THE EFFECT OF NETWORK EMBEDDEDNESS: SOCIAL INFLUENCE AND LATENT SPACE POSITIONS ON TEACHERS’ RESOURCE CURATION By Yuqing Liu A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Measurement and Quantitative Methods—Doctor of Philosophy 2022 ABSTRACT THE EFFECT OF NETWORK EMBEDDEDNESS: SOCIAL INFLUENCE AND LATENT SPACE POSITIONS ON TEACHERS’ RESOURCE CURATION By Yuqing Liu Few studies on teachers’ social networks have extended their scopes from schools to online, leaving gaps and the potential to study how school and district colleagues as well as online-only peers can exert a network influence on teachers’ online resource curation activities. These studies have underused the relational-event social-influence model along with the latent space model to estimate the social influence process of teachers’ online resource curation, while taking into account their latent positions for potential resource-mediated social selections. Also, few studies have defined the network embeddedness of teachers’ resource curation regarding the direct social context of interpersonal networks, as well as the indirect context of the teacher- resource two-mode social space. This dissertation attempted to use the relational-event social- influence model to estimate the online network influence on teachers’ resource curation activities, while accounting for a potential resource-mediated social selection process using the latent space model. Using a sample of 55 teachers from Waters School District in Indiana and their curation data on 81 resources across 48 weeks from 2016-17, I found a significant network exposure effect, specifically from online-only peers, after accounting for the potential resource- mediated social selection process. Several interaction effects of individual attributes and resource curation contexts have also been found to moderate the network exposure effect. In conclusion, teachers were influenced by their online networks when curating resources. Though both were significant, the resource-mediated social selection process was not confounded with the social influence process in the one-mode interpersonal network, suggesting that the two social contexts teachers are embedded in played different roles in affecting teachers’ resource curation. Copyright by YUQING LIU 2022 ACKNOWLEDGEMENTS I am extremely fortunate to be an advisee of yours, Dr. Ken Frank. Thank you for choosing me to be your student at the beginning of my program and being my steady support through the end of my doctoral study. To me, you are more than an academic mentor, a respectful man, and even more than a father. You are my role model in many senses of the word. Your genuine smile made me believe that there exists pure joy in every detail of the research process, which can power through any other difficulties in research and in life challenges. What I need to do is to always keep looking for those joys and turn them into a big engine of motivation. I sincerely appreciate the support and advice Dr. Kaitlin Knake brought me over the years. When I look back, I know that I made the right decision to join the Teachers in Social Media project, where I was given many freedoms, from making decisions on the statistical model details, to the way I could frame the manuscript and discuss the results. To me, you are a big sister of mine who not only brought me so many publication and presentation opportunities, but you are also a role model of hard working and caring for the family at the same time. You are such an icon who always keeps trying out different opportunities and sharing our work with all kinds of venues. I know that I will be on my own one day, but thinking of you gives me endless courage and energy, because you taught me to never give up and keep trying. My gratitude deeply goes to Dr. Sharhryar Minhas and Dr. Kim Kelly. Without your thoughtful comments, I would not have been able to catch my blind spots and think through some decisions I made throughout the dissertation—you prepared me to anticipate possible critiques that may come from a wider audience. Your direction and guidance carried me through the revision process, which was one of the most blessed and satisfying revision experiences I have ever had. v I also would like to extend my appreciation to Dr. Yuta Masuda, one of my project leaders and co-authors from The Nature Conservancy. You have the magic to set the bar high, but you can also break down the goal into small and actionable steps. It was such a fulfilling and invaluable learning experience to work with you. I want to express my deepest respect for those genuine conversations, and those rigorous, methodical, yet caring work sessions. Your work ethic became a lighthouse whenever I wanted to rush to the end - “remember, we keep editing until it is perfectly written.” Thanks Iliana, my writing coach, who might be the only person to read this dissertation twice beyond my dissertation committee. With your fun and vivid articulation of grammar rules, I started to enjoy the revision of my manuscript. You always had my back whenever I wanted to try something new and left me worry free with those complex sentence structures. Our revision sessions at one time became my motivation and reason to smile when thinking about the week ahead. Last but not least, I would like to thank my family, especially my husband, Kewei Wang, who accompanied my entire Ph.D. journey and carried me through all the difficulties and uncertainties. There were joys and tears along the way. You were there when my articles were published in journals. You were also there when I burned out and could not look at my face in the mirror. Thank you for being my role model and encouraging me to be brave, resilient, and independent. Thank you for your brutal honesty on my strengths and weaknesses. Without you, I would not be me and could not finish my Ph.D.. Period. In the end, my Ph.D. journey means so much more than a degree. I saw myself stop functioning many times, but soon after, I recovered and got back. The only thing I can say is that it was so worth it to take on this Ph.D. journey, despite all the tears, moments of giving up, vi burning out, and feeling anxious. Thank you Yuqing, you did a great job! Take this Ph.D. degree as a sign of your resilience, a proof of your hard work, and a boost of your confidence. Fasten your seat belt and let us travel to the future. vii TABLE OF CONTENTS LIST OF TABLES ·························································································· xi LIST OF FIGURES ························································································ xii INTRODUCTION ···························································································· 1 Motivations of This Dissertation ········································································ 2 Teachers’ Online Resource Seeking ···································································· 3 LITERATURE REVIEW···················································································· 5 Overview of the Literature Review ····································································· 5 Social Capital Theory and Social Learning Theory ··················································· 6 Social Capital Theory ·················································································· 6 Social Learning Theory ················································································ 7 Social Learning within Professional Learning Spaces ············································· 8 From Physical to Virtual: Teacher Networks in Online Social Platforms ························· 9 The Co-existence of Learning and Socialization in Online Social Spaces ························ 11 Implications of Social Learning Activities on Social Structures ································ 12 Teachers’ Resource Curation ··········································································· 13 Resource Curation as a Professional Learning Activity ·········································· 14 Curated Content as Digital Assets and Tacit Knowledge ········································ 14 Resource Curation as Knowledge Distribution ···················································· 15 Analyzing Teacher Resource Curation Two-Mode Network ······································· 15 Duality of Teachers and Social Learning Events in Two-Mode Networks ···················· 16 One-Mode Projection of Two-Mode Networks ··················································· 16 Preserving the Duality of Two-Mode Networks ·················································· 17 Social Influence and Social Selection ·································································· 17 Social Influence ························································································ 18 Social Selection ························································································ 18 Modeling the Social Influence Process ································································ 20 Egocentric Networks ·················································································· 20 Network Exposure Models ··········································································· 20 Dynamic Social Influence Process in the Framework of the Relational Event Model ·········· 22 Event History Model ·················································································· 22 Relational Event Model ··············································································· 23 Relational Event Model in Studying Tie Occurrence in Two-Mode Networks ··············· 23 Limitations of Current Two-Mode Relational Event Studies ···································· 24 Modeling Social Selection Process Using Latent Space Models ··································· 25 Disentangling Influence from Selection in the Two-Mode Network ······························ 27 Limitations of Using Mixed Triads to Estimate Social Influence Effects ····················· 29 DISSERTATION SIGNIFICANCE: INTEGRATING THE RELATIONAL EVENT MODEL WITH THE LATENT SPACE MODEL ······················································ 32 A Focus on Local Structural Parameters ······························································ 32 viii Combining Two Approaches ············································································ 33 CONCEPTUAL FRAMEWORK ········································································· 34 Double Network Embeddedness ········································································ 34 Latent Space Positions in Two-Mode Networks as an Outcome of Complex Mechanisms···························································································· 37 Bounded District Networks in an Unbounded Online Space ······································· 37 Conceptualizations of Online Resources in Social Media Platforms ······························ 38 The Standing of This Dissertation ······································································ 39 Hypotheses ································································································ 40 METHODS ··································································································· 41 Study Context ····························································································· 41 Pins - Resource Content and Social Spaces ························································ 43 Teachers’ Pinning Activity on Pinterest ···························································· 45 Pinterest Platform Effect ·············································································· 46 Data ········································································································· 49 Sample ····································································································· 52 Waters School District Characteristics······························································ 52 Sample Exclusion Criteria ············································································ 55 Analytical Strategy ······················································································· 58 Latent Space Approach with Multiplicative Effects ·············································· 58 Posterior Predictive Checks on the Model Goodness-of-Fit across Dimensionality ······ 61 Interpretation of Multiplicative Effects ·························································· 65 Clarifying Variation of Terminology across Latent Space Model Literature··············· 65 Estimation ··························································································· 68 Variable Description ····················································································· 71 Dependent Variable ··················································································· 71 Independent Variables ················································································ 73 Network Exposure ·················································································· 73 Network Exposure to School and District Colleagues and Online-Only Peers ············ 75 The Similarity of Latent Space Positions ························································ 75 Dealing with Missingness in the Similarity of Latent Space Positions ······················ 76 Covariates ······························································································· 77 Time ·································································································· 77 Extreme Resource Curation Weeks ······························································ 77 Teacher’s Career Stage ············································································ 77 Teacher’s Grade Level Taught ···································································· 78 Resource Category·················································································· 78 Resource Type ······················································································ 79 Resource Origin ····················································································· 80 Teachers’ Perceptions of Teaching ······························································· 81 Effective Teaching Disposition ································································ 81 Competency in Classroom Management ····················································· 81 Perceived Helpfulness of State Test Expectations ·········································· 82 Pervasive Beliefs among Teachers that Students Are not Motivated to Learn ·········· 82 ix Teachers’ and Resources’ Indicators ····························································· 82 Using the Relational Event Model to Estimate Network Influence ································ 83 Concerns for Controlling for Prior Behavior ······················································ 85 Model Specification for Testing the Network Exposure Effect ···································· 86 Models of Network Exposure Effects ······························································· 88 Models of Network Exposure Effects Interacting with Individual Attributes ················· 90 Models of Network Exposure Effects Interacting with the Resource Curation Context ····· 92 Models of Network Exposure Effects Interacting with Individuals’ Perceptions of Teaching································································································ 93 RESULTS ···································································································· 96 Visualization of Latent Space Positions ······························································· 96 MCMC Diagnostics ······················································································ 97 Variances of Teachers and Resources ································································· 99 Regression Results······················································································ 101 Network Exposure Effects ·········································································· 101 Moderating Effects of Individual Attributes on Network Exposures ························· 106 Moderating Effects of Resource Curation Context on Network Exposures ················· 110 Secondary Analyses on the Moderating Role of Teachers’ Perceptions of Teaching on Network Exposure Effects ····································································· 113 CONCLUSION AND DISCUSSION ·································································· 117 Discussion on Results with Caution·································································· 122 LIMITATIONS AND FUTURE DIRECTION ······················································· 125 APPENDICES ····························································································· 127 APPENDIX A. 81 Resources Curated by at Least Four of the 55 Waters School District Teachers During the 2016-2017 School Year ··································· 128 APPENDIX B. R Code for Latent Space Positions and Circle Plots ···························· 169 APPENDIX C. Circle Plots of Latent Positions for Each of the 48 Cumulative, Weekly Networks ············································································· 175 REFERENCES ····························································································· 222 x LIST OF TABLES Table 1 Waters District Comparison with Indiana School Districts and US School Districts ···· 54 Table 2 Posterior Predictive Checks on Model Goodness-of-Fit across Different Dimensionality ····················································································· 64 Table 3 Descriptive Statistics for Variables in the Regression Analyses ···························· 72 Table 4 Frequency Table of Teachers’ Outdegree and Resources’ Indegree ························ 83 Table 5 Regression Analyses for the Network Exposure Effects (N = 161,054) ················· 103 Table 6 Regression Analyses for the Interaction Effects of Network Exposure and Teachers’ Early Career Stage (N = 161,054) ··············································· 107 Table 7 Regression Analysis for the Interaction Effects of Network Exposure and Grade Level Taught (N = 161,054) ·························································· 109 Table 8 Regression Analyses for the Interaction Effects of Network Exposure and the Resource Curation Context (N = 161,054) ············································· 111 Table 9 Regression Analyses for the Interaction Effects of Network Exposure and Teachers’ Perceptions of Teaching ·························································· 115 xi LIST OF FIGURES Figure 1 Conceptualization of Learning and Social Elements of a Social Learning Event ········ 13 Figure 2 Reproduced Figure from Snijders et al. (2013) ··············································· 30 Figure 3 Double Network Embeddedness of Teachers’ Resource Curation ························· 35 Figure 4 Teachers’ Concurrent Embeddedness in Two-Mode Teacher-Resource Networks and One-Mode Interpersonal Networks ······················································ 36 Figure 5 An Example of a Teacher’s Pinterest Homepage············································· 43 Figure 6 An Educational Pin – Chatty Class? Try Blurt Beans! ······································ 45 Figure 7 Data Collection Procedure ······································································· 50 Figure 8 Data Collection Timeline ········································································ 51 Figure 9 Sample Exclusion Figure ········································································ 56 Figure 10 Analytical Roadmap ············································································ 59 Figure 11 Posterior Predictive Checks on the Sender and Receiver Heterogeneity across Models from k=1 to k=4 ······································································· 63 Figure 12 Susan’s Network Exposures to Resource GrowthMindset at Week Six ················· 74 Figure 13 Percentage of Resources in Each Content Category ········································ 79 Figure 14 Percentage of Resources in Each Resource Type ··········································· 80 Figure 15 Percentage of Resources by Origin ··························································· 81 Figure 16 Circle Plot of the Latent Space Positions of Teachers and Resources in the Cumulative, Weekly Network at Week Three ············································· 97 Figure 17 The Autocorrelation Plot of the Latent Space Model Estimation of the Cumulative, Weekly Network at Week 47 ················································· 98 Figure 18 The Trace Plot of the Latent Space Model Estimation of the Cumulative, Weekly Network at Week 47 ··········································································· 99 Figure A1. Resource-Classroom management1 ······················································· 128 xii Figure A2. Resource-Growth mindset1 ································································· 128 Figure A3. Resource-Classroom resource1 ···························································· 129 Figure A4. Resource-Growth mindset2 ································································· 129 Figure A5. Resource-Flexible seating1 ································································· 130 Figure A6. Resource-Classroom management2 ······················································· 130 Figure A7. Resource-Growth mindset3 ································································· 131 Figure A8. Resource-Character education1 ···························································· 131 Figure A9. Resource-Classroom management3 ······················································· 132 Figure A10. Resource-Flexible seating2 ······························································· 132 Figure A11. Resource-Writing1 ········································································· 133 Figure A12. Resource-Reading2········································································· 133 Figure A13. Resource-Classroom management6······················································ 134 Figure A14. Resource-Writing3 ········································································· 134 Figure A15. Resource-Growth mindset4 ······························································· 135 Figure A16. Resource-Writing2 ········································································· 135 Figure A17. Resource-Classroom management5······················································ 136 Figure A18. Resource-Classroom management4······················································ 136 Figure A19. Resource-Classroom resource2 ··························································· 137 Figure A20. Resource-Growth mindset5 ······························································· 137 Figure A21. Resource-Reading3········································································· 138 Figure A22. Resource-Reading1········································································· 138 Figure A23. Resource-Reading5········································································· 139 Figure A24. Resource-Math2 ············································································ 139 xiii Figure A25. Resource-Reading4········································································· 140 Figure A26. Resource-Math1 ············································································ 140 Figure A27. Resource-Character education2 ·························································· 141 Figure A28. Resource-Writing4 ········································································· 141 Figure A29. Resource-Fun project1 ····································································· 142 Figure A30. Resource-Character education3 ·························································· 142 Figure A31. Resource-Growth mindset8 ······························································· 143 Figure A32. Resource-Flexible seating3 ······························································· 143 Figure A33. Resource-Classroom management7······················································ 144 Figure A34. Resource-Growth mindset6 ······························································· 144 Figure A35. Resource-Classroom resource3 ··························································· 145 Figure A36. Resource-For parents1 ····································································· 145 Figure A37. Resource-Back-to-school1 ································································ 146 Figure A38. Resource-Growth mindset7 ······························································· 146 Figure A39. Resource-Reading11 ······································································· 147 Figure A40. Resource-Fun project2 ····································································· 147 Figure A41. Resource-Spelling2········································································· 148 Figure A42. Resource-STEM challenge2 ······························································ 148 Figure A43. Resource-STEM challenge1 ······························································ 149 Figure A44. Resource-STEM challenge3 ······························································ 149 Figure A45. Resource-Classroom resource4 ··························································· 150 Figure A46. Resource-STEM challenge4 ······························································ 150 Figure A47. Resource-Spelling4········································································· 151 xiv Figure A48. Resource-Math3 ············································································ 151 Figure A49. Resource-Math4 ············································································ 152 Figure A50. Resource-Writing5 ········································································· 152 Figure A51. Resource-Character education4 ·························································· 153 Figure A52. Resource-For parents2 ····································································· 153 Figure A53. Resource-Classroom management9······················································ 154 Figure A54. Resource-STEM challenge7 ······························································ 154 Figure A55. Resource-Back-to-school2 ································································ 155 Figure A56. Resource-Character education5 ·························································· 155 Figure A57. Resource-Classroom management8······················································ 156 Figure A58. Resource-STEM challenge5 ······························································ 156 Figure A59. Resource-Reading6········································································· 157 Figure A60. Resource-Reading7········································································· 157 Figure A61. Resource-Growth mindset11 ······························································ 158 Figure A62. Resource-Growth mindset10 ······························································ 158 Figure A63. Resource-Growth mindset9 ······························································· 159 Figure A64. Resource-Flexible seating4 ······························································· 159 Figure A65. Resource-Classroom resource5 ··························································· 160 Figure A66. Resource-Reading8········································································· 160 Figure A67. Resource-Back-to-school3 ································································ 161 Figure A68. Resource-Back-to-school4 ································································ 161 Figure A69. Resource-Growth mindset16 ······························································ 162 Figure A70. Resource-Spelling1········································································· 162 xv Figure A71. Resource-Reading10 ······································································· 163 Figure A72. Resource-Spelling3········································································· 163 Figure A73. Resource-Classroom resource6 ··························································· 164 Figure A74. Resource-Growth mindset12 ······························································ 164 Figure A75. Resource-Classroom resource7 ··························································· 165 Figure A76. Resource-Growth mindset14 ······························································ 165 Figure A77. Resource-STEM challenge6 ······························································ 166 Figure A78. Resource-Growth mindset15 ······························································ 166 Figure A79. Resource-Growth mindset13 ······························································ 167 Figure A80. Resource-Reading9········································································· 167 Figure A81. Resource-For parents3 ····································································· 168 Figure C1. Week Zero Network Circle Plot···························································· 175 Figure C2. Week One Cumulative Network Circle Plot ············································· 176 Figure C3. Week Two Cumulative Network Circle Plot ············································· 177 Figure C4. Week Four Cumulative Network Circle Plot ············································· 178 Figure C5. Week Five Cumulative Network Circle Plot ············································· 179 Figure C6. Week Six Cumulative Network Circle Plot ·············································· 