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INQUIRY COMMUNITY IN AN ACTIVITY THEORY FRAME Barbara Jaworski & Simon Goodchild Agder University College, Norway A developmental research project, Learning Communities in Mathematics (LCM) bases its activity on the theoretical concepts of inquiry and community. It seeks to create knowledge and improve practice in the learning and teaching of mathematics through developing inquiry communities between teachers in schools and didacticians in a university setting. Analysis of data requires a recognition of the complexity of socially embedded factors, and we draw on activity theory to address complexity and deal with issues and tensions related to learning within the project. This theoretical paper presents our early thinking in analysing inquiry community within an activity theory frame. We present a theoretical paper related to a research project, LCM1 (Learning Communities in Mathematics) introduced in previous papers. The theoretical basis of our project is community of inquiry which is addressed in Jaworski (2004, 2005 and in press). In Goodchild & Jaworski (2005), we introduced an activity theory frame for analysing data within the project; here we provide a more detailed theorisation. INQUIRY COMMUNITIES AND DEVELOPMENTAL RESEARCH Teachers and didacticians each bring specialised knowledge to developing teaching, and hence learning, of mathematics. Together we can use, and explore the use of this knowledge in order to improve the mathematical learning experiences of students in classrooms and to know more about the creation of good opportunities for learning. The words “together” and “explore” adumbrate the concept of inquiry community (Wells, 1999). Fundamentally, inquiry and exploration are about questioning: asking and seeking to answer questions. Together, we ask and seek to answer questions to enable us to know more about mathematics teaching and learning. Moreover, the asking of questions is a developmental tool in drawing students, teachers and didacticians into a deeper awareness of their own actions, motives and goals (Jaworski, 1994; Mason, 2001). Thus we engage in developmental research: research which both studies the developmental process and, simultaneously, promotes development through engagement and questioning. We recognise engagement in inquiry activity within a well defined community as a significant means of coming to know. Thus, a major aim of our critical questioning approach is to take us, as a community, deeper into knowing mathematics teaching and learning. Not only are research questions defined and explored (through suitable data collection and analysis), but the whole research process is subject to question and exploration. We look critically at our research activity while engaging in and with it (Chaiklin, 1993). 2006. In Novotná, J., Moraová, H., Krátká, M. & Stehlíková, N. (Eds.). Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education, Vol. 3, pp. 353-360. Prague: PME. 3 - 353 Jaworski & Goodchild Teachers in the project belong to particular school communities within the school system, functioning within educational norms in society, and a political framework. Everyday factors such as curriculum, school timetables, responsibilities of teachers, time and energy afford and constrain what is possible (Engeström, 1999). We would not describe such communities as communities of inquiry, although they might be termed communities of practice (Wenger, 1998)2. They are groups of people dedicated to specific activity with established ways of thinking and doing which may be questioned but are most often taken for granted in the everyday momentum. Didacticians belong to a university community in which research activity is a norm involving familiarity with inquiry at formal levels. As teacher educators, didacticians are expected to question and theorise teaching in schools. However, questioning or theorising their own activity (of teaching and research) may not be a community norm. Thus, a desire to generate communities of inquiry within the project requires a serious addressing of the activity and goals of these various communities and a searching for ways of generating the kinds of thinking and coming to know that we expect from inquiry activity (Cochran Smith & Lytle, 1999; Wells, 1999) The LCM project was designed by didacticians who sought funding and had initial responsibility for the project. Schools and teachers were recruited after funding had been secured (Jaworski, 2005). Initial activity was motivated by the need to establish a project community and to start to understand jointly what inquiry might mean within the project. Didacticians have designed activity to create opportunity to work with teachers, to ask questions and to see common purposes in using inquiry approaches that bring both groups closer in thinking about and improving mathematics teaching and learning. We design workshops, and tasks for workshops, through which parallel design