Enhancing mathematics teaching and learning in early childhood settings Maggie Haynes, Carol Cardno, and Janita Craw 2007 Teaching and Learning Research Initiative P O Box 3237 Wellington New Zealand www.tlri.org.nz © Crown, 2007 1 Acknowledgements First and foremost we wish to acknowledge the teaching teams at the three kindergartens: y Avondale Kindergarten: Marjo Whyte-van Diessen and team y Birdwood Kindergarten: Kathryn Palmer and Melanie Chaplin y Don Buck Kindergarten: Katrina Bone and Petra Wyrsch The kindergarten teachers are acknowledged in person, together with the names of their kindergartens, because it was their wish not to remain anonymous. We very much appreciated the input from our Advisory Committee: Dr Gregor Lomas (University of Auckland), together with Shelley Shennan and Deena Mayor (Auckland Kindergarten Association). We thank them for their valuable contributions to the project. We also thank our colleagues in the School of Education, Unitec Institute of Technology, for their support during the project and, in particular, we acknowledge the ongoing interest and acceptance of our involvement from our colleagues in the early childhood programmes. 2 Table of Contents Acknowledgements 2 1. Aims, objectives, and research questions 6 Aim 6 Objectives 6 Rationale 8 Research questions 9 2. Research design and methodologies 10 Action research defined 10 The collaborative learning process and research rigour 11 The action research settings 13 Doing action research—the process 14 Reconnaissance 15 Intervention 16 Evaluation 16 Data-gathering methods 16 Documentary analysis 16 Small-scale survey questionnaires 17 Reflective journals and diaries 17 Notes, emails, and photographs as evidence 17 Challenges for the researcher-facilitators 17 Challenges for the participants 18 Teachers becoming practitioner-researchers 18 3. Project findings 20 Introduction to the case studies 20 The case of Avondale Kindergarten: establishing a platform for making mathematics prominent 21 The kindergarten 21 Understanding the problem—the reconnaissance phase 22 Intervention phase—planning and monitoring new practices 28 Monitoring the Intervention 30 Evaluating the intervention and identifying the next steps 33 The case of Birdwood Kindergarten: enhancing collaborative mathematical partnerships between teachers and parents 38 The kindergarten 38 3 Understanding the problem—the reconnaissance phase 39 Intervention—planning and monitoring new practices 45 Monitoring the intervention 47 Evaluating the intervention and identifying the next steps 50 The case of Don Buck Kindergarten: growing teacher confidence in strategising for children’s mathematical learning 53 The kindergarten 53 Understanding the problem—the reconnaissance phase 54 Intervention—planning and monitoring new practices 63 Evaluation 71 End-point evaluation 72 Meta-analysis of the findings 74 Discussion of the findings related to the strategic value of the TLRI 74 Discussion of the findings related to the practice value of the TLRI 80 Summarising the findings: action research as a model for improving the teaching and learning of mathematics 85 Final words from the teachers 86 4. Limitations of the project and possible directions for future research 88 The kindergarten teacher as researcher 88 Time commitment for practitioners 88 Focus on mathematics within early childhood settings 88 Changes in personnel in collaborative early childhood teaching 89 Early childhood teachers’ own perceptions of limitations 89 Researchers maintaining consistency 89 Recommendations for future work and for the TLRI 89 Children’s mathematical outcomes 90 Moving beyond first order change 90 Pedagogical documentation and children’s voices 90 Broadening the knowledge domain of early childhood mathematics 91 5. How the project contributed to building capability and capacity 92 Research collaborators 92 Capacity and capability building 92 The early childhood teacher as researcher 93 Evaluating the process 95 6. References 98 References 98 Dissemination 101 Presentations generated so far by this research 101 4 Tables Table 1 Intervention plan: Avondale Kindergarten 28 Table 2 Document analysis Don Buck Kindergarten 58 Table 3 Intervention plan: Don Buck Kindergarten 65 Table 4 TLRI cluster evaluation execise—SWOT analysis 94 Figures Figure 1 QaAction research spiral 11 Figure 2 Cycle of research and action events 15 Images Image 1: The long and the longer dragon 31 Image 2: The cover of the mathematics book on display 31 Image 3: A page from the mathematics book 32 Image 4: Display of extracts from the Education Review Office report 42 Image 5: The wall display “making mathematics visible” 46 Image 6: The mathematics newsletter 49 Image 7: The mathematics “Parent’s Voice for Mathematics” form 50 Image 8: Audit list of the mathematical potential around the kindergarten 67 Image 9: Example of a mathematics poster in a curriculum area 69 5 1. Aims, objectives, and research questions Aim The overall aim of the project was to engage early childhood teachers in investigating and improving their expertise in the teaching and learning of mathematics. The intention of the project was to develop a research environment through which researchers and kindergarten teachers worked collaboratively, using action research methodology, to explore means by which mathematical outcomes for children could be maximised. The research arose from the premise that within the field of mathematics education, while much has been written about mathematical experiences of both learners and teachers in the compulsory (school) sectors of education, very little is documented on mathematical learning and teaching in the early childhood sector from the perspective of the teacher, and particularly within Aotearoa New Zealand. The project engaged the kindergarten teachers through one cycle of action research: from reconnaissance, through intervention, to evaluation. This provided them with opportunities to self- select a relevant issue in mathematics teaching and learning through exploration and reflection on their own mathematics knowledge, their personal dispositions towards mathematics, and their teaching strategies. It was expected that changes in practice would improve mathematical outcomes for children. It was hoped that the findings from this project would: y act as a useful learning tool for early childhood teachers across the wider early childhood education field by provoking them to consider the teaching and learning of mathematics in their own contexts; y contribute to the body of knowledge within mathematics education research both within Aotearoa New Zealand and internationally; and y broaden the action research field by increasing the possibilities for early childhood teachers to engage in action research. Objectives The overall objectives of the project addressed the strategic, research and practice principles of the Teaching and Learning Research Initiative (TLRI); specifically, through teachers’ increased 6 understanding of the processes of mathematics teaching and learning; by building capacity through teachers’ engagement in personalised and contextualised research; and through the teachers’ evaluation of both the mathematical and the action research aspects of the project. This was achieved through the kindergarten teachers applying a cycle of action research in order to improve their practice. An action research model was used to create, for each kindergarten teaching team, an independent framework for researching within their own kindergarten setting and community. Cardno (2003) describes how action research “creates the expectation that those involved will be researching a particular situation with the intent of taking action that will make a difference … [that] will bring about change or improvement” (p. 1). The partnership kindergartens that participated in this project were involved in the planning, discussion, and decision-making, as occurs at all stages of an action research process, as each team of teachers self-identified a focus for their action research. Hence the research provided a base for self-review which, according to McLachlan-Smith, Grey and Haynes (2000), fosters not only improvement but also empowerment in early childhood teachers. The objectives of each phase of the project were: y reconnaissance phase: to investigate what research and practice reveals in relation to enablers and barriers that enhance the quality of mathematics learning and teaching, through y working in partnership with the teachers in each kindergarten through the formation of three action research groups; y conducting a review of relevant literature that informs the research problem; y examining issues and conditions for teachers that create barriers to mathematics teaching and learning in their kindergartens; y identifying strategies that are successful, and skills needed, to enhance effectiveness in the teaching of mathematics; and y facilitating each kindergarten to plan an intervention. y intervention phase: to improve practice by intervening in the status quo, through y establishing a working theory of effective mathematics teaching and learning practice; and y involving whänau/families in an appreciation of conditions that support and enhance the possibilities for increased effectiveness in the teaching of mathematics. y evaluation phase: to conduct an evidence-based evaluation of the effectiveness of the intervention, through y planning for the evaluation events; and y reflecting on the effectiveness of change in the teaching and learning of mathematics. An action research approach to research does not aim for replication. However, in addition to documenting the mathematical journey for each individual kindergarten, it was also the 7 researchers’ objective to execute a meta-analysis of the three site-specific cycles of action research in order to: y establish similarities and differences between the findings in the three research settings; y strengthen the transferability of new knowledge; and y increase the rigour and validity of the project overall. Rationale In view of the ongoing government strategy to promote numeracy knowledge and skill development in the school sector in Aotearoa New Zealand, it is crucial that prestige be accorded to exploring issues that relate to effective mathematical learning and teaching in the years of early childhood education. It is important to undertake specific research within an early childhood pedagogy to establish guidelines for teachers that promote best, or wise, teaching practices: practices that improve the outcomes for children (Peters, 2001). Also, Savell and Davies (2001) emphasise how numeracy skills, and number competency in particular, are a necessary lead-in to further mathematical interest and achievement. They make the connection to Te Whäriki (Ministry of Education, 1996) by reminding us that in the early years children should “develop the expectation that numbers can amuse, delight, illuminate, inform and excite” (p. 78). Researchers such as Carr, Peters and Young-Loveridge (1994), Young-Loveridge, Carr and Peters (1995) and Wylie (2001) have for some time now highlighted the importance of young children’s mathematical competencies in the early years and how these impact on the children’s successes in learning mathematics later in the school years. Consequently, areas that need to be explored include: how mathematics teaching and learning is conceptualised in early childhood settings; what teachers’ attitudes are to providing learning experiences that support and extend mathematical learning; what helps and hinders effective teaching and learning; and what can be done to improve practices that enhance the learning outcomes for children. The need for teacher knowledge to support these issues has been identified by Parsonage (2001) who explored her kindergarten setting through the lens of the mathematics component of the New Zealand Curriculum Framework (Ministry of Education, 1992; Ministry of Education, 1993). The research described in this report built capacity for the kindergarten teachers by providing a framework within which they could investigate their capabilities: this included investigating their current knowledge and practice