Second Chance At First Life: Fostering The Mathematical and Computational Agency Of At-Risk Youth by Sneha Veeragoudar Harrell B.A. (University of California, Berkeley) 1998 M.A. (Columbia University) 2001 A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Education in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Dor Abrahamson, Chair Professor Michael Clancy Professor Andrea diSessa Professor Jabari Mahiri Spring 2009 Second Chance At First Life: Fostering The Mathematical and Computational Agency Of At-Risk Youth © 2009 by Sneha Veeragoudar Harrell Abstract Second Chance At First Life: Fostering The Mathematical and Computational Agency Of At-Risk Youth by Sneha Veeragoudar Harrell Doctor of Philosophy in Education University of California, Berkeley Professor Dor Abrahamson, Chair In the USA, women and many ethnic minority groups are underrepresented in Science, Technology, Engineering, and Mathematics (STEM) professions. Amidst the failure of federal responses, e.g., NCLB, to reach students by operating at the school level, this dissertation explores the viability of a campaign to reach each individual student and mobilize and empower them as agents in their own STEM learning. At an alternative high school serving predominantly at-risk underrepresented students evicted from mainstream education, I implemented Fractal Village, a critical/computational/constructionist-pedagogy (C3) learning environment of my design. Fractal Village, instantiated in the virtual-world "Second Life," constituted an empirical environment to research my emergent model of mathematical/computational agency (m/c) as well as an intervention aiming to foster such agency. Key research objectives were to: (1) study relations amongst cognitive, affective, material, technological, and social factors that would contribute to individual development of m/c agency; (2) 1 delineate design principles for fostering m/c agency; (3) implement a sustainable program in collaboration with school personnel. The student cohort engaged collaboratively in virtual-world imaginative construction activities each manifesting generative themes (Freire, 1968), to which the designers-as-teachers tailored mathematical and computer-science concepts, such that students appropriated the STEM content apropos of tackling their own emergent construction problems. Through the lens of three case studies, I argue that to build agency, students must develop both skills and dispositions—a spiraling inter-constructive growth. Student S., a self-professed gang member who could not imagine his post high school future at the beginning of the study, expressed interest in becoming an architect after learning basic programming concepts while constructing a virtual skyscraper. Student B., categorized as Special Education with an Individual Education Plan limiting his intellectual activity to 20-minute durations, realized for the first time ever that he could become an engineer after engaging in 110-minute demanding sessions. Student D, however, discontinued participation in the project, underscoring the imperative to sensitively evaluate in-coming students' skills and dispositions. I conclude that we can, and must, engage at-risk youth by helping them to build STEM identities, engaging their a priori m/c agency, and customizing skills and dispositions-related classroom discursive supports. 2 DEDICATION Dedicated with affection and deep gratitude to members of the Veeragoudar and Khemalapure families that have come before me, whose love, labour, and sacrifice has made my journey possible. A special thank you Mom and Dad for your caring, generosity, and devotion— your bravery and courage in your quest to provide your children opportunities knows no bounds. Thank you Veerendra for your love and support. Fox, thank you for love and faith. Lastly, I wish to recognize the importance of those individuals who will come after me, those on the margins who struggle and fight with honor for emancipation. i TABLE OF CONTENTS INTRODUCTION ........................................................................................................ 17 Conceptualizing M/C Agency ................................................................................... 19 Investigating Agency Through Designing and Implementing Fractal Village ............ 22 Research Questions................................................................................................... 26 Implementing & Studying Fractal Village: Methods and Findings Overview............. 27 Skills and Dispositions.............................................................................................. 29 Skills..................................................................................................................... 30 Dispositions .......................................................................................................... 30 Summary............................................................................................................... 32 Students’ M/C Agency Development ........................................................................ 33 Overview of Chapters ............................................................................................... 35 THEORETICAL FRAMEWORK................................................................................. 37 1. Pedagogical Commitment: Critical, constructionist, computational literacy (C3) + Imagination............................................................................................................... 37 2. Student Cognition as Situated, Distributed, and Embodied .................................... 43 3. Relevant literature pertaining to factors contributing to mathematical agency........ 44 From Theory to Design: Harnessing Visions of Change ............................................ 47 METHODS................................................................................................................... 49 Participants ............................................................................................................... 49 Materials................................................................................................................... 49 Technology ........................................................................................................... 49 Virtual Location.................................................................................................... 50 ii Journals................................................................................................................. 51 Procedure.................................................................................................................. 51 Pre-Intervention Procedure.................................................................................... 51 Assembling the Research Team......................................................................... 51 Locating a Research Site and Securing Access .................................................. 52 During-Intervention Procedure.............................................................................. 56 Extending an Invitation ..................................................................................... 56 Logins and Avatars............................................................................................ 57 Customizing the Curriculum.............................................................................. 57 Customizing Mathematical and Computational Content .................................... 58 Daily Debrief of Fractal Village Research Team Members ................................ 59 Extra-Curricular Activities ................................................................................ 59 Data collected ........................................................................................................... 60 Follow-Up Data .................................................................................................... 62 Data Analysis............................................................................................................ 62 Coding Scheme ..................................................................................................... 64 Interrater Reliability.............................................................................................. 67 RESULTS AND DISCUSSION.................................................................................... 68 Case Studies.............................................................................................................. 68 Overview .............................................................................................................. 68 Case Study One: Shahzor’s Agency Construction.................................................. 73 Snapshots: Beginning and End .......................................................................... 73 Family Background........................................................................................... 74 iii School History................................................................................................... 75 Relationship With the Researchers .................................................................... 77 Overview of Activity and Growth...................................................................... 80 Skill and Disposition Development...................................................................