activity can start to take place in schools. This design process is generative and transformative (Kelly, 2003). We use tasks necessitating inquiry to generate inquiry activity through which a joint community, with common goals can emerge. Workshops have encouraged all of us to do mathematics together, to inquire in tackling mathematical problems, to raise questions about learning and teaching and to start to think and plan for the classroom. In schools, teacher teams, with didactician support, follow up experiences from workshops to explore possibilities for inquiry activity in classrooms, engaging themselves in inquiry through their design of tasks for students. These words express, simply, aspects of the project design and of its implementation but they underestimate the complexity of the process and the problematic nature of interpreting project goals into the realities of engagement in the project (Goodchild & Jaworski, 2005; Jaworski, 2005). We see tackling issues and tensions as forming the essence of our learning: at a practical level, for the project to make progress; and, at a theoretical level, to conceptualise their role in our learning development, both theoretical and practical. It is here that we are exploring the use of activity theory as an analytical framework and toolbox. 3 - 354 PME30 — 2006 Jaworski & Goodchild ACTIVITY THEORY (AT) Key concepts and terms Activity theory develops from the work of Vygotsky, particularly his arguments that cognition arises through the internalisation of external operations that occur in sociocultural contexts (Vygotsky, 1978). In identifying an intermediate link in the stimulus-response process, Vygotsky proposed the notion of a “complex mediated act” which “permits humans … to control their behaviour from the outside. The use of signs leads humans to a specific structure of behaviour that breaks away from biological development and creates new forms of a culturally-based psychological process” (1978, p. 40, italics in original). Through consideration of sociocultural artefacts that mediate between stimulus and response, the idea of a complex mediated act has been developed further. For example, following “the tradition of the theory of activity proposed by A. N. Leont’ev”, Wertsch refers to “goal-directed action” and writes, “human action typically employs ‘mediational means’ such as tools and language”. He goes on to emphasise that “the relationship between action and mediational means is so fundamental that it is more appropriate, when referring to the agent involved, to speak of ‘individual(s)-acting-with-mediational-means’ than to speak simply of ‘individual(s)’” (1991, p. 12). A. N. Leont’ev makes the following point, “in a society, humans do not simply find external conditions to which they must adapt their activity. Rather these social conditions bear with them the motives and goals of their activity, its means and modes. In a word, society produces the activity of the individuals it forms” (1979, pp. 47-48). So, according to Wertsch (p. 27), rather than “the idea that mental functioning in the individual derives from participation in social life”, “the specific structures and processes of intramental processing can be traced to their genetic precursors on the intermental plane”. The key idea for us here is that human activity is motivated within the sociocultural and historical processes of human life and comprises (mediated) goal-directed action. According to Leont’ev, “Activity is the non-additive, molar unit of life … it is not a reaction, or aggregate of reactions, but a system with its own structure, its own internal transformations, and its own development” (p. 46). He proposed a three tiered explanation of activity. First, human activity is always energised by a motive. Second, the basic components of human activity are the actions that translate activity motive into reality, where each action is subordinated to a conscious goal. Activity can be seen as comprising actions relating to associated goals. Thirdly, operations are the means by which an action is carried out, and are associated with the conditions under which actions take place. Leont’ev’s three tiers or levels can be summarised as: activity ÅÆ motive; actions ÅÆ goals; operations ÅÆ conditions. Leont’ev writes emphatically about the movement of the elements between the ‘levels’ within an activity system: activity can become actions and actions develop into activity, goals become motives and vice-versa, similarly with operationsconditions. The crucial differences seem to be: first, goals are conscious, if the motive of activity becomes conscious it becomes a motive-goal; second, motive is about an energizing force for the activity and the actions, it is not something that is PME30 — 2006 3 - 355 Jaworski & Goodchild attained but rather drives the activity forward; on the other hand goals are results that can be achieved. Leont’ev writes “The basic ‘components’ of various human activities are the actions