180 Figure C7. Week Seven Cumulative Network Circle Plot ··········································· 181 Figure C8. Week Eight Cumulative Network Circle Plot ············································ 182 Figure C9. Week Nine Cumulative Network Circle Plot············································· 183 Figure C10. Week 10 Cumulative Network Circle Plot ·············································· 184 Figure C11. Week 11 Cumulative Network Circle Plot ·············································· 185 Figure C12. Week 12 Cumulative Network Circle Plot ·············································· 186 xvi Figure C13. Week 13 Cumulative Network Circle Plot ·············································· 187 Figure C14. Week 14 Cumulative Network Circle Plot ·············································· 188 Figure C15. Week 15 Cumulative Network Circle Plot ·············································· 189 Figure C16. Week 16 Cumulative Network Circle Plot ·············································· 190 Figure C17. Week 17 Cumulative Network Circle Plot ·············································· 191 Figure C18. Week 18 Cumulative Network Circle Plot ·············································· 192 Figure C19. Week 19 Cumulative Network Circle Plot ·············································· 193 Figure C20. Week 20 Cumulative Network Circle Plot ·············································· 194 Figure C21. Week 21 Cumulative Network Circle Plot ·············································· 195 Figure C22. Week 22 Cumulative Network Circle Plot ·············································· 196 Figure C23. Week 23 Cumulative Network Circle Plot ·············································· 197 Figure C24. Week 24 Cumulative Network Circle Plot ·············································· 198 Figure C25. Week 25 Cumulative Network Circle Plot ·············································· 199 Figure C26. Week 26 Cumulative Network Circle Plot ·············································· 200 Figure C27. Week 27 Cumulative Network Circle Plot ·············································· 201 Figure C28. Week 28 Cumulative Network Circle Plot ·············································· 202 Figure C29. Week 29 Cumulative Network Circle Plot ·············································· 203 Figure C30. Week 30 Cumulative Network Circle Plot ·············································· 204 Figure C31. Week 31 Cumulative Network Circle Plot ·············································· 205 Figure C32. Week 32 Cumulative Network Circle Plot ·············································· 206 Figure C33. Week 33 Cumulative Network Circle Plot ·············································· 207 Figure C34. Week 34 Cumulative Network Circle Plot ·············································· 208 Figure C35. Week 35 Cumulative Network Circle Plot ·············································· 209 xvii Figure C36. Week 36 Cumulative Network Circle Plot ·············································· 210 Figure C37. Week 37 Cumulative Network Circle Plot ·············································· 211 Figure C38. Week 38 Cumulative Network Circle Plot ·············································· 212 Figure C39. Week 39 Cumulative Network Circle Plot ·············································· 213 Figure C40. Week 40 Cumulative Network Circle Plot ·············································· 214 Figure C41. Week 41 Cumulative Network Circle Plot ·············································· 215 Figure C42. Week 42 Cumulative Network Circle Plot ·············································· 216 Figure C43. Week 43 Cumulative Network Circle Plot ·············································· 217 Figure C44. Week 44 Cumulative Network Circle Plot ·············································· 218 Figure C45. Week 45 Cumulative Network Circle Plot ·············································· 219 Figure C46. Week 46 Cumulative Network Circle Plot ·············································· 220 Figure C47. Week 47 Cumulative Network Circle Plot ·············································· 221 xviii INTRODUCTION Many studies in the fields of teacher networks and professional learning communities have found evidence of the importance and effectiveness of teachers relying on their network members as social capital and support for professional learning and development (Frank et al., 2004; Frank et al., 2011). Nevertheless, few studies have extended their network models from schools to online, leaving gaps and the potential for researchers to study how transcendent collegial relationships as well as purely online-established relationships can exert a network influence on teachers’ educational resource curation activities—a process of teachers’ seeking, sorting out, and saving resource content for professional purposes. This calls for actions to explore how teachers’ diversified online networks would affect their resource curation. Big data from social media provides educational researchers opportunities to study time- stamped teachers’ curation of resources in combination with their social interactions online (Vu et al., 2015; Liu et al., 2020). Depending on the types of network data collected, researchers either rely on one-mode interpersonal networks (Frank, 1995) or two-mode social event participation networks (Doreian et al., 2004; Field et al., 2006) to capture the network embeddedness of individuals’ activities. Nevertheless, teachers are often simultaneously embedded in these two types of networks, which jointly define teachers’ network embeddedness in a social space. Hence, missing any layer of this double network embeddedness will render bias in making inferences on the network effects of teachers’ resource curation. Beyond the availability of big data, advancement in social network analysis presents researchers a spectrum of network models, each with different capacities. Some can model network peers’ influence effects on teachers’ curation activity (such as relational event models) (De Nooy, 2011; Liu et al., 2020), and others can model the selection effects of teachers’ 1 resource curation tie formation along with the network dependencies on the overall network structures (such as latent space models) (Hoff et al., 2002; Snijders et al., 2013; Fujimoto et al., 2018). Nevertheless, the intricacy of teachers’ resource curation activity adds complexity for researchers to choose the appropriate network statistical model. Previous studies either framed teachers’ resource curation as an activity or relational event occurrence, subject to peer influence in their social contexts as well as other covariates such as time or within-teacher random effects (Liu et al., 2020). Teachers’ resource curation can also be regarded as a two-mode network tie— teachers are indirectly connected to one another via participating in the same social learning event (i.e., curating the same resource in online spaces)—which is also subject to structural dependencies of the overall network in one’s indirect social context. An incomplete view of teachers’ resource curation can constrain network scientists’ approach to specifying models to capture both peer influence and the impact of the overall two-mode teacher-resource network on teachers’ resource curation. Subsequently, the danger of ignoring the structural dependencies of teacher-resource network data can result in overestimating the peer influence effect (Xu, 2016). Thus, to address this issue, a model that incorporates both the exogenous social influence effect and the endogenous social selection effect would be needed to properly estimate how teachers’ resource curation is influenced by that of their network peers. Motivations of This Dissertation Equipped with big data capacities and acknowledging the importance of peer influence on teachers’ professional learning, it becomes critical to statistically test the salience of peer influence in the context of teachers’ resource curation on social media, while also controlling for 2 the teacher-resource network tie dependencies on the overall network structure. This dissertation attempts to use a latent space approach to estimate the latent positions of teachers and resources in the two-mode networks in an effort to account for tie dependencies on the overall network structure. Furthermore, a relational event model will be used to estimate the social influence effect of network peers on teachers’ resource curation while controlling for tie dependencies of teacher- resource networks using estimated latent positions. Such a model has the advantage of taking teachers’ double network embeddedness into consideration, capturing a more complete picture of teachers’ embeddedness in double-layered online social contexts—both their interpersonal networks and teacher-resource two-mode networks—and their subsequent impact on teachers’ resource curation. Teachers’ Online Resource Seeking Facing multiple challenges, teachers may seek resources and help from their collegial networks. Studies showed that collegial networks and teacher collaborations help reduce teacher burn-out (Russell et al., 1987), increase resilience (Frank et al., 2020), improve professional skills (Penuel et al., 2012), and make implemented school intervention more sustainable (Frank et al., 2011). In addition, support from network members is particularly crucial for teachers whose class composition includes mainly underrepresented students, as resources teachers have access to may not be adequate to meet the learning needs of students in these situations (Berebitsky & Salloum, 2017; Castro et al., 2010). The professional networks through which teachers access resources are often constrained by formal organizational boundaries. On the positive end, the professional networks at school solidify internal connections, strengthen teaching norms, and create consistent teaching practices 3 (Bidwell & Yasumoto, 1999; Bryk & Schneider, 2002). Nevertheless, regular interactions with the same group of school-based colleagues expose teachers to redundant information (Burt, 2001), which poses an issue when teachers need novel teaching ideas and inspiration to tackle constantly changing scenarios in the classroom (Krackhardt et al., 2003). Hence, it becomes crucial for teachers to connect to broader networks for new resources and knowledge. A typical way for teachers to make new connections, learn, and exchange ideas with one another is to attend professional development (Coburn & Russell, 2008). This relies on school and district leaders’ efforts to create opportunities for professional interactions, encouraging teachers to connect and sustain those relationships (Frank et al., 2011; Horn et al., 2020). Altogether, these professional trainings and professional learning communities play an essential role in bridging educators to those outside of their school organization, connecting them with broader networks of teaching professionals (Penuel et al., 2018). In recent years, social media has afforded teachers the opportunity to connect online with their school and district colleagues and with peers they may not be able to meet face-to-face. Digital platforms and social media deliberately encourage teachers to interact, express their opinion, and create and share educational resources they find useful (Greenhow & Galvin, 2020; Henderson et al., 2013; Pinterest Labs, 2022; Szeto et al., 2016). All of these have wide-ranging implications on teachers' engagement and interactions with peers in the teaching profession, as social media interactions are not bound by the organizational boundary of school, nor by geography (Torphy et al., 2020). 4 LITERATURE REVIEW Overview of the Literature Review In this section, I will first review how researchers draw on social capital and social learning theories to frame teachers’ networking activity and its subsequent influence on teachers’ professional learning efforts. This is to establish the empirical background for introducing literature surrounding the network influence model and the relational event model. Next, I will present literature on the co-existence of learning and socialization in online social spaces, in which I further evaluate studies that focus on the network structural implications of individuals’ social learning activities. This is to set the stage for reviewing latent space models when capturing the social structure of teacher-resource networks as teachers curate resources via social media platforms. Furthermore, I will review various perspectives employed by current literature to investigate teachers’ resource curation activity. Starting from Analyzing Teacher Resource Curation Two-Mode Network, the second part of my literature review focuses on the network theories and methods surrounding social influence and selection processes in the context of two-mode networks. This is to provide a prelude to my research questions concerning resource curation in the framework of teacher- resource two-mode networks. Specifically, I conducted this literature review on how teachers’ resource content curation can be impacted by the exogenous social influence process of their network peers’ curation activity, as well as simultaneously subject to the endogenous resource- mediated social selection process. For instance, Ms. Jane would be influenced by resources curated by her online peer, Susan, to whom she is directly connected; in addition, Jane is also subject to resources curated by Bob, to whom she encountered during her visit to a resource space that she may or may not be directly connected with. 5 Thereafter, I introduce the relational event model with network exposures as the methodological approach to study the dynamic social influence process, followed by theories and methods (e.g., the latent space approach) to model the resource-mediated social selection process—tie formation in two-mode networks. Lastly, I reviewed and commented on the research potential and limitations of current methods for disentangling the social influence process from the social selection process, with an aim to investigate the social influence effect of teachers’ resource curation while accounting for the endogenous resource-mediated social selection. Social Capital Theory and Social Learning Theory Research in social influence investigates the consequences of the network connections on one’s behavioral changes (Friedkin & Johnson, 2011). Several sociological and social psychology theories are rooted in and have developed through the intersection of social networks and social influence. Among these theories, social capital theory (Lin, 2019) and social learning theory (Bandura & Walters, 1977) are widely applied in social sciences and the field of education. Social Capital Theory The research of social capital regards individuals as active agents, reaching out to socially-connected others for information or support, in which the acquired resources are called their social capital (Coleman, 1988; Portes, 1998). Social capital comes in a variety of forms, including information, opportunities, motivations, and abilities (Adler & Kwon, 2002), which are regarded as resources that can be mobilized via the network. Empirical applications of social capital theory include job opportunities via personal contacts (Granovetter, 1973), financial transactional favors in a group of French bankers (Frank 6 & Yasumoto, 1998), and advice seeking among teachers at school (Frank et al., 2004; Penuel et al., 2009). Furthermore, two competing arguments in social capital theory, the effects of strong ties versus weak ties for acquiring information and support, were explored across different contexts (Friedkin, 1982; Liu et al., 2020). Studies indicated that strong ties improved the efficiency of social exchange due to mutual trust and group identification, lowering the transactional cost (Krackhardt, 2003), whereas weak ties promoted information dissemination based on diverse access to different sources (Bakshy et al., 2012; Ruef, 2002). In terms of social capital in teacher networks, studies have found that educational resources (Liu et al., 2020), the ability to interpret accountability pressure and curricular standards (Frank et al., 2020), and expertise in computer technology (Frank et al., 2004) were able to be mobilized in the network to increase teachers’ human capital. Teachers, as individual agents, also establish their networks outside of schools in online spaces, largely expanding the range of their social networks, in which social capital, such as educational resources, are accessed via online network connections (Kelly & Antonio, 2016; Torphy et al. 2020; Wesely, 2013). Thus, further investigation into the social capital embedded in individual teacher’s online networks is needed, which has implications on teachers’ professional learning and growth. Social Learning Theory Social learning theory describes a type of learning approach through observing others in one’s social contexts, leveraging the social nature of human learning (Bandura & Walters, 1977). Behind this, social influence functions as the underlying process through which actors observe and are influenced by others’ behavior (such as others’ resource curation activity), learn from their social contexts, and change their behavior or level of knowledge as a reflection of their learning outcome (e.g., teachers’ curation of a new resource). Insofar as some types of social 7 exposures are present, direct interactions are not necessary for social learning to happen (Rogers, 2003). In connecting social capital theory with social learning theory, social capital is a critical factor for the creation of human capital, in which the learning outcome is the human capital that has been developed by observing the activity of socially-connected others, with information and knowledge transmitted in the process (Adler & Kwon, 2002; Coleman, 1988). In fact, scholars have pointed to the direction of extending social learning research to incorporate a social network approach, increasing the analytical capacity of examining the social aspects of an individual’s learning (Haythornthwaite & De Laat, 2010). Social Learning within Professional Learning Spaces Some literature that is closely related to social learning theory and teacher networks is about teachers’ professional development and professional learning communities. Inside the professional learning community, one way for professional development to be promoted and sustained is to encourage discussions and collaborations among teachers (Coburn et al., 2012; Daly, 2010; Frank et al., 2011). Regarding the objective of teachers’ professional learning, it ranges widely, including technological skills (Frank et al., 2004), mathematical knowledge for teaching (Sun et al., 2014), instructional practice (Penuel et al., 2009), and curriculum implementation (Coburn & Russell, 2008), all of which were better achieved under the mechanism of social learning. Studies have found similar results for teachers participating and collaborating in online professional learning communities, which benefited teachers’ professional learning outcomes (El-Hani & Greca, 2013; Macià & García, 2016). To conceptualize the professional learning space, various frameworks have been developed, each with slightly different emphases on the network components, collaborations, 8 social exchanges, knowledge sharing, and learning. These efforts appeared as early as the Community of Practice in Lave and Wenger’s (1991) Situated Learning Theory and flourished with frameworks like the Distributed Learning Community (Haythornthwaite, 2002), Knowledge Sharing Community of Practice (Ardichvili et al., 2003), Knowledge Building Community (Scardamalia & Bereiter, 2006), Networked Learning Community (Jackson & Temperley, 2007), Networked Improvement Community (Bryk et al., 2011), Socialized Knowledge Community (Hu et al., 2018), etc. In conclusion, the information individuals acquire via interpersonal networks can be regarded as their social capital and the outcome of social learning. In summary, the above theories put into perspective the benefits and impacts of social interactions, which can be framed as the process of social influence to generate changes in individuals’ knowledge and behavior. From Physical to Virtual: Teacher Networks in Online Social Platforms Teacher networks inside a school boundary are often studied in organizational research. Schools and districts are natural social systems, in which teachers frequently interact, collaborate, strive for common goals, and face similar challenges (Frank et al., 2020; Penuel et al., 2009). Organizational boundaries demarcate a holistic social system, which sets individuals within a system apart from the outside by norms, culture, contexts (Coleman, 1988), and resource possession and distribution (Santos & Eisenhardt, 2005). Though each teacher’s experience could be unique, larger environments such as district- level policy, school norms, and student background are strong drivers of teachers’ resource- seeking patterns and teaching practices (Coburn & Russell, 2008; Torphy, Liu, et al., 2020). Within the natural boundary of schools and districts, a network of teachers evolves through regular interactions and relational expectations that colleagues would exchange ideas and share 9 knowledge. All of these have an impact on resource flow, professional learning, and the implementation of new professional practices within a social system. With the development of online platforms, virtual spaces that contain information about professional knowledge and social network functions began to gain teachers’ attention and soon became self-organized social learning communities. These types of online communities fundamentally distinguished themselves from the professional learning community held by districts and states, in terms of the size (Kelly & Antonio, 2016; Macià & García, 2016), network structures (Karimi, 2020), teachers’ initiative (Weseley, 2013) and flexibility in forms of collaboration (Seo & Han, 2013). As teachers began to use social media for professional purposes, they also expanded the pool for collegial relationships to online platforms. Lying on a continuum of personal relationships across physical and virtual space (Wellman, 2004), teachers self-organize and preserve their interactional patterns with school colleagues on social media (Chen et al., 2017). Consequently, the organizational boundary is also projected into an online space (Torphy, Liu, et al., 2020). Results from a study of teachers’ online interactional patterns on Pinterest indicated that teachers that were snowball sampled from a school district were densely connected, compared to teachers that were randomly sampled at the state level (Karimi, 2020). Wellman (1999) argued that online networks are not only desirable for supporting weak ties but also for maintaining strong ties. In the context of teacher networks, research has found that teachers maintain their relationships with close colleagues at school, as well as other school- based and district-based colleagues on Pinterest, sustaining a spectrum of relationships in the physical space via the online platform (Liu et al., 2020). In addition, online interactions with existing colleagues on social network sites increase both the bonding and bridging social capital 10 of individuals (Steinfield et al., 2009). In other words, online interactions simultaneously reinforce the existing relationships and expand one’s capacity to access expertise embedded in a collegial network. In an unbounded online space, teachers can express their networked individualism (Rainie & Wellman, 2012) and establish connections with peers encountered in the virtual space. In one study, teachers, on average, followed 150 individuals on Pinterest, among which approximately 97% were peers outside of their district boundaries (Liu et al., 2020). In a sense, teachers extensively expand their professional networks online, following individuals who are not in their original social circle for broader professional support and diverse sets of information. As most ties are specialized, each providing support in a few dimensions (Wellman & Wortley, 1990), diversifying and connecting to a wider range of online peers—beyond school and district colleagues—provides teachers access to copious educational resources that are created and shared by individuals with dedicated strength and various perspectives (Frank & Torphy, 2019). In fact, Wellman (1999) discussed two types of networks, comparing the densely-knit tightly-bounded network with the sparsely-knit loosely-bounded network, in which he argued that the latter becomes a dominant form of interactions and collaborations in virtual communities. The Co-existence of Learning and Socialization in Online Social Spaces Unlike teachers’ activities in physical spaces, online engagement greatly depends on the affordances of each social media platform. Various educational researchers have conceptualized each platform’s affordances based on teachers’ and students’ online experiences, including personal profiling, content creation, authentic learning, information searching, resource sharing, relationship building, socializing, social participation, collaboration, community building, and 11 evaluation and feedback (Greenhow & Galvin, 2020; Henderson et al., 2013; Szeto et al., 2016). It has been increasingly clear that the social participation feature in online platforms is essential to and inseparable from teachers’ online professional learning activities. When online resources function as both a source of knowledge and a social event, learning and socialization co-exist in the online space (Hu et al., 2018). Implications of Social Learning Activities on Social Structures Previous research has investigated the patterns of actors’ learning activities in a social space with respect to its implications on social structures. Using data on high school students’ course-taking patterns, Frank et al. (2008) argued that adolescents’ social contexts would be defined by those who took similar math courses, in which the aggregates of actors and courses jointly determined their local positions in a social space. In this study, math courses function as a primary learning opportunity and a subsequent social event through which individuals observe, conform to, and are influenced by decisions of peers in their local positions via common course participation. Similarly, Vu et al. (2015) took a social structural approach to study online learners’ contributions to discussion threads. Inside the online forum, learners can initiate a discussion thread to ask questions and receive responses and comments from other learners. Though mainly designed to leverage the learning assistance between learners in the online community, discussion threads contain the social network feature, which increases the likelihood of participants to further contribute to the same discussion thread. These studies illustrate that a learning event is both a learning and a social event, be it a course, a discussion thread, or an online resource, creating opportunities for individuals to interact and develop relationships (See Figure 1). Subsequently, these social learning 12 opportunities shape individuals’ common participation in future learning events throughout the entire learning process. Figure 1 Conceptualization of Learning and Social Elements of a Social Learning Event Teachers’ Resource Curation Resource curation stems from digital content curation, which describes a series of information-seeking and management activities, including selecting, sorting out, annotating, archiving, and sharing of digital content (Flintoff et al., 2014; Yakel, 2007). With the increased use of social media, resource curation has gained attention as people curate content on social media platforms (Baruch & Gadot, 2021; Villi et al., 2012). In education, teachers’ online activities of seeking educational resources and professional support are found to be a new form of professional learning and professional development (Carpenter et al., 2018; Greenhow et al., 2020; Manca & Ranieri, 2017; Trust et al., 2016). Previous research has employed several 13 different perspectives to investigate the phenomenon of teachers’ resource curation, concentrating on the curation activity, the resulting curated content, and the social process of the content curation (Cherrstrom & Boden, 2020). Resource Curation as a Professional Learning Activity Extant literature views teachers’ resource curation through resource-seeking and learning activities, driven by individual professional needs and interests in the form of personalized and self-directed learning (Carpenter et al., 2018; Gadot & Levin, 2012; Greenhow et al., 2020). Factors like grade level taught, teaching dispositions, and school and district contexts are found to be predictors of teachers’ common resource curation activities (Torphy, Liu, et al., 2020). Arguably, shared interests on specific content and the subsequent curation activity could also be due to some unobserved variables (Stephens et al., 2016), such as teaching styles and teachers’ resource preferences. Curated Content as Digital Assets and Tacit Knowledge As to the result of teachers’ resource curation activity, collections of curated content are considered as digital assets (Beagrie, 2008; Deschaine & Sharma, 2015; Yakel, 2007) and resource possessions of teachers (Liu et al., 2020). As curators often add a level of quality control and relevance during content curation (Flintoff et al., 2014), curated content is also viewed as a teacher’s tacit knowledge, appearing to be an outcome of a teacher’s professional learning efforts. In fact, scholars have attempted to analyze the quality of teachers’ online lesson planning via assessing their curated content with respect to the dimensions of resource cognitive demand and depth of knowledge (Hu et al., 2021). 