges of learning and teaching mathematics in the information era from a Vygotskian perspective. A systemic approach is taken to an investigation of the ways in which information technologies have changed the contexts for and forms of mathematical activity in society and the challenge that this change presents to mathematics educators at all levels.     

Exploring pedagogies to elevate inquiry: teaching action research in the third space

ABSTRACT

This study chronicles a semester long inquiry focused on the impacts of pedagogical strategies informed by the tenets of third space theory on my own practices and understanding of students’ learning outcomes in an action research course. As I applied new instructional strategies to promote discourse and critical inquiry, I reflexively explored how these approaches enhanced my impacts on students’ learning and praxis of action research. This paper first provides a brief introduction to third space theory and then describes how I infused this framework into my course approach, the different types of data collected and analyzed to gauge the impacts of new pedagogies, and findings that emerged. These are summarized in relation to the conditions that both undergirded and elevated students’ engagement, and directions for further research to advance the praxis of action research across teacher education contexts.     

Interpreting unproblematic high achievement in mathematics: towards theoretical reflexivity

This article contributes to the long-running discussion about the gendering of mathematics learning by exploring the social biographies of six exceptionally high-attaining mathematics students, four women and two men. In contrast to some prior studies, these students appeared to feel no need to downplay being ‘good at maths’ in order to maintain social credibility with their socially privileged peers. I attempt to make sense of their stories from two theoretical standpoints: (1) a post-structuralist approach that emphasises discourses that position mathematics as masculine and (2) an approach, based on Bourdieu, that asks how mathematics is valued in different school and peer group settings. I show how, as I worked with the data, my emphasis moved from the former to the latter, and suggest that research in gender and education has much to gain from theoretical reflexivity alongside personal and methodological reflexivity.     

Embracing and Harnessing the Intimate Connection Between Emotion and Cognition to Help Students Learn

Traditionally, cognition and emotion were believed to be independent systems; however, research in the cognitive and neurobiological sciences has shown that the relationship between cognition and emotion is both interdependent and extensive. This intimate connection between emotion and cognition is leading to a number of insights that have the potential to inform and transform educational practices at all levels—from the classroom to the curriculum to educational policy. The question that has been on my mind (and on my heart) is, as a teacher, how can I both embrace and harness the power of emotion to help my students’ learning be more meaningful, useful, and intrinsically motivated? In this article, I would like to share with you some of the effective practices that I have implemented in my classroom and how I have worked to intentionally embed the emotional aspect of learning into the framework of the courses I teach.     

Material encounters and media events: what kind of mathematics can a body do?

This paper contributes to research on the material dimensions of teaching and learning mathematics, arguing that perception is not sensory integration or synthesis of multi-modal information, but rather a speculative investment in specific material encounters. This approach entails sociopolitical consequences for how we work with dis/ability in mathematics classrooms because it foregrounds how the relationship between sense (as meaning) and sense (as sensation) can be fundamentally altered. I focus on how visual perception in mathematics can be reconceived in these terms, drawing principally on the philosophical insights of Michel Serres and Brian Massumi. This paper shows how philosophical work on perception can shed light on embodied mathematics, opening up discussion about the potentiality of the human body.     

A Model of Classroom Coping Strategies

This paper represents an attempt to construct a theoretical model with which to analyse the social context and genesis of classroom coping strategies, thereby linking macro‐ and micro‐factors. I approach this firstly through a critique of A. Hargreaves’ analysis which tends to emphasise macro‐factors and constraints on teacher action. I suggest that this analysis should be balanced and augmented by recognition of more independent and creative action in micro contexts. In the second part of the paper I develop Woods’ work on teacher survival by considering the use of the interactionist concept of ‘self and the phenomenological concept of ‘interests‐at‐hand’ as a means of defining the subjective meaning of ‘coping’, and its implication for classroom processes. I emphasise the importance of teacher biography. Finally a conceptual model which seeks to integrate many macro‐ and micro‐factors which bear on classroom coping strategies is presented.     

Whither social theory?

