Teaching Problem Solving in Engineering - CiteSeerX

On Teaching and Assessing Engineering Innovation*

Daniel Raviv+, Melissa Morris+, Karen Ginsberg++ +

Department of Electrical Engineering Department of Computer Science and Engineering Florida Atlantic University, Boca Raton, FL 33431 E-mail: [email protected] (561) 297 2773

++

Abstract This paper details data, analysis, and evaluation of one facet of innovation: ideation. Over the past six years college and high school students were exposed to several idea generation methods in an engineering problem solving course at Florida Atlantic University entitled: “Inventive Problem Solving in Engineering” (EGN 4040). Two different problems were given to the students in the beginning and towards the end of the semester, about which they were asked to generate ideas. They used different methods to solve the problems, some of which they learned in class, including the Eight Dimensional Methodology for Innovative Thinking that was developed and taught by the first author. This method focuses on idea generation and is a unified approach that builds on comprehensive problem solving knowledge from different disciplines. The different dimensions, namely Uniqueness, Dimensionality, Directionality, Consolidation, Segmentation, Modification, Similarity, and Experimentation provide problem solvers with new directions for solving problems. The paper starts with a brief overview of the methods that were taught in the class, and later focuses on assessment, including method, data, analysis, and interpretation of results. The analyzed results are based on the average number of solutions per student, the standard deviation, and the total number of different solutions. The results clearly indicate a consistent and significant improvement in idea generation. They show an average increase in the number of ideas by a factor of nearly two and a half produced by about 130 participants.

* This work has been supported in part by the National Collegiate Inventors and Innovators Alliance (NCIIA)

Proceedings of the 2005 American Society for Engineering Education Annual Conference & Exposition Copyright © 2005, American Society for Engineering Education

Introduction Creative thinking, innovations, and inventions are a part of everyday life. Finding effective ways to teach students to be creative and solve problems requires as much creativity and innovation in itself. Currently, there are many different kinds of thinking methods and methodologies that stimulate creative cognitive processes. Sometimes, however, it is hard to define creativity. As defined by Grossmon, Rogders, and Moore, “Creative thinking involves the ability to find solutions to problems by changing your point of view” 1. One way to teach innovation is to develop a systematic way of thinking or controlling patterns of thought. There are many different kinds of such methods. Some examples include TRIZ 2,3, Lateral Thinking 4, Mind Mapping 5, and the Eight Dimensional Methodology for Innovative Thinking 6,7,9. Another option is to have hands-on activities such as 3-D puzzles and group projects which encourage students to be more open-minded and to experience joy in their learning and ideas. All of these methods are part of the curriculum in the course “Inventive Problem Solving” taught at Florida Atlantic University (FAU). The goal of the course is to enhance the inventive thinking of students that they can use in all aspects of their careers. One partial measure of success is the ideation, or number of solutions that students can develop to solve a given problem. This paper describes a study of ideation performed over the past four years. The college and high school students involved were evaluated before and after learning several techniques of problem solving, as well as many other activities and ideas. The results and analysis of these evaluations are described in detail. Overview of Course The course “Inventive Problem Solving in Engineering” (EGN 4040) has been taught at FAU for the past eight years. While most students who enroll are engineering majors, some students majoring in the sciences, arts and humanities have participated in the course. In addition to college juniors and seniors, high school students have taken the course over the past five years. These students were either enrolled in the Advanced Academic Institute (AAI) or Engineering Scholars Program (ESP), both of which are intense summer programs. Methods Taught A large portion of the in-class teaching is devoted to teaching systematic ways of thinking. Students are exposed to TRIZ, Lateral Thinking, Mind Mapping and the Eight Dimensional Methodology for Innovative Thinking. Multiple methods are taught since some are not necessarily suited for everyone or for every problem. TRIZ, a Russian Acronym that translates into the Theory of Inventive Problem Solving is quickly becoming very popular and is being used by major corporations throughout the world. After studying over two million patents, the method’s creator, Altshuller, identified the main principles and knowledge that define the process for solving inventive problems. TRIZ makes use of this global patent database by providing specific steps for solving the problems2-3,7.