14 Resource Curation as Knowledge Distribution Facilitated by the visibility feature of the social media platform, content curation approximates resource sharing and distribution, in which the curated resources are available to other curators in broader online communities through various paths, e.g., searching, direct visiting, following, and platform recommendations (Zhong et al., 2013). Curators are regarded as knowledge brokers, in which the sharing activity in essence is to distribute the content forward and provide access to others (Cherrstrom & Boden, 2020; Villi et al., 2012). In the age of information excess, online resource curation, such as Open Educational Resources (OER), highlights its advantage on the collective efforts and network connections of trusted individuals who curate resources with some extent of quality control and are suitable under a given professional context (Bhaskar, 2016; Villi et al., 2012). Returning to Wellman’s argument on networked individualism, teachers assemble their personal networks for content curation on social media based on their needs, in which they define their social contexts and accumulate the social capital of educational resources via online personal connections. Analyzing Teacher Resource Curation Two-Mode Network Teachers’ online resource curation data belong to two-mode networks. A common approach to measure network structures of social interactions is via collecting one-mode network data—a single mode of teacher-to-teacher interactions or relationships. Yet, a different type of network data—two-mode network data (also known as affiliation networks or bipartite networks)—also has the capacity to capture teachers’ social interactions through tracing their attendance and engagement in social learning events, in which teachers and social learning events are the two modes of nodes that are tied in the network. In other words, instead of gathering the direct social interactions, two-mode network data collect individuals’ social 15 activities or affiliations with the social learning events (Borgatti & Everett, 1997; Doreian et al., 2004). Though teachers are not directly connected with one another, social learning events mediate and play a bridging role to connect individuals who participate in the same events (Fujimoto et al., 2018). Duality of Teachers and Social Learning Events in Two-Mode Networks As illustrated by Simmel (1955), the duality of modern social life encompasses both the individuals and their social group affiliation, in which individuals join social events based on shared interests, such as teachers curating the same resources on the social media platform based on shared interests, increasing their likelihood of forming interpersonal relationships. At the same time, social learning events can be characterized and grouped by shared members. In short, through individuals’ social event participation, a social structure of individuals can be implied as well as common characteristics of social events (Doreian et al., 2004; Field et al., 2006). One-Mode Projection of Two-Mode Networks The most classical method for interpreting implied social structures is to project the two- mode network into the one-mode network (Breiger, 1974), assuming teachers who participate in the same social event have interpersonal connections. The advantage of the projection method lies in its straightforward approach of converting and deriving social connections between teachers from their social event engagement. Nevertheless, several concerns have been raised regarding the projection method, such as loss of information on the event size and multiple co-occurrences between the same pair during the projection (Latapy et al., 2008). These issues turn the two-mode network structure issues into one-mode network tie weighting issues (Neal, 2013; Newman, 2001). In addition, the projection 16 method also has the tendency to over-represent the network density and the overall level of clustering (Opsahl, 2013). Preserving the Duality of Two-Mode Networks To address concerns in transforming two-mode into one-mode networks, several studies chose to preserve the duality of two-mode networks instead of removing the social events and reducing the data to one-mode networks. For example, Frank et al. (2013) took a meso-level approach, interpreting the two-mode network structure at the cluster level. Specifically, they define local positions from both actors’ and events as densely connected individuals and events within a cluster (Field et al., 2006; Frank et al., 2008). Beyond that, statistical network models have also been developed to study the social selection process and tie formation theories behind two-mode network configurations, such as two-mode relational event models (De Nooy, 2011) or latent space models that can be applied to analyzing two-mode networks (Hoff et al., 2002; Krivitsky et al., 2020). Social Influence and Social Selection Social influence and selection are two social processes that have been studied by network scientists to explain the interrelationships between network structures and individual behaviors. The social influence process, on one hand, describes how an individual’s behavior could be affected by the social network she is embedded in, e.g., how teachers’ resource curation can be influenced by their network peers’ in their social contexts (Liu et al., 2020). On the other hand, the social selection process investigates how individuals’ attributes—such as latent positions of teachers and resources in the context of teacher-resource two-mode networks—and their similarities, along with network dependencies on existing ties, can affect tie formation between any pair of nodes (Frank et al., 2008; Frank et al., 2013; Snijders et al., 2013). 17 Social Influence The social influence process allows us to conceptualize changes in individuals’ behavior as a result of interactions with others in their social networks (Burt, 1987; Friedkin & Johnsen, 2011). For example, changes in teachers’ resource curation activity can be conceptualized as a result of teachers interacting with and being influenced by others in their social context. Social influence depends on exposure, which occurs when individuals actively seek information based on perceived referent expertise (i.e., information-based social influence), or when individuals perceive a norm in a social group (i.e., norm-based social influence). Changes in behaviors or beliefs in these two scenarios are attributed to social influence theory (Guimond, 1997; Kaplan & Miller, 1987; Lord et al., 2001; Werner et al., 2008). In particular, the network ties between individuals function as a path for information to be transmitted or norms to be exerted, carrying the influence from one to another (Marsden & Friedkin, 1993). In summary, social (or network) embeddedness describes how one’s social surroundings can determine to whom and what information and resources one has access to, functioning as both an opportunity and a constraint (Coleman, 1988; Granovetter, 1973; Uzzi, 1996). Social Selection Topics in social selection investigate individuals’ interactions and the subsequent network structures as explained by factors such as individuals’ node-specific characteristics, homophily between two or more people’s node-specific attributes, preferential attachment (being attracted to popular others), and network dependencies among two or more ties. For example, social selection research investigates how latent attributes of teachers and resources predict the formation of teachers’ resource curation ties. To further elaborate, the explanatory factors cover 18 a range of parameters at varying levels, including micro-level nodal parameters (Bjorklund & Daly, 2021; De Choudhury, 2011; Wehrli, 2008), such as teachers’ tendency to actively curate resources in social space; dyadic attributes (Kossinets & Watts, 2009; McPherson et al., 2001; Spillane et al., 2012), such as the inherent similarity of values between teachers and resources; meso-level local structural parameters (Fujimoto et al., 2018; Robins et al., 2009), such as the clustering tendency among teachers and resources; and macro-level global structural parameters (Goodreau et al., 2009; Kadushin, 2012; Kossinet & Watts, 2006), such as teachers’ resource curation network densities. In other words, selecting with which social event an actor is affiliated can be determined by the attributes of the actors and the social events (Berardo, 2014), the consistency of inherent values between actors and social events (Frank et al., 2018; Newcomb, 1961), and the existing social ties that could potentially affect the formation of new social ties (Fujimoto et al., 2018; Snijders et al., 2013). Later in my dissertation, I will introduce the latent space approach, which relies on the estimation of latent positions of teachers and resources to account for a series of above-mentioned social selection mechanisms and network dependencies in teachers’ resource curation two-mode networks. Taken together, teachers’ resource curation can be affected by network structures in two ways, 1) direct social influence from connected others in the local network, 2) social selection process and tie dependencies in broader network structures, in which the current social activity of teachers’ resource curation is embedded. 19 Modeling the Social Influence Process Egocentric Networks Many studies have tested the effect of social influence via estimating the network exposure effect through the individual’s egocentric network data (Frank et al., 2004; Frank et al., 2020; Reddy et al., 2021). To represent one’s immediate local networks, the egocentric approach is used to capture interpersonal relationships that are centered at each sampled individual (the ego) and link to others (the alters) with whom the ego has direct connections (Granovetter, 1973). For instance, Liu et al. (2020) collected teachers’ egocentric network data and estimated the social influence effect from network peers on teachers’ resource curation. Different from the sociocentric approach, which measures the connections of a whole network, the egocentric approach focuses only on the targeted individual’s direct social context, to whom the actor is exposed and influenced by (Perry et al., 2018). Thus, egocentric networks are desirable for sampling one’s direct networks and modeling the social influence effect, which also requires additional information on the ego’s and alters’ behaviors and beliefs (Frank et al., 2020; Liu et al., 2020). Network Exposure Models Network exposure models, also called network autocorrelation models, have been developed to estimate the social influence effect while controlling for an individual’s prior behaviors or beliefs. Previous research on modeling social influences have proposed different weight matrices in creating the network exposure terms to reflect different influence hypotheses on the social processes, i.e., the degree to which individuals are influenced, such as in what way are teachers influenced by their online networks. 20 Several studies have conceptualized the network exposures as the mean level of the behaviors of the alters in an ego’s local networks, normalizing the total exposures by an ego’s network outdegree, e.g., teachers are influenced by the average level of curation activities of a certain resource in their direct social context (Fujimoto et al., 2011; Leenders, 2002; Marsden & Friedkin, 1993). These types of conceptualizations originate from research on population in a closed social space, such as social influence in the diffusion of innovation, in which all colleagues’ decisions and behaviors, adopting or not, are cognitively weighted by the egos to infer the current innovation adoption stage in their social environment (Burt, 1987; Valente, 2005). Indeed, close communities often stress group identities, encouraging conformity to norms as the underlying mechanism for social influence. Thus, normative influence is measured as the mean level of alters’ behaviors in one’s local network (Coleman, 1988). In contrast, studies with contexts in a vast open social space for information-seeking employ an unnormalized total network exposures approach, with the hypothesis that individuals absorb and learn in an accumulative fashion under informational influence (Liu et al., 2020). Specifically, as opposed to social norms that are subject to the consensus of a group of teachers (e.g., how teaching should be conducted in a classroom), teachers’ level of knowledge on a specific subject can only increase monotonically as they are exposed to an incremental amount of subjected-related content (i.e., teachers are under informational influence). The underlying assumption is that each additional network exposure to the information source contributes and cumulates into a stronger social influence on individuals’ level of knowledge and practices. In addition, emulation is another hypothesis for social influence to occur. Individuals in the workplace could be exposed to people they don’t directly interact with but still adopt their behavior to emulate them for competitive reasons (Burt, 1987). 21 When social networks (such as personal networks on social media) function as an information channel, as opposed to a collective that emphasizes group identities and norms, network influence is less about individuals changing their behaviors to conform to expectations and norms, and is more about adopting certain behaviors as a result of having access to information and knowledge (Coleman, 1988). To summarize, the underlying mechanism of social influence determines how the network exposures are mathematically formulated, which depends on the salience of the norms in the social contexts and individuals’ intentions for information-seeking. Dynamic Social Influence Process in the Framework of the Relational Event Model Event History Model To study the social influence process (such as how teachers’ resource curation is influenced by that of their network peers), longitudinal data are often required to distinguish behaviors at different time stages to make a causal statement on the network influence effect (Friedkin & Johnsen, 2011). Event history analysis is a type of analysis that incorporates and explicitly models the time dynamic of an occurrence of an event in a population in either a continuous or a discrete time frame (Singer & Willett, 2003). In applying event history analysis to investigate the network influence effect, several studies in the area of diffusion of innovation have framed the network exposure as a time- varying covariate, changing along the time span (Strang & Tuma, 1993; Strang, 1996; Valente, 2005). As alters choose to adopt the innovation at different time points, the social contexts of egos have changed accordingly, which leads to the occurrence of an ego’s adoption behavior. Beyond the time-varying peer influence, event history models also have the capacity to record temporal evolutions of the dependent variable as a series of observations leading up to the 22 final occurrence of an event (a change in states). This approach provides the potential to investigate the dynamic social influence process, along with the specification of network exposures as a time-varying covariate. As to my dissertation, instead of regarding innovation as the event of interest, I concentrate on the occurrence of educational resource curation across a group of teachers. Relational Event Model Following the event history model tradition, Butts (2008) tailored the hazard function and developed the relational event model (REM) to study the temporal dynamics of social network tie occurrence. In the relational event model, network ties are framed as the relational events. When a network tie between a teacher and a resource is established, a relational event occurs, and the state of a teacher-resource-curation tie changes. That is, the relational event tie is the hazard, and its occurrence or not and when is what we estimate. Specifically, the hazard function models a tie occurrence (i.e., a tie formation) at a certain time, which is conditional on the non-occurrence of that tie across all previous time episodes since the beginning of a study (De Nooy, 2011). In addition, depending on mechanisms of the tie formation, a relational event can also be modeled with covariates like time and network-specific parameters (such as individuals’ tendency to form a tie or latent space positions of each node) in an ongoing dynamic fashion. Relational Event Model in Studying Tie Occurrence in Two-Mode Networks De Nooy (2011) extended the relational event model to the two-mode network scheme, studying book reviewers’ selection of an author’s new book with respect to time, author’s node attributes, conformity of reviewers to authors (a tie-specific predictor), and other network parameters, such as two-path indirect connections. He further elaborated that snowball sampling 23 of the surrounding network environment across temporal and social dimensions would be needed given the relational event model is actor-based and local in nature. Thereafter, several studies have applied the relational event model to two-mode networks in the context of contributions to open-source software projects (Quintane et al., 2014), social learning in Massive Open Online Courses (MOOC) (Vu et al., 2015), favors in congressional collaborations (Brandenberger, 2018), and directors’ and firms’ board-interlock networks (Valeeva et al., 2020). Recognizing the tie dependency of existing relational events in two-mode networks, these studies took advantage of the time-ordered network data, testing hypotheses on various interaction-related tie formation mechanisms. Concretely, they followed the parameterization in the exponential random graph models (ERGM) tradition but leveraged the longitudinal capacity of the data, specifying network parameters that reflected the tie dependencies on both past as well as current relational events. Limitations of Current Two-Mode Relational Event Studies None of the two-mode relational event models described above incorporated the social influence process from one-mode networks into their frameworks. Yet, a recent study investigated teachers’ resource curation of resources on Pinterest, in which exposures to colleagues’ resource-seeking from one-mode networks were hypothesized as an explanatory factor and tested significant for the occurrence of relational events in two-mode networks—the occurrence of teachers’ curating a resource (Liu et al., 2020). In the study conducted by Liu et al. (2020), teachers’ resource curation was modeled as a two-mode relational event, in which a teacher’s hazard rate of resource curation was increased as more of her colleagues in the direct social surroundings began to curate the same resource. In a modified variation of their relational event outcome (frequencies of teachers’ resource curation), 24 results indicated that each network exposure to colleagues who curated a resource increased a teacher’s frequency of resource curation by 1.67 times. This was the first study that attempted to statistically test the social influence effect on the two-mode relational events of teachers’ resource curation by using one-mode networks and longitudinal observations to capture a constantly-evolving peer influence in teachers’ social contexts. The above two-mode relational event study did not address global network structural dependencies. As Valeeva et al. (2020) pointed out, a potential limitation of the relational event model is that it cannot capture the dependencies of a local network tie on other ties further away in the network, as actors may also respond to and coordinate with the networking activities of others outside of their local neighborhood. Thus, parameters that can capture the network dependencies among two-mode relational events are needed such that the social influence effect of teachers’ resource curation can be estimated holding constant the social selection effect. Xu and Frank (2020) have also developed a simulation-based sensitivity analysis to test the robustness of social influence effects against six forms of social selection mechanisms, such as homophily and transitivity, which could potentially confound with the influence effect. Specifically, they attempted to address the question of how network exposure effects might change if people select and establish ties based on different mechanisms. Modeling Social Selection Process Using Latent Space Models Beyond the development of network models for testing social influence effects on individuals’ behavior, a variety of statistical models have also emerged for tie formation and network structures of the social selection process. For instance, ERGMs deliberately specify each of the possible network configurations that are aligned with the social selection process in order to meet the partial dyadic dependence assumption (Robins et al., 2007; Snijders et al., 2006). 25 Nevertheless, Hoff et al. (2002) pointed out that model degeneracy and instability problems are less due to the estimation techniques, but more to the defects in models focusing on the global rather than local structures. They subsequently proposed latent space models as a solution. Latent space models (LSM, also called latent position models) view the probability of a tie as some function of a pair of individuals’ positions in a latent social space, in which the latent space positions represent individuals’ unobserved characteristics. Two distinct features of LSMs unfold as follows: First, LSMs built upon the concept of social space, adapted from geographical space to the space of social interactions, which uses the geometric distance between individuals to represent social dependence (Carrington et al., 2005). Social positions, in a similar fashion, are “evidenced in the social interactions of individuals as occupants of positions and performers of roles” (Faust, 1988). Second, the specific type of social space described in LSMs refers to “a space of unobserved latent characteristics that represents potential transitive tendencies in network relations” (Hoff et al., 2002). Using nodal latent positions (as a measure of unobserved characteristics) and dyadic distance or similarity between two individuals, the authors demonstrate the capacity to model the social processes under the premise that social ties are transitive in nature. In a sense, this method relies on the nodal and dyadic local structures as the building blocks and fundamental social dynamics for explaining and generating higher-order network configurations. See also Clarifying Terminology in Latent Space Model Literature under the Analytical Strategy section. To elaborate on the LSM logic, if node i and j have a tie, this implies that j and i are also close in the latent space, which captures the tendency for a reciprocal tie at the dyadic level. At the triadic level, if node i and j have a tie, as well as j and k, then i and k are not far away in the 26 latent space, thereby capturing the tendency for a triadic closure. In fact, Hoff et al. (2018) showed that the latent space approach effectively captures reciprocity and transitivity in cross- sectional network structures. Compared with ERGMs, LSMs use a model-based graphical representation of network relationship and social positions in a lower dimensional space, with an emphasis on an additional assumption of the transitive nature of ties in the social space. Extending the LSMs’ logic, LSMs can be generalized to scenarios other than transitivity that also satisfy this graphic configuration, such as structural equivalence (Faust, 1988). Therefore, networks that can be represented by the social processes of transitivity (structural influence) or structural equivalence (structural homophily), such as women social event participation of two-mode networks (Davis et al., 1941), are good contexts for using LSMs to account for the endogenous network selection process and network dependency in two-mode networks. Applying LSMs in the two-mode networks of teachers’ resource curation would account for the endogenous social selection processes, such as the observed four-cycle network configuration, of which two teachers and two resources are connected and structurally dependent on one another. Disentangling Influence from Selection in the Two-Mode Network In research cited in previous sections, social influence and selection were not fully separated in modeling the relationship between individual behaviors and network structures. For example, although structural homophily (also called structural equivalence)—a social selection process—is commonly drawn on to explain a tie formation where two individuals of similar network positions tend to form a relationship, it has been investigated as a social influence process in innovation adoption literature. Burt (1987) found that individuals followed those who occupied a similar network position and subsequently conformed their behavior. In fact, this 27 result captured a two-step social process—both selection and influence—such that the two are confounded with one another. Specifically, structural similarity generated some sense of relevance and indirect connectivity between two individuals. This type of connectivity further leads to social influence. In the scenario of teachers’ resource curation, the two-step social process would be that teachers’ connections via common visits to resource spaces represent social selection, which provides opportunities for subsequent social influence on teachers’ curating activity. Relatively recent studies have attempted to distinguish social influence from the social selection process (Fujimoto et al., 2018; Snijders et al., 2013), unfolding the complex chicken- and-egg problem by using structural homophily to explain tie formation in the presence of other existing ties, while partialling out the social influence effect. These studies also presented the multi-faceted nature of social event engagement behavior. That is, engaging in social events represents one’s social networks and behaviors, which is subject to network dependencies in the process of social selection, and is malleable to change in the process of social influence. Specifically, these studies have investigated the dynamics of one-mode and two-mode networks using the stochastic actor-oriented model (SAOM) (Fujimoto et al., 2018; Lomi & Stadtfeld, 2014; Snijders et al., 2013). With data on the co-evolution of one-mode and two-mode networks, Snijders et al. (2013) investigated the change of one’s employment preference as both a function of the exogenous effect of social influence from the advice network and the endogenous selection effect of structural dependencies inside the employment preference two- mode network. Using a parameter of between-network mixed triad, Snijders et al. (2013) found that the advice ties of one-mode networks lead to agreements among students regarding their employment preferences in two-mode networks, in which the between-network mixed triad is 28 composed of an advice tie (from one-mode networks) and two student-company preference ties (from two-mode networks). Similarly, Fujimoto et al. (2018) found that adolescent friendship (measured in fall 2010) led to common participation in sports activities (in spring 2011), interpreting the impact of one- mode networks on two-mode networks as social influence effects, also called “friendship-based context assimilation.” In their context, the process of social influence is found to be stronger than that of social selection. In other words, the process of “friendship leading to common sports participation” was more salient than the process of “common sports participation leading to friendship formation.” Furthermore, the authors were one of the first to use mixed triadic effects (i.e., a multivariate network term of transitive closure that integrates a single interpersonal tie with two social event affiliation ties) to parameterize the exogenous social influence effect (i.e., the effect of the one-mode on the two-mode network), while accounting for the endogenous social selection effect in two-mode networks (i.e., higher-order network configurations like the four- cycle parameter). Limitations of Using Mixed Triads to Estimate Social Influence Effects Compared with the two-mode relational event model used in Liu et al. (2020), the SAOM between-network-mixed-triadic-effect approach has several limitations. First, it does not specify the social influence process as a continuous time-varying covariate, in which the social influence of network peers cumulates in a time-dynamic fashion, and the estimation of the associated parameter leverages observations across multiple time periods in predicting changes in the hazard rate of teachers’ resource curation attributed to the social influence effect. 29 Second, using between-network-mixed-triad to approximate social influence assumes that influence would happen invariantly between any connected individuals as long as they have a shared sports activity (see Figure 2, the reproduced Figure from Snijders et al., 2013). This is due to the fact that the between-network-mixed-triad regards social influence as a network structural parameter, and not as a weighted combination between friendship network structures and friends’ prior level of behavior. In a sense, the multivariate mixed triad approach fails to explicitly model the social influence using network exposure terms, which would be a multiplication of both the one-mode network ties and alters’ prior behaviors. Figure 2 Reproduced Figure from Snijders et al. (2013) Third, as Snijders et al. (2013) pointed out, it would be challenging to distinguish empirically whether the ego influenced the alter, or vice versa on the common participation of the two-mode social events using SAOM’s between-network mixed triad. Fourth, the SAOM does not model the social influence process with respect to each specific social event choice or preference that has been passed via network connections. In fact, 30 Snijders et al. (2013) and Fujimoto et al. (2018) selected the most common social engagement activities in regard to their study contexts, i.e., employment preference among college students and sports participation among adolescents, which are social activities that would most likely be affected by advice-seeking relationships and friendships respectively. However, this approach would not be appropriate for contexts with diverse social engagement opportunities, of which each was determined by different social influence processes. Lastly, the SAOM adapts the ERGM approach for accounting for network dependency, which could inherit the problem of model degeneracies and estimation difficulties. Therefore, an extension of the two-mode relational event model, with approaches to control for the endogenous social selection process (i.e. latent space model), would be needed to estimate the time-dynamic social influence effect of teachers’ resource curation, while taking into consideration the latent positions of teachers and resources to account for network dependencies on the existing global structures of two-mode teacher-resource networks. 