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Preparing Teachers to Integrate Computer Programming Into Mathematical Problem Solving Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By David D. P. Ely, B.A., M.Ed. Education Teaching and Learning The Ohio State University 2016 Dissertation Committee: Dr. Patricia Brosnan, Advisor Dr. Christopher Stewart Dr. Lin Ding Copyright by David D. P. Ely 2016 Abstract Responding to the call of the Association for Computing Machinery (ACM) and the CS/10K Project for the development of models to train K – 12 Computer Science teachers, this study examined the effectiveness of a 3-week intensive summer workshop to prepare secondary mathematics teachers to integrate computer programming into mathematical problem solving. The workshop, using the C programming language, was built off of pedagogical principles that emphasized hands-on primary learning, a well- crafted sequential set of learning tasks, applications from mathematics, extensive group work, minimal lecturing, numerous discussions, and a focus on problem solving and logic instead of syntax, Specifically, the study examined if the workshop could effectively prepare and motivate secondary mathematics teachers to integrate computer programming into the study of classical probability problem solving. The teacher participants were measured on 1) their ability to solve probability problems with and without computer programming, 2) their self-efficacy to teach programming and probability, and 3) their change in motivation levels to integrate computer programming into their teaching of mathematics. Mathematics teachers from grades 7 -14 were the target audience for this workshop as they were deemed the most likely teachers to benefit from incorporating ii computer programming into the classroom. In order to connect with these teachers, classic probability was the chosen mathematical discipline for exploring computer programming. Probability is now taught at grades 6 and beyond in mathematics classrooms, yet many teachers are uncomfortable with the subject. Experimental probability through programming models and simulations offers an alternate route to the traditional, and sometimes unattainable, theoretical probability models. Using measurement tools of probability tests, surveys, and journal submissions, the study concluded that the workshop had 1) a significantly positive impact on improving the teacher’s performance of classical probability problems, 2) a significant increase in teachers’ comfort levels in using programming for probability problem solving, and 3) a significant increase in comfort and motivation to incorporate programming teaching. A follow-up on one of the teachers found he had successfully implemented portions of the workshop curriculum in a middle school class just two months after completing the workshop. iii Dedication For my mother Jeanette, whose endless support has made all of the difference iv Acknowledgments I wish to thank my advisor Dr. Patricia Brosnan for guiding me through the long and arduous Ph.D. process and for believing in my ideas and supporting my convictions. I wish to thank Dr. Lin Ding for inspiring me in the classroom and challenging my understanding of science. I wish to thank Dr. Christopher Stewart for over seven years of support, which he selflessly offered long after the focus of my studies changed from computer science to mathematics education. v Vita 2004 ………………....B.S. Mathematics & Computer Science, Lewis & Clark College 2006 ………………….M.Ed. Mathematics Education, Portland State University 2006 to present ………Licensed Advanced Mathematics Teacher, Oregon 2006 – 2008 …………Secondary Mathematics Teacher, West Linn High School, Oregon 2008 – 2011 …………Graduate Teaching and Research Associate, Department of Computer and Information Sciences, The Ohio State University Summer 2014.............Adjunct Instructor, Department of Mathematics & Statistics, Portland State University. 2011-2015 …………..Graduate Teaching Associate, Intern Supervisor, Department of Curriculum and Instruction, The Ohio State University 2015 –present ……….Sabbatical Replacement, Department of Mathematics and Computer Science, Lewis & Clark College Publications J. Mache, D. Ely, M. Gilbert, J. Gimba, T. Lopez and M. Wilkinson, Modifying the Overlay Network of Freenet-style Peer-to-Peer Systems after Successful Request Queries, Proceedings of the 37th Hawaii International Conference on System vi Sciences (HICSS) (Peer-to-Peer Ecommerce Systems and Applications Minitrack), 2004 D. Ely and J. Mache, The "Bread-Crumb" Algorithms: Improving the Performance of Freenet-style Peer-to-Peer Systems, Proceedings of the Oregon Academy of Science, 2004 Fields of Study Major Field: Education Teaching and Learning Specializations: STEM Education and Doctoral courses in Computer Science vii Table of Contents Abstract ............................................................................................................................... ii Dedication .......................................................................................................................... iv Acknowledgments............................................................................................................... v Vita ..................................................................................................................................... vi List of Tables ................................................................................................................... xiii Chapter 1: Introduction ...................................................................................................... 1 Why Mathematics Teachers .......................................................................................... 4 Teacher Workshop ........................................................................................................ 4 Problem Statement ........................................................................................................ 7 Why probability ....................................................................................................... 8 Theoretical vs. experimental methods .................................................................. 10 Modeling vs. simulation ........................................................................................ 12 Programming vs. statistical-software ................................................................... 14 Plan ............................................................................................................................. 16 Chapter 2: Review of the Literature................................................................................. 17 Challenges to Learning Probability ............................................................................ 17 Teachers’ Preparedness to Teach Probability ............................................................. 21 viii Ease-Of-Use vs. Learning Benefits of Technology and Programming ...................... 23 Simulation/modeling software .............................................................................. 24 General-purpose programming tools ................................................................... 28 Effective Training for Teaching Computer Programming .......................................... 32 Challenges to effective teacher preparation ......................................................... 32 Offering more effective preparation through CGI ................................................ 35 Training teachers in computer science ................................................................. 39 Probability and Computer Programming in Common Core State Standards ............. 41 Summary ..................................................................................................................... 44 Chapter 3: Design Description ......................................................................................... 46 Subjects ....................................................................................................................... 47 Workshop Description ................................................................................................ 48 Theoretical framework .......................................................................................... 49 Environment, length, and typical day ................................................................... 51 Instructional programming tasks .......................................................................... 53 I/O ................................................................................................................... 56 Mathematics constructs .................................................................................. 56 Conditional statements.................................................................................... 57 Loops ............................................................................................................... 58 Arrays .............................................................................................................. 60 Measurement Tools, Data Collection Methods, and Analysis .................................... 62 ix Tests ...................................................................................................................... 63 Surveys .................................................................................................................
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