that translate them into reality, We call a process an action when it is subordinated to the idea of achieving a result, i.e. a process that is subordinated to a conscious goal” (pp. 59- 60). Exemplifying AT terms and concepts in the LCM Project Here we exemplify briefly the concepts and terms above with reference to examples from the LCM project. These examples (rows in the table below) are deeply related to each other and so could be considered elements of one complex activity system. We separate them artificially to show elements of the three levels (the columns). Exemplification is an oversimplification, but serves the purpose of clarifying how we see these terms and concepts fitting our project and serving as a basis for analysis. In each case actions and operations are only examples of many possibilities. Activity (System) & Motive Developmental research, whose motive is to study developmental processes and, simultaneously, promote development in the learning and teaching of mathematics. A school, whose motive is to educate pupils. The LCM project as community of inquiry, with motive to provide the environment and modes of action for teaching development to be realised. Actions & Goals Asking researchable questions, collecting and analysing data leading to findings or outcomes related to new knowledge and/or practice. Operations & Conditions Making methodological decisions related to principled and effective ways of collecting and analysing data to address research questions. Organising teaching groups Choosing topics and and designing lessons to planning classroom tasks promote learning according to according to the school’s the declared curriculum. approaches to addressing the curriculum. (Planlegg et opplegg3) Creating opportunities for Teachers and didacticians working together and engaging working in groups in in inquiry to achieve a working workshops on mathematical community with practical problems to exemplify knowledge of inquiry inquiry processes and processes. develop common understandings. Mediation in goal directed action Within an activity system, goal-directed actions are mediated by tools and signs as represented by the basic mediational triangle deriving from Vygotsky and developed further by Leont’ev (Figure 1) (e.g., Engeström, 1999; Vygotsky, 1978). Here we see the human subject or group seeking to achieve a goal or object, mediated by some tool or sign where the nature of the tool or sign is deeply embedded in the activity. In recognition of this deep embeddedness, Engeström expanded the basic triangle to the “complex model of an activity system” (1999, p. 31) to recognise mediation by or through community, rules of activity and division of labour within the activity system. Each of the connections within the expanded triangle indicates possible 3 - 356 PME30 — 2006 Jaworski & Goodchild mediational means within the system. The double arrows throughout indicate dialectical dependencies between the elements of a system. TOOLS MEDIATING OBJECT SUBJECT SUBJEC OBJEC OUTCOM OUTCOM RULES COMMUNIT DIVISION OF Based on Vygotsky’s model of a complex mediated Engeström’s ’complex model of an activity Figure 1 Figure 2 LCM AS AN ACTIVITY SYSTEM Within the LCM project we engage in research that seeks to promote development in teaching and learning mathematics and to study that development. We believe this can be achieved through the development of an inquiry community comprising teachers and didacticians. This is the energizing force of the project, it is the motive for the activity of the project. The motive provides a rationale for the activity, and an incentive for the actions that comprise the activity. The actions are ‘energized’ by the motive but they are directed towards achieving some conscious goals, achievable results that will arise from the actions. For example, we want to achieve a sense of community, so we organise workshops and within those workshops opportunities for teachers and didacticians to meet together, work together and discuss together. Individual didacticians also spend time on their own seeking out mathematical activities for the workshops; in this action the goal is to find tasks that show potential to be of use. The result of this time spent is an ‘oppgave’3; neither the action nor the ‘oppgave’ is the central purpose of the project, but the motivation for the action of finding the tasks is the same ‘energizing force’ (motive) of the project. In the project activity system a number of mediational means are available to support or enable the actions that comprise the activity. For Vygotsky the main tool was language and the project seeks to develop a language of inquiry within the community. It has been emphasised that the asking of questions is fundamental to inquiry. In this respect the questions are an important tool or artefact within the envisaged activity system. The workshops, tasks, research literature, meetings of teachers in school or didacticians at the college also have a