in the area of mathematics and ways of increasing this knowledge; their ability to undertake research into the teaching and learning of mathematics at their kindergartens, allowing them to examine a significant issue related to their practice; and subsequently transferring their findings into the learning environment by implementing and evaluating action designed to improve the mathematical learning experiences for the children. Furthermore, improved mathematical outcomes at the kindergartens would have the potential to benefit the wider community of each kindergarten. These wider benefits of shared mathematical activity within whānau/family settings were evident in the literacy and numeracy campaign 8 (Ministry of Education, 1999). This research project provided opportunities for teachers to involve the whānau/families in their children’s mathematical thinking by making links to the home environment and involving the whānau/family in exciting opportunities to enjoy mathematical activity at home. In seeking ways to investigate the enhancement of children’s mathematical learning and development, the research was underpinned by the principles of Te Whäriki (Ministry of Education, 1996). Haynes (2000) identifies how the teaching and learning of mathematics in early childhood settings must remain firmly within the expected philosophical domain of early childhood education in Aotearoa New Zealand. This was reinforced by the teachers who were adamant that participation in the project would not jeopardise their normal philosophical and pedagogical practices. Thus this project enabled the kindergarten teachers to understand their own processes of teaching and learning and to view them from a mathematical perspective, to identify for themselves mathematical gaps in their own knowledge and to create forward-looking strategies for future possibilities in the teaching and learning of mathematics in their kindergartens as they relate to the values of the TLRI requirements. Research questions The overarching (macro) research question was: What do the participant kindergarten teachers know and practise in relation to the teaching and learning of mathematics, and how can this be improved? Research questions specific to each kindergarten were generated at each site, and are identified in the case studies (Section 3). Each kindergarten teaching team self-selected a relevant issue in mathematics teaching and learning, and focused on strategies for improvement. The site-specific (micro) research questions that arose were: y How can we establish a platform for making mathematics prominent? (Avondale Kindergarten); y How can we enhance a collaborative mathematical partnership between teachers and parents? (Birdwood Kindergarten); and y How can we grow teacher confidence in strategising for children’s mathematical learning? (Don Buck Kindergarten). 9 2. Research design and methodologies Action research defined With its many and often contested definitions and applications, the action research knowledge base is “an arena of debate” (MacNaughton, Rolfe, & Siraj-Blatchford, 2001) in which much of the educational action research literature relates to the compulsory schooling sector. Very little appears to have been published on the specific nature or form of action research used in early childhood education contexts, However, in one study by Carr, May, and Podmore (2000), there is reference to a spiral approach derived from the work of Kemmis and McTaggart (1988). More recent reports of action research (for example, Bulman, Cubey, Mitchell, & Wilson, 2005; Podmore, 2004) refer to action research cycles and action research processes without elaborating on the details that support their claims to conducting any specific form of action research. Action research is undoubtedly a form of practitioner research that has many meanings attached to it because it is used to describe a problem-solving approach that may be as simple as reflecting on and changing an aspect of one’s teaching practice, or as complex as embarking on a major evidence-based review of institutional management practice (Cardno & Piggot-Irving, 1996). In this project, a particular “developmental” form of action research was employed. This is described by Cardno (2003) as: action research that is carried out by or for educational practitioners within their own organisation in response to some aspect of professional work that needs to be developed, either within the classroom, across the school, or in the management of the organisation. (p. 1) In this research project, the broad problem that attracted both researcher and practitioner attention related to the need to enhance the teaching and learning of mathematics in early childhood settings. Action research was chosen as an appropriate methodology because its fundamental principles value professional practice and collaborative research partnerships between practitioners and researchers. Additionally, it enables theory building that acknowledges the primacy of the critique and generation of new knowledge in the practice context with a view to improving that practice (Elliott, 1991; Lomax, 2002; McNiff, 1988; McNiff & Whitehead, 2005; Mills, 2000). As Cardno (2003) asserts, “the aims of action research are twofold: to enquire into professional practice, and to use the knowledge and understandings thus gained for developmental purposes” (p. 21). Action research of this type is inherently collaborative and critical: collaborative because 10 it requires all the people associated with the issue to be involved as active participants; and critical because it requires practitioners to adopt a critically reflective stance in relation to their own theories of practice and consequently generate new knowledge that has both theory and practice value (McNiff & Whitehead, 2005). The process of action research is intended to be planned and systematic, proceeding in a cyclic process that moves through stages of investigating and analysing a problem, to planning a change strategy and then implementing this, followed by an evaluation of the effectiveness of the change. This end-point reflection could lead into a reclarification of the problem, or revelation of deeper or further dimensions of the problem that warrant another formal cycle of investigation (research), intervention (action) and evaluation (in the form of monitoring or review or more research to collect data for these processes), and so on. Hence, action research is often depicted as an ongoing spiral (Cardno, 2003, p. 13) and participants could well embark on another cycle of research and action as a consequence of identifying new or recurring issues related to the original problem they set out to solve. This cycle is depicted in Figure 1. Qa Figure 1 QaAction research spiral The collaborative learning process and research rigour Facilitated action research of the type employed in this project engages the action research group in action learning. Zuber-Skerritt (1993; 2002) notes that the term ‘action learning’ (often used synonymously with the term “experiential learning” because of shared philosophical assumptions about adult learning) is associated with reflecting on personal practice: It offers us a method of raising our learning from the unconscious to the more conscious levels through techniques of questioning that probe and illuminate what many of us assume or ignore about our own prefiguring of what we learn. This conscious use of the learning process can thus make tacit knowledge more explicit. (Zuber-Skerritt, 2002, p. 118) 11 This is what is needed to understand problems/challenges in action research and to negotiate changed action. Because action researchers in educational settings work with adults (key practitioners and their professional colleagues), the principles of action learning are acknowledged to be at the heart of the process. In the case of this project, the researchers were expected to be familiar with the general principles of both action research and action learning. In this project, each meeting of the action research group was an action learning episode. However, action research demands more than action learning. According to Zuber-Skerritt (1993), action research involves action learning but the process is “more deliberate, systematic and rigorous, and it is always made public” (p. 46). She asserts that the rigour of action research demands explanations of the methodology and use of methods for gathering data so that it can be scrutinised (Zuber-Skerritt, 2002). Similarly, Wallace (1987) contends that action research requires a formalised approach to data gathering and must be published to achieve its status as research as opposed to other forms of organisational development. It is this consistently identifiable standard of reporting the research project that distinguishes action research from the less formal processes of action learning. Action researchers are also concerned with strengthening the rigour and credibility of their studies. As Janesick (2000) asserts: Validity in the quantitative arena has a set of technical microdefinitions, and the reader is most likely well aware of those. Validity in qualitative research has to do with description and explanation and whether or not the explanation fits the description. In other words, is the explanation credible? In addition, qualitative researchers do not claim that there is only one way of interpreting an event. There is no one “correct” interpretation. (p. 393) In essence, what counts in establishing validity in this kind of research is “the extent to which what you say is credible and trustworthy” (McNiff & Whitehead, 2005, p. 91) is borne out by the evidence displayed and its authentication. An aspect of internal rigour (or validity) relates therefore to efforts to assure verification by the practitioners themselves of the evidence included in reports to confirm the integrity of the project. In this project, the practitioners were asked to provide feedback on their particular case study draft and this was incorporated into the final version of each case. Each case reported in this research report is unique in terms of the particular situation researched. Action research makes no claims about its ability to transfer data or generalise from a specific situation to the whole populations (external validity). Instead, the fact that it relates to a particular situation is a purported strength, lending it a high degree of relevance for participants. And the immediacy with which a solution can be applied invariably makes it popular with practitioners who value its practical worth. This is not to say that the learning occurring in one case of action research may not interest or benefit those who did not participate. Indeed, as is the intent of this research project, by reporting these case studies and making the accounts public, action research ideas can reach, and be transferable to, other practitioners in similar settings. 