Copyright is owned by the Author of the thesis. Permission is given for a copy to be downloaded by an individual for the purpose of research and private study only. The thesis may not be reproduced elsewhere without the permission of the Author. Impact of collaborative planning for mathematics and anticipating student responses to problems on teacher beliefs, knowledge and practice A thesis presented in partial fulfilment of the requirements for the degree of Master of Education at Massey University, Palmerston North, New Zealand Jenna Louise Crowley 2017 ABSTRACT Six teachers engaged in collaborative planning for mathematics lessons that allowed for student- generated responses to problems. As part of their planning they anticipated a range of possible strategies students could use to solve problems and possible student misconceptions. This study explored how the teachers perceived these practices affected their beliefs and the teaching approaches they enacted in their lessons. The study also examined the affordances and barriers of collaborative planning and anticipating on teacher learning. Mathematics education literature recommends a move toward student inquiry approaches in order to improve outcomes for all learners. Relevant literature was reviewed, illustrating the importance of providing the conditions required to enable teacher learning and change. Evidence was provided of the role of dissonance, teacher confidence and knowledge of both mathematics content and pedagogy, and effective leadership and systems of support. Teacher collaboration was identified as a potential catalyst for change. A qualitative case study method was chosen as most appropriate for this study. A range of data was collected and analysed, including semi-structured interviews with all of the participants. Researcher field notes and documentary data allowed for triangulation. Ethical principals were strictly adhered to. The study revealed some resistance to change and the constraints of teachers’ prior learning and existing beliefs and practices on the outcomes of the collaborative planning intervention. The study demonstrated teachers’ experimental approach to enacting new practices in mathematics lessons and their adherence to their current teaching practices and beliefs about grouping students for learning. Noteworthy benefits of anticipating and collaborative planning were increased teacher confidence to allow student-generated solutions to problems and increased teacher knowledge of mathematics strategies. These benefits were attributed to teachers learning from each other while collaboratively planning. The results revealed teacher collaboration was perceived as an affordance to change and highlighted a number of factors which acted as barriers to teacher change. Identified barriers included either too much or too little dissonance experienced by teachers, attitudes towards risk and the desire to conform, and gaps in teacher knowledge of mathematics. The results offered insights into the effects of school culture and the design of professional learning experiences for teachers. ii ACKNOWLEDGEMENTS I would like to acknowledge and thank the many people who have made this study possible. Most importantly I wish to thank the teachers who participated in the study and acknowledge the value of their contributions to the study and to my own learning. I appreciate the time and effort that each of you put in and your willingness to share so openly with me. I give acknowledgement and thanks to my supervisors, Dr Roberta Hunter, Dr Jodie Hunter, and Dr Glenda Anthony. You have all shown me patience, belief and support, both personally and professionally. Your suggestions and guidance have shaped the final presentation of this thesis. Bobbie, your contribution to my growth and personal development over the last twelve years has been invaluable, and will always be remembered. Finally, I must acknowledge and thank my family and friends for coming on this journey alongside me. To my husband, Warren Snalam, who held everything together around me, I would like to say thank you for being my partner and my supporter. I want to thank my mother, father, and sister for their encouragement and unwavering belief in me. Lastly, I wish to express my sincere appreciation to my friend Becks, for her advice and input into my writing; and to Laurayne, who helped me get over the finish line. This study would not have been possible without any of the people mentioned here, and I acknowledge the collective effort that has gone into this thesis. Arohanui ki a koutou. iii TABLE OF CONTENTS ABSTRACT ii ACKNOWLEDGEMENTS iii TABLE OF CONTENTS iv CHAPTER 1: INTRODUCTION 1.1 Background to the study 1 1.2 Research objectives 3 1.3 Overview 4 CHAPTER 2: LITERATURE REVIEW 2.1 Introduction 5 2.2 Planning practices and the role of anticipation 5 2.3 Teacher change 6 2.3.1 Generative teacher change 7 2.3.2 Dissonance 7 2.3.3 Vision 8 2.3.4 New Knowledge 8 2.3.5 Relevance 9 2.3.6 Leadership 10 2.4 Professional learning communities 10 2.4.1 Culture of collaboration 10 2.4.2 Collective inquiry 11 