role as ‘mediating artefacts’. The rules of the activity system, now, include rules underpinning rigorous research and rules governing teachers’ and students’ work in school, such as following the national curriculum. However, through the project we anticipate that our understanding of the developmental research paradigm will grow and as teachers engage to a greater degree in teaching characterised by inquiry processes it is PME30 — 2006 3 - 357 Jaworski & Goodchild possible that their interpretation of the curriculum ‘rules’ may change. At the outset of the project, there were a number of separate communities, the community of didacticians and a number of school communities, each pursuing their own activity largely independent of the others. In coming together within the project it was recognised by each community that we can learn together and develop our practice. The final item in Engeström’s model is ‘division of labour’. Inevitably in the envisaged activity system didacticians, teachers and students will have distinct roles that engage them in different tasks and actions. As teachers increasingly recognise and value their own research potential and didacticians participate in school and classroom, we anticipate that the division or labour will change. Thus we see, and expect to see, developments in the activity system as we engage in it. THE TRANSFORMATIVE NATURE OF THE ACTIVITY SYSTEM The LCM project emerges from a vision of an activity system whose motive is to engage, collaboratively, didacticians, teachers and students in developing and researching the teaching and learning of mathematics through processes of inquiry. At the time the project was proposed, this activity system did not exist, nor did it exist when the proposal began to be implemented. Now, halfway through the initial funding period, an activity system exists but we question the extent to which it fulfils what was envisioned. The vision is of a coherent community of co-learners taking roles relevant to the nature of their participation with responsibility as partners within the project. For example teachers and didacticians might be both insider and outsider researchers: insiders, as they seek to explore and develop their own practice and outsiders as they explore characteristics in their students’ learning and understanding of mathematics, or in the activity of their co-participants (Jaworski, 2005). The words above point not only to possible divergence between original goals and current activity, but to the transformative nature of the process in which we engage and the problematic nature of what we experience. In promoting development of inquiry communities we are motivated by theoretically warranted visions of transformation in mathematics teaching and learning. In the reality of project implementation, we recognize people, relationships, existing systems, ways of being and thinking and obstacles to change. Every event emerging in research embodies a complex story (e.g., Goodchild & Jaworski, 2005). We learn about the development of inquiry communities as teachers and didacticians act together and embrace notions of inquiry. We have talked about using inquiry as a tool leading to development of inquiry as a way of being (Jaworski, in press). We see ‘inquiry as a tool’ in many circumstances within the project. For example, tasks designed for workshops promote joint asking of questions and associated exploration. Tasks, questions and exploration are tools mediating activity. Use of these tools involves goal directed actions comprising condition-related operations. However, ‘inquiry as a way of being’ is a motive-goal (i.e., where the motive becomes conscious) of activity, rather than an outcome from it. Achieving an inquiry stance is ongoing and problematic. 3 - 358 PME30 — 2006 Jaworski & Goodchild Our developmental process is a struggle with developing thinking related to intransigencies in everyday activity. While workshop activity might prove inspirational in illuminating concepts of inquiry, and promote associated actions in school activity, the actions and emergent thinking contend with the demands of school activity, and established ways of thinking about it. Reports at a workshop of actions deriving from the previous workshop, reveal activity and thinking that both indicates elements of progress, and reveals limitations and constraints in vision and practice. As the project progresses, our analysis of data both charts the nature of development and reveals the problematic nature of that development. We are submerged in the complexity of relationships, interactions, demands from established communities with their deeply embedded ways of thinking, and our ongoing struggles with changing thinking and practice according to theoretical principles. We both recognize our situation as a complexity of activity systems, and draw on analytical frameworks in AT to navigate the complexity. The AT triangle offers a unit of analysis for all levels of the project. Its