12 The “research” demand in action research is met when a collaborative research group embarks on a systematic and evidence-enriched process with the aim of examining and improving practice. In this project, in order to ensure the integrity of the developmental action research process, the research group (practitioners and researchers) attended to all of the following. They: y used existing knowledge to inform problem understanding; y engaged in action learning to generate focus research questions; y collected and authenticated evidence in a process of ongoing verification; y intervened to change practice paying attention to both theory and best practice; y monitored the effectiveness of changed practice and emerging new theories of practice to draw conclusions and to chart future directions; and y reported the project (presentations and publication). Such practitioner-researcher partnerships create a big demand for the professional partners. Participation requires a considerable commitment on the part of already busy practitioners even when the process is facilitated by a consultant or external academic researcher. Yet both the researchers and the practitioners in this project wanted to engage in rigorous action research. This is a dilemma inherent in practitioner research in general, and action research in particular. On the one hand proponents of action research wish to promote the methodology as a practical and appropriate tool for institutional-based change that is manageable and sustainable. Yet, on the other hand, academic action researchers often find themselves needing to defend the methodology as a rigorous form of qualitative research that has scholastic credibility as well as practice relevance. Furthermore, action research is generally presented as an ongoing process (Cardno, 2003; Kemmis & McTaggart, 1988), spiralling beyond an initial cycle to deeper or further cycles and thus implying that the end of one project is a platform for embarking on a new cycle of action research. This gives rise to an often untested assumption that practitioners will be able to continue to apply an action research approach in resolving problems/challenges of practice after the conclusion of the formal project. It behoves academics and consultants who provide action research opportunities in the first place to consider these challenges for practitioners and to create conditions and motivation that will assist these practitioners to make critical choices about whether or how they can sustain the momentum of action research beyond a formal “supported” or “funded” professional development programme, or research project. The action research settings This TLRI project involved three academic researchers from Unitec Institute of Technology and the teaching teams at three West Auckland kindergartens in 2005. The project activity began in December 2004 and concluded in mid-2006. The head teachers at all three kindergartens were known to the project director and these kindergartens were among the many partnership centres that contributed to the Unitec Institute of Technology early childhood teacher education programme by accepting students for practicum and field-based learning. 13 In the project, a research partnership was established between the teaching teams from the three kindergartens and the three academic researchers who guided the overall project. The academic researchers engaged in a facilitated research process with each kindergarten action research group comprising head teacher and teaching staff. Although both the academic researchers and the kindergarten teachers were researchers in the project, for the purposes of this report the academic researchers are identified as the researcher-facilitators and the kindergarten teachers as the participants. The following kindergartens were approached in October 2004 about the possibility of participating in the project and agreed to be named in the proposal for this project: y Avondale Kindergarten (head teacher and two teachers); y Birdwood Kindergarten (head teacher and one teacher); and y Don Buck Kindergarten (head teacher and one teacher). The Auckland Kindergarten Association (AKA) approved the researcher-facilitators gaining access to the three kindergartens in the project. Ethics approval to conduct research at the three sites was granted by the Unitec Research Ethics Committee prior to the start of the project. All site-based meetings were arranged to minimise intrusion of the research into the daily life of the kindergartens. Hence all researcher-practitioner meetings were scheduled after session times. The researcher-facilitators, however, who were each allocated to one specific kindergarten, paid visits to the kindergartens during session times in order to collect and verify data. Ethical practice in facilitated action research projects requires the researcher-facilitator to take responsibility for getting the participants to check the data they have contributed. This was done in every case. Drafts of the case studies were sent to participants and their views were incorporated in the final version. At the start of the project, the intention was to ensure anonymity for the kindergartens. However, because the three kindergarten teams participated in a public dissemination event mid-way through the project (research symposiums and conferences where they were named in the course of presenting progress reports of the research), they themselves decided to forego anonymity in the final reporting. This disclosure of sites and names was subsequently approved by the AKA. The participation of these practitioners in the project was financially supported. A grant was made to each kindergarten to defray the costs of appointing relief staff to compensate for the time spent in meetings with the researchers, data gathering, communication and other research-related activities. Doing action research—the process Because action research occurs as a dynamic, unfolding process of enquiry and action it is depicted as a cycle of events. In externally supported developmental action research (Cardno, 2003) of the kind that took place with these kindergartens, a facilitation schedule was agreed (four 14 site-based meetings between February and October 2005) to ensure that meetings with the researcher-facilitator occurred at regular points throughout the year. Each of these meetings was a half-day action learning event. The meetings were used to progress the research through the various stages of an action research cycle. In addition all participants at the three kindergarten sites came together for two full-day cluster meetings. One of these meetings was held before the start of the project to introduce participants to the methodology of action research. A final meeting in November 2005 allowed all participants to contribute to an evaluation of their specific research project outcomes and to overview the process they had experienced. This was in keeping with developmental action research which constitutes a cycle of research and action events incorporating action learning and data collection. This cycle is depicted in Figure 2. Figure 2 Cycle of research and action events Accounts of how a cycle of action research was implemented in each of the three kindergarten settings is elaborated in the case studies that form the next section of this report. In brief, in each kindergarten the participants completed a phase of reconnaissance (investigation and analysis); intervention (planning and action); and evaluation (reflecting on the process and outcomes). Reconnaissance In the reconnaissance phase (approximately February to May 2005) each kindergarten’s action research group engaged in facilitator-led action learning with the researcher. This involved investigation and analysis of the problem that required an understanding of the theory and practice of mathematics teaching and learning. It guided the group towards a clear articulation of the research questions: the focus for collecting data. To achieve this clarity of focus for the action research, all three researcher-facilitators used a consistent systematic problem analysis exercise in a facilitated action learning meeting. Through subsequent communication and team effort, the researcher-facilitators and participants assembled the evidence needed to confirm the focus. 15 Intervention A further two action learning meetings (between June and August 2005) allowed the action research groups to firm up an intervention plan that was unique to each kindergarten and begin its implementation. All three researcher-facilitators guided this phase using similar templates for planning. Participants at each site were in regular communication with their assigned researcher- facilitator throughout. Evaluation During October and November 2005, action learning focused on evaluation and reflection. In this final phase each of the groups participated in a site-based meeting and then in November all participants and researcher-facilitators came together for a final cluster meeting. The key purpose of this phase was to assist the participants with the monitoring of their change strategies, and further assembly of evidence, that would aid their reflection on the effectiveness of both the intervention in particular and what engagement in the total project had achieved for them. Data-gathering methods In the reconnaissance phase and in some cases also in the evaluation phase of each of the three research projects, participants and researcher-facilitators used documentary analysis across all three projects. In addition the participants used a range of data-gathering methods within the bounds of each project. These included small-scale surveys and the assembly of data in the form of reflective journals, note-keeping, emails to researcher-facilitators, photographs and other material that was considered to be evidence. As Waterman, Tillen, Dickson, and de Koning (2001) assert, in action research “qualitative data from multiple perspectives in the form of reflective notes, diaries, interviews and documentary evidence may be preferred” (p. 16). Documentary analysis Documentary analysis (Bell, 1999; Wellington, 2004) is viewed as an extremely effective approach for reviewing policy and regulation guidelines at the start of an action research project (Cardno, 2003) as part of the problem-understanding phase. Because the teachers in all three kindergartens needed to become familiar with the core documents (common to all kindergartens) that contained references to mathematics teaching and learning, and expectations held of teachers, these documents were analysed by both the researcher-facilitators and the participants in each kindergarten. In the case of Don Buck Kindergarten this analysis was extended in depth to the mathematics curriculum document (Ministry of Education, 1992) in the form of an audit of the mathematics potential in the learning environment. 16 Small-scale survey questionnaires Questionnaires (Jenkins, 1999) can be a quick and relevant way of surveying opinion. Their use in action research is generally to collect descriptive qualitative data that contributes to problem reconnaissance. These instruments can also be used as end-point evaluation to assess the extent to which planned change has been effective. Carefully constructed questionnaires, similar to structured interview instruments, are most appropriate to use with small samples. The participants at all three kindergartens made use of recently collected survey data (by external agencies such as the AKA) or conducted small-scale surveys in the form of questionnaires to whānau/parents. In the case of Birdwood Kindergarten, a parent survey was used in the reconnaissance phase and again in the evaluation phase. Reflective journals and diaries Each kindergarten team kept a journal of their action research journey, noting events, reflection on plan achievement, and self-critique of practice. Additionally, at the closure of the project each head teacher contributed a reflective summary of what they felt they had achieved overall during the project. Notes, emails, and photographs as evidence Participants in the project kept notes on team meeting discussions, on reflections on their practice, and on actions undertaken and monitored in the intervention phase. Emails were also used to update the researcher-facilitators and to record actions associated with monitoring and evaluating the intervention, especially in the case of Avondale Kindergarten. Photographic evidence was used throughout to illustrate and confirm anecdotal evidence and record agreed changes. Challenges for the researcher-facilitators For the three researcher-facilitators in the project the following issues emerged in the application of action research methodology in kindergartens: y ensuring nonintrusiveness of the project on the day-to-day practices of head teachers and teachers; y balancing a systematic and structured approach to the research with the need for flexibility, in order to maintain the process as a dynamic approach that could be responsive to the immediate needs of a particular setting; y maintaining comparability between sites in relation to the way three different researcher- facilitators applied the action research methodology; y absorbing and responding to new learning as the application of the “developmental action research” process unfolded; and 17 y coping with site-based factors such as staff turnover which was experienced in two kindergartens. Challenges for the participants