31 DISSERTATION SIGNIFICANCE: INTEGRATING THE RELATIONAL EVENT MODEL WITH THE LATENT SPACE MODEL A Focus on Local Structural Parameters Careful thoughts are given to network models that concentrate on local structures in comparison to global network structures. In fact, De Nooy (2015) provided his perspective on why he shifted the focus from global to local network structural parameters. In his view, “the overall network structure of interactions is merely a by-product of how social actors respond to their local network context” (p. 2). De Nooy (2015) argued that the relational event model provided a straightforward framework for modeling the dynamics of local ties as a function of different types of social processes, e.g., reciprocation and triadic balance in time-varying interaction contexts, of which each can be formulated as independent variables in a regression analysis. As a framework for longitudinal network data analysis, the REM displays its advantage compared to the cross- sectional counterparts of ERGM. Hoff et al. (2002) had similar concerns in modeling a variety of network parameters representing the overall network structures. Instead, they took a local structure approach by controlling for the latent positions of nodes in a social space. That is, the LSM approach decomposes the entire network sociomatrix to account for network dependencies by estimating specific parameters at the nodal level, instead of including complex higher-order network parameters (i.e., configurations with at least three network ties). Because LSMs are developed for analyzing cross-sectional network data, this approach attempts to model the tie formation at a local level using the nodal latent positions to account for a diversity of social selection processes, such as reciprocity and transitivity (Hoff et al., 2018). 32 The advantage of the LSM lies in its emphasis on how local ties function as building blocks—with tendencies of grouping and clustering for potential subgroup creation—which generate emergent overall network structures. This logic also leads to simplified network models with one term of (dis)similarity between latent positions of nodes at the dyadic level, without estimating each network configuration for all possible social selection mechanisms. In summary, the view of modeling two-mode network data through local network parameters is congruent between Hoff et al. (2002) and De Nooy (2015), both acknowledging and making connections between local network parameters and its contribution to or dependency on the final configuration of the entire network structure. Combining Two Approaches In my dissertation, I propose to combine a relational event model with a latent space approach in modeling teachers’ resource curation in the framework of teacher-resource two- mode networks. Specifically, the LSM offers the flexibility to reduce a variety of social selection processes in teachers’ engagement with social learning events to a similarity measure between the latent space positions of teachers and resources. Subsequently, the REM with estimated latent positions will further allow me to model the exogenous social influence effect, while also accounting for the endogenous selection effect. In connecting two approaches, we are empowered to leverage both the temporal dynamic capacity of modeling social influence in the two-mode relational event setting, along with a simplified approach to account for network dependencies of local ties on their global network structure. 33 CONCEPTUAL FRAMEWORK This dissertation focuses on investigating the social dynamics of teachers’ online resource curation, particularly the social influence process of network peers’ curation activity while acknowledging the resource-mediated social selection process during teachers’ engagement with online resources in a social space. Previous studies have situated teachers’ resource curation under the bigger theme of teachers’ use of social media, in which social media functions as a technology tool and an online platform for teachers to continue their professional practices of resource seeking, lesson planning, social interactions, community building, and classroom teaching (Carpenter et al., 2018; Hu et al., 2021; Manca & Ranieri, 2017; Trust et al., 2016). In contrast, this dissertation concentrates on the network embeddedness of teachers’ resource curation. Specifically, I conceptualize teachers’ resource curation as teachers’ professional learning activity, impacted by online peers’ curation activity in their immediate interpersonal networks, as well as teachers’ participation in a social learning event—a type of social engagement that increases teachers’ likelihood of interactions, impacted by teachers’ latent space positions in a holistic teacher-resource two-mode network. Double Network Embeddedness In a sense, teachers experience double network embeddedness in an online social space (see Figure 3), which simultaneously affords teachers the opportunity to build personal connections and conduct the social activity of resource curation (see Figure 4). The first layer of network embeddedness exists in teachers’ direct interpersonal social contexts, in which teachers are exposed to resources curated by their network peers in the one-mode network. Furthermore, the social activities of teachers’ resource curation define the second layer of network embeddedness, in which online resources play the role of social learning events, connecting 34 teachers who curate the same resource. In other words, teachers are embedded in a social context co-determined by teachers and resources, while teachers themselves are indirectly connected to each other. The two-mode social space captures teachers’ latent space positions and resources that flow in teachers’ online neighborhoods, which further impacts what resources teachers may curate in the online space. Figure 3 Double Network Embeddedness of Teachers’ Resource Curation Note. The upper social space is defined by one-mode interpersonal networks, in which teachers are embedded and curate resources as a consequence of the direct social influence from their network peers. The lower social space is defined by two-mode teacher-resource networks, in which teachers are embedded and curate resources as a result of their latent space positions in a broader network environment. Dashed lines represent one-mode network ties of interpersonal connections between individuals. Solid lines represent two-mode network ties of teachers’ resource curation. 35 Figure 4 Teachers’ Concurrent Embeddedness in Two-Mode Teacher-Resource Networks and One-Mode Interpersonal Networks Note. This figure integrates two layers of network embeddedness from Figure 3 into one holistic frame to display the full scope of teachers’ embeddedness in a social space, which allows teachers to interact with both people and resources at the same time. The inner circle displays teachers’ resource curation as embedded in a two-mode teacher-resource network. The outer circle displays teachers’ curation as influenced by and embedded in a one-mode interpersonal network. In Figure 3, I separately presented the two layers of network embeddedness of teachers and their resource curation activity, highlighting opportunities and constraints brought by each type of network. In fact, when teachers are allowed to interact concurrently with other individuals and resources on a social media platform, both layers of network embeddedness occur at the same time. This means teachers’ resource curation is subject to network peers’ social influence in one-mode networks and their local network positions in two-mode networks in an inseparable fashion. Thus, I integrate the two layers of teachers’ network embeddedness in 36 Figure 4 to show teachers’ concurrent embeddedness in two types of networks in their social curation process. Latent Space Positions in Two-Mode Networks as an Outcome of Complex Mechanisms Latent space positions of teachers and resources in two-mode networks could be an outcome of both the selection and the influence mechanism. First, due to cognitive consistency, homophily, and structural equivalence, teachers of a kind select similar resources, reinforcing their positions in the latent space based on personal preferences and orientations, i.e., their unobserved latent attributes. Second, seeing what resources colleagues curate is equivalent to knowing their personal preferences and professional orientation. Teachers are more likely to be influenced by individuals who are aligned with their professional views, thereby more likely to select resources curated by them. In short, the latent space positions of teachers and resources carry various types of information on whether and why teachers would select certain resources, observed as the realization of the two-mode network structures. Bounded District Networks in an Unbounded Online Space Mixed findings exist on whether teachers collaborate with colleagues from schools and districts within online social media. Some indicate that teachers’ online activities on social media platforms, such as Pinterest, are mainly individual actions with few communications and collaboration, while others suggest that teachers collaborate online with other educators both within their district and around the world (Carpenter et al., 2018; Greenhow et al., 2020). I argue that school districts maintain their social salience even when teachers extend their professional relationships to the online space. In other words, teachers are embedded in a network of school 37 and district colleagues in the online space, in which they keep track of and are influenced by their colleagues’ resource curation activity. In combination with the framework of double network embeddedness, teachers’ curation activities are affected by the direct network influence from the one-mode online networks, as well as their latent space positions and nearby resources in two-mode teacher-resource curation networks. As district organizational boundaries are projected online, teachers from the same district are viewed as actors in a bounded district network in an unbounded online space. Conceptualizations of Online Resources in Social Media Platforms This dissertation leverages three conceptual understandings of the resources and operations in teacher resource curation networks. First, curated resources include tacit knowledge that are exchanged between individuals. In this view, resource curation amounts to teachers’ professional learning activities. Subsequently, the cumulation of curated resources equals the increase in teachers’ tacit knowledge. Second, resources are conceptualized as social learning events, from which social structures emerge. Curating the same resource on the online platform increases teachers’ likelihood of interactions in the resource curation space, which would further enhance their professional relationships. Third, the curated resources are viewed as observations of teachers’ latent attributes, reflecting their preferences and professional orientations. Teachers with similar latent attributes may curate resources alike, naturally drawn close to similar others and preferred resources in the two-mode teacher-resource social space. 38 The Standing of This Dissertation Previously, Liu et al. (2020) investigated how teachers were influenced by their school and district colleagues’ resource curation activity on social media. Using a sample of teachers who expanded their professional relationships from physical to virtual space, the authors tested the direct collegial influence in the online space. Specifically, they focused on the online collegial network influence of the blue actors in the upper social space in Figure 3. Nevertheless, their study only investigated the interpersonal network embeddedness (i.e., the first layer in Figure 3) and overlooked the social dynamics and impact of the two-mode teacher-resource networks (i.e., the second layer in Figure 3), which could confound with the network influence from the one-mode network. Building upon Liu et al.’s (2020) framework, this dissertation attempts to study teachers’ resource curation as they are embedded in both one-mode interpersonal networks and two-mode teacher-resource networks. Furthermore, this dissertation will expand the scope of teachers’ ego- centric interpersonal networks by including both school and district colleagues (i.e., core blue actors in Figure 3), and online peers (i.e., peripheral actors in Figure 3), testing the overall network exposure effects on teachers’ resource curation. Altogether, teachers’ resource curation is impacted by all network members’ curation activity in their online interpersonal networks, both from colleagues in their school district and online-based peers (i.e., the first layer of network embeddedness in Figure 3). Furthermore, teachers’ resource curation is impacted by their latent space positions in a two-mode teacher- resource network, in which the online two-mode network boundary includes teachers from the same district, considering its social salience (i.e., the second layer of network embeddedness in Figure 3). 39 Hypotheses To test the social influence effect, I developed the two hypotheses below. Hypothesis 1 directly tests the peer influence effect on teachers’ resource curation, while hypothesis 2 tests the same social influence effect while taking into account the resource-mediated social selection process during teachers’ resource curation in teacher-resource two-mode social space. Hypothesis 1—Teachers’ resource curation is influenced by the direct network exposure to online peers in egocentric one-mode networks. Hypothesis 2—The social influence effect of teachers’ resource curation remains significant after taking into account the resource-mediated social selection effect in the teacher- resource two-mode social space. Hypothesis 3—Teachers’ online resource curation is influenced more by online-only peers compared to the network influence from their school and district colleagues. 40 METHODS In this section, I will introduce the study context, the data source, the sample, the variables, and the analytical strategy used to test my hypotheses. In particular, the study context section will introduce where the empirical study settings were situated, specifically the characteristics of the Pinterest social media platform. Next, the data section will describe what types of network connection, resource curation and individual attributes data were collected and when they were collected. Furthermore, the sample section will introduce who were sampled and how they were sampled, including both a sample of teachers and a collection of resources. Finally, the analytical strategy section will introduce the statistical models employed to estimate and test the hypotheses. Study Context This dissertation is situated around Pinterest, a visual discovery engine and an image- based social media platform, which allows users to create, search, and save image-based content onto their user-defined boards. On Pinterest, image-based resources are called “pins,” and users who conduct the pinning activities are called “pinners.” Based on its platform statistics, Pinterest has 444 million monthly average users and 330 billion pins. Pinning activities on Pinterest describe individuals’ behavior of saving and curating image-based content onto their boards in a way that makes sense to them. Thus, I will use pins and resources, as well as pinning, saving and curating interchangeably in this dissertation. According to descriptions from Pinterest’s website (2022), pinners use Pinterest mainly for idea inspiration, in which they look for a wide range of ideas, including food and drink, beauty, home décor, and more. Though Pinterest was not originally created for searching and sharing education-related resources, a study of elementary school teachers’ use of social media 41 gathered data on their actual collection of resources, indicating that 77% of the sampled 90 teachers used Pinterest at least once a month for professional purposes (Hu et al., 2018). As a social media platform, Pinterest affords teachers the opportunity to follow one another, visit each other’s homepage, and track resources that have been pinned by others beyond the teachers’ own resource curation activities. Thus, Pinterest provides a natural setting for social network scientists and educational researchers to study the social network effect on teachers’ resource curation. Figure 5 displays an example of a Waters District teacher’s Pinterest homepage. This teacher has followed 133 online peers and has been followed by 330 individuals, which formed her online personal network on Pinterest. The bottom of the page displays the resources pinned by this teacher, which have been sorted into boards under different themes. For instance, boards such as “Easter,” “word families,” “Monthly project,” “Classroom,” and “100th day” contained varying numbers of educational pins this teacher has found useful and saved for later use for teaching-related activities. 42 Figure 5 An Example of a Teacher’s Pinterest Homepage Pins - Resource Content and Social Spaces According to Pinterest (2022), a “curated pin” is a bookmark of loved content people saved to their personal boards. Moreover, not only is a pin a content or resource, Pinterest also assigns each pin its own webpage, in which the comments section allows individuals to comment, reply, and like a pin, covering a variety of social engagement activities. Thus, each curated pin can be viewed as an online social space, in which teachers can interact, exchange ideas, and build relationships. Altogether, pins function as online social learning events, in which teachers can acquire knowledge as a way of professional learning through their pinning activities and interact with others by visiting and engaging within the resource space. A closer look at a pin’s resource space would disclose a variety of content-specific information, including the pin title, pin description, resource image, link to the original creation website, and the content creator. It is worth noting that each pin also contains information on 43 which person saved this pin to one of her personal boards at this round of pinning. To further explain, each pin serves as a documentation of a specific individual’s saved resource and her pinning activity that was uniquely identified on Pinterest by its pinning time, the specific pinner, and its pinning board. In other words, this individual-pinning-specific information reveals to teachers the pinning activity conducted by their network peers, which reflects the curation activities in their social contexts. For situations like various teachers curating the same resource, we would expect that, across several uniquely identified pins, their content-specific information remains the same, while the individual-pinning-specific information would change if we were to compare pins that have originated from the same educational resource but were pinned and circulated via different teachers. Figure 6 exhibits the most prevalent resource pinned by teachers in the Waters School District. I used it as an example to showcase a pin’s resource space. This pin was originally created by Miss Giraffe on missgiraffesclass.blogspot.com before being introduced to the Pinterest platform. The title of the pin is “25 Chatty Class Classroom Management Strategies for Overly Talkative Students,” followed by a four-line pin description. There are 16 comments left in the comments section in different forms of texts or images, a majority of which are feedback on or adaptations of the original resources from individuals who tried this idea in their professional contexts. At the bottom of the page is the pinning-specific information, which displayed the name of a teacher from Waters District, who saved this pin to her Classroom Management board. I blurred this teacher’s username and photo to protect her data privacy. 44 Figure 6 An Educational Pin – Chatty Class? Try Blurt Beans! Teachers’ Pinning Activity on Pinterest There are several ways for teachers to identify resources to pin onto their personal boards. Inside Pinterest, teachers can browse their home feed or use the search bar to find and pin relevant resources based on their interests. Moreover, during the process of teacher-resource interaction, teachers can trace the pinner of this resource and find other content that has also been curated by this pinner via visiting her board or homepage. In a sense, this feature potentially generates network dependencies of further two-mode teacher-resource interactions, which is 45 initiated through visiting the same resource space and expanding to curating more resources from the pinner they encountered in previous rounds of pinning. Teachers can also pin resources directly from others who they follow in their personal networks, either by visiting their network peers’ homepage or by browsing personalized Updates, in which Pinterest lists resources pinned by their network peers in chronological order. This following-follower relationship creates an opportunity for social influence effects to occur via interpersonal one-mode networks, in which teachers’ pinning activities can be influenced by those with whom they are connected online. Beyond resource curation inside Pinterest, teachers can also browse and pin image-based resources from external websites, such as Educator Blogs or Teacher-to-Teacher Markets (Torphy et al., 2020), onto their personalized Pinterest boards. Alternatively, teachers can trace resources from Pinterest to external websites and pin them at their creation origin back on Pinterest. In other words, teachers can store and organize resources that are circulated within Pinterest and materials that are created and posted on external websites in one place by pinning them onto their Pinterest boards for a whole collection of curated educational resources. For teachers’ resource curation data used in this dissertation, only 1.54% of pins (seven out of 456) are resources teachers pinned from external websites, which indicated that teachers mostly curate resources within Pinterest. Pinterest Platform Effect The platform effect refers to the invisible hand of the behind-the-scenes Pinterest recommender system, which affects what resources teachers will be recommended and suggested based on their previous search results, pinning activities, and individuals they followed on personal networks. According to Pinterest Labs (2022), they use featured technologies to 46 enhance their personalization models, which are further explained below, including AutoML (a content relevance ranking model), Interest Taxonomy (a taxonomy-based content understanding system), PinSage (a graph convolutional neural network for web-scale recommender systems), and PinnerSage (a clustering algorithm-based user embedding framework). All machine learning models target personalizing teachers’ resource curation experience by considering teachers’ previous resource interaction patterns to recommend content that can best fit teachers’ interests. For instance, if a teacher starts with “first grade math” in her search box, Pinterest will return results like “first grade no-prep math game for the year,” “math 1st grade addition worksheet” etc., with the help of AutoML, to expand the query to other similar queries. As a teacher continues to click on different first-grade-math related pins, each of her interactions with the pin helps the machine learning system—Interest Taxonomy—to understand more about the pin and identify topics that better capture the teacher’s interest, which is also used to recommend additional relevant content. Then, once the teacher browses through her home feed, Pinterest suggests more first-grade-math inspiration according to her interests. The recommender system works in an iterative fashion, as it gathers and analyzes teachers’ resource curation data in each round of teachers’ pinning activities. The PinSage algorithm also leverages pinning data from other users who are similar to that teacher regarding their search query in order to continue refining the personalization model. Subsequently, resources that have been pinned by similar others based on the resemblance of their previously curated content will also be suggested to the teacher on their home feed. Likewise, as that teacher starts to create and organize content onto boards, PinnerSage 47 recommends her saved pins and boards to others’ search queries who are also interested in content relevant to first grade math. Since the data span of this dissertation for teachers' resource curation on Pinterest was from 2016 to 2017, I traced back to the documentations on the Pinterest recommender algorithm from 2016. This documentation indicated that Pinterest used an earlier recommender algorithm to suggest pins their users may like based on their previous pinning activities. Regarding the above-mentioned four Pinterest recommender algorithms, I found that the earliest time PinSage was documented was around 2018, while AutoML, Interest Taxonomy, and PinnerSage were documented around 2020 as the earliest time they could be found on the Internet (Cui & Shrouty, 2020; Hamilton et al., 2017; He, 2018; Pal et al., 2020; Wang, 2020; Ying et al., 2018). In summary, Pinterest applied their earlier version of the recommender algorithm to suggest similar pins in 2016, and further developed a more comprehensive recommender system over the years. Hence, Waters district teachers were subject to the Pinterest platform effect when curating educational resources from 2016 to 2017, though the recommender system was not fully developed at the time. In a nutshell, Pinterest’s backend recommender system plays an important yet invisible role, accentuating the clustering effect among similar resources and similar teachers. Specifically, teachers are recommended with resources of similar content on top of their tendency of seeking similar resources that are aligned with their professional values and preferences (see cognitive consistency, Newcomb, 1961). Oftentimes, the clustering effect captures a series of complex higher-order network structural dependencies. In other words, Pinterest catalyzes the phenomenon of cognitive consistency and higher-order network dependencies with its machine learning models. 48 As resources often function as a social space, individuals who curate similar resources more than expected may also have a higher likelihood of encountering one another, thereby expediting their process of relationship development. Thus, similar teachers tend to cluster as they curate similar resources. In the long run, two-mode-network-wise, the platform effect may cause homogeneity in the types of resources teachers curate and the polarization of groups of teachers as they tend to curate narrowed themes of resources that gather a similar group of teachers. Data The data used in this dissertation came from two sources, survey data and Pinterest big data, which were part of the efforts from two collaborative projects: Study of Elementary Mathematics Instruction (SEMI) and Teachers in Social Media (TISM). The SEMI team first employed surveys to collect data on Waters School District teachers (see Sample section below for more descriptions on teachers from the Waters School District) and the TISM team subsequently identified them on Pinterest. The flow chart in Figure 7 shows how survey and Pinterest data were collected in a consecutive manner. 