CASE-STUDIES OF TEACHERS COLLABORATING TO IMPLEMENT A CULTURALLY-RELEVANT PROBLEM-SOLVING RICH MATHEMATICS UNIT IN FOUR CLASSROOMS IN THE COMMONWEALTH OF THE NORTHERN MARIANA ISLANDS A DISSERTATION SUBMITTED TO THE GRADUATE DIVISION OF THE UNIVERSITY OF HAWAI‘I AT MĀNOA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN EDUCATION MAY 2014 By Dora Borja Miura Dissertation Committee: Joseph T. Zilliox, Chairperson Julie Kaomea Neil A. Pateman Beatriz D’Ambrosio Tom Craven ABSTRACT I chronicled the journeys of four teachers in three elementary schools in the Commonwealth of the Northern Mariana Islands (CNMI). To support the teachers in the implementation process, I created a series of focused collaboration sessions for them. These sessions first introduced the teachers to the idea of ethnomathematics and the potential of adopting culturally-relevant approaches, and later provided support during implementation. In order for me to understand the impact of the collaboration sessions and the implementation process on the teachers' beliefs about mathematics, teaching and curriculum, I created four case studies, one for each teacher, and employed cross-case analysis to form my conclusions. My analysis of the case studies showed that the teachers believed that the focused collaboration sessions and the implementation process effectively changed their teaching, their attitudes and knowledge of mathematics, and their understanding of curriculum. I recommend that others adopt a similar focused collaboration approach as a form of professional development for teachers interested in different approaches to teaching mathematics and developing curriculum. Keywords: Problem-solving mathematics, ethnomathematics, Saipan, CNMI, teachers, case study ii TABLE OF CONTENTS Abstract .............................................................................................................................. ii Chapter 1. Introduction ................................................................................................... 1 Rationale for the Study ................................................................................................ 1 History of Education in the CNMI ............................................................................. 1 Current CNMI Curriculum ......................................................................................... 4 Chapter 2. Literature Review .......................................................................................... 8 Problem-Solving Rich Mathematics ........................................................................... 8 Culturally-Relevant Mathematics ............................................................................ 11 Chapter 3. Methodology ................................................................................................ 15 Purpose of the Study .................................................................................................. 15 Methods ....................................................................................................................... 15 Chapter 4. Outcomes of the Study ............................................................................... 20 Study Participants ....................................................................................................... 20 Procedures and Data Gathering ............................................................................... 21 Limitations of the Study ............................................................................................ 25 The Case Studies ......................................................................................................... 26 Introduction ............................................................................................................. 26 Case Studies ............................................................................................................. 26 First grade teachers ............................................................................................ 30 Fourth grade teachers ........................................................................................ 32 Reflection session in October with all teachers .............................................. 33 Focus on first grade teachers ................................................................. 33 Focus on fourth grade teachers ............................................................. 36 First grade planning sessions ............................................................................ 38 First grade implementation of unit: Heidi ...................................................... 45 First grade implementation of unit: Tara ........................................................ 50 First grade implementation of unit: Collaboration Session 1 ....................... 51 First grade implementation of unit: Heidi ...................................................... 56 First grade implementation of unit: Heidi and Tara ..................................... 60 First grade implementation of unit: Tara ........................................................ 61 First grade implementation of unit: Collaboration Session 2 ....................... 62 First grade implementation of unit: Heidi ...................................................... 64 First grade implementation of unit: Tara ........................................................ 67 First grade implementation of unit: Collaboration Session 3 ....................... 73 First grade implementation of unit: Heidi ...................................................... 80 First grade implementation of unit: Tara ........................................................ 81 First grade implementation of unit: Collaboration Session 4 ....................... 87 First grade implementation of unit: Heidi ...................................................... 90 First grade implementation of unit: Tara ........................................................ 92 First grade implementation of unit: Collaboration Session 5 ....................... 95 Fourth grade planning sessions ........................................................................ 97 Fourth grade implementation of unit: Roxy ................................................... 99 Fourth grade implementation of unit: Mindy ................................................ 99 Fourth grade implementation of unit: Collaboration Session 1 ................. 100 Fourth grade implementation of unit: Roxy ................................................. 101 iii Fourth grade implementation of unit: Mindy .............................................. 104 Fourth grade implementation of unit: Collaboration Sessions 2 & 3 ........ 105 Fourth grade implementation of unit: Roxy ................................................. 107 Fourth grade implementation of unit: Mindy .............................................. 110 Fourth grade implementation of unit: Collaboration Session 4 ................. 113 Fourth grade implementation of unit: Roxy ................................................. 113 Fourth grade implementation of unit: Mindy .............................................. 114 Fourth grade implementation of unit: Collaboration Session 5 ................. 115 Fourth grade implementation of unit: Roxy ................................................. 115 Fourth grade implementation of unit: Mindy .............................................. 117 Themes ............................................................................................................... 119 Problem-solving rich mathematics .................................................... 119 Questioning techniques ....................................................................... 120 Manipulatives ........................................................................................ 126 Enduring understandings ................................................................... 135 Cultural pit stops .................................................................................. 143 Confidence ............................................................................................. 147 Chapter 5. Discussion and Conclusions ................................................................ 154 Revisiting the Case Studies ................................................................................. 155 The Role of Culture .............................................................................................. 157 My Participation and What I Learned ............................................................... 159 Final Thoughts ...................................................................................................... 160 Appendices ................................................................................................................ 162 Appendix A ........................................................................................................... 162 Appendix B ............................................................................................................ 164 Appendix C ........................................................................................................... 170 Appendix D ........................................................................................................... 171 Appendix E ...........................................................................................................