Lateral thinking involves changing one’s perception. This method “. . . is concerned not with playing with the existing pieces but with seeking to change those very pieces. Lateral thinking is concerned with the perception part of thinking. This is where we organize the external world into the pieces we can then 'process'.” 8 This method is practiced by having the students as a class come up with a list of items taken for granted at a restaurant, eliminating one item at a time, and then brainstorming ideas for a “new restaurant” that exploit the lack of the items . Mind mapping involves using works, phrases and pictures to branch from a central idea or problem to many solutions or related ideas. The result is a central core that has branches that break off as more detailed ideas are generated. Using this method, students are asked to solve a variety of problems including how to deal with a hungry mosquito in the room. Here students are introduced to a problem, e.g., “There is a mosquito in the room and it bothers you.” They list ideas, and then collectively come up with a category-based pictorial mind-map of the different solutions. Ideas range from the initial idea of slapping the mosquito to less obvious solutions such as burning down the house (with the mosquito inside). The Eight Dimensional Methodology for Innovative Thinking is a combination of many types of problem solving techniques. This unified approach is quick to learn and can easily generate many unique and high-quality ideas in a short period of time. “You explore solutions in eight different thinking directions, one at a time. In each direction, or dimension, you are guided through multiple questions or suggestions that stimulate your mind and that may lead to solutions.”6 The dimensions are 1) Uniqueness, 2) Dimensionality, 3) Directionality, 4) Consolidation, 5) Segmentation, 6) Modification, 7) Similarity, and 8) Experimentation. A major portion of the lectures is devoted solely to this method, which include solving 3-D puzzles and engaging in team-based games and tasks that relate to each dimension. Students use this method to solve several problems, including “how to improve a sprinkler system” and “create an ideal neighborhood”. For more information on this method, readers are encouraged to refer to a previous paper written by the first author 9. Class Activities Besides simply teaching creatively, there are many activities designed to encourage selfexploration and interpersonal skills. To do this, the class includes many team-based and handson activities.10 These activities help to enhance the concepts taught and put into practice what the students have just learned, as well as providing new experiences. In addition, students frequently are required to move about the room and enjoy thinking in a non-lecture environment. Students participated in individual and group activities designed to stimulate their minds (Figure 1). While they consider problems and explore solutions, they are learning new concepts in thinking. These activities include solving mechanical 3-D puzzles, each of which emphasizes one or more problem solving techniques. Throughout the class, students solve brainteasers, which allow them to use methods they just learned in class and help to maintain interest and concentration during the lectures. Occasionally, activities allow students to leave the classroom. In one such activity, groups of two to three students are charged with the task of measuring the height of a tall building using only a 12-inch ruler, a sheet of paper, a pencil and an 8 by 8-inch flat mirror. The teams then present their solutions to the class so students can appreciate the


wide range of ideas and innovations. This activity also emphasizes that many problems have more than one solution and that there are more solutions than “one right solution”. Daily, “Puzzlebusters” 14 are given as homework. These brainteasers allow students to work individually or in small groups on a daily basis outside of the scheduled class time. Questions such as “How can you distribute six pennies in three paper cups so that each cup contains an odd number of pennies?” reinforce inventive thinking by continuously stimulating students’ minds. Other assignments include performing Internet or patent searches to find inventions, products or advertisements that utilize each sub-strategy of the Eight Dimensional Methodology for Innovative Thinking. After these, students come up with their own solutions to new problems using all eight dimensions and the relevant sub-strategies. The integration of several methods and activities are included with the so-called “Speed Bump Problem”. First, student groups use mind mapping to brainstorm the problems that speed bumps cause (i.e., spilled drinks and suspension wear). After doing this, students find many solutions to improve speed bumps using the Eight Dimensional Methodology. Finally, the groups pick solutions and actually design, build and implement them. (Usually they build scaled down versions with RC cars.) This takes the students through the entire process of innovative problem solving from observing and defining the problem to evaluating the solution.

