AN EXAMINATION OF THE POTENTIAL OF SECONDARY MATHEMATICS CURRICULUM MATERIALS TO SUPPORT TEACHER AND STUDENT LEARNING OF PROBABIILITY AND STATISTICS by Joshua E. Williams B. S., Clarion University, 2000 M. S., Salisbury University, 2006 Submitted to the Graduate Faculty of The School of Education in partial fulfillment of the requirements for the degree of Doctor of Education University of Pittsburgh 2016 UNIVERSITY OF PITTSBURGH THE SCHOOL OF EDUCATION This dissertation was presented by Joshua E. Williams It was defended on September 7, 2016 and approved by Dr. Ellen Ansell, Associate Professor, Instruction and Learning Dr. James Greeno, Emeritus Professor, Standford University Dr. Mary Kay Stein, Professor, Learning Science and Policy Dissertation Advisor: Dr. Margaret S. Smith, Emeritus Professor, Instruction and Learning ii Copyright © by Joshua E. Williams 2016 iii AN EXAMINATION OF THE POTENTIAL OF SECONDARY MATHEMATICS CURRICULUM MATERIALS TO SUPPORT TEACHER AND STUDENT LEARNING OF PROBABIILITY AND STATISTICS Joshua E. Williams, EdD University of Pittsburgh, 2016 The Common Core State Standards for Mathematics (CCSSSM) suggest many changes to secondary mathematics education including an increased focus on conceptual understanding and the inclusion of content and processes that are beyond what is currently taught to most high school students. To facilitate these changes, students will need opportunities to engage in tasks that are cognitively demanding in order to develop this conceptual understanding and to engage in such tasks over a breadth of content areas including probability and statistics. However, teachers may have a difficult time facilitating a change from traditional mathematics instruction to instruction that centers around the use of high-level tasks and a focus on conceptual understanding and that include content from the areas of probability and statistics that may go beyond their expertise and experience. Therefore, curriculum materials that promote teacher learning, as well as student learning, may be a critical element in supporting teachers’ enactment of the CCSSM. This study examines three secondary mathematics curriculum materials with the intention of determining both the opportunities they provide for students to engage in high-level tasks and the opportunities for teacher learning. Tasks in the written curriculum materials iv involving probability and statistics as defined by the CCSSM will be examined for evidence of these opportunities. The results of this examination suggest that one of the three secondary mathematics curriculum materials, Core-Plus Mathematics Project (CPMP), contains high-level tasks addressing many of the probability and statistics standards from the CCSSM. A second curriculum, Interactive Mathematics Program, also contains high-level tasks but has far fewer high-level tasks than CPMP. The third curriculum, Glencoe Mathematics (GM), addresses many of the probability and statistics standards from CCSSM but does so with low-level tasks. None of the three curricula provides ample opportunities for teacher learning in the areas of anticipating student thinking and providing transparency of the pedagogical decisions made by the authors when designing the materials. v TABLE OF CONTENTS ACKNOWLEDGEMENTS .................................................................................................. XXII 1.0 RESEARCH PROBLEM ............................................................................................ 1 1.1 CCSSM WILL NECESSITATE CHANGE IN MATHEMATICS EDUCATION ........................................................................................................................ 2 1.2 CURRICULUM MATERIALS WILL PLAY A VITAL ROLE .................... 5 1.3 CCSSM MAY REQUIRE STUDENT ENGAGEMENT IN HIGH-LEVEL TASKS ............................................................................................................................... 7 1.4 TEACHER LEARNING MAY BE NECESSARY ........................................... 9 1.5 CURRICULUM MATERIALS ARE ONE POTENTIAL SOURCE FOR TEACHER LEARNING .................................................................................................... 11 1.6 PROBABILITY AND STATISTICS ARE IMPORTANT CONTENT AREAS ............................................................................................................................. 13 1.7 PURPOSE AND RESEARCH QUESTIONS ................................................. 17 1.8 SIGNIFICANCE ................................................................................................ 19 1.9 LIMITATIONS .................................................................................................. 20 1.10 SUMMARY ........................................................................................................ 21 2.0 REVIEW OF LITERATURE ................................................................................... 23 2.1 PROBABILITY AND STATISTICS ............................................................... 24 vi 2.1.1 Probability and statistics are important ................................................... 25 2.1.2 Probability and statistics are difficult to teach......................................... 26 2.1.3 Misconceptions are widespread across content and among everyone ... 30 2.2 GUIDELINES FOR ASSESSMENT AND INSTRUCTION IN STATISTICS EDUCATION REPORT ........................................................................... 34 2.3 COMMON CORE STATE STANDARDS AND PROBABILITY AND STATISTICS ....................................................................................................................... 38 2.3.1 Probability and statistics in curricula and standards .............................. 38 2.3.2 Interpreting Categorical and Quantitative Data (S-ID) .......................... 40 2.3.3 Making Inferences and Justifying Conclusions (S-IC) ............................ 45 2.3.4 Conditional Probability and the Rules of Probability (S-CP) ................ 48 2.4 TEXTBOOK STUDIES .................................................................................... 52 2.4.1 Analysis of probability in textbooks .......................................................... 53 2.4.2 Textbook studies in mathematics education ............................................. 55 2.5 EDUCATIVE CURRICULUM ........................................................................ 57 2.5.1 The birth of educative curriculum materials ........................................... 58 2.5.2 Design heuristics for educative curriculum .............................................. 61 2.5.3 Educative curriculum and CCSSM ........................................................... 67 2.5.4 Educative curriculum in mathematics education .................................... 68 2.6 HIGH-LEVEL TASKS ..................................................................................... 71 2.6.1 Establishing the importance of tasks......................................................... 72 2.6.2 The relationship between cogntive demands of tasks as set up and implemented ............................................................................................................... 74 vii 2.6.3 High-level tasks and student learning ....................................................... 76 2.7 SUMMARIZING CHAPTER 2........................................................................ 78 3.0 CHAPTER 3: METHODOLOGY ............................................................................ 81 3.1 PURPOSE AND RESEARCH QUESTIONS ................................................. 81 3.2 TEXTBOOK SELECTION .............................................................................. 82 3.2.1 Glencoe Mathematics (GM) ....................................................................... 83 3.2.2 Core-Plus Mathematics Project (CPMP) .................................................. 86 3.2.3 Interactive Mathematics Program (IMP) ................................................. 91 3.3 METHODOLOGY ............................................................................................ 94 3.3.1 Identifying the items to be analyzed .......................................................... 97 3.3.2 Identifying the level of cognitive demand ............................................... 102 3.3.3 Identifying educative opportunities for teachers ................................... 106 3.3.4 Reliability measures .................................................................................. 111 3.4 HOW THE DATA RELATES TO THE RESEARCH QUESTIONS ........ 112 4.0 RESULTS ................................................................................................................. 117 4.1 DESCRIPTION OF TASKS AND ITEMS ................................................... 119 4.2 ONLINE STANDARD IDENTIFICATION LEADING TO ITEMS THAT DIDN’T CORRESPOND ................................................................................................. 128 4.3 GLENCOE MATHEMATICS ....................................................................... 130 4.3.1 Question 1 .................................................................................................. 132 4.3.2 Question 2 .................................................................................................. 135 4.3.3 Question 3 .................................................................................................. 139 4.4 INTERACTIVE MATHEMATICS PROGRAM ........................................