What is the place of social theory in mathematics education research, and what is it for? This special issue of Educational Studies in Mathematics offers insights on what could be the role of some sociological theories in a field that has historically privileged learning theories coming from psychology and mathematics as the main theoretical frames informing research. Although during the last 10 years the term “socio-cultural” has become part of the accepted and widespread trends of mathematics education research when addressing learning, this issue gathers a collection of papers that depart from a “socio-cultural” approach to learning and rather deploy sociological theories in the analysis of mathematics education practices. In this commentary paper, we will point to what we see to be the contributions of these papers to the field. We will do so by highlighting issues that run through the six papers. We will try to synthetize what we think are the benchmarks of the social approach to mathematics education that they propose. We will also take a critical stance and indicate some possible extensions of the use of social theory that are not addressed in this special issue but nonetheless are worth being explored for a fuller understanding of the “social” in mathematics education.     

Mentor, Mentee and Mathematics: A Story of Professional Development

In this paper, I critically examine my role as a mentor to a group of mid-career mathematics teachers, to better understand how mentoring practices influence teacher learning. The teachers taught mathematics to Grades 5 or 6. They planned and taught lessons to promote conceptual understanding of mathematics through the use of discussions, and reflected on their own and pupils' learning in the process. The study lasted for a year. It draws on qualitative data from sources such as semi-structured interviews, participant observation, and teachers' reflective journals. As a mentor/researcher I found that in the case of mentees' perception of the mentor as a problem solver or evaluator of performance learning was inhibited, whereas mentor and mentee relationships established on mutual trust supported mentees' personal and professional growth. The close work with the teachers also gave me insights into aspects of learning influenced by teachers' beliefs and understanding of mathematics and of how learning takes place. The study has implications for other such teacher education initiatives, particularly in the context of developing countries like Pakistan. This revised version was published online in July 2006 with corrections to the Cover Date.     

Who is not multilingual now?

What is the relationship between research into multilingualism and research concerned more generally with language and communication in mathematics education? Diversity in linguistic practices is universal in modern society and poses problems for teaching and learning even in apparently monolingual contexts. Research in multilingualism and mathematics education offers constructs and insights that can inform research and pedagogy more widely.     

Adapting the boundaries in primary physical education: an account of my learning,my educational influence and improved practice

In this paper I explore how I have come to theorise my work as a critical emancipatory practice as a lecturer in primary physical education (PE). I give an account of what I understand to be the epistemological foundations and practices of practitioner research and my potential educational influence in my own and other practitioner-researchers’ learning. I explain how I have generated my living educational theory of practice and discuss the changes in my learning from a propositional approach towards a dynamic epistemology of practice that is grounded in inclusional and dialogical ways of knowing. Within my paper I position myself as a professional educator and researcher, and share the exciting and transformational experiences of teaching and learning in evolving action research cycles of practice. I view my learning to date as an active act, working with the novice teachers I support to offer improvement and change in our future practice. I celebrate my reconceptualised view of education as a learner from within my practice and explain my move from knowledge transfer to knowledge co-creation. I make an original contribution to educational knowledge by explaining how I try to inspire others to research their practice and contribute to a new scholarship of educational enquiry.     

Making sense of power relations in a Malaysian English-as-a-second-language academic writing classroom

The role of power in an English-as-a-second-language classroom has yet to be fully explored by an action research practitioner, especially in a Malaysian higher education setting. This study aims to contribute to this gap by working within an academic literacies perspective to teaching academic writing, which propagates the understanding of power-relational, socio-cultural and epistemological conditions for effective teaching and learning. As the teacher in this classroom, I focus on how power-relational conditions play out. To activate the power conditions, I used a teaching principle in Teaching English to Speakers of Other Languages (TESOL)-negotiated interaction to reduce power-based mismatches between participants in a teaching or learning relationship in my classroom, drawing upon Kumaravadivelu’s work on post-method pedagogy for TESOL; that is, not being bound by any specific method of teaching. In analysing the different types of power that were operational in my classroom, wider implications of power that operate beyond the classroom level and how they impacted teaching and learning decisions were found to be highly illuminating. The action research methodology used for this study enabled me to reflect critically on my detailed diary recordings and student letter and interview collections, which in turn impacted on my teaching decisions as each teaching cycle was completed. My reflections also help shape my evolving identity as a teacher-researcher throughout this ongoing Malaysian action research journey.     