49 Figure 7 Data Collection Procedure As this dissertation was part of efforts to study teachers’ Pinterest use for educational resources, the method of how teachers’ Pinterest accounts were identified and validated can be found in Figure 5 of Torphy et al.’s (2020). Regarding the research ethics of teachers’ survey and big data use, we went through the process of de-identifying teachers’ names and their Pinterest handles to generate random teacher personal identifiers (PID). Ultimately, the de-identified teacher administrative and social media data were used for research purposes to protect each individual’s confidentiality. The survey data were collected in a progressive fashion, in which Waters District teachers were surveyed over three consecutive years from Fall 2014 to Spring 2017 (see Figure 8). Multiple cohorts of teachers participated in different waves of the survey, though a small group of teachers has been sampled repeatedly over time. I combined teachers from different cohorts and their survey responses for more complete information on teachers from Waters District. Using survey data, we collected information on teachers’ school district membership as 50 well as their characteristics, such as their career stage, grade level taught, and so on. Teachers’ school district membership was later used to delineate the boundary of the Waters School District on Pinterest’s unbounded social space. Figure 8 Data Collection Timeline In contrast to the survey data, Pinterest big data was collected retrospectively. Though the online archival data was accessed in September 2017, it provided the opportunity for educational researchers to gather teachers’ pinning data starting from the opening of their Pinterest account. Therefore, this dissertation leveraged the capacity of big data to collect Waters District teachers’ detailed time-stamped Pinterest curation data of educational resources from July 1, 2016, to June 1, 2017, covering the 2016-17 school year (see Figure 8). This takes into account teachers’ tendency to use the summer for lesson preparation and resource-seeking in advance of the beginning of the academic year. This data was used to construct both the teacher-resource two- mode network data as well as the data frame for the relational event model of teacher-resource network ties. We also downloaded Waters District teachers’ Pinterest ego-centric network data including whom they were following by September 2017 (see Figure 8). This was to identify to whom Waters District teachers were exposed in terms of the educational resources in their social context. Ideally, the best time to collect teachers’ network data was on or before July 1, 2016, making sure that the network peers’ social influence was exerted through an existing tie at the 51 time of the Waters District teachers’ resource curation. Alternatively, if teachers’ Pinterest following network was found to be relatively stable over time, I could use the network measure in September 2017 as a proxy for teachers’ network data in 2016. Comparing teachers’ 2017 and 2018 network data, I found a 95.16% consistency of teachers’ network composition over the two years. Among 8129 ties of the 55 Waters District teachers’ ego-centric networks, 7736 ties existed across both years (95.16%), with 188 dissolving ties in 2017 (2.31%) and 205 emerging ties in 2018 (2.52%). Due to the limitation at the time of data collection, I only have data downloaded from 2017 through 2018. Based on the examination of network stability across these two years, I assume that teachers’ ego-centric networks were also stable from 2016 to 2017. Thus, I used network data in 2017 as a proxy for teachers’ network data in 2016. Once the network peers were identified, we traced to and downloaded their time-stamped Pinterest curation data from June 24, 2016, to May 25, 2017 (see Figure 8). I further subset network peers’ curation data on a selected set of educational resources, of which four or more Waters District teachers visited the resource spaces and curated these resources (see more details in the sample exclusion criteria section later). To make a causal statement about the social influence effect, the study design took advantage of the longitudinal time-stamped data and gathered network peers’ curation data one week earlier than that of the Waters District teachers to avoid potential confoundedness in the cross-sectional data. Sample Waters School District Characteristics My final analytical sample consists of 55 teachers from nine elementary schools in one Indiana district (Waters District by pseudonym). Based on the reported 2016-17 student 52 demographics from the National Center for Education Statistics (NCES), the Waters School District serves a population of students that are 51.6% male; 27.7% White, 49.9% Black, 13.9% Hispanic, and 0.7% Asian (see Table 1). Moreover, 38.7% of students are eligible for free or reduced lunch. In addition, 3.4% of students in Waters District are English language learners, and 8% of students are in special education. Regarding school-level characteristics, Waters District has a student-to-teacher ratio of 13.96. Among all 18 schools in the district, 83.3% are identified as Title I schools. A sample of teachers from each of the nine elementary schools in Waters District are included in this dissertation. I compared the student and school characteristics of Waters District to 289 Indiana regular school districts with operating elementary schools (see Table 1). Other than the same proportion of male students, Waters District differs from an average regular school district in Indiana across several characteristics. Specifically, Waters District has 55.5% less White students, 45.7% more Black, 6% more Hispanic, and 0.4% less Asian. Furthermore, Waters District has 0.5% less students eligible for free or reduced lunch, 2% more English language learners, and 0.4% less special education students than an average Indiana school district. Compared to the student-to-teacher ratio of 12.25 in an average Indiana district, a ratio of 13.97 in Waters District marked that teachers in the sampled district taught 1.72 more students on average. In contrast to 29.2% of Title I schools in an average Indiana school district, 83.3% of the schools in Waters were Title I schools. 53 Table 1 Waters District Comparison with Indiana School Districts and US School Districts Waters Indiana regular school US regular school District districts districts Obs Mean Std Obs Mean Std Dev Dev Sex – %Male students 0.516 289 0.516 0.014 12,893 0.515 0.037 Race – %White students 0.277 289 0.832 0.184 12,893 0.702 0.276 Race – %Black students 0.499 289 0.042 0.106 12,893 0.069 0.152 Race – %Hispanic students 0.139 289 0.079 0.100 12,893 0.146 0.207 Race – %Asian students 0.007 289 0.011 0.024 12,893 0.021 0.051 %Students eligible for Free 0.387 289 0.392 0.017 12,696 0.447 0.115 Reduced Lunch %English Language Learners 0.034 263 0.014 0.022 9,746 0.032 0.049 %Special Education students 0.080 289 0.084 0.017 12,612 0.073 0.027 Student-to-teacher ratio 13.969 289 12.249 3.655 12,893 12.119 18.940 %Title I schools 0.833 289 0.292 0.294 12,845 0.385 0.388 Beyond the comparisons with Indiana school districts, I also compared the student and school characteristics of Waters District to 12,893 regular school districts with operating elementary schools across the United States (US; see Table 1). Likewise, the proportion of male students remained similar in the sampled district as compared to an average school district in the US. Regarding students’ race composition, Waters District has 42.5% less White, 43% more Black, 0.7% less Hispanic, and 1.4% less Asian. Furthermore, Waters District has 6% less students eligible for free or reduced lunch, 0.2% more English language learners, and 0.7% more special education students. With a student-to-teacher ratio of 12.12 from an average US school district, teachers in Waters District taught on average 1.85 more students comparatively. Lastly, Waters District has 44.8% more schools that were Title I, compared to an average US school district (38.5%). Additional information about Waters District’s demographics is provided on the NCES dashboard of education demographic and geographic estimates. Based on data from 2015 to 2019, about one-fifth of the families had income below the poverty level (22.7%) and 21.9% of 54 families received Food Stamps/SNAP benefits. 76.2% of households have broadband Internet. Regarding family types, 43% of families had a Female householder with no husband present, followed by a Married-Couple (41%), a Cohabitating-Couple the next (9%), and a Male householder with no wife present the least (7%). For parents of children in public schools, the median household income was $48,057; 81.7% of them were in the labor force. With respect to parents’ educational attainment, a majority were parents with some College or an Associate’s degree (37.9%) and High School graduates (31.2%), followed by parents with less than a high school diploma (16.1%) and parents with Bachelor’s degree or higher (14.8%). Sample Exclusion Criteria Teachers investigated in this dissertation were originally sampled by the Study of Elementary Mathematics Instructions (SEMI), which aimed to investigate early career teachers’ math instructions and their egocentric collegial networks at school. Using a convenience sampling approach, 123 total elementary teachers from the Waters District agreed to participate in the SEMI study. This sample was further explored to study teachers’ resource curation in an online social space, i.e., Pinterest, a social media platform, under the Teachers in Social Media project (TISM). Thus, teachers who did not have a Pinterest account were excluded (n=27; see Figure 9). In addition, this dissertation focused on teachers’ resource curation and their online networks during the 2016-17 school year. Therefore, teachers who were not actively curating educational resources during this period were excluded (n=26). 55 Figure 9 Sample Exclusion Figure Furthermore, this dissertation regarded teachers’ resource curation as two-mode networks, in which resources are considered as social learning events to connect teachers in online space. Thus, the social learning event size (also considered as the prevalence of a resource among teachers in the Waters District) functioned as a criterion to screen out teachers who only curated resources with a learning event size of one (i.e., resources that were sought by themselves alone). Due to the duality of teachers and resources in the two-mode networks, whether a resource can be qualified as a social event was determined by the number of teachers that have visited and potentially connected in the social space. Therefore, resources with a social learning event size of one were subsequently excluded, as they did not provide a social space for two or more teachers to connect. 56 Ultimately, 70 Waters District teachers shared 5,169 unique educational resources, among which 87.04% were resources that were only curated by a single teacher. Hence, 4,499 resources with a prevalence of one teacher curating, i.e., having a social learning event size of one, were excluded from the two-mode networks. Subsequently, 3 teachers who only curated resources with a social learning event size of one were excluded, as they were isolated nodes from the entire two-mode social networks and thereby not socially embedded in the two-mode network space (see Figure 9). Moreover, 589 less-prevalent educational resources were also excluded due to the following concerns in estimating the latent factor model and the relational event model. First, resources that were curated by very small portions of teachers (i.e., two or three teachers relative to 67) in the two-mode networks played a periphery role in determining the primary network structures, while they largely expanded the network size from 136 nodes (55 teachers and 81 resources) to 737 nodes (67 teachers and 670 resources), potentially causing estimation issues in identifying the latent space positions of teachers and resources in the latent factor model. Second, resources with low curation prevalence or incidence were equivalent to a low hazard rate in relational event models. As teachers’ resource curation was modeled across multiple resources and across multiple time points, low incidence of resource curation also created the problem of excess zeros in the logistic regression estimation process, potentially causing models not to converge. Considering the estimation difficulties, this dissertation set the bounds of the two-mode networks with common resources that were curated by at least four teachers in the Waters District. Therefore, 589 resources were further excluded due to low curation prevalence, i.e., 57 resources curated by two or three teachers. Subsequently, 12 teachers who curated only low prevalence resources were further excluded (see Figure 9). Finally, a sample of 55 teachers and 81 resources was used to represent the joint teacher- resource social space (see Appendix A for 81 resources). For teachers’ characteristics, with respect to their school positions, 23 are early career teachers, 27 mentor colleagues, three instructional coaches, one principal and one uncategorized teacher. In addition, descriptive statistics on teachers’ grade level taught indicated that 7.27% of teachers instructed kindergarten, 30.91% first grade, 23.64% second grade, 12.73% third grade, 7.27% fourth grade, 3.64% fifth grade, and 1.82% sixth grade. Thus, led by more than half of the teachers from first and second grades (54.55%), there were more teachers sampled from lower grades than from higher grades in this dissertation. Analytical Strategy Latent Space Approach with Multiplicative Effects A latent space approach with multiplicative effects (also called bilinear effects or multiplicative interactions) was employed to first estimate latent positions of teachers and resources in an unobserved social space (see the analytical roadmap in Figure 10). Then the multiplicative effect of teachers’ and resources’ latent positions was used to account for the network dependency of teacher-resource curation ties in a holistic network structure (Hoff et al., 2002; Hoff, 2005; Hoff, 2009; Hoff, 2018). Specifically, the latent positions were a reduced-rank k-dimensional representation of the original m by n sociomatrix of two-mode teacher-resource network data via singular value decomposition (m represents teachers as rows; n represents resources as columns). Regarding the multiplicative effect Zi′Zj, it is calculated as the inner 58 product of teacher i’s and resource j’s vectors of latent positions, which represents the similarity of teachers’ and resources’ latent characteristics over a k-dimensional space. Figure 10 Analytical Roadmap A teacher who carries similar characteristics with a resource has a higher chance to curate that resource and thereby establish a two-mode network tie. For example, the circle plot in the result section (Figure 16) displayed that teacher-26 and -36 curated the resources math-2, STEM challenge-1 and classroom resource-1, with two-mode network ties between them, thus being plotted together. This indicated that the two teachers may have a tendency to curate math and STEM related resources, hence sharing similar characteristics with the resources in these 59 categories. Using R package-latentnet, I fit the latent space model with bilinear effects (Krivitsky et al., 2020) (see Appendix B for the R code). To recap the data structure of a two-mode network sociomatrix, rows are teachers and columns are resources. The data in each cell captures whether teacher I curates resource j. Though sociomatrices record tie-level connections between teachers and resources, a singular value decomposition regards the curated resources of teachers as teachers’ characteristics (i.e., treating resource columns as teachers’ characteristics) and patterns of teachers being attracted to resources as the resources’ characteristics (i.e., treating teacher rows as resources’ characteristics). Therefore, by decomposing sociomatrices, the tie-level connection patterns of teachers and resources are translated into node-level latent characteristics of teachers and resources. In turn, the nodal parameters inherently contain teachers’ and resources’ latent positions relative to others in the entire unobserved social space. Subsequently, their similarities (in a form of vectors’ inner product) are used to account for complex network dependencies that involve connections to and between other teachers and resources, of which teachers and resources are embedded. A previous study showed that homophily between teachers’ teaching disposition led to similar resource-seeking patterns on Pinterest (Torphy et al., 2020). Hence, I chose the latent space approach, in which similarities between teachers and resources are modeled by the multiplicative effect, founded on the assumption that homophily or consistency of inherent values between teachers and resources are the driving force behind the resource-mediated social selection process. 60 Equation 1 is a logistic regression—a probability model for binary network outcomes—to estimate the latent positions Zi and Zj. Teacher-resource tieij in equation (1) was the binary network tie between teachers and resources. Logit P(teacher-resource tieij=1) = β + Zi′Zj (1) Zi and Zj are latent positions of teacher I and resource j over a k-dimensional latent space, of which each is an m×k and an n×k matrix respectively. Based on the model fit indices, i.e., Bayesian Information Criterion (BIC), I selected k=2 (a two-dimensional Euclidean space) to represent the latent space of teachers and resources. Note that, according to the latentnet package, BIC can be safely used to select which fixed effect to include, but it is not clear whether BIC is appropriate to be used to select the dimension of latent space (Krivitsky et al., 2020). Therefore, I also relied on the Markov Chain Monte Carlo (MCMC) diagnostics of latent space models from k=1 to k=4, specifically the density of the log likelihood, the autocorrelation plot, and the trace plot. Results indicated that except for the week zero estimate (which favored k=1), all other 46 weeks’ estimations favored k=2. For model consistencies, I chose k=2 as the dimensions for all latent space models’ estimations. Posterior Predictive Checks on the Model Goodness-of-Fit across Dimensionality. In addition, I conducted the posterior predictive checks to evaluate the goodness-of-fit of the latent space models with different dimensionality (Figure 10). The resulting simulated networks from the latentnet were initially in a format of an n by n matrix, with teachers and resources in both rows and columns (i.e., as both senders and receivers). As the latentnet did not set the constraint on the tie generation between different node sets, I further subset an m by n matrix from the upper right corner of the original simulated networks, to make available the simulated two-mode networks. This approach was equivalent to specifying structural zeros in the original sociomatrix 61 in places where the tie value was not applicable. Overall, this preprocessing of the simulated networks was the approach to take for those who wanted to evaluate other two-mode specific network statistics, like the two-mode versions of betweenness and eigenvector centrality, average distance, and transitivity measures. Based on a sample of 1000 simulated networks for each of the k=1 to k=4 estimated latent space models, I compared a distribution of the predictive sender heterogeneity (the left graph in Figure 11) and receiver heterogeneity (the right graph) to the actual values from the observed teacher-resource two-mode network at week 47. The blue line in Figure 11 denoted the actual value and the red denoted the mean of values from the simulated networks. The shaded intervals represented 90 and 95 percent credible intervals. Visual checks indicated that as the dimensionality k increased, the mean of the predictive sender heterogeneity in red approached closer to the actual value in blue. For receiver heterogeneity, no clear sign of better fit between models of different dimensionality was revealed through visual checks. Thus, I further conducted the one sample t-test and interpreted the results below. 62 Figure 11 Posterior Predictive Checks on the Sender and Receiver Heterogeneity across Models from k=1 to k=4 In general, the posterior predictive checks showed that the latent space models tended to overestimate the sender and receiver heterogeneity (i.e., teacher and resource heterogeneity). Results from the one sample t-test showed that k=4 provided the best fit for recovering the sender heterogeneity in the observed network, in which the actual value was 0.0988 and the mean from 63 1000 simulated networks was 0.1066 with a t-ratio of 29.504 (Table 2). In this scenario, k=2 was the third best fitted model. Table 2 Posterior Predictive Checks on Model Goodness-of-Fit across Different Dimensionality Sender heterogeneity Receiver heterogeneity Actual Mean value from t-ratio Actual Mean value from t-ratio value simulated networks (df=999) value simulated networks (df=999) 0.0988 0.0308 k=1 0.1436 166.36 0.0545 124.02 k=2 0.1245 92.695 0.0555 160.35 k=3 0.1115 43.938 0.0545 173.75 k=4 0.1066 29.504 0.0538 160.04 In terms of recovering the observed receiver heterogeneity, the one sample t-test result indicated that k=1, with a t-ratio of 124.02, provided the best model fit, in which the actual value was 0.0308 and the mean of the simulated networks was 0.0545. Nevertheless, the model with k=3 generated the same mean (i.e., 0.545) as the model with k=1, yet with a larger t-ratio. This was because the standard deviation for the column mean (i.e., receiver heterogeneity) of the model with k=1 was wider than that of k=3, thus k=1 had a smaller t-ratio—an indicator for a better fit model. This was reflected in the spread of the distribution of the receiver heterogeneity for k=1 (a wider spread over 0.08) compared to k=3 (a narrower spread over 0.07) (see Figure 11). In other words, the model with k=3 had a smaller standard deviation on the column mean, therefore having a larger t-ratio—an indicator for a model less than the best fit. The predictive performance of the last three models from k=2 to k=4 was close. With respect to the comparison of model dimensionality, k=2 appeared to be the third best fitted model in both scenarios. Though k=2 may not provide the best fit for capturing the sender and receiver heterogeneity (according to the one sample t-test in Table 2), it was the model with the most stable estimation based on visual checks of the MCMC trace plots and autocorrelation plots. Therefore, I chose k=2 as the dimension for the latent space model. 64 Interpretation of Multiplicative Effects. The multiplicative term Zi′Zj is a similarity measure between two vectors of latent characteristics of teacher Zi and resource Zj. A larger multiplicative effect indicates Zi and Zj are similar in their directions, weighted by magnitudes of the vectors. In the context of this study, the magnitude of a teacher’s vector represents a teacher’s social activity tendency to attend learning events, i.e., curate resources in the online social space of Pinterest. Likewise, the magnitude of a resource’s vector represents a resource’s prevalence among the group of Waters District teachers. For example, if teacher i is prone to curate classroom management resources, and resource j falls into the category of classroom management, we would expect to see a larger- than-expected multiplicative effect as vectors Zi and Zj were laid in a similar direction in a k- dimensional latent space. In addition, the multiplicative effect becomes larger if teacher i actively seeks more educational resources in the social space in general and resource j is popular with more teachers curating it. Clarifying Variation of Terminology across Latent Space Model Literature. Across various phases of latent variable model development, different names have been created in relation to variations of the same technique. To avoid confusion, I will briefly sort out these model terms below. Terms in literature like latent space approach, latent position methods (Hoff et al., 2002), latent variable models (Hoff, 2008; 2018), latent eigenmodel (Hoff, 2007), and latent factor models (Hoff, 2009; 2018) all refer to the technique of singular value decomposition (e.g. m by n two-mode networks) or eigen-decomposition (e.g. n by n one-mode networks) of the observed sociomatrix, with differences of analyzing symmetric versus non-symmetric latent positions as well as one-mode versus two-mode networks. These models are used to compute the singular (or eigen) vectors of teachers and (or) resources as k-dimensional vectors of node-level 65 latent characteristics. In this dissertation, I chose to use the term latent space approach to keep consistent with the language used in Hoff et al. (2002) R package-latentnet (Krivitsky et al., 2020), which provides the option to fit two-mode networks with multiplicative effects. Terms like latent positions are used interchangeably with latent characteristics of teachers and resources, both of which carry the meaning of latent attributes and latent features of nodes in an unobserved latent social space. Furthermore, once the sociomatrix decomposition has been done, terms like bilinear effects (Hoff et al., 2002; Hoff, 2005), projection model (Hoff et al., 2002), and multiplicative effects (Hoff, 2009; 2018) refer to variations of inner products of two latent positions. These are similarity measures of node-specific parameters between teachers and resources, with differences in whether they normalize the magnitude of resource vectors, or in directed one-mode network settings, calculating two latent positions for each person of both their sender’s and receiver’s roles. According to Hoff (2005, 2018), the “multiplicative effect” is a more generalized form of the “bilinear effect.” Thus, I preferred the term multiplicative effect for its generalizability and straightforward naming after its functional form—the inner product multiplication of two vectors. Terminology like latent space approach includes both distance model and multiplicative (bilinear) effects model, in which the former regards a network tie as a function of distance between latent positions of teachers and resources in a Euclidean space; the latter models a network tie as a function of vector similarity between teachers and resources, represented by their latent positions in a Euclidean space. The estimated latent positions in a multiplicative effect model contain both the direction and magnitude of the teacher- and resource-vectors. The inner product between two vectors represents their similarity and is predictive of the probability of a teachers’ resource curation tie. In general, latent space is an approach to visualize teachers’ 66 and resources’ unobserved nodal positions in a latent social space via observed network connections and structures. In contrast, the latent factor model, a further developed multiplicative-effect latent space model, is a specific framework for analyzing directed network data. Though both relying on the inner product parameter, the latent factor model departed from the multiplicative-effect latent space model in that the former estimates two vectors for each node—both a sender’s and a receiver’s latent characteristics—while the latter estimates only one vector (not distinguishing the sender and the receiver role) for each node as node-specific latent characteristics. Thus, the latent factor model focused on directed network data (e.g., non-symmetric one-mode networks), while the multiplicative-effect latent space model is more appropriate for undirected network data (e.g., two-mode networks are considered as a type of undirected network). Specifically, latent factors refer to the extracted n-latent dimensions through decomposing an observed sociomatrix and extracting the corresponding n-biggest singular vectors as the new coordinates. In this scenario, latent positions refer to the extracted factor scores of nodes and are often visualized in a circle plot (a variation of biplot for network data). As to the notation for representing the positional parameters, I chose Zi and Zj to represent teacher i’s and resource j’s vectors of latent positions, consistent with the notation in Hoff et al. (2002) and Hoff (2005), which are the two foundational sources of latent space approach development literature. Though the recent development in Hoff (2018) specified the generalized multiplicative effects as UiTVj, his main concern is to differentiate two feature vectors (i.e., two latent positions) of the same person i, (i.e., vector Ui and Vi) in asymmetric one- mode networks, in which each person can be simultaneously a sender and a receiver, occurring twice in the latent space. Nevertheless, due to distinct features of two-mode networks in my 67 dissertation, each network tie can only be sent from teachers and received by resources. Hence, only one latent position for each node will be estimated. Therefore, vector Z is adequate to represent the latent positions of both teachers and resources without confusion; there is no need to use U and V to represent senders’ and receivers’ latent positions separately. In summary, I chose the latent space approach with multiplicative effect to refer to the technique that estimates latent positions of teachers and resources and calculates the inner product of two vectors to account for network dependency. In combining with estimating the social influence effect, a stepwise approach will be taken to first estimate the latent positions of teachers and resources using the latent space model; then I account for its multiplicative effect in the relational event model when estimating the social influence effect of teachers being exposed to their network peers’ resource curation. Therefore, I acknowledge the potential pitfall that the stepwise estimation procedure will not be able to simultaneously update the social influence effect and the latent position estimates at the same time. Estimation. The latent space approach with multiplicative effects assumes that, conditional on the latent positions of teacher i and resource j in a nonlinear multiplicative fashion, each teacher-resource network tie is conditionally independent of one another. Equation 2 is the likelihood function for a conditional dyadic independence model, in which the binary outcome—teacher-resource two-mode network tie—followed a Bernoulli distribution. %&'() (𝜽),!" ) !" %&' (∑!#" )!" (𝜽),!" ) 𝐿(𝑌; 𝜃) = 𝑃! (𝑌 = 𝑦) = ∏"$# 𝑃(𝑦"# |𝜃) = ∏"$# -.%&'() =∏ (2) !" (𝜽)) !#"(-.%&'()!" (𝜽))) Equation 3 incorporated the model specification from (1) to (2), in which I explicitly specified and substituted the function of parameters 𝜂"# (𝜃) = 𝛽 + 𝑍"2 𝑍# . %&' (∑!#"(3.4!$ 4" ),!" ) 𝐿(𝑌; 𝜃) = 𝑃! (𝑌 = 𝑦) = ∏"$# 𝑃(𝑦"# 2𝑍" , 𝑍# , 𝛽) = ∏!#"(-.%&'(3.4!$ 4" )) (3) 68 Equation 4 is the log-likelihood function of (3), which was maximized to get the maximum likelihood estimates of latent positions Zi and Zj. log P(Y|𝑍, 𝛽) = ∑"$#(:𝛽 + 𝑍"2 𝑍# ;𝑦"# − log (1 + exp (𝛽 + 𝑍"2 𝑍# ))) (4) The Bayesian method, in combination with the Kullback-Leibler divergence, was used for estimating the latent positions of teachers and resources. Regarding the estimator, the minimum Kullback-Leibler (MKL) estimates of (Z, 𝛽) were produced, which minimized the posterior mean of the Kullback-Leibler divergence from the true model. The true model refers to the model with parameters given by the posterior expectation of the network graph under the mean-value parameterization of the exponential family model. Briefly speaking, the Kullback- Leibler divergence is a general measure of the difference between two distributions—the joint probability of the posterior distribution of the network graph with parameter 𝜙 (i.e., from the true model) versus that distribution with parameter 𝜂, in which 𝜂=(Z, 𝛽) (i.e., the MKL that needs to be estimated). According to Shortreed et al. (2006), the minimization problem of the Kullback- Leibler divergence with respect to 𝜂 then becomes a maximization problem, which is simplified 567 () $ 8[:|:%&' ]) to finding the value of 𝜂 (i.e., Z, 𝛽) that maximizes =()) . Furthermore, Shortreed et al. (2006) indicated that the posterior mean E[𝑌|𝑌>?