University of New Mexico UNM Digital Repository Organization, Information and Learning Sciences Electronic Theses and Dissertations ETDs Fall 11-15-2018 LEARNING STATISTICS THROUGH GUIDED BLOCK PLAY: A PRE- CURRICULUM IN STATISTICAL LITERACY Robert P. Giebitz University of New Mexico - Main Campus Follow this and additional works at: https://digitalrepository.unm.edu/oils_etds Part of the Early Childhood Education Commons, Educational Psychology Commons, Elementary Education Commons, Indigenous Education Commons, Organization Development Commons, and the Statistics and Probability Commons Recommended Citation Giebitz, Robert P.. "LEARNING STATISTICS THROUGH GUIDED BLOCK PLAY: A PRE-CURRICULUM IN STATISTICAL LITERACY." (2018). https://digitalrepository.unm.edu/oils_etds/53 This Dissertation is brought to you for free and open access by the Electronic Theses and Dissertations at UNM Digital Repository. 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Robert Giebitz Candidate Organization, Information & Learning Sciences Department This dissertation is approved, and it is acceptable in quality and form for publication: Approved by the Dissertation Committee: Patricia Boverie, Chairperson Nick Flor Karl Benedict Sylvia Celedón-Pattichis LEARNING STATISTICS THROUGH GUIDED BLOCK PLAY A PRE-CURRICULUM IN STATISTICAL LITERACY By ROBERT GIEBITZ B.S., Basic Sciences, New Mexico Institute of Mining and Technology, 1980 M.S., Management/Human Resources Management, Florida Institute of Technology, 1989 DISSERTATION Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Organization, Information & Learning Sciences The University of New Mexico Albuquerque, New Mexico December, 2018 iii ©2018, Robert Giebitz iv Dedication Knowledge is as wings to man’s life, and a ladder for his ascent. Its acquisition is incumbent upon everyone. Endeavor to the utmost of thy powers to establish the word of truth with eloquence and wisdom and to dispel falsehood from the face of the earth. – Bahá’u’lláh v Acknowledgements My heartfelt gratitude to: My committee chair Patsy for her continual support, guidance, and encouragement. Sylvia, Nick, and Karl for serving on my committee and giving great feedback. Bob for many cups of coffee and a ton of great music. Lani, Greg, Ruth, and Cheryl each of whom had a special gift along the way. Chris and Linda who cleared many obstacles and kept me on track. Doris and Nora, partners in making the invisible visible with statistical tools. Linda, Linda, and Theo, my Dalian friends who helped me get started. My students at Dong Cai Da Xue who reminded me it was time to go back to school. Especially my wife Amalia for years of unwavering support and encouragement. vi LEARNING STATISTICS THROUGH GUIDED BLOCK PLAY A PRE-CURRICULUM IN STATISTICAL LITERACY By Robert Giebitz B.S., Basic Sciences, New Mexico Institute of Mining and Technology, 1980 M.S., Management/Human Resources Management, Florida Institute of Technology, 1989 Ph.D., Organization, Information & Learning Sciences, University of New Mexico, 2018 ABSTRACT Learning to use data to investigate the world and make decisions has become an essential skill for all citizens. Play and curiosity are powerful motivators for learning. Inquiry – the process of asking questions and seeking answers – can engage the natural curiosity of young learners and motivate early learning. Recent research in statistics education has shown that children as young as 4 and 5 years old can learn to collect, organize, and interpret data they acquire through observation, counting, and measuring in a process of guided inquiry. Guided block play has been used for over 100 years to enable children to interact with mathematical structures paving the way for abstract understanding. Jerome Bruner conjectured that playing with a concept in concrete form prepares the mind for later abstract understanding and can begin at any age. Interaction with an embodied concept engages sensorimotor faculties and initiates neuronal activity that leads to useable knowledge grounded in experience. The frequency distribution is a core concept of statistics. Simple wooden cubes can be arranged on a ruler in the form of an embodied frequency distribution. This multiple case study explores how interaction with concrete representations of data structures in guided block play vii can engage learners in grades K-2 and lay a foundation for understanding a data set as an aggregate with emergent properties of shape, spread, and center. Activity Theory provides a flexible theoretical framework for describing the interactions and explaining the outcomes of a series of exploratory tutorial sessions. It is further conjectured that this early experience with embodied learning enjoyed in the first years of formal schooling may prevent statistics anxiety and misconceptions in later years. viii Table of Contents List of Figures ....................................................................................................................... xiii List of Tables ......................................................................................................................... xv Chapter 1: The Statistical Literacy Imperative ................................................................... 1 Data Literacy and Statistical Literacy ........................................................................... 1 Data-Driven Decision-Making and Dialogue ............................................................... 3 Data Visualization ......................................................................................................... 4 The Challenge of Developing Statistical Literacy, Reasoning and Thinking ............... 7 Transformation of Society .......................................................................................... 12 Learning through Movement, Play, and the Use of the Hands ................................... 14 Exploring a Pre-curriculum in Statistical Literacy ..................................................... 15 Chapter 2: Literature Review .............................................................................................. 18 Inquiry, Knowledge, and Logic .................................................................................. 18 Knowledge is the Outcome of an Inquiry Process .......................................... 20 Science and Common Sense Share Common Ground .................................... 22 Science is Packaged in a Cultural Wrapper .................................................... 23 Inquiry-Based Teaching and Learning ............................................................ 25 Movement, Cognition, and Thinking with the Hands................................................. 26 Kinesthetic Consciousness and Symbolic Thought Evolved through Movement ........................................................................................... 27 The Hand Played a Decisive Role in the Evolution of Cognition .................. 29 Cognition is Embodied, Situated, and Distributed...................................................... 31 Play ......................................................................................................................... 34 ix Play-based Learning........................................................................................ 36 Learning through Block Play .......................................................................... 37 Statistics Education ..................................................................................................... 39 The Challenges of Teaching and Learning Statistics ...................................... 39 The GAISE Framework .................................................................................. 41 Learning Statistics with Manipulatives ........................................................... 43 A Conceptual Framework for Building Statistical Literacy ....................................... 44 Activity Theory ............................................................................................... 45 Learning Trajectories ...................................................................................... 46 Chapter Summary ....................................................................................................... 47 Chapter 3: Methods .............................................................................................................. 49 Study Design ............................................................................................................... 49 Exploratory Case Study Methods ................................................................... 49 Multiple Case Studies ..................................................................................... 51 Dynamics of the Learning Sessions ................................................................ 52 Participants ...................................................................................................... 52 Data Collection ........................................................................................................... 54 Videotaping and Interaction Analysis ............................................................. 54 Analytic Rubrics ............................................................................................. 55 Structure of