‘Doing’ Persuading: Actively Constructing Knowledge,Voice and Self

I explore a series of incidents in my English classroom, which occurred while I was preparing my students for their high-stakes GCSE English Language exam (‘Paper 2: Writers’ viewpoints and perspectives’). I thereby attempt to confront some of my own failings and biases with regard to non-fiction and the teaching of persuasive writing in particular, as well as to unleash the huge potential I now believe it offers, when combined with the multi-voiced space of a classroom, for creative play and the productive skills of English. In doing so I argue, drawing on Vygotskian notions of the internalisation of concepts and the developmental benefits of play, that in order for truly ‘productive’ learning to occur, students need agency and a sense of empowerment to construct knowledge together, and to experiment with and develop their understanding of and flexibility with their own ‘voice’.     

Collaborative research for assessment for learning

This paper reports on a collaborative research study between three secondary teachers and two university researchers, initiated by the teachers, into the practice and impacts of assessment for learning in science, geography and history classes. The research provides insights into how teachers and researchers can collaborate to develop a research and practice agenda. The study illustrates the need for a dynamic interconnection between the personal, micro or school-related level and the macro or policy level factors. The findings highlight the importance of external support, shared teacher knowledge and beliefs, professional experimentation, and shared reflection on student responses to classroom innovations.     

How inconvenient assumptions affect preservice teachers’ uptake of new interactional patterns in mathematics: analysis and aspiration through a bifocal lens

In this paper, I highlight the inadequacies of contemporary theoretical and philosophical orthodoxies to fully address pedagogic change. The required change is in mathematics education, and it has to do with enabling preservice teachers, upon graduation, to rework extant power relations in implementing new interactional patterns that centre the mathematics and the learner in dynamic, productive interaction. I interpret data from published research and my own teaching using psychological, overlaid with poststructuralist, constructs of the relationship between knowledge and action. In data interpretation I read through the words for a psychological interpretation (meaning), and I look at the words for poststructuralist indications of subjectification and identity formation (related to how well students recognise themselves as full participants in the combined discourses of mathematics and education). I have my cake and eat it; contradictory notions of the learner and learning to teach in innovative ways are held together to demonstrate (a) how it can happen that a teacher educator’s aspirations can be held ransom to constituted assumptions that inconveniently work against change, and (b) how the recognition that humanist assumptions, mathematical proficiency and agency are discursively constituted (Davies, 1990) can suggest avenues for change in teacher education.     

Unpacking a Liturgical Framing of Desire for the Purposes of Educational Research

Much of the public discourse on education arguably reinforces the assumption that most stakeholders share the same desires for teaching and learning—desires reflecting a liberal paradigm that stresses individualism, control, and efficiency. But there are other desires, and additional empirical research informed by a Vygotskian sociocultural theory of learning could enrich this discourse. In my view, such research could benefit from a framework of desire compatible with the theory's central assumptions of learning as socially situated in cultural practices, teleological, and transformational. To this purpose, I offer a liturgical framing of desire put forth by James K. A. Smith, which treats humans as essentially desiring beings and defines desire as a potent force formed through participation in communal practices that orient practitioners' hearts (eros) toward particular futures (telos). I show how this framing satisfies key features of sociocultural theory and highlight two examples of how desire has been qualitatively examined and where the framing might enrich further examinations of education settings.     

Digital Art Making as a Representational Process

In this article I bring artistic production into the learning sciences conversation by using the production of representations as a bridging concept between art making and the new literacies. Through case studies with 4 youth media arts organizations across the United States I ask how organizations structure the process of producing autobiographical digital art through a focus on representational tasks and how learning can be traced by examining youth artists' representations over time. Using a distributed cognition framework I analyze data on the process of making digital art in terms of the macro and micro tasks performed in order to identify occasions for external representation construction and use across organizations. I then examine how individual youth engage in these macro and micro tasks by producing representations that demonstrate their understanding. These analyses show that youth media arts organization production processes engage young artists in a representational trajectory that begins with developing a story about the self, moves toward a focus on how the tools of the medium afford representation of that story, and culminates in digital representations that reflect an understanding of the relationship between story and tools.     