For the participants in this highly collaborative and new experience as practitioner-researchers there were also challenges. These are summed up by the participants as follows: y frustration associated with a formal problem analysis phase (reconnaissance), when they felt they could have made suggestions for solutions, but instead experienced what they considered an unexpectedly long drawn-out phase leading to clarification of the issue; y frustration their hopes of focusing on “mega” issues (for example, social conditions beyond their control but known and difficult to tackle) were not the immediate focus of the project, in spite of their realisation that a project of this scope could realistically address only an issue that could be dealt with; and y “a time commitment, although anticipated, that was demanding”. This was associated mainly with the additional paperwork, data collection, and assembly of the evidence throughout the project. Teachers becoming practitioner-researchers If action research is to be valued by both research and practice communities then it must be committed to the development of practitioners as researchers as well as changers of practice. In the application of action research methodology across three kindergarten sites the academic researchers in this project endeavoured to make the partnership a real learning experience for all. We have asked our practitioner partners to articulate what it has meant for them to make the transition from being practitioners concerned with improving practice to becoming practitioner- researchers who both improve practice, add to their own knowledge of their theories of practice, but above all add knowledge that can be disseminated to the community of theory and practice knowledge that constitutes the domain of early childhood research. Our practitioner partners assert that this research has led to the following practitioner-research outcomes. They have: y learnt a new process which can be applied in other situations; y developed awareness of using evidence in everyday practice in order to improve this; y been made to feel more accountable about the changes they make; y been challenged to be more collaborative in their teaching teams; y acknowledged that they are on a learning journey; and 18 y been motivated by the knowledge that their research and action can make a difference to both themselves and others if it is in the public domain. A significant part of the learning journey for the three kindergarten head teachers in this project was their willingness to attend two research dissemination events in December 2005. All three head teachers presented the progressive findings of their action research journeys in public forums at the annual symposium for New Zealand Research in Early Childhood Education (NZRECE) and the annual conference of the New Zealand Association for Educational Research (NZARE) in Dunedin. 19 3. Project findings Introduction to the case studies Action research provides a means for achieving a research aim that is two-fold. Firstly, such research sets out to investigate the status quo. Secondly, once knowledge about the status quo is established, findings from this initial phase of the process are used to improve practice. Furthermore, because action research is iterative in nature, these projects proceed to a stage of evaluating improvements made with a view to basing further change on evidence. Consequent on these findings, the project might establish a new focus in which further research is conducted as a prelude to further action, and so on. Unlike traditional, large-scale projects that are established around answering a general research question, action research has both macro (overarching) and micro (specific to a setting) research questions. In the case of this project the macro research question related to all three kindergartens that participated in the project. The macro research question that guided the project asked: y What do the participant kindergarten teachers know and practice in relation to the teaching and learning of mathematics, and how can this be improved? The key micro research questions specific to each kindergarten were: y How can we establish a platform for making mathematics prominent? (Avondale Kindergarten); y How can we enhance a collaborative mathematical partnership between teachers and parents? (Birdwood Kindergarten); and y How can we grow teacher confidence in strategising for children’s mathematical learning? (Don Buck Kindergarten). The focus for the research in each kindergarten was established in the reconnaissance (investigation) phase of the action research process. The findings in relation to each kindergarten are presented as individual case studies: y the case of Avondale Kindergarten: establishing a platform for making mathematics prominent; y the case of Birdwood Kindergarten: enhancing collaborative mathematical partnerships between teachers and parents; and y the case of Don Buck Kindergarten: growing teacher confidence in strategising for children’s mathematical learning. 20 In action research, the critical concern is to use knowledge generated in the process of assembling evidence, discussion, and reflection to illuminate and understand the problems/challenges of practice. Whilst commonalities and significant differences between sites also generate important findings, it is the knowledge of site-specific practice that informs and guides change. In this section, the three case studies are documented to show how each kindergarten set out to answer their unique research question followed by a meta-analysis of findings and discussion informed by the theory base. The case of Avondale Kindergarten: establishing a platform for making mathematics prominent The kindergarten At the time this research project began, Avondale Kindergarten in suburban Auckland was staffed with three full-time permanent teachers and a teacher aide. The kindergarten works with an average of 45 children in the mornings and 40 in the afternoons and experiences a high rate of turnover with almost half of each cohort in each term being “new” to the group. The children come from a diverse range of ethnic backgrounds. A snapshot of ethnic mix in March 2005 showed morning session children comprised Samoan (20), Indian (17), Mäori (9), Tongan (9), European (8), Chinese (4) and six other ethnic groups. This kindergarten is located beside a primary school that has a decile 2 rating indicating a socio-economic composition that is at the low end of the scale. Many of the children are from new immigrant families with approximately half of the children in each cohort speaking English as their second language and one-tenth of each cohort not being English speakers at all. Whānau/parents mirror this linguistic diversity and whilst many are keen to volunteer help in kindergarten activities, this help is often limited by the language barrier. A further barrier is that as new immigrants, many of the Indian mothers that offer to help are unfamiliar with the Aotearoa New Zealand early childhood curriculum and the education system in general. The head teacher comments that “they are seldom able to assist with the supervision of children and rarely able to help them to explore in a mathematical way”. The teaching team of Avondale Kindergarten was interested in participating in this research project because, as well as having a connection with the project director in the course of their studies in early childhood education, they were motivated to improve mathematics teaching and learning in their setting. The head teacher and other team members had been concerned throughout the 2004 year that the team was not attending sufficiently to the teaching, and therefore the learning, of mathematics. All three teachers were interested in joining a project that would allow them to study this dissatisfaction with mathematics teaching in a systematic way. 21 Understanding the problem—the reconnaissance phase The facilitation of this action research process began with an orientation on developing an understanding of the problem situation and one of the main challenges for the researcher- facilitator was to guide participants to explore the dimensions of the problem and rein in their instinctive need to implement a ready-made solution. For example, initially the head teacher was drawn to the idea of conducting a survey. She stated: The solution I was thinking of at the time was carrying out a survey with the parents and trying to find ways to involve them and work on the children’s dispositions. In terms of the action research model that guides this project (Cardno, 2003), the participants engaged in guided dialogue and data gathering to reconnoitre the terrain of the problem or challenge. They did this to gain both a wide and deep understanding of the complexity of the issues and the factors that had made it difficult to resolve their specific problem in past attempts. The reconnaissance phase for Avondale Kindergarten involved two discussion sessions (3 hours each) interspersed by the collection of data by the participants to further inform their understanding. Analysis of the problem Guided by the researcher-facilitator, the teaching team talk was funnelled from a broad ranging exploration of the problem from the perspective of each participant to a narrowing down of key aspects which could be agreed by all three team members. The vague sense of frustration that permeated all three participants’ consideration of what was problematic for them was distilled at the end of the first discussion session (February, 2005) to be expressed as follows: The problem for us is that it is hard to be a teacher of mathematics in a setting where there are several barriers. Several spreads of brainstormed ideas noted on whiteboard were themed and re-themed to gain a clearer picture of the dimensions of the problem—and in particular the barriers that the group felt were part of their problem. The agreed problem dimensions recorded at the end of this session were: y social factors (the transient nature of the population, ethnic diversity, and the attendant language barriers especially for new immigrants; consequent limitations to whānau/parent involvement in assisting with teaching; some children’s ethnic-related dispositions that might be counter to those associated with mathematics learning, such as taking initiative to explore); y working conditions (high student to staff ratio; lack of time to devote to mathematics teaching because social conditions made it necessary to prioritise the learning of boundaries or rules for socialisation; all team members having been in these roles for only one or two years and still developing as a team; insufficient capable whānau/parent voluntary help); 22 y system expectations (plethora of demands from multiple stakeholders; balancing act needed to sift specific requirements from general directions; uncertainty about whānau/parent expectations because of diversity of values/cultures); and y self expectations (wanting to be good teachers of mathematics yet sometimes not confident about ability; anxiety about subject knowledge—what mathematics is and how to teach it in early childhood settings). Much discussion was focused on the issue of having little control over the conditions that prevailed at Avondale Kindergarten. As one participant said: If we agree that we can’t be effective mathematics teachers in this culture then it’s a problem we can’t change. That means we can’t be a better maths teacher because of the barriers. I think we need to improve ourselves to get over these barriers. And another confirmed the belief that: If we don’t see how the social factors are ever going to change then we have to look at ourselves. That could be the way to start to look at solutions. Thus, very early in the process of exploring the dimensions of the problem, the teaching team was critical of their own description of the issue, realising that they had no power to influence prevailing socio-cultural conditions. This realisation enabled them to take a more pragmatic view where they, as the teachers, accepted that their own practice could be the focus of the project. They now recognised that an immediate constraint related to