@ ] can be accurately obtained from the MCMC samples. The Bayesian method is used for estimating the posterior probability distribution of the latent positions of teachers and resources. The set-up for the Markov Chain allows 10,000 iterations for burn-in, which were discarded and not used for the posterior density. Drawing every 10th of the sample from a 40,000-sample Markov Chain, the posterior density of the parameters contained an ultimate sample of 4000. 69 The latent position Z is set to be a mean-zero random effect. As the network size increased, the prior distribution for the latent space variance also increased and was proportional to the number of nodes in the network. With respect to the specific cumulative, weekly network at week 47, the prior distribution for the overall latent space variance is scale-inverse-chi-squared (11.66, 17), with 11.66 as the number of Chi-squared degrees of freedom and 17 as the scaling parameter. These are the parameter values chosen by the latentnet. In other words, the mean for the latent space variance is set at 20.52, with a variance of 109.92, considered as an informative prior. According to Krivitsky and Handcock (2008), a larger value of the latent space variance leads to “lower belief in cluster separation,” and a lower value of the latent space variance degrees of freedom represents “greater diversity in within-group variation.” They further illustrated that too high a prior latent space variance “leads to clusters blurring together,” while too low a variance “creates posterior mode in which all the clusters are concentrated at a point, causing the fit to collapse.” Since I only estimated a model with one cluster, treating all teachers and resources in the same group, blurred clusters are less of a concern. Thus, specifying the variance at a value higher than 17 can be another alternative. Regarding the variance degrees of freedom, an alternative specification can be a value higher than 11.66, as I did not expect any diversity in within-group variation, given that I only fit a model of one group. I also fitted a model with an uninformative prior of scale-inverse-chi-squared (1, 100). The model converged, indicating the posterior density did not strongly depend on the prior. In fact, a 55 by 81 network has 4455 tie-level observations. This means the posterior density was dominated by the likelihood function of the data and was less influenced by the prior specification. Beyond the latent space variance, the prior distribution on the intercept 𝛽 is normal (0, 9). 70 The MKL estimates have been shown to be superior to the other three alternative latent position estimates, i.e., the maximum likelihood, the posterior mean, and the posterior mode. First, the MKL estimates produced more consistent network statistics, like density, compared to the observed networks, indicating that the MKL estimates are a better representation of the latent positions. This is particularly true when comparing the MKL estimates to the posterior mean and the posterior mode estimates. Second, due to statistical averaging and use of prior information, oftentimes models with MKL estimates will be closer to the true model, compared with the maximum likelihood estimate (Shortreed et al., 2006). Third, as the 2020 latentnet package indicated, MKL estimates were used as the default methods. Thus, I chose the MKL estimates as the positional estimates of teachers and resources in the latent space. Variable Description Dependent Variable Regarding teachers’ resource curation, I used whether teachers pinned a particular resource or not as the dependent variable (M=0.002, SD=0.047; see Table 3). With the longitudinal data capacity, I transformed teachers’ time-stamped resource curation data into a time frame of 48 weeks, each week indicating whether or not a teacher pinned a resource (Singer and Willet, 2003; De Nooy, 2011). Along with 55 teachers’ resource curation data over 81 resources, the complete data framework for the dependent variable is on the basis of all three dimensions, i.e., 55 teachers x 81 resources x 48 weeks = 213,840 observations. A value of one indicates whether teacher i pinned resource j at week t. 71 Table 3 Descriptive Statistics for Variables in the Regression Analyses N M or SD Min Max Percent Teachers’ resource curation (i.e. teacher- 185,145 0.002 0.047 0 1 resource ties) Network exposures Network exposure (overall) 185,145 0.093 0.858 0 44 Network exposure to school-and-district 185,145 0.009 0.105 0 3 colleagues Network exposure to online-only peers 185,145 0.084 0.850 0 44 Similarity of teachers’ and resources’ latent 144,117 -0.197 0.769 -5.012 5.068 positions (vectors’ inner product) Missing indicator for the similarity of latent 185,145 0.222 0.415 0 1 positions Low curation volume indicator 48 0.167 0.377 0 1 High curation volume indicator 48 0.167 0.377 0 1 Teachers in early career stages 55 0.418 0.498 0 1 Grade 48 Lower-elementary 21 43.75% Mid-elementary 20 41.67% Upper-elementary 7 14.58% Resource type 81 Subject-Specific 31 38.27% Classroom Management 17 20.99% Classroom Resource 12 14.81% Social & Emotional Learning 21 25.93% Resource origin 81 Educator’s Blogs 57 70.37% Teacher-To-Teacher Consumption Markets 12 14.81% Periphery Online Secondary Sites 6 7.41% Educational Organizations 6 7.41% Teachers’ perceptions of teaching Effective teaching disposition 42 3.024 0.517 2 4 Competency in classroom management 39 3.256 0.549 2 4 Perceived helpfulness of state test 41 3.268 1.049 1 5 expectations Pervasive beliefs among teachers that 38 1.789 0.991 1 4 students aren’t motivated to learn In addition, the relational event model assumes that the event of teachers pinning a particular resource can only happen once in the time of a study. Thus, once teachers pinned a certain resource, they hit the hazard of resource curation. These teachers will no longer stay for 72 further pinning of the same resource and are dropped out of the risk set. This is a reasonable assumption as teachers’ resource curation activity is mainly to search, store, and organize resources on their personalized Pinterest boards to be used in the future. Based on this model assumption, I censored teachers’ resource curation data after the week of them pinning a specific resource, resulting in 201,315 observations. Lastly, not all resources were created before the beginning of the study. I further tailored the data frame, deleting observations of teachers’ resource curation for the week in which resources had not been made available to pin based on the resource creation time (final observations were 185,145). Independent Variables Network Exposure. Teachers’ network exposure—Σi’teachers’ following network tieii’×online peer’s resource curationi’j(t-1) —is defined as the number of times an online network peer i’ curated the resource j at an earlier week t-1, summed over all network peers of teacher i (M=0.093, SD=0.858; see Table 3). In other words, the network exposure term is composed of two elements: network connections between teacher i and network peer i’, and resource curation activities conducted by peer i’. The network exposure term was designed to be resource-specific and time-specific, in which only network members’ curation activities on the same resource in the most recent week were qualified as teachers’ exposed network influence. For example, Susan has a network of two peers with Rachel and Deb, who pinned resource GrowthMindset at week three and week five respectively. The network exposure of Susan to resource GrowthMindset at week six would be a value of one. In this scenario, only Deb’s curation of this resource is counted as Susan’s network exposure due to Deb’s pinning in the most recent week (at week five), which directly precedes Susan’s week six resource curation activity (see Figure 12). 73 This is because Susan is most likely to be exposed to resources pinned by her online networks in the most recent week, as Pinterest ranks and recommends the most recently curated resources of network peers to be displayed on Susan’s main page and in her notification updates. I also created a cumulative network exposure measure, aggregating all network peers’ curation activity on the same resource since the beginning of the study. The zero-order correlation indicated that the network exposure of the most recent week was positively and significantly correlated with the cumulative network exposure at r=0.679—each of them was positively correlated with the dependent variable, i.e., the first occurrence of a teacher curating a resource, at 0.015 and 0.013 respectively. Figure 12 Susan’s Network Exposures to Resource GrowthMindset at Week Six The dynamic nature of online peers’ curation activities and subsequently teachers’ network exposure to their curated resources illustrated a constantly changing resource curation social environment in teachers’ online networks. This dissertation regards resources curated by network peers in the most recent week as having the most salient social influence effect on teachers’ resource curation activity in a given week. Teachers on average connected with 144.07 people on Pinterest, and on average received 0.093 network exposures per resource each week. 74 The maximum teachers’ network exposures from online networks to a resource in a given week was 44. Network Exposure to School and District Colleagues and Online-Only Peers. To test hypotheses on separate network exposure effects from school and district colleagues, as well as online-only peers, I split each weekly overall network exposure term into two, based on whether the exposures were from school and district colleagues (M=0.009, SD=0.105; see Table 3) or from online-only peers (M=0.084, SD=0.850; see Table 3). So, for every one network exposure from school and district colleagues, teachers received 10 times the amount of network exposures from online-only peers. Teachers on average connected with 5.65 school and district colleagues, and 138.42 online-only peers. The maximum network exposures teachers received in a given week from school and district colleagues and from online-only peers were three and 44 respectively. Descriptive statistics indicated that the network exposures teachers received from each group were proportional to the number of people in that group. The Similarity of Latent Space Positions. The similarity of teachers’ and resources’ latent positions was calculated using the inner product of vectors of teachers’ and resources’ positions along two dimensions of the latent space (M=-0.197, SD=0.769; see Table 3). Considering the time dynamic of two-mode networks of teachers and resources, their latent positions were likely to be changed in a weekly manner as more teachers joined to curate a variety of resources, and more resources became available as time elapsed. In addition, teachers’ resource curation ties at week t not only depended on other curation ties in the current week but was also subject to the impact of teachers’ curation ties formed in the weeks since the beginning of the study. Therefore, the latent space positions of teachers and resources were calculated in a weekly and cumulative fashion. For the first week (i.e., week zero), teachers’ and resources’ 75 latent positions and their similarities were only based on the two-mode network of that week. From the second week (i.e., week one) to the 48th week (i.e., week 47), latent positions and their similarities were computed from a cumulative curation network that aggregates network ties from previous week(s) to the current week; for example, the cumulative two-mode network in the second week combines ties from the first and second week. This is to account for network dependencies accumulated over time. Dealing with Missingness in the Similarity of Latent Space Positions. Though ultimately 55 teachers and 81 resources were present in the two-mode networks over the period of one school year, not all teachers curated resources from the beginning of the study, nor had all resources been pinned in the first week. Hence, both were absent in the two-mode network in the early weeks until teachers gradually joined to pin resources in the social space and resources were introduced by teachers to the two-mode network. In these scenarios, teachers and resources as nodes in two-mode networks were missing, further creating a missing-tie issue between teachers and resources, causing the missingness of their latent positions and similarities in the given week. Yet, teachers experienced a hazard of pinning a particular resource even though their latent positions were not identified. To avoid listwise deletion in estimating the network exposure effect, I assume that latent positions among absent teachers and resources are the least similar in any given cumulative, weekly two-mode network. In other words, they are the least likely to have a resource curation tie. I imputed the minimum value of the observed similarity of latent positions between teachers and resources in a given week to those teachers and resources that are absent in that two-mode network. I also included a missing indicator (M=0.222, 76 SD=0.415; see Table 3) in the final model to account for the variation in teachers’ resource curation attributed to the measurement inaccuracy in the variable similarity of latent positions. Covariates Time. I chose weeks to be the natural time unit as teachers tended to systematically curate resources for lesson planning and instructions on a weekly basis. The first week (July 1, 2016) was set to be a value of zero, as the starting point of planning for the upcoming school year. The following weeks were arranged in sequence to week 47 (June 1, 2017) based on the Waters district school calendar. Extreme Resource Curation Weeks. Previous research has found seasonal effects and fluctuations on teachers’ resource curation activities during different times of year (Torphy et al., 2017). Thus, I created two indicator variables to account for lowest and highest curation volumes at the weekly level. I used the cut-off score based on teachers’ curation volumes at the 17.44 and 84.71 percentile to distinguish the lowest and highest volumes. Specifically, if a week has teachers curating resources less than three times, that week is labeled as one of the weeks with the lowest curation volumes. They are the weeks of December 2, December 9, January 20, March 3, and of April 7 through the week of April 28 (covering the entire month of April). Likewise, if a week has teachers pinning resources more than 15 times, that week is labeled as one of the weeks with the highest curation volumes. They are the weeks of July 1 through the week of July 22 (the entire month of July), and the weeks of August 12, August 26, December 30, and March 24. Teacher’s Career Stage. According to Torphy et al. (2020), using a sample of 100 teachers from four school districts, they found that teachers in different career stages (i.e., early career teachers compared to experienced teachers) tend to curate resources differently, with early 77 career teachers having an online resource portfolio similar to those of others in their local area, while experienced teachers have a more independent resource portfolio. Hence, I created an indicator variable, labeling if a teacher is in an early career stage (i.e., those who were in their first three years of teaching) (M=0.418, SD=0.498; see Table 3). Teacher’s Grade Level Taught. Previous studies have found that the grade level taught significantly predicts the curation similarity between teachers (Torphy et al., 2020). This finding indicates that teachers from different grades tend to seek different resources. Thus, I included the grade level taught to reduce its confoundedness with the network influence effect as teachers are more likely to follow network peers in the same grade who appeared to curate the same resources. Due to concerns of the non-linear relationship between the grade level taught and teachers’ resource curation, I further grouped grades into three categories: lower grades (grades kindergarten to one; 43.75% of the teachers; see Table 3), mid grades (grades two to three; 41.67% of the teachers), and upper grades (grades four to six; 14.58% of the teachers). The category lower grades was set to be the reference group. Resource Category. Resource content was coded based on the pin description and the text and graphs embedded in the pin image. There were 13 resource categories found in the coding process. Results indicated that the most prevalent resource content was Growth Mindset (19.75%), succeeded by Reading (13.58%) and Classroom Management (11.11%) (see Figure 13). The second tier of frequently curated resources included STEM Challenge (8.64%), Classroom Resource (8.64%), Writing (6.17%), and Character Education (6.17%). Lastly, resource content that was curated by less than 5% of the Waters school district teachers were in categories such as Spelling (4.94%), Math (4.94%), Flexible Seating (4.94%), Back-to-school (4.94%), For Parents (3.7%), and Fun Project (2.47%). The coded resource categories were used 78 for displaying the name of the resources and their latent positions on the circle plot of weekly, cumulative two-mode networks. Figure 13 Percentage of Resources in Each Content Category Resource Type. I further combined the 13 content categories into four broader resource types (see Figure 14). The most prevalent resource type was the Subject-Specific (38.27%; see Table 3), including Reading, STEM Challenge, Writing, Spelling, and Math. The second leading type was Social and Emotional Learning resources (25.93%), including Growth Mindset and Character Education. Next was Classroom Management-relevant resources (20.99%), including Classroom Management, Flexible Seating, and Back-to-school. The least frequently curated type was Classroom Resource-relevant resources (i.e., facilitating materials) (14.81%), including Classroom Resource, For Parents, and Fun Project. In summary, when resources were coded at the broader content level, the most prevalent resources shifted from Growth Mindset to Subject- Specific resources. The combined resource type was used in the final relational event model to account for variations in teachers’ resource curation attributed to teachers’ preferences of certain types of resources. Subject-Specific resource was set to be the reference group. 79 Figure 14 Percentage of Resources in Each Resource Type Resource Origin. As a content curation platform, Pinterest pooled a variety of image- based content from websites outside of its platform. This content embodied the standing and professional beliefs of the original content creators. Thus, I adopted the coding framework developed by Torphy et al. (2020) to characterize resources based on their resource origin (aka secondary online sites). Categorizing 81 resources into four groups, the classification results indicated that 70.37% of the resources were originally from Educator Blogs, e.g. Missgiraffesclass (see Table 3, Figure 15). The next group was resources from Teacher-to- Teacher Consumption Markets (14.81%), e.g. Teacherspayteachers; followed by resources from Periphery Online Secondary Sites (7.41%), e.g. YouTube and Facebook; and Educational Organizations (7.41%), e.g. Scholastic. Compared with the percentage distribution of the resource origins of 140,287 coded pins in Torphy et al. (2020)’s article, data in this dissertation contained 12% more resources from Educator Blogs, a similar percent of resources from Teacher-to-Teacher Consumption Markets and Educational Organizations, while having 11.5% fewer resources from Periphery Online Secondary Sites. Educator Blogs was set to be the reference group. 80 Figure 15 Percentage of Resources by Origin Teachers’ Perceptions of Teaching. Four items from the Waters District teachers’ survey on their perceptions of teaching were used in the exploratory analyses on the interaction effect of network exposure and teachers’ perceptions of teaching. Teachers’ survey data were combined across cohorts that responded in one or more waves of the survey from 2014 to 2017. For those who participated in multiple years, I used their responses in 2016 to best align with their resource curation activities during the same year. Though the survey was to measure teachers’ perceptions on mathematics instruction, elementary teachers tend to teach multiple subjects at the same time. Thus, I used their survey responses as a proxy for their general perceptions of teaching. Effective Teaching Disposition. The original survey item was in a 4-point Likert scale and asked teachers to what extent did they agree with the following, “when the mathematics grades of students improve, it is often due to their teacher having found a more effective teaching approach” (M=3.024, SD=0.517; see Table 3). Competency in Classroom Management. This 4-point Likert scale item asked about the perception of teachers’ general teaching ability regarding to what extent they agreed with “if a 81 student in my class becomes disruptive and noisy, I feel assured that I know techniques to redirect him/her quickly” (M=3.256, SD=0.549; see Table 3). Perceived Helpfulness of State Test Expectations. This 5-point Likert scale item asked “on average across all of your mathematics lessons when you most recently taught, to what extent did expectations associated with state math tests support or inhibit your ability to enact your math lessons” (M=3.268, SD=1.049; see Table 3). Pervasive Beliefs among Teachers that Students Are not Motivated to Learn. This item asked, on a 5-point Likert scale, about what percentage of teachers at your school shared the following belief, “students at this school just aren’t motivated to learn” (M=1.789, SD=0.991; see Table 3). Teachers’ and Resources’ Indicators. To account for possible unique resource curation patterns specifically related to certain teachers or resources, I generated teachers’ and resources’ indicator variables. In the context of network analysis, teacher- and resource-effects are also called sender- and receiver-effects, which captures teachers’ tendency of curating a resource and resources’ tendency of being curated. To simplify the number of indicators used for teachers and resources, I created indicators based on teachers’ outdegree and resources’ indegree (i.e., the number of ties sent by teachers and the number of ties received by resources). See Table 4 for the teachers’ outdegree and resources’ indegree frequency table. For example, if Mary and Bob were both curating seven different resources, they would be labeled with a value of one on the same indicator for an outdegree of seven. A similar approach was used to group and label resources based on having the same number of teachers curating certain resources. A likelihood ratio test showed that the model controlling for all teachers’ and resources’ fixed effects (with 134 fixed effects) is not significantly different from the simplified model that only controlled for indicators 82 of teachers’ outdegree and resources’ indegree (with 25 fixed effects), χ2(109)=18.38, p>.05. Hence, I chose the parsimonious specification with similar model performance. Table 4 Frequency Table of Teachers’ Outdegree and Resources’ Indegree N Percent Teachers’ outdegree 55 1 12 21.82% 2 3 5.45% 3 5 9.09% 4 6 10.91% 5 3 5.45% 6 7 12.73% 7 3 5.45% 8 3 5.45% 10 1 1.82% 11 1 1.82% 12 1 1.82% 13 3 5.45% 17 1 1.82% 22 1 1.82% 23 1 1.82% 24 1 1.82% 30 1 1.82% 31 1 1.82% 33 1 1.82% Resources’ indegree 81 4 43 53.09% 5 16 19.75% 6 11 13.58% 7 5 6.17% 8 3 3.70% 9 1 1.23% 12 1 1.23% 13 1 1.23% Using the Relational Event Model to Estimate Network Influence Using a logistic regression for discrete-time relational event models, I estimated the network exposure effect on teachers’ resource curation, while accounting for similarities of latent positions between teachers and resources in an unobserved two-mode social space. P(teacher- resource tieijt=1|teacher-resource tieijs=0, sdata frame->matrix data_week_matrix<-as.matrix(as.data.frame.matrix(data_week_contingency)) network <- as.network(data_week_matrix, matrix.type="adjacency", bipartite=T) ######grab the username and resource in the order of the network data, then turn them into a vector for node names user<-rownames(data_week_matrix) resource<-colnames(data_week_matrix) user.resource<-c(user, resource) network.vertex.names(network) <- user.resource #analyze #lfm.fit<-ergmm(network ~ bilinear(d=2)) #assess model fit before extracting latent positions lfm.fit.d1 <- ergmm(network ~ bilinear(d=1), control=ergmm.control(burnin=10000)) lfm.fit.d2 <- ergmm(network ~ bilinear(d=2), control=ergmm.control(burnin=10000)) lfm.fit.d3 <- ergmm(network ~ bilinear(d=3), control=ergmm.control(burnin=10000)) lfm.fit.d4 <- ergmm(network ~ bilinear(d=4), control=ergmm.control(burnin=10000)) #create a null vector bic <- c() #extract bic bic[1]<-summary(lfm.fit.d1)$bic$overall bic[2]<-summary(lfm.fit.d2)$bic$overall bic[3]<-summary(lfm.fit.d3)$bic$overall bic[4]<-summary(lfm.fit.d4)$bic$overall print(bic) week<-i-1 model_dimension<-c(1:4) model_bic[[i]]<-data.frame(cbind(model_dimension, bic, week)) #note: turn vector into the data.frame before assigning them to model_bic outside of the “for loops” #to extract latent positions, I need the iteration number or the week number, and the node name latent_position_d1_list[[i]]<-data.frame( cbind( data.frame(summary(lfm.fit.d1)$mkl$Z), user.resource, week) ) latent_position_d2_list[[i]]<-data.frame( cbind( data.frame(summary(lfm.fit.d2)$mkl$Z), user.resource, week) ) latent_position_d3_list[[i]]<-data.frame( cbind( data.frame(summary(lfm.fit.d3)$mkl$Z), user.resource, week) ) latent_position_d4_list[[i]]<-data.frame( cbind( data.frame(summary(lfm.fit.d4)$mkl$Z), user.resource, week) ) 170 #extract MCMC diagnostics, 1.autocorrelation plot; 2.traceplot&posterior density #See if I have convergence in the MCMC setwd("~/Dropbox/Dissertation/Results/r output/MCMC Diagnostics/Dimension 1") pdf(paste0("MCMC Diagnostics week ",week," d1.pdf")) mcmc.diagnostics(lfm.fit.d1) setwd("~/Dropbox/Dissertation/Results/r output/MCMC Diagnostics/Dimension 2") pdf(paste0("MCMC Diagnostics week ",week," d2.pdf")) mcmc.diagnostics(lfm.fit.d2) setwd("~/Dropbox/Dissertation/Results/r output/MCMC Diagnostics/Dimension 3") pdf(paste0("MCMC Diagnostics week ",week," d3.pdf")) mcmc.diagnostics(lfm.fit.d3) setwd("~/Dropbox/Dissertation/Results/r output/MCMC Diagnostics/Dimension 4") pdf(paste0("MCMC Diagnostics week ",week," d4.pdf")) mcmc.diagnostics(lfm.fit.d4) #clear off the dev.list() if it is not empty, which is R's inner place to store all the plots in this session while (!is.null(dev.list())) dev.off() print(dev.list()) #close off the pdf file generating process } #based on a list of generated data frames, append them all and generate an overall data file df.bic <- rbindlist(model_bic) df.latent.position.d1 <- rbindlist(latent_position_d1_list) df.latent.position.d2 <- rbindlist(latent_position_d2_list) df.latent.position.d3 <- rbindlist(latent_position_d3_list) df.latent.position.d4 <- rbindlist(latent_position_d4_list) #note: for each week of the network, select the best fitting model of a specified dimension with minimum BIC #extract MCMC diagnostics to evaluate MCMC convergence #latent positions #clean BIC library(dplyr) # in dplyr pipes, mutate = create a new variable, group_by = within a group, filter = subset data, select = keep selected variables. min.BIC <- df.bic %>% group_by(week) %>% mutate(min_BIC = min(bic)) %>% mutate(minBIC_indicator = case_when(min_BIC==bic ~ 1, min_BIC!