2.4.3 Student learning 11 2.4.4 Action and results orientation 12 2.5 Teacher collaboration 12 2.5.1 Shared beliefs 13 2.5.2 Respectful challenge 13 2.5.3 Risk-taking and enquiry-mindedness 14 2.5.4 Facilitation 14 2.5.5 System-level support 15 2.5.6 Benefits of teacher collaboration 15 2.6 Teacher knowledge 16 2.7 Impact of teacher confidence and efficacy on teacher practice 17 iv 2.8 Summary 17 CHAPTER 3: RESEARCH DESIGN 3.1 Introduction 19 3.2 Methodology 19 3.3 Case study 20 3.4 Role of the researcher 21 3.5 Data collection 21 3.5.1 Interview 22 3.5.2 Observation 22 3.5.3 Documentary data 22 3.5.4 Setting and sample 23 3.5.5 Research schedule 24 3.5.6 Reliability and validity 25 3.6 Data analysis 26 3.7 Ethical considerations 27 3.8 Summary 28 CHAPTER 4: FINDINGS 4.1 Introduction 30 4.2 Teachers’ beliefs and prior learning 30 4.3 Teacher confidence and self-efficacy 33 4.3.1 Planning practices and the role of anticipation 33 4.3.2 Working as a team 34 4.3.3 Desire to conform 35 4.4 Teacher knowledge 36 4.4.1 Mathematics knowledge 38 4.4.2 Curriculum knowledge 38 4.5 Use of student responses 39 4.6 Teacher experimentation 41 4.7 Summary 42 CHAPTER 5: DISCUSSION AND CONCLUSION 5.1 Introduction 44 5.2 Analysis of barriers to teacher change 44 5.2.1 Teacher beliefs and prior learning – The individual teacher 45 v 5.2.2 Teachers’ prior learning and the role of dissonance 45 5.2.3 Teacher beliefs and critical inquiry 46 5.2.4 Perceived pressure on teachers – The school 47 5.2.5 School norms and collegial expectations 47 5.2.6 Perception of risk 48 5.2.7 Time pressure 49 5.2.8 Teacher experimentation – The learning activity 49 5.2.9 Teacher knowledge 50 5.3 Analysis of affordances to teacher change 51 5.3.1 Working as a team 52 5.3.2 Planning practices and the role of anticipation 52 5.3.3 Expectations of teachers 53 5.4 Limitations and implications 53 5.5 Opportunities for further research 54 5.6 Conclusions 54 5.6.1 Affordances to teacher change 54 5.6.2 Barriers to teacher change 55 5.7 Summary and concluding thoughts 56 REFRENCES 58 APPENDICES Appendix A: Initial Interview (I#I) questions 66 Appendix B: Final Interview (I#F) questions 67 Appendix C: Sample of teacher weekly planning (Phase 1) 69 Appendix D: Collaborative planning questionnaire (Phase 2) 70 Appendix E: Lesson sequence and teacher reflective questions 71 Appendix F: Example of completed planning template 72 Appendix G: Sample of coding and memoing 74 Appendix H: Teacher information letter 76 Appendix I: Example – Task 5, GLoSS Interview 1 78 LIST OF TABLES 3.1 Summary timeline of data collection 23 vi CHAPTER ONE INTRODUCTION 1.1 BACKGROUND TO THE STUDY Mathematics achievement in New Zealand The current New Zealand mathematics education achievement statistics are cause for concern. In 2014 and 2015 New Zealand participated in two large international studies – the Trends in International Mathematics and Science Study (TIMSS), and the Programme for International Student Assessment (PISA). The results of these studies show current mathematics education practices in New Zealand schools are not significantly raising student achievement (Ministry of Education, 2017). Also problematic is that the gap between low and high achievers has widened significantly since the 2010/11 TIMSS. For example, for both of the tracked groups - Year 5 and Year 9 students, the range has increased, indicating growing inequity in educational outcomes for young people (Caygill, Hanlar, & Singh, 2016a, 2016b). Furthermore, Maori and Pasifika learners had lower average mathematics achievement than non-Maori and non-Pasifika learners, respectively. The growing gap between low and high achievers, and disparities in educational success for Maori and Pasifika learners have led researchers to question what is needed to improve the teaching and learning of mathematics in New Zealand schools. Effective mathematics teaching Widely-held understandings of what constitutes effective mathematics teaching and learning have changed in recent times from teacher-driven instruction to student inquiry approaches. The professional learning and development landscape for teachers in New Zealand has also changed over the last two years, from a centrally managed national delivery programme to an individual school directed approach. The aim of mathematics professional development initiatives for teachers is to improve teaching and learning. Beginning in the year 2000, in-service primary and intermediate school teachers were provided with the training and resources known as the Numeracy Development Project (Ministry of Education, 2008a). More recently, studies have found additional specific pedagogies and practices that teachers can enact to better address the needs of diverse learners in their classrooms (Anthony & Hunter, 2017; Averill & Clarke, 2013; Bills & Hunter, 2015; Bishop, Berryman, Powell, & Teddy, 2007; Boaler, 2016; Hunter, 2007; Stein, Engle, Smith, & Hughes, 2008; Stigler & Hiebert, 1999; Sullivan & Lilburn, 2004; Van de Walle, Karp, & Bay-Williams, 2016) Many current providers of professional learning draw on these