their admission that they were often overwhelmed by the variety of expectations they felt they had to cope with. These expectations were communicated by whānau/parents and by official documents. This problem identification phase provided them with an opportunity to sift through a range of issues that had an effect on their teaching, and the children’s learning, of mathematics. Expectations ranged from their own aspirations as professionals, to whānau/parent expectations and the expectations of the system under which they operated. Some data assembly and analysis was called for. The team agreed that they needed to assemble and review data that was available to them in the form of previous reviews of practice, and documents pertaining to expectations related to the effective teaching and learning of mathematics, before the next facilitated meeting (March, 2005). Summary of previous reviews In 2004, Avondale Kindergarten had participated in a survey of parents conducted by the AKA. The results provided a snapshot of whānau/family views (n = 22) at that time. Respondents represented every ethnic group involved in the kindergarten with the largest group (a quarter of respondents) being of Indian ethnicity. Of significance to this research project was the finding about the extent to which the kindergarten was meeting expectations of whānau/parents in relation to a range of aspects such as curriculum and teaching philosophy, developing social skills, and so on. The expectation that the kindergarten provide reading, writing and mathematics skills scored 23 the lowest ratings of all aspects of this kindergarten’s provision. Seven respondents perceived provision was below their expectations. The newly constituted teaching team at Avondale Kindergarten had discussed this finding and consequently examined both their own practice and their knowledge of the whānau/parent body that might have implications for the kinds of teaching practice valued by whānau/parents. One of the difficulties they were encountering related to whānau/parents with Indian and Chinese experiences of extremely formal pre-school education, and their difficulty to adjust to the Te Whäriki (Ministry of Education, 1996) way: a philosophy of play as the platform for learning. Nevertheless, this team was not prepared to ignore the message inherent in the survey results and turned an eye on their own practice in an effort to be responsive. In June 2004, the newly appointed head teacher had led a self-review of mathematics teaching with the team. Her team had brainstormed what was currently being done, identified the gaps, discussed the reasons the gaps existed, and planned some changes. These changes led to making mathematics teaching more explicit, including the increased use of specific mathematics language and concepts, informing whānau/parents more specifically about what was being done in mathematics teaching, engaging in professional development to increase teacher confidence in mathematics teaching, and accepting the invitation to participate in this action research project to increase the effectiveness of mathematics teaching and learning. Documentary analysis—system and kindergarten levels A range of documented expectations guides the teaching and learning of mathematics in all kindergartens. In reviewing the documents relevant to the three site-based action research projects reported here, the researchers completed an analysis of common system level documents pertinent to all three sites and the results were shared with the practitioners. This was a useful exercise as it served the purpose of refreshing familiarity with these well known documents. However, involvement in an analysis that focused on extracting references to mathematics teaching and learning guidance revealed that the participants from Avondale Kindergarten were not familiar with this aspect of the documents. They were not making use of the documents to increase their understanding of expectations but were happy to consider doing this in the future. Presentation of the documentary analysis summary led to a dialogue that focused on the notion of “dispositions” to both learning and teaching. The team was keen to revisit the documents that explained what was important and what was expected. These participants agreed strongly that the official documents confirmed the importance of “disposition” in children and that they wished to take greater note of this in their focus on improving mathematics teaching and learning. The isolation of learning and teaching expectations in official documents (for example, see Auckland Kindergarten Association Service Delivery Manual, AKA, 2003) reiterated for them that the idea of disposition is raised in the context of teachers deciding what to assess in relation to a child’s learning. This reinforced the expectation held at a systemic level that teachers should both understand the notion and apply it in daily 24 activity. For the team this clearly identified for them the expectation held at system level that those who make management and teaching decisions should recognise that “dispositions are important ‘learning outcomes’. They are encouraged rather than taught” (Ministry of Education, 1996, p. 44). As well as appreciating the opportunity to revisit the plethora of documents that officially guide their practice, this teaching team was self-critical of their earlier belief that the problem they sought to address was just too big to deal with. They revisited their stance on making themselves the focus of the project. It was evident to them that their management and teaching decisions could be refocused to consider not only the encouragement of mathematical disposition in children but also in themselves, as teachers. They commented that: The teaching dispositions go hand-in-hand with the children’s dispositions. They talked about their own dispositions to teaching mathematics: For me personally, confidence with mathematics is an issue because I always found maths very hard when I was at school. It wasn’t my favourite subject … it’s not my passion or something I would immediately choose to do. We can’t ignore the teacher’s ability. As a consequence of this analysis of documentary evidence, the teaching team at Avondale Kindergarten was better informed about where expectations came from in a system where there were many levels of stakeholders. They were also clear at this point that they were accountable for meeting these expectations at the system level, local level, and institutional level. At the system level, the government agency for institutional review, the Education Review Office (ERO) would expect that their programme planning and implementation was of a high quality. Affirmation that they were meeting criteria set by ERO for offering a programme with variety was contained in this kindergarten’s most recent ERO report which confirmed that mathematics language and concepts were incorporated throughout the programme. At the local level, the AKA would expect delivery of a high quality programme and local whānau/parents would have expectations of mathematics teaching and learning that were communicated to them, on behalf of the affiliated institutions, in the AKA pamphlet “What do I learn at kindergarten?”. At the institutional level, the teaching team’s concern, once these national and local expectations were isolated, was related to the high expectations they had set for themselves to match espousals of effective teaching and learning with actions that led to demonstrable learning outcomes for children. They acknowledged that in relation to mathematics teaching they had not articulated these expectations amongst themselves, in a way that would reinforce their commitment or help them to communicate this to whānau/parents: For parent expectations, mostly we observe what parents do and say and we haven’t written it down. 25 One of the particular challenges for this team was a diversity of expectations from whānau/parents. They talked about the parent who “dragged the child to the teaching table and made them sit and do writing work” and the parent who “carried the child to the teaching/learning situation and placed her next to the teacher”. Then there was the other extreme: whānau/parents who were never sighted and both parents and children with no English language capability. Some of the frustration for this teaching team lay in the very nature of the context in which they operated: a highly ethnically diverse and transient community and the high child–teacher ratio. The research team took a critical stance related to their own practice when it came to two-way communication of expectations. Firstly, they believed they could make better use of whānau/parental comment and expressed aspirations than was currently the case. Secondly, they felt that they often missed opportunities for communicating their expectations to whānau/parents. This related to both what they expected from children and from whānau/parents, in terms of creating learning opportunities outside kindergarten time. Emerging themes By the end of the second facilitated meeting in this reconnaissance phase, the Avondale team was beginning to understand the nature of the complex problem they faced in enhancing mathematics teaching and learning. They had steered away from their earlier position of feeling that the barriers (largely the sociocultural factors in their community) were where they should focus. They had adopted a more pragmatic approach in their decision to focus on themselves, the teachers, as a place to begin. Because they had initially felt overwhelmed by the range of expectations they had to meet as teachers, they also decided to focus on ways in which mathematics could be given more prominence—starting with it featuring regularly and often in day-to-day activities: We can’t change social factors but we need to work with these to the best of our ability. You often have to try to overcome, work around the social factors to show the system. And because you have these high system expectations the danger is that you focus on the able children in the group. An ongoing concern for the team was that they felt they were held accountable by the AKA for demonstrating the extent to which they were meeting expectations in relation to every child’s learning. Yet, for many children (those with both sociocultural and linguistic barriers that militated against self-initiation of mathematics exploration) they felt they were falling short of what was expected of them. One participant said: So you can show we are meeting the goal but we might only be meeting it with a few children. Teaching ability comes out with able children. Focus on the teachers They decided to describe what competent teaching of mathematics in this kindergarten would require. The following statement was compiled. 26 A competent teacher of mathematics: y has a good knowledge of mathematics concepts and language; y is able to judge the linguistic and mathematics ability of each child; y is able to “draw out” the mathematics in day-to-day activities and follow this up—for example at mat time; y plans for mathematics in each kindergarten area; y has the commitment to teach mathematics concepts and language on an ongoing basis; y is able to adapt the teaching of mathematics to a range of ability; y is able to supervise and teach rules and routines on an ongoing basis, including teaching how to use and look after equipment; y is able to reflect, record and document children’s mathematical learning; y is able to relate children’s mathematical learning to whānau/parents face-to-face on a daily basis; and y is able to involve whānau/parents by being specific about how they can help their children’s mathematical learning by being communicative and encouraging. The participants in this team were highly committed to improving their practice and two of the three had participated in AKA professional development activities focused on mathematics teaching. One participant was completing an undergraduate paper on the teaching of mathematics for credit towards a Bachelor of Education degree, this having been the case a few years previously for the other teacher. They were critically self-reflective of their current practice. As one said: I don’t tend to focus on maths because I’m not very confident in that. I don’t really like maths. When I looked at my learning stories I tended to focus on other areas although I have now done learning stories focused on maths now that I am starting to bring maths into everyday activities. And another says: The children weren’t doing it because we weren’t doing it. In short, the decision to make changes by “starting small” and by turning the spotlight on themselves led to changed action that was both immediate and incremental. Making mathematics prominent The team discussed their wish to “draw out” the mathematics in their daily activities, to “talk mathematics”, to “plan for mathematics”. They shared with one another their attempts to act on the decision to make mathematics prominent in their planning and action: I wasn’t doing it every day but since we talked about it the other day I’ve tried it every day. It also turns into action when you are using maths language with the children—like today— when the children started jumping and we talked about how long it was, making it wider. I was asking them to make it wider, jump further, because I was thinking of maths. That’s where we are slipping it into activities. 