=bic ~ 0, 171 TRUE ~ NA_real_)) #subset data, only keep the models from each week with a minimum bic min.BIC.model.dimension <- min.BIC %>% filter(minBIC_indicator==1) %>% select(week, model_dimension) %>% arrange(week) #post-latent position analysis results cleaning df.latent.position.final<-df.latent.position.d2 %>% mutate(week2 = case_when(week<=40 ~ week, week>=41 ~ week+1, TRUE ~ NA_real_)) %>% select(-week) %>% rename(week=week2, z1=X1, z2=X2) ########output latent factor model results######## setwd("/Users/yuqingliu/Dropbox/Dissertation/Data/Processed data") library(foreign) write.csv(df.latent.position.final,"weekly latent position estimates 060322.csv", row.names = FALSE) ############second part################ #create circle plots library(amen) library(tidyverse) library(stringr) par(mar = c(1, 1, 1, 1)) setwd("/Users/yuqingliu/Dropbox/Dissertation/Data/Processed data/") #load the latent position data load("/Users/yuqingliu/Dropbox/Dissertation/Code/R/dissertation R.RData") #read in the original teacher-resource two-mode network data data<-read_excel("/Users/yuqingliu/Dropbox/Dissertation/Data/Processed data/weekly network data over 47 weeks.xlsx",sheet="Sheet1") #node labels teacher<-data[, c("username","userid")] teacher<-unique(teacher) resource<-data[,c("link", "resource_category_label")] resource<-unique(resource) #in the latent position data, create an indicator to indicate if the node is a resource or a teacher rspattern<-"http" df.latent.position.final$rs_indi<-str_detect(df.latent.position.final[['user.resource']], rspattern) df.latent.position.final$rs_indi<-as.integer(df.latent.position.final$rs_indi) 172 #no new tie added in week 41, so the cumulative weekly network at 41 = week 40, append week 41 to the data frame week41 <- df.latent.position.final %>% filter(week==40) %>% mutate(week=week+1) df.latent.position.v2 <- rbind(df.latent.position.final, week41) %>% arrange(week) #generate plot titles plot_title<-df.latent.position.v2 %>% select(week) %>% distinct() %>% arrange() %>% mutate(title = case_when (week==0 ~ paste0("Week ",week," Network Circle Plot"), week>0 ~ paste0("Week ",week," Cumulative Network Circle Plot"), TRUE ~ NA_character_) ) plot_title<-pull(plot_title, title) #set the directory path for the circle plot setwd("~/Dropbox/Dissertation/Results/R latent space model/circle plot") pdf("circle plot with title.pdf", width = 9, height = 6) #for teachers' latent position data, merge in the label of teachers' nodes teacher.latent.position<- df.latent.position.v2 %>% filter(rs_indi==0) %>% select(-rs_indi) %>% rename(username=user.resource) %>% left_join(y=teacher, by=c("username")) #for resources' latent position data, merge in the label of resources' nodes resource.latent.position<- df.latent.position.v2 %>% filter(rs_indi==1) %>% select(-rs_indi) %>% rename(link=user.resource) %>% left_join(y=resource, by=c("link")) #the loop to generate 48 cumulative, weekly teacher-resource network circle plots my_list <- c(0:47) for (i in 1:length(my_list)) { #part 1. estimated latent positions #note the latent positions are already based on network data accumulated up to the given week, week==i-1 is the right one #sort latent positions of teachers by userid; sort latent positions of resources by resource_category_label #teacher.U is the row/sender factor to enter in the circle plot; resource.V the column/receiver factor teacher.U<-teacher.latent.position %>% filter(week==i-1) %>% arrange(userid) %>% select(z1,z2) teacher.U<-data.matrix(teacher.U) 173 resource.V<-resource.latent.position %>% filter(week==i-1) %>% arrange(resource_category_label) %>% select(z1,z2) resource.V<-data.matrix(resource.V) #(doesn't help much) add the number of teachers and resource together, later used to scale the plot for better visualization #nodes <- dim(teacher.U)[1] + dim(resource.V)[1] #part 2. original network adjacency matrix data2<-data[which(data$week<=i-1), c("userid","resource_category_label")] #task: tidy up data2 based on whether the node has latent positions, using right_join #first, grab teachers and resources that have latent positions at a given week t.w.position<-teacher.latent.position %>% filter(week==i-1) %>% arrange(userid) %>% select(userid) r.w.position<-resource.latent.position %>% filter(week==i-1) %>% arrange(resource_category_label) %>% select(resource_category_label) #second, merge with data2 to only keep teachers and resources with estimated latent positions data2<- data2 %>% right_join(y=t.w.position, by=c("userid")) %>% right_join(y=r.w.position, by=c("resource_category_label")) #turn network edgelist to adjacency matrix data2 <- table(data2) class(data2)<-"matrix" #plot circplot(data2, U = teacher.U, V = resource.V, row.names = rownames(data2), col.names = colnames(data2), plotnames=TRUE, lcol = "dark gray", bty="u", #vscale=0.9, #pscale=1.75,mscale=0.5, #jitter = 0.1 * (nodes)/(1 + nodes), ) #add in the plot title title(main=paste0(plot_title[i]), cex.sub=2) } while (!is.null(dev.list())) dev.off() print(dev.list()) 174 APPENDIX C. Circle Plots of Latent Positions for Each of the 48 Cumulative, Weekly Networks Figure C1. Week Zero Network Circle Plot Week 0 Network Circle Plot 11 Writing4 For parents1 853 40 CharacterReading9 Reading11Writing3 education1 Spelling4 Flexible seating4 Back−to−school3 ClassroomFun project2 management9 ClassroomMath2 management5 20 33 9 4632 Reading2 24 Back−to−school1 Reading10 Classroom management3 49 27 50 4 12 28 7 Flexible 422Flexible seating1 seating2 Reading4 52 175 Figure C2. Week One Cumulative Network Circle Plot Week 1 Cumulative Network Circle Plot 8 ForReading11 parents1 40 Writing3 ClassroomSpelling3 32 resource4 Character Flexible education4 seating4 Reading6 28 12 Spelling4 Reading9 ClassroomWriting4 management5 Classroom management9 Back−to−school3 Character education1 Spelling2 Reading2 46 Classroom For parents2 Back−to−school1 management3 Math2 Fun project2 Flexible seating2 2453 Reading10 27 36 26 49 9 Flexible seating1 Reading4 20 33 42 44 1 74 2 11 50 5230 176 Figure C3. Week Two Cumulative Network Circle Plot Week 2 Cumulative Network Circle Plot 27 20 33 2812 Flexible seating2 3 Reading10 46 Spelling2 Back−to−school3 32 Reading6 Classroom Fun project2resource4 42 Classroom resource3 Flexible seating4 Flexible seating1 50 Spelling3 55 75 Reading4 1 2 30 52 Classroom 819 management9 47 4 44 9 11 40 Reading11 For parents1 Writing3 Writing4 Classroom resource1 Spelling4 49 21 Character Character Classroom education1 Reading9 education4 management5 Growth mindset13 Growth Classroom mindset4 Back−to−school1 Growth management3 mindset8 For Classroom 53 parents2 Reading2 resource2 Math2 36 26 24 177 Figure C4. Week Four Cumulative Network Circle Plot Week 4 Cumulative Network Circle Plot 28 46 32 Classroom Spelling2 Classroom resource5 resource4 Reading6 12 mindset7 Back−to−school3 11 Fun Growthproject2 Classroom management9 Classroom 33 management5 Classroom Spelling3 management4 Flexible2023 seating2 Character Growth education5 For Writing3 parents1 mindset240 8 Reading11 Spelling4 Character education4 22 54 27 Back−to−school4 Character education1 Reading9 425541 Writing419 3 Classroom Reading10 resource3 47 STEM Math2 STEMchallenge1 challenge3 50 137 Growth Growth Classroom mindset4 mindset8 resource2 STEM challenge6 53 Classroom resource1 2 Flexibleseating4 Flexible seating1 For parents2 Reading2 52 Back−to−school1 Back−to−school2 26 Growth mindset5Growth mindset13 9 17 36 21 Classroom Reading4 44 management3 53049 24 35 178 Figure C5. Week Five Cumulative Network Circle Plot Week 5 Cumulative Network Circle Plot 9 5312 44 Math2 2640 46 23 Fun project2 Growth mindset7 Growth STEMmindset2 Character education5 challenge1 Classroom resource2 Writing4 Growth Growth mindset4 mindset8 Reading9 Classroom management5 Spelling4 Reading11 ClassroomCharactermanagement9 education4 54 20 Reading6 Back−to−school3 Character Spelling2 28 education1 For Classroom parents1 resource4 Writing332 8 4 1 22 Spelling3 Classroom resource5 36 STEM STEM challenge6 challenge3 55 33 ForReading4 parents2 Back−to−school4 Classroom management4 19 7 13 Flexible seating4 Classroom resource3 Reading2 Back−to−school1 Growth mindset13 Back−to−school2 2111 250 Classroom Flexible Flexible Growth management3 mindset5 seating2resource1 Reading10 seating1 347 52 4 9 4227 Classroom 535 30 17 24 179 Figure C6. Week Six Cumulative Network Circle Plot Week 6 Cumulative Network Circle Plot 9 26 44 23 10 2554 38 22 1 Classroom management5Growth mindset7 Reading7 5533 20 17 7 13 Classroom resource2 11 Classroom resource5 Growth STEM Growth Math2 mindset8 challenge1 mindset4 52 23 Growth mindset2 Character 12 education5 42 14 50 For parents1 Character Reading11education4 Writing4 47 5 Flexible Classroom seating4 resource3 35 Growth mindset5 Reading9 40Reading6 Classroom Back−to−school3 resource4 Flexible seating1 Classroom Writing3 36 STEM management9 Spelling3 challenge6 Flexible seating2 STEM challenge7 STEM challenge3 Writing2 Reading4 Classroom Reading10resource1 30 8 Spelling2 Back−to−school1 Growth Reading2 mindset13 Classroom Back−to−school2 Fun project2 Math1 management3 21 27 53 Back−to−school4 For parents2 Spelling4 28 Character Classroom education1 management4 3219 46 24 49 4 180 Figure C7. Week Seven Cumulative Network Circle Plot Week 7 Cumulative Network Circle Plot 3320 11 22 55 7 13 17 5223 42 38 Growth mindset5 Flexible Classroom 47 50 seating4 resource3 5 29 14 Fun project2 54 30 Classroom resource5 Growth mindset7 23 Flexible Flexibleseating1 27 seating2 21 25 STEM challenge7 Classroom 944 management5 Reading10 35 4 1 Classroom resource1 49 Classroom resource6 Back−to−school1 Back−to−school2 Growth 24 mindset13 Classroom 26 Math2 resource2 Reading2 Math1 Growth mindset2 STEM Growthchallenge1 mindset8 Classroom management3 Growth mindset4 46 For parents1 Classroom Spelling4 management4 10Character education5 Character Back−to−school4 For education1 parents2 12 Classroom Reading11 Writing4 Spelling3 Reading7 STEM Reading6 Character Classroom STEM management9 Writing2 Reading4 Spelling2 challenge3 challenge6 education4 resource4 40 Writing3 Back−to−school3 Reading9 19 36 53 8 28 32 181 Figure C8. Week Eight Cumulative Network Circle Plot Week 8 Cumulative Network Circle Plot 19 46 32 Classroom Character 53 For Classroom STEM parents2 management4 education1 Spelling4 47 management3 challenge1 Growth mindset4 24 Spelling2 Growth Back−to−school4 mindset8 Growth Growth mindset15 mindset10 Math1 Reading2 26 36 Classroom STEM management9 challenge3 Reading7 Reading1 STEM Writing2 challenge6 Back−to−school1 Back−to−school2 Spelling3 Writing3 Reading6 Reading9 Back−to−school3 Classroom Growth resource1 mindset13 Reading4 Growth Character 28 mindset12 education4 35 Classroom Writing4resource4 Reading10 Growth mindset2 8 Spelling1 40 Character Growth Writing1 education5 mindset1 45 23 Classroom Reading11 resource2 For Classroom STEM parents1 management8 challenge7 Flexible Flexible seating130 seating2 4927 Growth 12 mindset16 21 14 29 Flexible seating4 Classroom resource6 50 Growth 10 mindset7 23 42 Classroom resource3 52 Growth mindset517 13 7 Classroom Classroom Math2 Fun project2 55 management5 resource5 38 4420 25 1 11 9 22 54 33 182 Figure C9. Week Nine Cumulative Network Circle Plot Week 9 Cumulative Network Circle Plot 24 46 53 2636 Classroom 19For Classroom 47 Growth STEMGrowth parents2 mindset4 management3 mindset10 Back−to−school1 Reading2 Math1 challenge1 management4 Growth mindset15 Reading4 Back−to−school2 Classroom resource1 Spelling4 Back−to−school4 Growth mindset13 Reading9 Reading10 Character education1 Math2 32 Growth mindset8 STEM challenge3 Spelling2 Flexible 5 seating2 35 Classroom STEM management9 challenge6 Reading1 Writing2 Flexible seating1 30 Reading6 Back−to−school3 Spelling3 Writing3 Writing4 427 Character education4 28 mindset12 Flexible seating4 Growth Classroom Character resource4 education5 Reading7 49 21 29 14 50 Classroom resource3 3 42 Growth STEM mindset1 challenge7 23 52 GrowthClassroom 8 mindset2 40 Spelling1 resource2 Writing1 17 Reading11 12 Classroom management8 13 For parents1 Classroom resource6 7 Growth mindset16 2 4455 20 25 Growth mindset7 22 11 9 54 Classroom Growth Fun management5 mindset5 project2 Classroom resource5 1 10 38 33 183 Figure C10. Week 10 Cumulative Network Circle Plot Week 10 Cumulative Network Circle Plot 8 32 2840 46 19 Classroom Growth Character Growth Spelling3 Growth Writing2 For Writing3 STEM Reading6 STEM management9 Writing1 parents1 mindset12 Spelling2 mindset8 mindset2 Reading1 education4 challenge3 Writing4 challenge6 Back−to−school3 Reading11 Classroom STEM Spelling1 resource4 challenge7 Classroom Character management4 Spelling4 education1 Back−to−school4 For STEMparents2 challenge1 Growth Character education5mindset16 Growth mindset1 Growth mindset15 Growth Classroom Growth mindset4 management3 Math1 4724 mindset10 Reading7 Classroom resource6 Back−to−school2 Reading253 Back−to−school1 Growth Classroom 12 mindset5 management8 Classroom resource1 26 Growth38 mindset7 Reading9 Growth mindset1317 Classroom resource2 23 Growth mindset9 10Fun project2 Reading10 Reading4 36 5 Classroom Classroom resource5 Flexible seating1 33 management5 Math2 Flexible seating229 35 2 Flexible seating4 30 Classroom resource3 1427 1 21 50 49 95422 25 20 44115541613 42 52 3 7 184 Figure C11. Week 11 Cumulative Network Circle Plot Week 11 Cumulative Network Circle Plot 3653 12 Math2 Reading4 STEMSTEM Reading9 challenge1 26 STEMchallenge6 challenge3 Writing4 Character education5 28 44 Classroom 49 resource6 Classroom resource4 1 Classroom resource5 Back−to−school3 Reading6 STEM challenge7 Classroom 9 resource3 Growth Writing2 mindset8 5521 Reading1 Character For education4 parents2 6 Spelling2 Spelling1 Spelling3 40 25 13 722 Classroom Classroom Classroom Growth 32 mindset13 management9 19 management3 management4 Back−to−school4 52 20 Growth Writing3 mindset12 Reading11 Math1 Spelling4 11 54 5027 39 Flexible 3 42 4 seating4 Character Growth Growth education1 mindset15 mindset4 Back−to−school1 Reading2 For Growth Growth Character parents1 mindset2 mindset16 education3 Growth Growth Classroom Reading7 Back−to−school2mindset7 Writing1 mindset10 management8 24 46 Flexible 14 Flexible 16 30 seating1 Growth seating2 mindset5 Growth mindset9 8 29 Reading10Growth Classroom ClassroomFun management5mindset1 Classroomresource1 project2 resource2 17 35 23 52 4738 33 10 185 Figure C12. Week 12 Cumulative Network Circle Plot Week 12 Cumulative Network Circle Plot 2749 50 42523 44 30 21 55 Classroom resource5 11 36 Flexible Flexible seating1 seating2 Classroom Classroom resource6 resource3 Flexible 1 13 seating4 79 53Reading4 12 Math2 622 25 Reading10 20 Reading9 54 STEM 17 challenge1 26 39 Growth mindset13 14 STEM Writing4 STEM challenge6 challenge3 4 STEM challenge7 29 Classroom Charactermanagement3 education5 For Classroom 28 parents2 resource4 Reading6 Math1 35 Back−to−school1 Back−to−school3 Classroom management5 Classroom resource2 Back−to−school4 Growth Classroom 24 mindset8 Reading2 management4 19 Writing2 23 Growth Character Classroom mindset15 Spelling2 education4 Spelling3 management9 Spelling4 Classroom Fun management8 project2 16 33 Character Growth Spelling1 Back−to−school2 education1 mindset12 Character education310 Growth 40 Growth 32 mindset4 Reading1 Reading11 For Growth Math3 Growth Writing3 Growth Growth mindset2 Growth mindset5 Writing1 parents1 Classroom Growth mindset1 mindset9 mindset7 mindset16 Reading7 resource1 mindset10 4738 2 5 46 8 186 Figure C13. Week 13 Cumulative Network Circle Plot Week 13 Cumulative Network Circle Plot 10233338 47 825 464032 16 Classroom Growth Growth Growth Reading7 Growth Growth Math3 mindset7Writing1 mindset10 mindset2 Reading1 Reading11 mindset16 mindset5 resource1 Writing3 Writing2 Growth For Spelling1 mindset12 parents1 28 Fun project2 Spelling3 19 Classroom GrowthGrowthmindset1mindset9 Classroom management8 Character Growth management9 Spelling2 Character education4 education1 mindset4 Character education3 Back−to−school3 Reading6 Spelling4 Growth Character 1224 mindset8 education5 Classroom management5 35 Classroom resource4 Classroom resource2 Classroom Growth management4 mindset15 Back−to−school4 Back−to−school2 ForReading2 parents2 Math1 26 Back−to−school1 Classroom STEMmanagement3 challenge7 29 Writing4 STEM STEM challenge3 challenge6 STEM challenge1 Growth mindset13 17 Reading9 Reading10 Flexible seating2 4 Flexible Reading4seating1 39 14 Math2 54 20 25 6 1 922 Classroom Flexible Classroom Classroom seating4 resource3 resource5resource6 53 36 755 13 43 44 1121 49 30 52 342 50 27 187 Figure C14. Week 14 Cumulative Network Circle Plot Week 14 Cumulative Network Circle Plot 26 53 36 30 17 2750 Growth Flexible STEM Reading10 Reading9 Flexible mindset13 seating1 challenge1 STEM Reading4 challenge7 seating2 42 3 24 Writing4 Back−to−school1 STEM challenge3 STEM challenge6 Math2 Flexible seating4 52 Classroom management3 Reading2 Math1 49 19 5 parents2 Classroom resource3 29 Back−to−school2 For 21 Growth mindset15 117 Classroom resource6 Back−to−school4 Classroom management4 43 Classroom resource5 2 13 55 Spelling4 44 Growth Character32 4640 12 mindset4 education1 14 28 Growth mindset8 Writing1 ClassroomFor parents1 47 resource1 25 39 Classroom 8 Spelling3 Back−to−school3 Character GrowthReading6 Classroom 35 education4 mindset10 management9 Spelling2 Character education5 resource4 19 22 Writing3 Reading11 6 Spelling1 Reading1 20 Growth Growth Growth Growth mindset2 Writing2 mindset5 mindset12 mindset16 54 Growth Growth Reading7 Growth mindset1 Reading3 mindset7 Math3 mindset3 23 Fun project2 Growth Classroom Character 38 Classroom mindset9 management8 education3 management5 16 1033 Classroom resource2 4 188 Figure C15. Week 15 Cumulative Network Circle Plot Week 15 Cumulative Network Circle Plot 12 28 Character Classroom Writing2 Reading1 Reading6 education5 Back−to−school3 Spelling1 resource4 33 Character Reading11 Growth Growth Character Fun education4 mindset9 mindset12 Reading3 education3 project2 38 40 1632 Growth Reading7 Growth Growth Growth Classroom mindset3 Spelling2 mindset16 Spelling3 Math3 mindset11 mindset7 management9 8 31 Classroom GrowthWriting3 Growth Classroom Classroom mindset8 management8 mindset2 STEM challenge3 resource2 management5 10 23 Growth Growthmindset5 mindset1 6 46 For parents1 Writing1 47 STEM challenge6 19 Character Growth Growth mindset4 education1 mindset10 Spelling4 2 ClassroomWriting4 management4 Back−to−school4 For parents25 Classroom Growth mindset15 resource12624 Classroom Back−to−school2 Reading2 Back−to−school1 management3 Math1 91 Math2 35 20 54 Classroom resource5 22 STEM challenge1 44 45 2539 Classroom resource6 5513 4 FlexibleGrowthseating1 Reading10 Reading9 mindset13 7 4321 11 ClassroomFlexible 49 Flexible resource3 Reading4 seating4seating2 STEM challenge7 17 52423 50 2714 29 3653 30 189 Figure C16. Week 16 Cumulative Network Circle Plot Week 16 Cumulative Network Circle Plot 28 33 Classroom Classroom Writing2 Reading1 Growth Reading6 Classroom resource4 management1 Character mindset9 Spelling1 Character Back−to−school3 Spelling2 Growth Fun education338 management5 Reading3 education4 mindset3 project2 16 4032 Character Classroom Reading11 education5 Growth Growth Growth Growth Growth Growth management9 mindset11 Reading7 Spelling3 mindset7 Writing3 mindset12 mindset16 Math3 Growth STEM challenge6 Classroom mindset8 mindset2 mindset5 management8 8 12 STEM challenge3 Classroom Growth resource2 mindset1 10 parents1 23 For Writing1 Writing4 31 Character Growth 46 education1 mindset10 Growth mindset4 Spelling4 6 Classroom management4 For parents2 47 Back−to−school4 19 Classroom resource1 Growth mindset15 292 STEM challenge1 Back−to−school2 5 2624 Classroom Math1 Reading2 management3 Back−to−school1 35 1 Math2 Reading4 9 Classroom 22 resource5 Growth mindset13 445439 20 45 17 25 Classroom resource6 Flexible Flexible Reading10 Reading9 seating1 seating2 36 55 13 Classroom resource3 Flexible STEM challenge7 53 seating4 71149 4321 4 14 30 52 342 50 27 190 Figure C17. Week 17 Cumulative Network Circle Plot Week 17 Cumulative Network Circle Plot 21 42 43 35250 27 554811 45 713649 4 145330 25 54 39 2220 44 1 challenge7Classroom resource3 Flexible seating4 9STEM 36 Flexible seating2 Reading9 Flexible seating1 Classroom resource6 Reading10 17 Classroom resource5 Growth mindset13 31 Reading4 35 Classroom Reading2 Back−to−school1 management3 Math1 Math2 Back−to−school2 Classroom Classroom resource1 management1 Classroom management6 Growth mindset15 12 Back−to−school4 Growth ClassroomFor mindset10 parents2 24 5 management4 29 Spelling42 Reading1 Character education5 STEM challenge3 Growth mindset4 Character education1 47 Classroom STEM resource4 challenge6 Writing2 Reading6 Back−to−school3 19 Spelling1 CharacterMath4 Growth Reading11 Classroom Fun Writing4 STEM Growth Growth Growth Growth mindset9 Classroom Growth Writing3 education4 Classroom Spelling2 management9 Reading3 management5 project2 Character challenge1 mindset11 Spelling3 Growth For mindset1 Writing1 mindset5 management8 education3 mindset3 parents1 mindset12 mindset16 Reading7 2346 28 Classroom Growth Growth Growth resource2 mindset8 mindset2 mindset7 Math3 26 10 16 40 33 38 32 8 191 Figure C18. Week 18 Cumulative Network Circle Plot Week 18 Cumulative Network Circle Plot 28 33 12 Character Classroom Reading6 Writing2 STEM education5 challenge3 Back−to−school3 Math4 Fun project2 resource4 38 Growth Spelling1 Classroom Classroom management5 mindset9 resource6 STEM challenge6 Character Growth Growth Classroom Growth Growth education4 Reading7 Spelling2 mindset12 mindset7 Reading11 management7 mindset16 Spelling3 mindset11 40 Growth Classroom Growth Growth Growth Character Classroom mindset3 Reading3mindset8 mindset2 mindset5 management9 education3 management8 Math3 Writing3 328 Classroom management6 Growth mindset1 For parents1 Classroom 16 10 resource2 Writing1 23 Character Growth Reading1 GrowthSpelling4 education1 Writing4 mindset4 mindset10 Classroom management4 For parents2 Back−to−school4 46 Classroom resource5 Growth management1 Classroom mindset15 Classroom resource1 9 1 22 54 Classroom management3 Back−to−school2 47 20 Math2 Math1 Reading2 19 44 Back−to−school1 STEM challenge1 Reading4 2 45 55 48 2539 29 11 26 24 5 13 49 Classroom resource3 Growth mindset13 35 7 43 FlexibleSTEM seating4 challenge7 Reading9 21 6 FlexibleReading10 seating2 Flexible seating1 36 43117 53 52 42 14 30 3 27 50 192 Figure C19. Week 19 Cumulative Network Circle Plot Week 19 Cumulative Network Circle Plot 12 26 28 Classroom STEM resource5 challenge3 STEM challenge1 36 STEM STEM Math2 challenge6 challenge7 Character Classroom education5 Writing4 resource4 Reading6 Back−to−school3 Writing2 44 1 Classroom Character resource6 Spelling1 education4 40 948 Classroom Growth management7 Reading11 Spelling3 mindset8 11 49 Classroom Growth management6 Math4 mindset6 22 Classroom Growth Spelling2 For Growth parents1 mindset11 Reading3 management9 Writing3 mindset12 725 Growth GrowthMath3 mindset16 mindset9 20 45 39 55 436 For parents2 32 13 21 5453 Growth Growth Classroom Reading7 mindset2 mindset7 Writing1 Funmanagement4 42 Classroom resource3 Growth Back−to−school4 Character Spelling4 Reading1 mindset5 project2 8 education1 STEM challenge5 52 Growth mindset433 327 Character Growth 19 education3 mindset1538 50 Reading9 Flexible seating4 Growth Classroom Classroom Classroom mindset1 Math1 management3 management8 management1 resource2 46 Flexible seating2 Growth Classroom mindset10 Classroom management5 23 Flexible seating1 Reading10 Reading2 Back−to−school1 Back−to−school2 Reading4 Growth mindset3 10 16 3014 17 4 Classroom resource1 Growth mindset13 4724 353129 52 193 Figure C20. Week 20 Cumulative Network Circle Plot Week 20 Cumulative Network Circle Plot 16 2410 47 25 23 29 35 46 Classroom Growth Reading2 Back−to−school2 Classroom 38 Back−to−school1 Classroom resource1 mindset3 management5 Classroom resource2 Reading4 Growth management1 mindset13 31 Growth Growth Classroom Character Growth 33 26 Math1 mindset1 mindset10 management8 education3 mindset15 36 Growth Growth19 Writing1 mindset4 mindset5 17 Growth 8For Character Growth Classroom Reading1 education1 Spelling4 mindset7 mindset2 Reading7 management3 parents2 Reading10 Flexible seating1414 Back−to−school4 STEM Classroom Fun project2 challenge1 management4 30 Growth Growth Growth Classroom Writing3 Math3 mindset9 mindset16 mindset12 management9 Reading3 For Growth parents1 mindset11 32Reading11 Growth Classroom Spelling2 Growth STEM mindset6 challenge3 mindset8 management6 Math4 Spelling3 Reading9 50 Flexible seating4 52 40 Character Spelling1 education4 Flexible seating2 273 53 39 Classroom management7 Writing4 42 54 Writing2 Classroom resource6 Reading6 Back−to−school3 Classroom 45 55 625 13 resource3 STEM challenge5 21 43 20 Classroomeducation5 Character resource4 22 9 51 28 48 7 44 4911 Fun project1 STEM challenge6 1 STEMMath2 challenge7 Classroom resource5 12 194 Figure C21. Week 21 Cumulative Network Circle Plot Week 21 Cumulative Network Circle Plot 28 3246 5 840 24 19 2 23 Growth STEM Classroom 26 Back−to−school3 Character Classroom Spelling4 mindset4 Reading1 Writing1 Spelling3 challenge3 Reading6 STEM challenge6 Reading2 education1 resource4 management7 Character Classroom For 31 parents1 Reading3 47 education4 Spelling1 management6 Classroom Classroom Back−to−school2 resource6 management4 Growth ClassroomSpelling2 Classroom mindset8 management9 Growth management1 mindset6 Writing2 38 STEM 12 Back−to−school4 Writing4 For Math1 challenge1 parents2 Writing3 Character Growtheducation5 Reading11 16 mindset11 Growth Growth Growth Classroom Growth Growth Growth mindset2 mindset15 mindset5 Math3 resource1 mindset16 mindset12 mindset1033 ClassroomBack−to−school1 management3 Growth Growth mindset1 mindset7 Reading7 10 GrowthMath4 Classroom mindset9 management8 36 STEM 17 challenge7 Reading4 Character Fun education3 project2 Growth mindset13 Growth mindset3 Reading9 Reading10 Classroom management5 Classroom 29 resource2 Flexible Flexibleseating1 STEM challenge4 seating2 Classroom STEM resource3 challenge5 Math2 Flexible 53 seating4 30 49 35 55 Classroom resource5 524227 50 3 11 Fun project1 4 14 21743 6 44 51 13 14839 152522 945 20 54 195 Figure C22. Week 22 Cumulative Network Circle Plot Week 22 Cumulative Network Circle Plot 10 33 1638 47 23 Classroom Classroom Character Growth Growth FunGrowth management5 mindset3 Math4 project2 Growth Growth Growth Growth Growthmindset1 mindset9 management8 education3 Reading7 Classroom resource1 mindset7 mindset5 mindset10 Math3 mindset12 mindset16 Classroom 29 resource2 Growth Classroom mindset2 Writing3 Reading11 Growth Growth Growth For Classroom mindset15 mindset11 2 40 management9 mindset6 Writing2 parents1 management1 Reading3 35 Classroom Growth Reading2 STEMSpelling2 CharacterWriting1 Spelling1 Character challenge6 management6 mindset8 education48 education5 31 Reading1 Spelling3 46 5 Growth Character mindset4 education1 14 STEMSpelling4 Classroom challenge3 32 management7 Back−to−school3 Reading6 4 Classroom resource4 Classroom Classroom management4 resource6 Back−to−school2 Writing4 28 54 456 Back−to−school4 STEM challenge1 19 24 20 22 939 For parents2 Math1 25481 Back−to−school1 Classroom management3 26 15 51 Fun project1 44 1343 STEM challenge7 49 12 721 Classroom resource5Flexible STEM Reading4 challenge4 11 Flexible STEM Flexible Growth seating4 Classroomchallenge5 Math2 seating1 seating2 Reading10 mindset13 Reading9 resource3 17 36 503 52 27 42 53 55 30 196 Figure C23. Week 23 Cumulative Network Circle Plot Week 23 Cumulative Network Circle Plot 32 28 19 24 46 5 Classroom STEM management4 challenge3 STEM 26 challenge1 8 Writing1 Back−to−school3 Growth STEM Reading1 mindset4 Classroom Reading6 Spelling3 For resource6 parents2 Writing4 Back−to−school2 Back−to−school4 Classroom Classroom resource4 management7 challenge6 Spelling4 40 Character Classroom Character Classroom 2 management1 Spelling1 Reading2 Reading3 Writing2 GrowthSpelling2 For parents1 31 Character education1 Classroom education4 management6 mindset8 education5 Math1 Back−to−school1 management3 Classroom Growth management9 Reading11 mindset15 Reading4 12 Growth Growth Writing3 mindset11 mindset5 STEM 49 challenge7 Growth Growth Growth 23 Math3 mindset2 Growthmindset16 mindset6 mindset12 Growth mindset13 Reading10 Reading9 36 Growth mindset10 Classroom Growth resource1 mindset7 Flexible 17 seating1 Flexible seating2 Growth38 16 Reading7mindset1 33 47Math4 Growth mindset9 Classroom STEM challenge5resource3 Math2 STEM challenge4 Classroom 10 Character education3 Fun project2 management8 Flexible seating4 5530 53 Growth mindset3 52 42 27 Classroom resource5 3 Classroom management5 50 Classroom 29 resource2 11 35 7 4321 Fun project1 13 44 6481 144 25 922 51 15 45 54 3920 197 Figure C24. Week 24 Cumulative Network Circle Plot Week 24 Cumulative Network Circle Plot 23 408 46 32 24 47 16 ClassroomClassroom Character Growth Character management6 Reading1 mindset4 Spelling1 management9 STEM education2 31 education4 challenge3 19 38 For Reading2 Reading11 5Back−to−school2 Growth 29 Growth Writing3 Growth parents1 mindset6 Math3 Classroom mindset11 Character mindset8 Writing2 Reading3 management2 Spelling2 Spelling3 Writing1 education1 Spelling4 Growth Growth 10 Growth Classroom Growth Classroom mindset2Classroom mindset16 mindset12 resource1 mindset7 mindset10 management1 Character Classroom education5 Math1 Classroom resource6 management7 management4 28 Growthmindset15 mindset5 49 Growth GrowthSTEM Reading7 challenge6 mindset1 Back−to−school1 Back−to−school4 26 33 Classroom management8 Classroom For management3 parents2 Reading6 Growth Character mindset9 Classroom Fun project2 resource2 education3 Back−to−school3 Classroom STEM resource4 Writing4 17 challenge1 Growth 2 Math4 mindset3 Classroom management5 STEM 35 challenge2 Reading4 12 Reading9 36 Math2 Growth mindset13 53 Flexible Flexible 14 seating2 seating4 FunSTEMproject1 Reading10 Flexible Classroom seating1 resource3 challenge7 STEM STEM challenge4 challenge5 Classroom resource5 45 5413 342 2255930 20 11 25 48 7 639451 27 43 1 2144 50 52 15 198 Figure C25. Week 25 Cumulative Network Circle Plot Week 25 Cumulative Network Circle Plot 2 35 5 33 31 STEM challenge7 10 49 Classroom STEM Classroom management5 challenge2 Classroom management1 Growth management2 mindset3 Math4 Fun project2 3816 Flexible 14 Flexible Flexible seating4 seating1 seating2 STEM Growth Growth Classroom Classroom Character challenge6 mindset9 mindset15 management8 resource1 education3 3 Classroom 55 resource3 Growth Growth Growth mindset1 Back−to−school2 Growth mindset5 Reading7 mindset10 mindset7 Reading2 STEM challenge5 Growth Growth Growth Growth mindset2 mindset16 mindset12 Reading11 For Math3mindset6 parents1 Character education2 42 13 7 Classroom management7 2940 4723 54 Classroom STEMReading1 Classroom management9 resource6 Writing3 challenge3 STEM3045 11 challenge4 Growth Growth mindset4 mindset11 8 52 50 Growth mindset8 Classroom resource2 Reading3 20 22 Classroom Character management6 Math1education4 46 27 9 25 15 6 Character education1 Spelling2 Spelling1 Spelling4 24 5121 1 Reading10 4 Classroom Classroom Back−to−school1 Spelling3 Writing1 32 management4 management3 39 48 43 Writing2 Back−to−school4 44 For parents2 Character education519 Classroom resource4 Fun project1 Classroom resource5 Growth Math2 Back−to−school3 STEM Reading4 mindset13 challenge1 Reading6 Writing4 1728 26 Reading9 53 36 12 199 Figure C26. Week 26 Cumulative Network Circle Plot Week 26 Cumulative Network Circle Plot 35231 5 33 1038 16 Classroom Classroom management1 STEM Growth management5 Classroom STEM Character challenge6 challenge7 mindset3 23 management2 Math4 education3 STEM challenge2 Growth Growth Classroom Classroom mindset9 mindset1 resource5 management8 Reading2 408 55 14 Growth GrowthFun Classroom Math3 Growth mindset5 project2 Reading4 mindset15 resource1 Back−to−school2 mindset10 Reading7 Flexible 3Flexible 4549 Classroom seating4 seating2 resource3 GrowthGrowth Growth Growth mindset747 mindset6 mindset16 mindset2 Flexible STEM challenge5 seating1 Growth Reading3 mindset12 Reading11 Character 29 education2 For parents1 7 Growth mindset11 Classroom Classroom resource6 management7 Reading1 42 13 52 challenge4 ClassroomSTEM