studies and other recent mathematics education research. Teachers require 1 continuing access to quality professional support to change their beliefs and classroom practices if New Zealand is to address the current disparities in student outcomes. The challenge of change along a continuum of practices Alongside the implementation of the Numeracy Development Project, there is now an internationally recognised move to include more inquiry-based discourse approaches within the mathematics classroom. The specific approach the researcher had been advocating within recent in-service professional development included the enactment of pedagogical practices described by O'Connor, Michaels, Chapin, and Harbaugh (2016), Stein et al. (2008), and Hunter (2007). These practices included using ‘Talk Moves’ to encourage productive academic discourse amongst students, providing students with worthwhile mathematical problem-solving tasks to work on in mixed-ability groups and allowing student-generated responses to be the focus of the lesson, and teachers planning collaboratively to anticipate a range of possible student solutions to tasks before teaching them. The underlying drive behind the current study was the desire to better support teachers to change their beliefs and enact teaching practices aligned with current research in mathematics education, in order to improve results in mathematics for all students. Punch and Oancea (2014) encouraged researchers to “be philosophically mindful in research, including questioning their assumptions, inquiring into alternatives, checking their arguments, and analysing their concepts” (p. 20). This is consistent with Schön (1983), who said the modern professional needs to constantly question and reflect upon their practice. The research questions addressed in the current study arose from the researcher’s reflection on practice. Worthwhile mathematical tasks: From anecdote to case study Effective teaching should result in student learning. Researchers have pointed to the importance of task design in enabling student learning in mathematics (Choy, 2016). According to Anthony and Walshaw (2007), an effective mathematical task must be deliberately created to support mathematics learning; be sufficiently challenging for all students; and provide “opportunities for students to investigate mathematical structure, to generalise, and to exemplify” (p. 140). Best practice, cognitively challenging mathematical tasks are difficult for teachers to create; Choy (2016) states that, “to improve task design skills, teachers often engage in collaborative lesson planning activities” (p. 421). The aim of the current study was to explore how collaborative planning affected teacher beliefs and enacted practices through a case study investigation. 2 The value of anticipating student responses Stein and her colleagues (2008), explain that the practice of anticipating can support teachers to manage the challenge of enacting more effective classroom pedagogy during their lessons. The planning practice of anticipating is one of five practices recommended by Stein and her colleagues (2008); the other four practices relate to teacher actions during mathematics lessons. Anticipating takes place prior to lessons as part of planning for teaching, and involves teachers predicting a range of possible student strategies for solving a problem. The anticipated strategies can be informed by observations of students’ thinking, as well as teachers’ own mathematics and curriculum knowledge. Furthermore, Stein and her colleagues (2008) stated that enacting these five specific practices (including anticipating) can improve teachers’ sense of efficacy, as they become more adept at facilitating learning through discussion of student-generated solutions to problems during mathematics lessons. The current study sought to explore the impact of anticipating during collaborative planning sessions involving a team of teachers working together, with the ultimate aim to expand on current understandings of the effects of these practices. 1.2 RESEARCH OBJECTIVES The purpose of this qualitative study was to investigate teachers’ experiences of collaborative planning for mathematics problem-solving lessons, using planning practices based on the work of Smith, Hughes, Engle, and Stein (2009). The particular practice that was the focus of the collaborative planning intervention was anticipating. A case study research design explored collaborative planning sessions as they occurred within the context of a New Zealand primary school. The objective of the research was to develop understanding of how collaborative planning affected teacher beliefs and practices enacted in mathematics lessons, from the teachers’ perspectives. The study also sought to understand the benefits and/or disadvantages of collaborative planning, in particular, the impact of this practice on teacher knowledge. The ultimate goal of this research was to add to the literature surrounding supporting teacher learning and thereby contribute to reducing educational disparities for learners of mathematics. 3