27 I was finding it a bit hard at first. I was doing something with dollies and I thought I didn’t really do much maths because it wasn’t a maths activity. Then M said, take a step back the next time it happened. And I thought about it and I got them started on counting the finger and toes, thinking which dolly is bigger. It went somewhere else. It’s ticking in a bit more for me in everyday activities. So I think maths first and then do the activity and then that’s a maths activity. This team engaged in a high degree of critical reflection. They examined and rejected a theory of practice that had been adopted to excuse their neglect of mathematics in everyday activities. It was a theory of practice adopted in what they felt were insurmountable contextual constraints created by language and cultural barriers. In adopting a new theory of practice which allowed them to work with the sociocultural constraints, they recognised that they had, in part at least, contributed to the status quo that they uncovered for themselves. In essence, they had learnt that if they focused on their practice consistently, this could lead to change and better mathematical learning experiences for children. Intervention phase—planning and monitoring new practices A facilitated meeting (May, 2005) was held specifically for the purpose of planning an intervention: a range of strategies for changed practice that could be monitored. The team devised a formal plan (Table 1) and also made a commitment to continue the practice changes to which they were now committed. These new practices had already begun during the reconnaissance phase and focused on the participants “drawing out the mathematics” in everyday activities. Table 1 Intervention plan: Avondale Kindergarten GOAL All teachers to make mathematics teaching a prominent priority. OBJECTIVES OUTCOMES ACTIONS RESOURCES & BUDGET DATE 1. Consultation with system managers to communicate prominence of mathematics (for inclusion in advertisement) May/June 2. Head teacher involvement in appointment process April 3. Add "maths is important" statement to kindergarten information documents (for appointment) May 4. Provide early professional development to strengthen confidence in mathematics teaching Up to $1000 August/ September To develop an induction process for the kindergarten to sustain commitment to mathematics being prominent 1. Continuation of emphasis on mathematics 2. Awareness of commitment to prominence accorded to mathematics 3. Effective contribution to kindergarten curriculum 5. Continue to plan sustain- ability and emphasis on mathematics 28 Teachers The team brainstormed several strategies that they intended to implement straight away. These included giving the planning of mathematics (weekly and long term) more significance’ the creation of a “mathematics book” that would be on display for whānau/parents, teachers and children; and a continuation of the whole team making an effort to put mathematics foremost as a learning outcome for children. The following comments give voice to the direction of the teacher talk: Planning for maths teaching is first, drawing out maths should happen as a result. Team meetings must be time to plan for maths teaching. I will write in “build on strategies”. It would be good if we write how we got to that success. Put the strategies in the team meeting records. Because the children in this kindergarten do not often initiate mathematical thinking, teachers are required to plan for maths teaching. Right, so for example, to be able to teach the children the language—mathematical language and concepts, you have to know what the basic concepts are in the first place and we have to know which language to use. And for that we have to look at each area and brainstorm about—like—what kind of match we could bring to certain games and activities. Planning for maths has helped me also. Driving to kindergarten I think what maths could be in the activity I am doing today. For example, “directions”. With that thought in my mind I start the activity. Then it depends on which child comes to me and their level of English. In the course of discussing the various strategies that this team wanted to initiate, the head teacher expressed her concern about sustaining the commitment that everyone had made to the new emphasis on mathematics in their day-to-day work. It was now known that two of the team of three would be moving to new positions by the end of June. None of the team members wanted to lose the momentum that was now evident. One suggested: Perhaps have a chat with P who is going to interview people for the positions here to see if she is aware of the different things that we are doing so she can choose the best applicants in terms of this. The team agreed that whilst the AKA had a general induction programme for new appointees to kindergarten positions, there was no specific process at the institutional level that could be used to communicate and clarify an expectation as particular as the one that now pertained to mathematics teaching and learning being accorded prominence. Induction of new teachers Closely related to the focus on teachers was the concern that kindergarten level structures and systems would need to be robust to sustain the commitment to mathematics being given prominence. This was a particular challenge in an environment that not only had transient families 29 but also high staff changeover. The team devised a formal plan to use as a basis for the development of an induction process that would support their curriculum goal. Monitoring the Intervention From June to August 2005, the kindergarten team continued to build on their early efforts to “draw out the mathematics” in their everyday activity. The researcher-facilitator was in regular telephone contact and visited the kindergarten in late July to observe mathematical activity and record progress towards the goal of making mathematics prominent. The team provided the researcher-facilitator with opportunities to observe changes they were making in their daily practice as relevant to the teaching and learning of mathematics. They continued to keep records of their management and teaching decisions related to mathematics, and their production of new documents developed to meet the objectives of the intervention plan. These items were evidence that could be validated by the researcher-facilitator as the intervention and associated monitoring proceeded in tandem. One aspect of evidence related to efforts to keep up the momentum in making mathematics happen and making it visible. Another aspect of evidence related to the changes made to sustain this commitment regardless of staff changes, by developing a sound foundation for induction that brought mathematics teaching and learning into prominence. Focus on teachers The researcher-facilitator was able to observe innovations that had been introduced and continued to be refined. These included participants’ endeavours to integrate mathematics language and concepts into everyday activities far more than had hitherto been their practice. Some photographs capture this greater emphasis. For example, to increase mathematics thinking in everyday experiences, when children made a long dragon and then others joined in to make it longer (see Image 1), the participants engaged in relevant mathematical dialogue throughout the progress of the learning experience. Mathematics was to be made a prominent feature of the kindergarten scene. The teachers established what they called the “mathematics wall” with resources that could be pointed out to the children to facilitate learning of a variety of concepts. The participants compiled the “mathematics book” primarily for a whānau/parent audience with pages dedicated to explaining aspects of mathematics learning in the curriculum and how this learning could occur at home. The book was prominently on display and within easy access. Pages were regularly added and material updated (see Images 2, and 3). As one of the team stated: We are in the process of making it visual for parents as well. Notice board, carpentry, technology, laminating, photos. 30 Image 1: The long and the longer dragon Image 2: The cover of the mathematics book on display 31 Image 3: A page from the mathematics book Focus on the induction of new teachers The head teacher acted on the formal action plan for establishing an induction process that would strengthen the goal of according prominence to mathematics. She prepared a “Kindergarten Profile” for the AKA Professional Services Manager to use in advertising vacancies at Avondale Kindergarten. In this profile, as well as describing the nature of the kindergarten and its community, there was specific mention of the Commitment to Mathematics and Involvement in Mathematics Research, drawing attention to the following as important competency criteria: y planning and reflections on planning with a focus on mathematics; y ability to judge linguistic / mathematical ability of the children; y knowledge of and teaching of mathematics concepts and language; y adapting teaching to a range of ability; y skill to supervise and be consistent; and y willingness to be involved in professional development. The following statements were also made about the emphasis on mathematics within the appointment documentation: 32 Teaching mathematics concepts and language is our first teaching goal for many of the children. Because the children do often not initiate mathematical thinking, teachers are required to plan for mathematical thinking. This means that the teacher needs to be aware of the mathematics curriculum and “draw out” the mathematics and use mathematical language whenever a possibility occurs. The following are also important: • planning learning experiences with an eye on mathematical potential helps developing mathematics concepts and language; • teachers looking through mathematical lenses helps involve the children in thinking mathematically and doing investigations; and • teachers using mat time to recapitulate for all children the mathematical learning that has been going on, teaching and highlighting specific mathematics concepts. (Centre Document, 2005) Evaluating the intervention and identifying the next steps A final site-based meeting for the purpose of formally evaluating the intervention strategies was held in early August 2005. The participants and the researcher-facilitator had been monitoring change throughout the intervention and the team was adamant that they would continue to do this as part of their normal planning and reflection on teaching. In relation to the induction aspect of the intervention, this end-point meeting had two objectives: firstly, to set some criteria by which the team could judge the effectiveness of their plan to introduce an induction process to sustain the focus on mathematics; and secondly, to prompt the team to collect evidence about the impact of changed practice. In the case of Avondale Kindergarten, by the time this meeting was held, there were two new staff members in the team—both relievers. The first part of the meeting was used to familiarise these new participants with the research project’s progress to date and bring them on board. The head teacher anticipated that by the beginning of October there would be two permanent new members in her team. One of the relieving teachers at this meeting shared her views about the newly developed induction process as she had experienced it over the two weeks she had been employed. Yes it was good. I got the information and I was able to take the information home. But I think the book [Displaying Mathematics] was helpful. Definitely helpful as an on-the-spot resource to use. I can use it by myself, with the children—a multi-purpose book. And another point she raised related to the whole team demonstrating the commitment to making mathematics teaching prominent: The teaching team needs to be doing the same thing. If one teacher is doing all the work with maths, consistently focused, and the other teacher is not comfortable with maths so that could be a concern. As long as all teachers are on board with it then there is no problem. 