UNIVERSITY OF CALIFORNIA, MERCED What am I supposed to do? Problem Finding and its impact on Problem Solving. A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Cognitive and Information Sciences by Daniel Matthew Holman Committee in charge: Professor Jeffrey Yoshimi, Chair Professor David C. Noelle Professor Michael Spivey 2018 Copyright © Daniel Holman, 2018 All rights reserved The Dissertation of Daniel Matthew Holman is approved, and it is acceptable in quality and form for publication on microfilm and electronically: Co-Chair (if applicable) Chair University of California, Merced 2018 iii Dedicated to my mom, dad and sister, without whom I would not have been able to reach this point, and whose love, support and belief in me have been invaluable. I also dedicate this work to the many friends, family members, colleagues and communities that have supported and encouraged me to succeed. I am immensely grateful to you all, and fully aware of how I fortunate I am to have more names to list than I possibly could. iv Chapter 1 : Problem Finding and Problem Solving .......................................... 1 1.1 Definition of Problems .............................................................................................. 3 1.2 The Problem Cycle .................................................................................................... 6 1.3 Prior Experimental Work ........................................................................................ 13 Chapter 2 : Literature Review ........................................................................... 17 2.1 Problem Finding ...................................................................................................... 19 2.1.1 Problem Discovery ........................................................................................... 20 2.1.2 Defining Problems ........................................................................................... 22 2.2 Problem Solving ...................................................................................................... 24 2.2.1 Insight Problems .............................................................................................. 24 2.2.2 Insight vs. Noninsight ....................................................................................... 32 2.2.3 Analogous Problem Solving ............................................................................. 37 2.2.4 Experts .............................................................................................................. 40 2.2.5 Procedural Problems ....................................................................................... 42 2.2.6 Understanding vs. Repeating ........................................................................... 44 Chapter 3 : A Taxonomy of Problem Types ..................................................... 46 3.1 Elaboration of Problem Features ............................................................................. 48 3.2 The Problem Types .................................................................................................. 54 Chapter 4 : Experimentation ............................................................................. 62 4.1 Two Models of Problem Solving in a Simple Game ............................................... 64 4.2 Experimental Setup ................................................................................................. 68 4.3 Experimental Conditions ......................................................................................... 72 4.3.1 Conditions ........................................................................................................ 73 4.3.2 Experimental Implementation .......................................................................... 77 4.3.3 Logging Player Data ........................................................................................ 78 4.4 Dependent Variables ............................................................................................... 81 4.5 Results ..................................................................................................................... 83 Chapter 5 : Conclusion ..................................................................................... 100 v TABLE 1: ALL PROBLEMS BUT PROBLEM 8 CAN BE SOLVED WITH B-2C-A, BUT 7 AND 9 CAN BE SOLVED WITH A+C; 6, 8 AND 10 WITH A-C ( ADAPTED FROM LUCHINS, 1942). .......................................................... 30 TABLE 2: CLASSIFICATION OF PROBLEM TYPES .............................................................................................. 53 TABLE 3: THE FOUR PROBLEM VARIATIONS SELECTED FOR USE IN OUR EXPERIMENT. .................................... 73 TABLE 4: EXPERIMENT CONDITIONS ............................................................................................................... 73 TABLE 5: DEPENDENT VARIABLE DESCRIPTIONS ............................................................................................ 81 TABLE 6: SUMMARY OF THE SIX MAIN LINEAR REGRESSION MODELS REPORTED IN THIS SECTION. NOTE THAT IN EVERY CASE BUT TIME SPENT THAT PROBLEM TYPE WAS A SIGNIFICANT PREDICTOR OF BEHAVIOR. .............................................................................................................................................................. 84 vi FIGURE 1: THE PROBLEM CYCLE ...................................................................................................................... 6 FIGURE 2: THE EXPERIMENTAL ENVIRONMENT. .............................................................................................. 15 FIGURE 3: THE TWO-STRING PROBLEM. ......................................................................................................... 26 FIGURE 4: THE BOX AND CANDLE PROBLEM.. ................................................................................................ 31 FIGURE 5: GRAPH OF INSIGHT VS. NON-INSIGHT. ........................................................................................... 34 FIGURE 6: THE TUMOR AND LASER PROBLEM ................................................................................................ 38 FIGURE 7: PARALLELOGRAMS. ........................................................................................................................ 45 FIGURE 8: GEARS PROBLEM ............................................................................................................................ 55 FIGURE 9: WATER-JUG PROBLEM. .................................................................................................................. 56 FIGURE 10: THE TOWER OF HANOI. ................................................................................................................ 57 FIGURE 11: THE TRAVELING SALESMAN PROBLEM. ....................................................................................... 58 FIGURE 12: AN EXAMPLE OF THE ROGUE-LIKE GAME. ..................................................................................... 69 FIGURE 13: THE ENTIRE GAME WORLD. ........................................................................................................... 71 FIGURE 14: OPENING A WALL BY PRESSING A BUTTON.. ................................................................................. 72 FIGURE 15: CLEAR PROGRESS, AND UNCLEAR PROGRESS ................................................................................. 75 FIGURE 16: A DETAILED PLOT OF ONE’S ACTIVITY IN THE GAME.. .................................................................. 79 FIGURE 17: PLOTS OF THE GAME GRID. ........................................................................................................... 80 FIGURE 18: THE LENGTH OF TIME PLAYERS SPENT IN THE GAME. ................................................................... 85 FIGURE 19: TIME SPENT FOR ALL SUBJECTS. ................................................................................................... 86 FIGURE 20: TIME SPENT FOR ALL FOUR CONDITIONS USING ONLY THE SUBJECTS WHO FOUND ALL EIGHT RED BUTTONS. ............................................................................................................................................... 87 FIGURE 21: A HISTOGRAM OF THE TOTAL PERCENT OF THE GAME BOARD VISITED BY PLAYERS.. ................... 88 FIGURE 22: PERCENT OF THE GAME BOARD VISITED BY PARTICIPANTS. .......................................................... 90 FIGURE 23: PERCENT OF THE GAME BOARD VISITED BY SUBJECTS WHO FOUND ALL RED BUTTONS. ............... 91 FIGURE 24: HISTOGRAM OF THE NUMBER OF PATHS TAKEN BY PLAYERS. ...................................................... 91 FIGURE 25: PATHS ........................................................................................................................................... 92 FIGURE 26: THE NUMBER OF PATHS TAKEN BY PLAYERS IN THE COURSE OF PLAYING THE GAME. .................. 94 FIGURE 27: HISTOGRAM OF PLAYERS PRESSING BUTTONS MULTIPLE TIMES.. ................................................. 94 FIGURE 28: AVERAGE BUTTON REVISITS ......................................................................................................... 96 FIGURE 29: HISTOGRAM OF HOW MANY BUTTONS PLAYERS WERE ABLE TO FIND AND PRESS. ........................ 96 FIGURE 30: THE TOTAL NUMBER OF RED BUTTONS FOUND BY PARTICIPANTS. ................................................ 98