In Search of Ways to Improve Practicum Learning: Self-Study of the Teacher Educator/Researcher as Responsive Listener

Abstract

Teacher education programs that appear to be more successful work to thread practicum experiences and on-campus courses with an eye to achieving overall program coherence. As part of a funded research project centred on understanding how teacher candidates perceive quality in their practicum experiences and, by extension, in their professional learning, focus groups were recruited for a series of discussions that extended over an academic year. I undertook this self-study in an attempt to examine the conditions for learning that made these focus groups so successful by virtue of participants’ commitment, engagement, focus and drive to become the best teachers they could possibly be. Self-study was an avenue for me to develop insights into my practice and to identify ways to move forward to become a more effective teacher educator who could model and scaffold responsive listening and relationship-building for future teachers. The two questions driving this self-study were “How does adopting and promoting a listening perspective improve participants learning?” And “What is transformative about responsive listening?” Identifying and challenging my assumptions were initial steps in understanding what a listening perspective entails, the importance of authorizing student perspectives and developing their pedagogical voices. Responsive listening became a means to interrogate my practice, to reframe my experience, to work in and from action, and to become more comfortable with the uncertain spaces where deep learning can occur – for myself and for those whom I teach. In so doing, I came closer to appreciating the possibilities for transformation.     

‘Don't talk about what you don't know’: on (not) conducting research with/in Indigenous contexts

This article raises the recurrent question whether non-indigenous researchers should attempt to research with/in Indigenous communities. If research is indeed a metaphor of colonization, then we have two choices: we have to learn to conduct research in ways that meet the needs of Indigenous communities and are non-exploitative, culturally appropriate and inclusive, or we need to relinquish our roles as researchers within Indigenous contexts and make way for Indigenous researchers. Both of these alternatives are complex. Hence in this article I trace my learning journey; a journey that has culminated in the realization that it is not my place to conduct research within Indigenous contexts, but that I can use ‘what I know’ – rather than imagining that I know about Indigenous epistemologies or Indigenous experiences under colonialism – to work as an ally with Indigenous researchers. Coming as I do, from a position of relative power, I can also contribute in some small way to the project of decolonizing methodologies by speaking ‘to my own mob’.     

Building the wall brick by brick: one prospective teacher’s experiences with mathematics anxiety

Mathematics education researchers have investigated mathematics anxiety in prospective elementary teachers. While many of these studies have focused on the bodily sensations and emotions of mathematics anxiety, particularly those felt in assessment situations, opportunities remain to investigate how prospective elementary teachers interpret their experiences with mathematics anxiety and connect them over time to compose personal histories of mathematics anxiety. Currently, over 90 % of elementary teachers in US schools are women, and women have been shown to suffer more from mathematics anxiety than do men. In this article, I analyze how one woman prospective elementary teacher described, explained, and related her experiences of mathematics anxiety across her personal narratives of learning mathematics as a K-12 student and of learning to teach mathematics as a college student in a teacher preparation program. My research demonstrates that experiences of mathematics anxiety may persist beyond assessment situations to influence women prospective elementary teachers’ larger mathematical histories. I also show that women prospective elementary teachers may interpret mathematics anxiety as specific fears (e.g., loss of opportunities for social participation) and may develop particular coping strategies related to those fears. Finally, I point out that while a coping strategy may be used consistently across K-12 mathematics learning and undergraduate teacher preparation, and may even offer a woman prospective elementary teacher some relief from mathematics anxiety, it may also limit her mathematics learning and professional development. To conclude, I present implications of my research for mathematics teacher educators.     

Conceptualising Resources as a Theme for Teacher Education

In this report, I examine resources and their use in school mathematics. I do so from the perspective of mathematics teacher education and with a view to the practice of school mathematics. I argue that the effectiveness of resources for mathematical learning lies in their use, that is, in the classroom teaching and learning context. The argument pivots on the concepts of school mathematics as a hybrid practice and on the transparency of resources in use. These concepts are elaborated by examples of resource use within an in-service teacher education research project in South Africa. I propose that mathematics teacher education needs to focus more attention on resources, on what they are and how they work as an extension of the teacher in school mathematics practice. In so doing, the report provides a language with which mathematics teacher educators and mathematics teachers can investigate teachers' use of resources to support mathematical learning in particular and diverse contexts. This revised version was published online in September 2006 with corrections to the Cover Date.