33 The head teacher confirmed that the AKA had used the documentation she had provided which explained the emphasis on mathematics in the appointment process. She had made a point of discussing this very early on with the relieving teachers. First thing I focused on is putting the kindergarten profile together and making sure that for new people coming on board that they know that maths is important in this kindergarten. I have given X and Y material to read—the list we made about teaching maths. We sort of discussed what is important—children’s language problems, often don’t know the concepts and mathematical words. And we talked about how when we see maths happening, to bring it back at mat time and talk about it to consolidate using mathematical concepts in the work and making it clear for the other children as well. She had started to include a focus on “reflecting about mathematics” in every planning and reflection meeting with the team. In fact, a new column was created to record mathematics aspects in the “Daily Sheets” that recorded mathematical experiences and offered a basis for reflection and forward planning. This was working well according to the head teacher because: Then we write down what each teacher has observed in daily activities, then it is each teacher’s responsibility to follow up on that. So each teacher individually plans/thinks how we can go further with that activity. How can you expand what children are already doing. And in relation to induction, she said: The induction plan really consists of telling the teachers that this is important, we are involved in research. I have also given them material to read—on maths in this kindergarten and what a competent teacher is in this kindergarten from a maths perspective. So—what I also believe is, it’s good not to leave it to just one meeting but to have continuity—for the longer period because it doesn’t stay with just one meeting. Maths focus has to be born. I have notified the teachers that this is the focus. You have also to give them the opportunity to think about and to see how they can live with it. If I bring it back daily / weekly in planning we can see what we are thinking about beforehand. I think it’s in that that we can improve the maths as a team. New teachers come in with new ideas and we think about these new ideas too. A critical concern arose at this point in the project. This was that the head teacher was now the sole practitioner in the action research, and she was concerned about maintaining the momentum of the project. A further concern, shared by the researcher-facilitator, was the sustainability of change in a situation where staff turnover was a constant challenge. Hence, the head teacher was concerned not only about maintaining momentum in the short term, but also about the recurring issue of the induction of each new staff member into this kindergarten’s values, and its moral and theoretical commitment to make mathematics prominent. The tenacity and commitment of this head teacher to continue with the project in the face of daunting and recurring barriers is to be commended. Many others would have given up at this point but the belief of this leader in the “rightness” of the new theory of practice was unshakeable. The current action research group acknowledged that, in addition to further monitoring of change, it needed to do a more formal evaluation of the head teacher’s efforts to highlight mathematics in 34 the induction process. The relievers suggested that it would be useful to review efforts at two specific points: three weeks after appointment and once the new teacher was six weeks into the job. A set of questions was developed by the team for the head teacher to use in order to get feedback from the new teachers: The questions for evaluating induction effectiveness (3 weeks after starting) were: y What was your initial reaction to the appointment documentation (focus on mathematics)? y What has helped you to meet this expectation (during your induction)? y What has challenged you (during your induction)? y What can we do together to improve this? The questions for evaluating induction effectiveness (6 weeks after starting) were: y Are we including mathematics in our planning? y What has been the mathematics that has been focused on in the last few weeks? y What has been missed out/could have been done in more depth? y Have mathematical concepts/language been followed up on at mat time? y Have mathematical learning stories been written up and displayed? y What else can we do to focus on mathematics—which strand, learning experience, game? Ongoing evaluation The head teacher’s standardised sets of questions to use in reviewing the induction process were trialled with Y (one of the relievers) at the end of August 2005. She emailed the researcher- facilitator a record of this discussion which is reproduced below: E-mail message: I have evaluated the induction with my other reliever today. First we talked about the routines. We are finding that we are recording the daily activities most of the time, although I am finding that if I don’t put it on the table in our lunch break, it gets forgotten. It is not feasible to reschedule this till after the afternoon session, because of other meetings and tasks. Weekly planning discussion: We decided to write any “links to maths” under the heading “links to Te Whäriki”. Y (the reliever) told me she was happy about the maths focus when she first heard about it, because “in each activity we can introduce maths”, and “ maths gives a lot of possibilities” (with its 5 strands it gives a variety of areas you can work with). It was quite clear to Y what was expected, especially after having read the handout “Maths in our kindergarten”, which she found quite clear. (So this has helped the induction.) 35 The amount of information given was just right. I hadn’t given Y the information of maths in each kindergarten area. She thought it a good idea to put this into an induction folder, for the teacher to read when ready or needed. Y is planning beforehand for maths possibilities in her activities. This is working well for her. What is not working? Y finds that the children are not taking a lot of initiative to write numbers. Between August and November 2005, this kindergarten was challenged by further staffing changes. By the middle of October, two permanent appointments had been made but by the time the researcher-facilitator met the team again in mid-November, one of these teachers had resigned. The head teacher nevertheless carried out her commitment to implement a review of the induction process with the two new permanent teachers, A and B, and incorporated this into a series of meetings. She reported the following: Discussion on 11/10/05 A and B have read the information on “Maths in our kindergarten”. We have discussed the following: • draw the maths out in children’s play • maths games (perhaps mosaic tiles / hopscotch game / spider game) • record/display maths learning (A3 paper) • show at mat time what they have made. Compare/discuss the maths aspect of the project • keep up daily records on maths in special column on daily sheets. Discussion on 18/10/05 Mentioned the Mathematics Book and forward planning for maths in each area. Discussion on 25/10/05 • maths needs more focus • collect learning stories • improve documentation related to maths • include maths game/activity on writing table • filing tray in office for maths learning stories. 36 End-point evaluation In mid-November 2005, the current Avondale Kindergarten teaching team met with the researcher-facilitator once again to look at what had been achieved in terms of change strategies since the meeting in August. The head teacher was accompanied to this meeting by the one remaining new permanent staff member and was still relying on a reliever to complete the teaching complement. The two teachers from Avondale Kindergarten summarised the evidence that showed what had changed in their practice as they pursued the action research goal. This is presented under the headings of documentation, planning and display: y documentation: − mention of mathematics in staffing advertisement − statement of competent mathematics teaching (kindergarten-specific) − evaluation questions to frame ongoing review of induction process y planning: − daily and weekly planning to “draw out the mathematics” − term evaluation of teaching plans − creation of special mathematics section in planning outlines y display: − mathematics display book − mathematics display wall − mathematical learning stories on display − attractive displays of mathematics equipment Overall, the teachers at Avondale Kindergarten believe they have gone some way to “developing a system for keeping mathematics alive, keeping it in the centre of the picture”. The importance of a “system” is borne out by the continuing difficulty this kindergarten has in retaining staff. The practitioners who were involved in this research (past and present team members) were very concerned to put something enduring in place. Their hope is that future teachers will succour and sustain this endeavour to enhance mathematics learning and teaching despite socio-cultural barriers. This will only happen if the teachers themselves make a concerted effort to keep the prominence of mathematics alive and well. 37 The case of Birdwood Kindergarten: enhancing collaborative mathematical partnerships between teachers and parents The kindergarten The Birdwood Kindergarten is located in West Auckland and, at the time of this research project, was staffed by two full-time permanent teachers. The teachers operate a roll that caters for up to 30 children in morning sessions and up to 30 in afternoon sessions. However, the actual number of children on the roll frequently falls below this capacity and also, there is a consistent pattern of irregular attendance of children who are on the roll. The 2005 Education Review Report revealed that the ethnic make up of the kindergarten community included Mäori (12), Samoan (12), New Zealand European (8), Tuvalu (4), South East Asia (4), Tongan (1), Fijian (1), Cook Island (1), Niuean (1), and Zimbabwean (1). Many of the families have lived in the area for some time creating a relatively stable community environment—it is not uncommon to have a family’s first, second and third child in attendance at the kindergarten. In some instances the second generation of children from a family are enrolled. The kindergarten is located beside a primary school that has a decile 1 rating indicating a socioeconomic composition that is at the lowest end of the scale—a 2004 AKA Parent Survey revealed that the biggest majority (44%) of families earn under $25,000 with a small number (4%) earning over $69,000. At the time of this research project, the two teachers at Birdwood Kindergarten had had a long- term working relationship: They had been working together as a team for nearly five years. The teacher holding the position of head teacher had been there for more than 12 years. Although an administrator is employed for four hours each week, the teachers undertake added administrative and management tasks that would normally have been done by a whānau/parent committee. The Birdwood Kindergarten community has, for several years, experienced difficulty in forming a whānau/parent committee. The participants were interested in participating in this research project because, as well as having had working relationships with members of the research team in the course of their own studies (upgrading to a teaching degree in early childhood education) and professional development, they were motivated to develop their understandings and their practices to improve the mathematics teaching and learning in their kindergarten. The participants were concerned that the community was unaware of the extent and potential for mathematics learning and teaching that happens in the early years and, in particular, that happens in the kindergarten. In order for mathematics teaching and learning to be effective for children it was crucial, they felt, that the kindergarten community—the whānau/parents and the school’s new entrant teacher—be both informed and involved. The participants shared a desire to “involve them on our journey”; they were convinced that collaboration was the key to creating a “culture of mathematics teaching and learning” for young children—in the kindergarten and in the home setting. Further, it was this collaborative approach that, they believed, would “support the (child’s) transition to school” and their ongoing learning in mathematics. 