value lies in the possibility of exploring the mediating elements and the dialectical relationships between elements. As the project is intended as developmental research the concern is to engineer, monitor and research changes within the activity system. Engeström suggests that contradictions and tensions take a central role as sources of change and development and thus the model can be used as both development and research tool in that it draws attention to those points where contradictions or tensions exists, whether these be within the elements or the dialectical relationships between the elements and thus prompts “a search for solutions … (that) reaches its peak when a new model for the activity is designed and implemented” Engeström (1999, p. 34). Engeström refers to this process as “the expansive cycle” (ibid. p. 33). It is easy to be discouraged when plans do not result in envisioned outcomes. Particularly in the activity in schools, there have been many obstacles to realisation of teams of teachers working in inquiry modes. The developmental nature of the project is that we work with the perceived obstacles and through this work relationships develop and forms of activity emerge that could not have been predicted in the original design. We work with what we have, and rethink according to theoretical principles and emerging reality. Periodically, in the cycles of activity and thinking, a recognisably new way of acting and thinking emerges, and becomes new activity. We see this as an expansive cycle. Its importance for the project is twofold. Firstly it is manifested in a build up of tension with transformative power in that it promotes a new wave of activity with clear actions and goals. Secondly, and possibly most powerfully, it creates new learning in which we gain new insights to theoretical realisation in social and historical complexity. References Chaiklin, S. (1993). Understanding the social scientific practice of understanding practice. In S. Chaiklin & J. Lave (Eds.), Understanding practice (pp. 377-401). Cambridge: Cambridge University Press. PME30 — 2006 3 - 359 Jaworski & Goodchild Cochran Smith, M. & Lytle, S. L. (1999). Relationships of knowledge and practice: teacher learning in communities’. In A. Iran-Nejad & P. D. Pearson (Eds.), Review of Research in Education (pp. 249-305). Washington: American Educational Research Association. Engeström, Y. (1999). Activity theory and individual and social transformation. In Y. Engeström, R. Miettinen & R-L Punamäki (Eds.), Perspectives on activity theory (pp. 1938). Cambridge: Cambridge University Press. Goodchild, S. & Jaworski, B. (2005). Identifying contradictions in a teaching and learning development project. In H. L. Chick & J. L. Vincent, (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (pp. 41-47). Melbourne, Australia: University of Melbourne. Jaworski, B. (1994). Investigating mathematics teaching. London: Falmer Press. Jaworski, B. (2004). Insiders and outsiders in mathematics teaching development: The design and study of classroom activity. In O. Macnamara & R. Barwell (Eds.), Research in Mathematics Education: Papers of the British Society for Research into Learning Mathematics: Vol 6 (pp. 3-22). London: BSRLM. Jaworski, B. (2005). Learning communities in mathematics: Creating an inquiry community between teachers and didacticians. In R. Barwell and A. Noyes (Eds.), Research in Mathematics Education: Papers of the British Society for Research into Learning Mathematics, Vol. 7 (pp. 101-119). London: BSRLM Jaworski B. (in press). Theory and practice in mathematics teaching development: Critical inquiry as a mode of learning in teaching. Journal of Mathematics Teacher Education, 9(2). Kelly, A. E. (2003). Research as design. Educational Researcher, 32 (1), 3-4 Leont’ev, A. N. (1979). The problem of activity in psychology. In J. V. Wertsch (Ed.), The concept of activity in Soviet psychology (pp. 37-71). New York: M. E. Sharpe. Mason, J. (2001). Researching your own classroom practice. London: Routledge Falmer. Vygotsky, L. S. (1978). Mind in society. Cambridge MA: Harvard University Press. Wertsch, J. V. (1991). Voices of the mind. Cambridge MA: Harvard University Press. Wells, G. (1999). Dialogic inquiry. Cambridge: Cambridge University Press. Wenger, E. (1998). Communities of practice. Cambridge: Cambridge University Press. Notes 1 The LCM Project is supported within the KUL Programme (Knowledge, Education and Learning) of the Norwegian Research Council. Project number 157949/S20. 2 We have demonstrated a fundamental difference between community of practice and community of inquiry (e.g., Jaworski, in press). Space does not allow articulation here. 3 Key Norwegian concepts and terms have entered into our vocabulary and are difficult to replace simply in English. Planlegg et opplegg refers to teachers’ planning of tasks for the classroom, and their resulting lesson plans. Tasks and all their related feature are called oppgaver. 3 - 360 PME30 — 2006