management9 Writing3 46 24 challenge3 STEM 11 Growth Classroom Growth Character mindset4 management6 mindset8 Spelling1 Math1education4 54 30 Character Spelling2 Writing1 Spelling4 32 education1 Classroom Spelling3 management4 Writing2 Back−to−school4 Back−to−school1 50 22 Classroom ForWriting4management3 parents2 20 Character education5 Classroom resource4 159 27 6 25 Reading10 Reading6 Back−to−school3 51121 48 STEM challenge1 Classroom 17 19 resource2 39 41 44 4 43 Fun project1 Growth mindset13 Math2 Reading9 28 53 26 12 36 200 Figure C27. Week 27 Cumulative Network Circle Plot Week 27 Cumulative Network Circle Plot 28 26 17 STEM Reading6 challenge1 36 Classroom19 Back−to−school3 Character 6 For Classroom parents2education5 Classroom resource4 Writing4 Writing2 management3 resource2 Reading9 Math2 12 Classroom Character Spelling3 Writing1 Back−to−school4 management4 Spelling1 Back−to−school1 Spelling4 For education4 Spelling2 parents3 Fun Growthproject1 mindset13 Character Classroom Growth education1 management6 mindset8 53 STEM Character Growth Writing3 Math1 challenge3 education2 mindset4 Classroom management9 Reading1 29 Classroom 32 management7 46 24Reading11 Classroom Growth resource6 mindset11 444 39 41 1 43 4851 21 8For 40 47 parents1 25 15 279 Growth mindset12 20 Growth 23 Growth Reading3 Growth mindset16 mindset2 mindset6 Reading10 22 5450 Growth mindset7 38 Reading7 16 1130 10 Growth mindset10 13 42 52 33 Growth Classroom mindset5 Reading4 Back−to−school2resource1 7 Growth Classroom Growth Growth Character Classroom Fun mindset1 management8 Math3 Reading2 mindset15 mindset9 education3 management2 project2 STEM challenge4 45 Classroom5 STEM challenge6 Math4 Growth mindset3 Classroom management1 STEMresource5 Flexible STEM seating4 challenge7 challenge5 Classroom resource3 55 3 49 Classroom 31STEM Flexible management5 Flexible seating1 seating2 challenge2 14 235 201 Figure C28. Week 28 Cumulative Network Circle Plot Week 28 Cumulative Network Circle Plot 26 28 12 6 36 Character education5 Reading6 Back−to−school3 STEM challenge1 Math2 Writing2 Spelling117 Fun project1 Spelling3 Character education4 Writing4 Spelling2 53 Reading9 Classroom management6 Classroom resource4 19 Growth Character Classroom Classroom Classroom mindset8 education2 For parents2 management9 Back−to−school4 32 resource6 management4 Reading11 Growth STEM Growth Spelling4 mindset6 challenge3 mindset11 44 51 48 4 1 Character Growth GrowthFor education1 mindset16 mindset12 parents1 41 9 43 Reading3 Reading1 1525 20 21 22 Growth Growth Classroom mindset4 mindset2 Classroom Writing3 8 46 resource5 management340 39 Growth Classroom Funmindset7 Reading7 project2 management7 Writing1 Growth Growth Math3 mindset9 mindset538 Classroom resource2 Math4 23 5445 11 Reading4 Classroom For parents3 management2 Math1 Back−to−school1 27 GrowthGrowth Classroom Character mindset1 mindset3 management8 47 2916 education3 33 50 13 Growth Growth mindset10 mindset15 Reading2 24 STEM 14 challenge4 Classroom Back−to−school2resource1 STEM challenge6 10 427 Classroom Classroom management1 management5 STEM challenge7 52 30 STEM Reading10 Flexible Classroom seating4 challenge5 resource3 2 Flexible Flexible STEM seating1 seating2 Growth challenge2 mindset13 315 3 55 49 35 202 Figure C29. Week 29 Cumulative Network Circle Plot Week 29 Cumulative Network Circle Plot 54 22 2115 39 941 2543 20 514414 48 50 13 27 1145 53 427 30 14 52 36 STEM challenge4 Fun Reading9 project1 355 Math2 12 Reading10 49 STEM challenge5 26 Flexible Flexible seating4 Classroom Flexible resource3 seating1 seating2 Growth Character 28 education5 STEMmindset13challenge2 Reading6 Back−to−school3 STEM challenge1 6 35STEM challenge7 Writing2 ClassroomClassroom 31 management1 management5 Writing4 Spelling1 Spelling3 Classroom resource2 5STEMReading2 Classroom challenge6 Back−to−school2 resource1 Classroom Growth Spelling2 Character management6 education4 mindset8 2Growth Classroom For resource4 parents2 Reading11 Character Classroom Growth Growth mindset15 Growth ClassroomForeducation3 mindset1 Reading4 Reading7 Growth Math1 Growth Back−to−school1 Classroom Growth Math3 mindset3 Character Classroom mindset10 Growth Classroom management2 Character mindset5 Growth For STEM Reading3 management8 parents3 Spelling4 Growth mindset9 Growth management3 education2 mindset11 management4 education1 management9 Back−to−school4 parents1 mindset12 challenge3 mindset2 Writing3 Classroom resource6 mindset6 mindset16 17 19 Classroom Growth Growth Math4Writing1mindset4 mindset7 Classroom resource5 Reading1 management7 Fun project2 1024 33 29 16 47 38 40 32 23 46 8 203 Figure C30. Week 30 Cumulative Network Circle Plot Week 30 Cumulative Network Circle Plot 32 46 40 47 8 29 19 Reading1 2316 Character Classroom Classroom CharacterGrowth For ClassroomGrowth Growth STEM For Classroomeducation4 management9 Writing1 management6 mindset16 mindset6 mindset4 challenge3 Reading3 parents1 Spelling4 Writing3 Classroom education2 parents2 Reading11 Back−to−school4 resource6 management7 management4 Growth Classroom mindset7 management8 Back−to−school1 38 17Character Spelling1 GrowthGrowth Growth Spelling2 Spelling3 Growth Classroom Writing2 mindset8 Growth Growthmindset2 mindset12 resource4 education1 mindset11 For Fun project2 parents3 Reading7 Reading4 Growth Growth ClassroomMath1 mindset1 mindset5 mindset9 mindset10 management3 24 10 33 Writing4 Character education5 Growth Classroom Character Math3 Classroom Growth resource5 mindset15 management2 education3 mindset3 Math4 28 Reading6 Back−to−school3 Classroom Reading2resource1 Back−to−school2 Classroom resource2 STEM challenge1 2 STEM challenge6 Classroom management55 6 Classroom management1 31 26 35 STEM challenge7 36 12 Math2 STEM Growthchallenge2 mindset13 Flexible seating2 Fun project1 Flexible Classroom Flexible STEM seating1 resource3 seating4 challenge5 49 53 Reading9 Reading10 55 3 4 STEM challenge4 14 4439481 41 30 925 51 4322202 1 7 42 52 15 54 45 11 27 5013 204 Figure C31. Week 31 Cumulative Network Circle Plot Week 31 Cumulative Network Circle Plot 14 345 55 49 35 Flexible STEM Growth Flexible challenge2 mindset13 seating1 seating2 Classroom management5 31 5 Flexible Classroom STEM Classroom seating4 resource3Classroom challenge5 resource52 management1 52 7 Reading10 Classroom management2 Reading2 33 10 16 STEM 30 challenge4 Growth Character STEM mindset3 Math4 Fun education3 Back−to−school2 24 challenge6 project2 42 Classroom Math3resource1 23 38 13 Growth Growth Growth mindset15 mindset10 mindset9 Reading4 Reading7 5027 11 Growth Growth mindset5 mindset18 Math1 54 Growth Classroom Classroom Classroom mindset7 Formanagement8 management7 management3 46 parents3 22 Growth Reading3 Reading1 4740 29 32 mindset12 20 1521 Growth Growth Classroom Classroom mindset2 mindset6 resource6 Writing3 resource4 25 43 948 Back−to−school1 STEM Growth Classroom Classroom challenge3 mindset4 management6 management4 51 1 41 Classroom Growth Character Character For Spelling4 mindset16 Writing1 Writing2 management9 Back−to−school4 education4 education1 parents1 4439 Character For Growth Reading11 Spelling2 education2 parents2 mindset11 4 Growth Spelling3 mindset8 Spelling1 Flexible seating3 53Fun project1 Reading9 Classroom Back−to−school3 STEM Reading6 Character education5 Writing4 resource2 challenge7 19 Math2 STEM challenge1 17 1236 26 6 28 205 Figure C32. Week 32 Cumulative Network Circle Plot Week 32 Cumulative Network Circle Plot 22 54 50 11 13 42 27 30 52 15 20 51 92521 48 43 challenge47 STEMReading10 355 1 4945 41 44 14 STEM challenge5 Flexible 439 Flexibleseating4 seating1 Flexible seating2 35 FunReading9 project1 STEM Growthchallenge2 Classroom resource3 mindset13 53 31 Math2 5 Classroom management5 Classroom resource5 2 1236 Classroom management1 26 Classroom management2 Reading2 33 STEM challenge1 Classroom 6 resource2 Growth Character Classroom STEM Fun mindset3 Math4 challenge6 16 education3 Back−to−school2 10 resource1 Growth Growth Math3 Growth project2 mindset9 mindset10 mindset15 STEM challenge7 Back−to−school3 28 Writing4 Growth Growth Classroom Growth Growth mindset1 mindset5 Reading4 Reading7 Flexible seating3 management8 mindset6 mindset7 3824 CharacterReading6 education5 Growth Classroom Classroom ClassroomGrowth STEM Reading11 Spelling1 Reading3 For Math1 Reading1 parents3 mindset2 management4 management7 mindset12 management6 Classroom management3 challenge3 23 Character Growth 19Classroom Spelling3 Character Classroom Writing3 mindset8 Growth Back−to−school1 Growth Writing2 Writing1 Back−to−school4 Growth For resource6 education1 mindset4 education4 management9 mindset16 mindset11 parents1 Spelling4 Spelling2 Classroom resource4 17 For Character parents2 education2 Reading5 29 47 46 8 3240 206 Figure C33. Week 33 Cumulative Network Circle Plot Week 33 Cumulative Network Circle Plot 8 32 40 46 47 Character 23 Character Classroom For Character Growth parents1 education1 Spelling2 Writing1 Spelling4 Reading11education2 management6 Writing3 mindset11 Writing2 17 29 Growth Classroom Classroom 24 Classroom Growth Classroom Classroom Classroom Reading3 STEM Reading1 Classroom 38 Growth mindset2 management4 management8 education4 Back−to−school4 For parents3 For Growth Back−to−school1 Growth Spelling1 management9 Spelling3 parents2 mindset4 challenge3 management7 mindset8 Reading5 resource6 mindset16 mindset12 management3 resource4 19 Growth Growth 10 16 Growth Growth Reading4 Flexible mindset1 mindset7 Reading8 Reading7 Growth mindset6 mindset5 seating3 mindset10 Reading6 28 Back−to−school3 Character Growth Classroom 33 STEMFun Math1 Math3 education3 mindset15 resource1 challenge6 project2 Character education5 Writing4 Growth Math4 Back−to−school2 Growth mindset9 Reading2mindset3 Classroom management2 STEM challenge7 6 Classroom Classroom Classroom resource5 2 management1 management5 STEM Classroomchallenge1 resource2 26 5 36 12 STEM Classroom31 challenge2 resource3 Math2 Flexible Growth 35 49 seating2 mindset13 Fun project1 Flexible seating1 Reading9 53 Flexible seating4 STEM challenge5 45 5514 394 3 STEM Reading10 challenge4 7 141 44 52 30 21 48 4325 9 51 42 13 27 11 54 22 20 15 50 207 Figure C34. Week 34 Cumulative Network Circle Plot Week 34 Cumulative Network Circle Plot 35 49 3 31 STEM ClassroomFlexible Flexible Flexible Flexible Growth STEM seating15545 challenge2 seating4 resource3 seating2 mindset13 challenge5 seating3 ClassroomClassroom 5 Spelling1 Classroom management1 management5 Math1 resource5 STEM challenge4 Reading10 14 Growth Growth Math4 Reading2 mindset9 mindset3 42 Back−to−school2 2 752 30 Classroom Growth Classroom STEM management2 Math3 mindset15 resource4 33 Funmanagement4 challenge6 13 ClassroomGrowth Character Classroom Classroom mindset10 education3 project2 management3 resource1 27 50 24 Growth Reading7 Growth 10 mindset6 mindset5 Reading4 11 16 54 Growth Growth Classroom mindset1 mindset7 management8 Reading8 Reading1 Reading3 38 4315 21 22 23 20 Growth Classroom 8 17 mindset12 management7 Back−to−school1 25 9 51 48 1 Growth ClassroomWriting2 mindset16 resource6 Reading5 44 41 Growth Classroom 40 32 STEM Growth Character mindset2 Back−to−school4 challenge3 management6 mindset4 education4 Writing3 Reading9 4 For Growth 46 Forparents1 mindset11 Spelling4 Reading11 parents3 39 Classroom Character For management9 education1 Spelling3 parents2 Spelling2 53 Character Growth 28 education2 mindset8 Writing1 Fun project1 47 19 Reading6 Character Back−to−school3 education5 Writing4 STEM Classroom Math2 612 challenge1 resource2 29 STEM challenge7 36 26 208 Figure C35. Week 35 Cumulative Network Circle Plot Week 35 Cumulative Network Circle Plot 3 55 45 4935 STEM 7 14 Flexible Flexible STEM STEM seating1 seating4 Classroom challenge2 challenge5 Flexible challenge4Growth Flexible resource3 seating2 mindset13 seating3 42 52 Classroom 31 resource5 30 13 Reading10 Classroom management1 ClassroomSpelling1 management5 5 50 11 Classroom Growth management2 mindset9 Reading2 STEM 2 challenge6 Back−to−school2 27 Growth mindset3 Math4 54 Growth Character mindset15 education333 15 22 43 Growth Math3 Reading4 mindset10 20 25 51 21 948 Growth Growth Classroom Classroom mindset1 mindset5 16 resource1 management8 Reading7 Reading8 10 38 4114 44 Growth Growth mindset6 Fun project2 mindset7 Classroom Math1 24 23 management4 39 Reading3 Growth mindset12 8 Classroom Classroom GrowthReading1 Growth mindset16 mindset240 resource4 management7 53 6 GrowthReading5 For mindset11 parents3 Reading11 Classroom resource6 Classroom For parents1 STEM challenge7 Writing3 management6 Fun project1 Classroom ClassroomGrowth Character mindset4 STEMWriting1 challenge3 management9 17 management3 46 education4 32 Reading9 Character Writing2 education2 Back−to−school1 Back−to−school4 Growth Spelling4 mindset8 1236 STEM Math2 For Spelling3 Character challenge1 Spelling2 parents2education1 26 Classroom Reading6 Writing4 Character resource2 Back−to−school3education5 29 47 28 19 209 Figure C36. Week 36 Cumulative Network Circle Plot Week 36 Cumulative Network Circle Plot 53 44 41 4 151 39 21 4825943 15 1236 6 20 22 26 275450 11 Fun project1 Math2 Reading9 13 Reading1030 STEM 28 challenge1 Classroom resource2 42 52 19 17 STEM challenge4 Back−to−school3 47Writing4 7 Reading6 STEM challenge5 For parents2 Flexible 55 seating1 CharacterSpelling2 education5 Spelling3 Flexible seating4 ClassroomBack−to−school1 Character 29 management3 Back−to−school4 Spelling4 education1 mindset133 Growth seating2 Classroom Growth STEM Character Writing2 management9 mindset8 challenge3 Reading5 education4 STEMFlexible 45 challenge2 Character GrowthFor Classroom education2 mindset4 parents1 Writing1resource6 Classroom resource3 Classroom46 Writing3 Growth Classroom management6 Reading11 Growth mindset11 Reading1 mindset16 resource4 32 Classroom Growth Classroom Growth STEMmanagement7 mindset2 Reading3 For management4 mindset12 challenge7 parents3 Classroom Flexible seating3 management51449 35 Classroom Growth Classroom Growth Math1 Growth GrowthReading8 Growth Classroom Growth Character Growth Classroom resource1 mindset7 Reading7 management8 Reading4 Writing5 STEM mindset15 mindset1 Math3mindset5 mindset3 Math4 management2 mindset6 education3 mindset10 Back−to−school2 Fun challenge6 Reading2 project2 management1 Spelling1 Classroom resource5 31 Growth mindset9 4023 38 25 824 1633 10 210 Figure C37. Week 37 Cumulative Network Circle Plot Week 37 Cumulative Network Circle Plot 31 35 3 494555 5 14 33 2FlexibleSTEM Classroom challenge5 resource3 Flexible Flexible Growth seating3 seating47 seating2 mindset13 Classroom 16 Growth STEM Classroom mindset9 resource5 management5 Flexible seating15242 challenge2 Classroom 10 Spelling1 management1 30 38 Reading2 STEM challenge4 13 50 Classroom 24 Back−to−school2management2 Fun project2 Reading10 CharacterFor Growth Growth 8 Math4 education3 parents3 mindset3 mindset6 Reading4 Growth STEM Classroom Growth Growth mindset15 challenge6 Math3 management8 mindset10 mindset5 Growth Classroom Growth 23 Math1 mindset1 Writing5 Reading8 Reading7 resource1 mindset7 11 54 27 Classroom Growth Classroom management4 mindset12 Reading3 resource4 Classroom Growth Classroom Growth Growth management7 Reading1 mindset2 mindset11 Writing2 mindset16 management6 40Writing3 22 20 Writing1 4315 CharacterFor Classroom Growth parents1 Reading11 resource6 mindset4 education4 9 Character Classroom STEM Reading5 Spelling4 education2 challenge3 management9 25 48 51 21 39 Growth Character Classroom mindset8 Spelling2 education1 management3 Spelling3 Back−to−school1 Character Back−to−school4 For education5 parents2 1 441 Fun project1 44 STEM challenge7 3246Reading6 Back−to−school3 Writing4 Reading9 29 STEM Classroom challenge1 resource2 Math2 53 17 47 28 6 36 19 2612 211 Figure C38. Week 38 Cumulative Network Circle Plot Week 38 Cumulative Network Circle Plot 542722 15 20 394394851 25 2144 41 14 11 53 50 13 42 30 36 527 Fun project1 12 Reading10 26 Math2 Reading9 6 STEM 49 challenge4 55 14 45 STEM challenge1 28 3 Flexible Flexible seating1 seating4 19 47 Flexible seating2 35 challenge5 Back−to−school3 STEM challenge2 STEM Writing417 Reading6 Growth mindset13 Classroom Growth resource3 31 mindset9 For Classroom parents2 management3 Spelling3 Classroom management5 Spelling2 Back−to−school4 Back−to−school1 Character Spelling4 Classroom Character Character STEM education1 resource2 education5 education4 challenge3 Classroom Flexible 5 management1 seating3 Classroom Character GrowthReading11 management9 education2 Reading8 Reading1 mindset8 Classroom For Growth parents3 Spelling1 Classroom Classroom Classroom management2 Reading4mindset3 resource5 resource1 Growth For Classroom mindset4 parents1 Writing3 Writing2 resource6 management6 management7 Reading5 Writing1 Classroom resource4 Growth Classroom Classroom Back−to−school2 CharacterReading2 Growth STEM Growth mindset15 education3 Math4 Reading7 mindset6 challenge6 Growthmanagement4 mindset11 management8 Growth mindset2 STEMMath1 challenge7 mindset16 Reading3 2 GrowthGrowth Fun Growth 38 mindset1 Math3 GrowthGrowth mindset5 project2 Writing5 mindset10 mindset12 mindset7 4632 331016 2329 40 8 24 212 Figure C39. Week 39 Cumulative Network Circle Plot Week 39 Cumulative Network Circle Plot 31 314 35 47 45 STEM 5 Flexible Flexible Flexible challenge5 seating2 seating1 seating4 STEM 55 challenge4 Classroom STEM Classroomchallenge2 resource2 resource3 52 Classroom Classroom 29 38 Growth For Classroom management2 2 management1 management5 mindset9 parents3 7 42 13 Growth Reading4mindset1 30 39 Classroom Classroom Character Growth 10 resource1 management8 education3 mindset3 16Fun project2 50 54 49 Growth 33 Growth STEM Growth Reading2mindset6 mindset14 challenge6 mindset5 Back−to−school2 Writing1 4 11 15 22 9 25 Growth Growth 23 Growth Growth Math4 Classroom mindset10 resource5 mindset7 Math3 mindset11 mindset15 20 43 48 Growth 8 Reading7 mindset2 Writing5 Spelling1 Reading5 51 27 41 144 Growth Growth mindset12 Reading3 mindset16 Reading1021 Classroom Classroom 40 For management4 Writing3 parents1 Growth Flexible management6 mindset13 seating3 Classroom Character 2446 management7 education2 53 ClassroomGrowthReading1 Classroom management9 Reading11 Character resource6 education5 mindset4 Growth mindset8 36 32 Character Writing2 Reading8 education1 Spelling4 Spelling2 Fun project1 Character STEM Classroom education4 challenge3 Math1 Spelling3 resource4 For parents2 STEM challenge7 Back−to−school1 Math2 6 Back−to−school4 Classroom Reading6 management3 Writing4 Reading9 STEM challenge1 26 12 Back−to−school3 17 1928 213 Figure C40. Week 40 Cumulative Network Circle Plot Week 40 Cumulative Network Circle Plot 5 38 292 10 163323 Classroom Classroom For Reading4 management1 Classroom resource1 management2 parents3 8 Classroom 31 Classroom STEM Growth Classroom Growth ClassroomGrowth management5 Character Classroom challenge2 Growth Fun Growth mindset9 resource3 resource2 STEM resource5 Growthmindset1 mindset3 mindset6 education3 Math4 Back−to−school2 Reading2 Growthproject2 mindset5 management8 mindset10 challenge6 mindset14 Math3 Spelling1 Writing1 40 STEM challenge5 Growth Growth Growth Growth Reading5 mindset15 mindset7 mindset11 Reading7 Writing5 mindset2 24 Flexible seating2 Growth mindset16 14 Classroom Reading3 Growth mindset12 management4 46 Flexible 47 3 35 seating1 Flexible seating4 Flexible Classroom seating3 management6 Classroom Writing3 management7 ForReading1 parents1 Character 32 education5 STEM challenge4 Character Classroom Classroom education2 Math1 management9 Reading11 Growth resource6 mindset4 45 55 Growth mindset8 Reading8 Writing2 STEM Character Spelling4 Character challenge3 education4 education1 Spelling2 STEM challenge7 Spelling3 Classroom resource4 7 Back−to−school4 Back−to−school1 For parents2 Reading6 52 Classroom Writing4 17 management3 42 Classroom Back−to−school3 resource7 1315 39 30 4 Growth mindset13 54 50 49 STEM challenge1 Reading9 19 Reading10 28 22 25 11 20 943 48 Math2 51 4127 1 Fun project1 44 21 6 53 36 1226 214 Figure C41. Week 41 Cumulative Network Circle Plot Week 41 Cumulative Network Circle Plot 5 38 292 10 163323 Classroom Classroom For Reading4 management1 Classroom resource1 management2 parents3 8 Classroom 31 Classroom STEM Growth Classroom Growth ClassroomGrowth management5 Character Classroom challenge2 Growth Fun Growth mindset9 resource3 resource2 STEM resource5 Growthmindset1 mindset3 mindset6 education3 Math4 Back−to−school2 Reading2 Growthproject2 mindset5 management8 mindset10 challenge6 mindset14 Math3 Spelling1 Writing1 40 STEM challenge5 Growth Growth Growth Growth Reading5 mindset15 mindset7 mindset11 Reading7 Writing5 mindset2 24 Flexible seating2 Growth mindset16 14 Classroom Reading3 Growth mindset12 management4 46 Flexible 47 3 35 seating1 Flexible seating4 Flexible Classroom seating3 management6 Classroom Writing3 management7 ForReading1 parents1 Character 32 education5 STEM challenge4 Character Classroom Classroom education2 Math1 management9 Reading11 Growth resource6 mindset4 45 55 Growth mindset8 Reading8 Writing2 STEM Character Spelling4 Character challenge3 education4 education1 Spelling2 STEM challenge7 Spelling3 Classroom resource4 7 Back−to−school4 Back−to−school1 For parents2 Reading6 52 Classroom Writing4 17 management3 42 Classroom Back−to−school3 resource7 1315 39 30 4 Growth mindset13 54 50 49 STEM challenge1 Reading9 19 Reading10 28 22 25 11 20 943 48 Math2 5141 27 1 Fun project1 4421 6 53 36 1226 215 Figure C42. Week 42 Cumulative Network Circle Plot Week 42 Cumulative Network Circle Plot 44 41 1 51 21 25 920 48 43 11454 5013 22 39 27 30 1549742 52 53 Reading10 Fun project1 55 4547 36 12 STEM challenge4 266 14 3 35 Math2 Reading9 Flexible Flexible seating1seating4 STEM challenge1 Flexible seating2 STEMchallenge2 STEM challenge5 31 28 19 Classroom Growth mindset9 resource3 ClassroomWriting4 resource7 Classroom resource5 Back−to−school3 Reading6 Classroom Classroom Reading2 management1 management5 Formanagement2 parents3 5 Classroom For management3 parents2 Back−to−school1 Back−to−school4 Classroom Character Classroom Classroom resource2 Growth mindset13 education3 management8 17 Spelling3 STEM Character STEM challenge7 Spelling2 Spelling4 Classroom education1 challenge3 resource4 Growth Growth STEM Growth Growth Growth Growth Math3 Fun Classroom mindset1 Reading4 project2 mindset3 resource1 challenge6 mindset6 mindset14 mindset15 Back−to−school2 Writing5 Spelling1 mindset10 382 Growth Reading11 Classroom Character Character Classroom Classroom Growth Character mindset8 education4 Classroom For Writing2 Reading8 Classroom Growth Growth education2 Flexible Growth mindset4Math1 education5 Reading1 mindset11 Reading7 Math4 mindset7 management6 management4 Growth parents1 Writing3 mindset5 seating3 Reading3 management7 management9 Growth mindset22916 mindset12 resource6 Writing1 Reading5 Growth mindset16 10 33 23 3246 40 24 8 216 Figure C43. Week 43 Cumulative Network Circle Plot Week 43 Cumulative Network Circle Plot 17 3246 For 19 Reading6 Classroom Classroom parents2 Character STEM Spelling3 management3 Character Classroom Growth Classroom Back−to−school4Spelling2 Back−to−school1 STEM education4 Reading8 challenge3 Writing2 education1 Character resource7 Growth mindset13 management9 mindset8 resource4 Reading1 Reading11 Spelling4 GrowthReading9 mindset4 challenge7 education5 4024 Back−to−school3 28 Writing4 Character Classroom Classroom education2 resource6 Writing3 management7 For parents1 Classroom Growth Classroom management6 mindset16 management4 Writing1 8 STEM challenge1 Growth Growth Reading3 Flexible mindset12 Math1 mindset2 seating3 Reading5 GrowthReading7 Growth mindset11 mindset723 6 Writing5 26 Math2 36 Growth Growth Growth Growth mindset5 mindset10 Spelling1 mindset1416 mindset15 33 2910 12 Growth Classroom Math4 mindset6 Back−to−school2 management8 Math3 Reading4 Growth Character GrowthSTEM Classroom mindset138 education3 challenge6 Fun mindset3 resource1 project2 Fun project1 Classroom management2 Reading2 For parents3 2 Classroom Classroom management5 management1 Classroom resource5 53 Growth Classroommindset9 resource2 Classroom resource3 STEM STEM challenge5 challenge2 5 Flexible seating2 1 21 44 41 Flexibleseating1 Flexible seating431 48 51 43 925 2720 2211 Reading10 STEM challenge4 394 54 35 47 14 50 30 13 15 52 49 45 55 3 427 217 Figure C44. Week 44 Cumulative Network Circle Plot Week 44 Cumulative Network Circle Plot 55 524249 13 7 30 50 15 335 45 47 54 3911 14 20 4 222551 9 27 43 48 31STEM challenge4 41 144 Flexible seating1 Reading10 21 Flexible seating4 Flexible 5 seating2 STEM challenge2 STEM challenge5 53 Classroom Growth resource3 mindset9 Classroom Classroom Classroom For38 management1 resource2 Classroom resource5 management5 parents3 2 Reading2 Fun project1 Classroom Classroom Growth 29 Growth management2 resource1 mindset1 mindset3 Character Classroom STEM Growth Reading4 Math3 education3 Funchallenge6 project2 management8 mindset6 Spelling1 Back−to−school2 Math2 12 Growth Growth 1016 Growth Growth Math4 33 Reading7 mindset14 mindset10 mindset5 mindset15 Writing5 36 Growth Growth mindset7 mindset11 626 Growth Reading5 Flexible seating3 mindset2 STEM challenge1 Classroom 23 Growth GrowthReading3 Writing1 mindset12 mindset16 management4 Classroom Classroom management6 ForWriting3 parents1 management7 8 Character ClassroomReading1 Growth Character Classroom Growth education2 resource6 Reading11 Reading9 Math1 mindset4 education5 management9 Spelling4 Writing2 Spelling2 Classroom mindset8 Writing4 Back−to−school3 Reading6 Back−to−school1 resource7 28 Character STEM Classroom Character Back−to−school4 Reading8 Classroom Spelling3 education1 For challenge3 resource4 STEM management3 parents2 challenge7 education4 Growth mindset13 19 24 40 46 17 32 218 Figure C45. Week 45 Cumulative Network Circle Plot Week 45 Cumulative Network Circle Plot 19 Writing4 2612 Back−to−school3 Classroom ClassroomGrowthSTEM challenge1 resource7 mindset13 management3 Math2 36 For 17 Back−to−school4 parents2 Reading6 STEM challenge7 Back−to−school1 Fun project1 6 Character Character STEM Spelling3 Reading9 Spelling2 28Spelling4 education1 education4 challenge3 Growth Classroom GrowthReading11mindset8 management9 Math1 Reading8 mindset4 53 32 Character Character 46 Classroom Reading1 education5 education2 resource4 Classroom Classroom Writing2 For parents1 Writing3resource6 management7 Classroom Writing1 40Reading5 management6 44 41 37 1 Growth 24 mindset16 4721 Classroom Growth Reading3 management4 mindset12 4851 9 25 Growth Growth Flexible mindset2 8Classroommindset11 seating3 resource2 43 39 20 22 427 23 Writing5 11 54 Growth STEM Growth Growth mindset7 Reading7 challenge6 mindset15 mindset10 Reading10 Growth Growth mindset5 mindset14 Math4 Math3 50 15 30 13 Growth Classroom Back−to−school2 Growth mindset6 management8 Reading4 1029Funmindset1 3316 Spelling1 42 Classroom resource1 752 project2 Growth Character Classroom mindset3 education3 Reading2 2 For management2 38 parents3 49 Classroom Classroom Growth management5 management1 Classroommindset9 resource5 45 ClassroomSTEM Flexible STEM 5 challenge2 resource3 seating2 Flexible Flexible STEM challenge5 seating4 seating1 challenge4 55 14 35 31 3 219 Figure C46. Week 46 Cumulative Network Circle Plot Week 46 Cumulative Network Circle Plot 19 Back−to−school3 17 Reading8 Writing4 STEM challenge1 Classroom Reading6 Back−to−school4 For STEM Spelling3 parents2 management3 challenge7 Back−to−school1 Math2 26 Character Classroom Growth Character Growth STEM28 Spelling4 Spelling2 Reading9 Reading11 education1 resource7 mindset8 education4 mindset4 challenge3 12 36 Classroom Character 32 Writing3 Reading1 Math1management9 education2 Fun 6 project1 Classroom For Character 46Writing1 management7 Writing2 parents1 education5 Classroom Classroom Growth management6 resource6 mindset16 Growth mindset13 53 Classroom Classroom Growth 40Reading5 Growth management4 resource4 mindset12 Reading3 mindset2 Growth Flexible mindset11 seating3 37 Growth 24Reading7 mindset7 44 41 1 21 8 Growth mindset5 48 4351 9 25 Growth Growth mindset15 Classroom mindset14 management8 20 22 427 39 Growth Growth 23 16 mindset10 mindset1 11 54 Back−to−school2 STEM Growth Spelling1 29Math4 challenge6 mindset6 7 10 Character 33 Classroom Reading4 Math3 Classroom 38Fun education3 resource5 project2 resource1 47 ClassroomGrowth For management2 2Classroom mindset3 Reading2 parents3 Writing5 resource2 13 50 30 15 Classroom management1 Classroom management5 Reading10 4252 Growth 5 mindset9 Classroom STEM Flexible STEM resource3 challenge2 seating2 Flexible challenge5 Flexible STEM seating4 seating1 challenge4 31 45 14 49 55 335 220 Figure C47. Week 47 Cumulative Network Circle Plot Week 47 Cumulative Network Circle Plot 10 33 23 8 24 40 32 16 46 2 29 Growth GrowthSTEM GrowthGrowth Reading7 mindset3 mindset6 Math4 mindset5 Flexible Fun Spelling1 Growth mindset7 Writing1 project2 Reading3 challenge6 mindset15 Growth seating3 mindset12 mindset11 17 Growth Classroom Classroom Character 38 Reading4 Back−to−school2 Reading2 Growth Classroom Growth mindset1 resource3mindset10 education3 Math3 ClassroomGrowth Classroom Classroom mindset2 Classroom resource5 management8 Classroom Classroommanagement4 mindset14 resource2 mindset16 Writing3resource4 management7 Reading5 management6 resource6 Classroom Classroom For management2 Writing5 parents3 resource1 Character Classroom Reading1 For Growth Growth STEM parents1 Reading11 28 mindset4 education2 management9 Writing2 mindset8 challenge3 Reading9 Classroom 5 management5 Character CharacterSpelling2 STEM education5 Reading8 education4 Spelling4 challenge7 Spelling3 Math1 Classroom Growthmanagement1 Flexible mindset9 seating2 Character Classroom Back−to−school4 education1 resource7 Back−to−school1 STEM Growth mindset13 STEMchallenge5 challenge2 Classroom Reading6 For management3 parents2 Back−to−school3 31 7 Flexible seating4 Flexible 3 seating1 Writing4 STEM challenge1 STEM35 challenge4 55 19 49 5214 Math2 45 Fun project1 Reading10 26 42 6 3612 30 5013 54 47 53 15 3911 43 48 4 37 2225 20 927 5144 1 4121 221 REFERENCES 222 REFERENCES Adler, P. 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