38 Understanding the problem—the reconnaissance phase This action research project began with a facilitated orientation towards developing a deeper understanding of the challenge ahead. It was essential, at this stage of the project, that the participants engage in a dialogue and data gathering process to gain both a wider and deeper understanding of the complexity, and of the issues, involved in their identified problem and to increase their understanding of why, in the past, any attempts to resolve these issues or change their practices may have met with difficulty. This reconnaissance phase for Birdwood Kindergarten involved two discussion sessions (3 hours each) interspersed with a data collection by the participants to further inform their understandings. Analysis of the problem After considerable dialogue that involved a wide-ranging exploration of the issues that enabled both participants to share their perspectives, a process of funneling took place. This guided process involved a narrowing of the key aspects that both participants agreed were at the heart of their action research problem. It was quickly evident they both believed that in order to improve the learning and teaching of mathematics in the kindergarten, it would need to be done in collaboration with whānau/parents and be consistent and responsive to children’s ongoing mathematical learning when they go to school. This led to their rationale for deciding that both the whānau/parents and the school’s new entrant teacher be involved in some way. With these ideas in mind, they formulated their first action research statement: How are we going to educate ourselves, the children and the kindergarten community to develop a collaborative knowledge and capability of learning and teaching mathematics in early childhood? Ideas from brainstorming were noted on a whiteboard and then themed and re-themed to gain a clearer picture of the dimensions of the problem—and in particular of the issues that the participants felt contributed to their problem. The focus of this discussion and data gathering involved considerable soul searching. The participants identified their own attitudes towards, and experiences with, mathematics as being influential in their approaches to mathematics teaching and learning. Hence the decision, though they felt it somewhat ironic, to make mathematics the focus of the current teaching journey. One participant wrote: Some years ago I was confronted with my mathematical disposition when I came across an early school report … alongside number … all I remember, is the word “poor”. The other participant described similar experiences: I need to look at my maths demons from years gone by and fight them head on, I hope to change my opinion of myself. I need to believe that I have the capability to create fun and rich mathematical experiences across the curriculum for our young students. Hence, at this early stage in the process of exploring the dimensions of the problem, the participants were critically aware of the impact that environmental experiences might have on 39 mathematics learning, and consequently on their teaching of mathematics. With their own experiences in mind, they questioned the kind of environments that might be prevalent in their diverse kindergarten community and, as a result, the mathematical experiences children might receive. They wondered: … whether (the children) actually come from an environment that encourages and supports their mathematical learning? They questioned whether many of the whānau/parents or the school’s new entrant teacher had an understanding, and therefore an appreciation, of the possible mathematics teaching and learning that took place in the kindergarten. This was particularly true, they proposed, of those for whom the Aotearoa New Zealand early childhood education “structure” was new or unfamiliar: Many families do not understand the concept of children learning through play … see the more formal school setting as the way to learn. Therefore, by the end of the session, the agreed dimensions of the problem were: y community mathematical knowledge and capability: that whānau/parents and the school’s new entrant teacher are aware of, understand, and appreciate the mathematics learning and teaching of mathematics in the kindergarten; and that there was uncertainty about whānau/parent expectations about mathematics teaching and learning in the early years because of diversity of values and cultures; y teachers’ mathematical knowledge, capability and manageability: being confident and able to recognise the mathematics component, and therefore the potential, in everyday experiences and to use the resources available; being able to document and make visible (i.e. display) the learning and teaching of mathematics in the kindergarten, in ways that are useful for informing whānau/parents and the school’s new entrant teacher of the mathematics learning and teaching that does happen in the early years; and y children’s mathematical knowledge and capability: that both teachers and whānau/parents are aware of children’s competencies, knowledge, skills, and attitudes in mathematics, and can support and extend them. In the next step of the problem identification phase, the participants assembled and reviewed available and relevant data. This specific site-based data analysis included previous reviews of practice and documents pertaining to expectations related to the effective teaching and learning of mathematics in a kindergarten. At this point they decided they needed to include whānau/parents in the data gathering process. They felt that in order to establish a collaborative approach, it was essential to both inform whānau/parents of the research project and open up some discussion to invite whānau/parents to share their ideas and be involved. Therefore, they decided to devise a whānau/parents survey, with an introduction and an explanation, to begin this process. 40 Summary of previous reviews Earlier, in 2004, Birdwood Kindergarten had participated in an AKA survey that had explored how the whānau/parent community viewed the kindergarten’s provision of care and education for their children. The results provided an indication of whānau/parents’ views (47% responded) and these respondents represented every ethnic group involved in the kindergarten community. Of significance to this research project was the extent to which the kindergarten was meeting whānau/parent expectations in relation to particular aspects, such as curriculum and teaching philosophy. These data revealed that whānau/parents’ expectations in reading, writing and mathematics skills scored a varied response—a considerable number of respondents felt that their expectations were exceedingly “well met”; for half the respondents their expectations were “met”; but for others (about one-fifth of respondents), provision was “below expectations”. The participants at Birdwood Kindergarten had discussed this finding. It had, at the time, provoked them to examine their own practices and their knowledge and understandings of the whānau/parent kindergarten community in order to understand what may have influenced the “below their expectations” responses expressed in the survey. They queried whether these responses suggested that the kinds of teaching and learning practices more highly valued, by many of the kindergarten community whānau/parents, might be similar, or the same, as those that are reinforced by the home intervention programme (HIPPY New Zealand, 1992) that was well- known in the community. HIPPY, as the teacher-participants understood it, provided a more structured and formal method of early childhood education with a greater emphasis on a skills- based approach. In contrast, the participants advocated a curriculum with a play-based philosophy and an integrated and holistic approach to learning and teaching. Nevertheless, the teachers were prepared to accept the challenges inherent in the AKA’s survey results and in their understanding of the importance of early mathematics learning and teaching for all children in the community. It was with this in mind, when the opportunity arose, that they started on this mathematics project. Yet it was, as one teacher said, “a journey I thought I would never see myself make”. At the system level, an Education Review Office (ERO) review was carried out at the time of the reconnaissance phase of this research project. The results of this review provided the participants with generic feedback on their performance in the area of teaching and learning mathematics. The ERO report (2005a) affirmed that, according to the high quality criteria set by the ERO office, “early literacy and numeracy … strongly underpin the teaching programme” (p. 2) in the kindergarten. This report stated that: The teachers support children to understand the fundamentals of numeracy. They provide for children to count, to classify and sort items and display numbers in prominent places in the centre. Children appear to have a good grasp of number and are beginning to use numeracy in their play. (p. 5) These comments were extracted from Education Review Office report, highlighted and displayed for the whānau/parents to read within the kindergarten environment (see Image 4). 41 Image 4: Display of extracts from the Education Review Office report However, the participants remained self-critical and were interested in increasing their competencies in their own teaching practices that would enable them to enhance children’s mathematical learning and foster children’s dispositions towards mathematics—they were keen to: Take advantage of situations that might arise [for children mathematically] to create a sense of enthusiasm for the children. [Take] action to continue with new resources or resources to address different mathematics concepts. Documentary analysis—system and kindergarten levels Although an emphasis on learning and teaching of mathematics in a kindergarten relies on teachers’ knowledge and understanding, a range of documented expectations also guide it. The researchers completed an analysis of the common system documents pertinent to all three sites (further detail is included in the case study of Avondale Kindergarten). In the case of Birdwood Kindergarten, presentation of a summary of the analysis of the system level documentary led to a dialogue about the kinds of teaching and learning documentation they were expected to produce in support of the teaching practices in the kindergarten. The participants were keen to explore the expectation that they use a variety of methods to document their teaching and learning processes. They were interested in increasing the variety of documentation that they 42