Figure 1: Students participating in group exercises Personal discovery and appreciation of diversity are important in allowing students to communicate and work with one another to develop ideas. Students “discover” themselves through Myers-Briggs testing to determine their own personality type and then see the variety within their own class. In another activity, Nedd Herrmann’s Diversity Game 11, students individually negotiate for cards that describe themselves with three adjectives, and then share their adjectives with their classmates to get a different perspective on the wide variety of personalities. These activities lead students to become more appreciative of the diversity of


different kinds of thinkers. The latter example, in particular, also helps encourage students to appreciate diversity in a fun, hands-on manner. Teaming and risk-taking are also important components of the course. Three LegoMindstorm® robot competitions help to develop teaming skills. Here, students work in groups of three to four to design robots to complete a specific task such as get out of a maze (Figure 2) or climb a rope. In these competitive events, some teams create creative, risky designs in order to gain an edge. This concept is iterated throughout the class by encouraging different ideas to be heard. It encourages students to be more creative, rather than following unspoken rules.

Figure 2: LegoMindstorm® competitions

The activities in the course provide students with skills important in areas such as engineering and business. Working in teams, communication, and creative thinking are all encouraged. Many of the activities during the class are the medium used to teach new concepts in thinking. These activities enhance the learning experience in the course, and most likely increase the creativity of the students. A paper published by the first author will be of interest for readers wanting more details about some of these class activities10.

Evaluation Method The ideation results are generated from responses from two questions given to students in the Inventive Problem Solving course. The first, “Where Are You?”, states “You are somewhere in the USA. How would you find your location? List ideas.” 12 The second, “The Jumping Problem,” states “JJ lived in an apartment located on the sixth floor of a building. He opened the window, looked down and … OH NO! … Jumped! His friend ZZ ran to the scene, and was surprised to discover that JJ was NOT hurt! Can you explain the mystery?” 13 The question sheets given to the students are in Figures 3 and 4.


Where Are You? You are somewhere in the USA

How would you find your location? List ideas Copyright © 1999, 2000, by Daniel Raviv, All Rights Reserved

Figure 3: “Where Are You?” problem sheet

The Jumping Problem JJ lived in an apartment located at the sixth floor of a building. He opened the window, looked down and ... Oh No ... JUMPED ! His friend ZZ ran to the scene, and was surprised to discover that JJ was NOT hurt !

Can you explain the mystery?

Copyright © 2000, by Daniel Raviv, All Rights Reserved.

Figure 4: “The Jumping Problem” problem sheet


As an interesting exercise for the reader, write down as many solutions to these problems as you can before continuing. Then compare with the student’s solutions described in this paper and in the Appendix. The evaluation data was collected in two stages during each course. During the first day of class, the students were split evenly into two groups, A and B. Group A was given the “Where Are You?” problem and Group B was given “The Jumping Problem.” Towards the end of class, after being taught several of the problem-solving methods and being involved in various activities, these questions were given again. However, Group A was given “The Jumping Problem” and Group B was given the “Where Are You?” problem. During both evaluation periods, the students worked individually, and were told to generate as many ideas as they could. They were not told to use any specific method for generating their ides. It was emphasized that the number of solutions produced would have no impact on the students’ grades. They were also told that there were no “right or wrong” answers. In addition, the students were given the time they needed to generate their ideas, generally about 15 to 20 minutes. Every effort was made to insure that the students did not feel that they were under pressure during both periods. After the students had finished, their answers and problem sheets were collected. To avoid sharing of ideas after the first evaluation, the students were immediately given other assignments to work on.

Results It should be noted that the results were collected and compiled by the teaching assistants of each class. In order to avoid any identification of participating students, the data given in this paper has been combined from all classes. However, the pattern of the overall data closely matches that of the individual classes. The number of solutions per student, the standard deviation, and the total number of different types of solutions were determined for each set of questions. As can be seen in the Appendix, some solutions were very similar. It was sometimes difficult to define a “different” solution. Some seemed too similar and were combined, while others were left as different solutions. It is up to the individual to decide if jumping into a (presumably, stationary) pile of feathers is really different than jumping onto the back of a (presumably, mobile) truck filled with feathers. In this respect, the actual number of different solutions can not be known for sure, but the results show a clear pattern despite a few uncertainties. There was some difficulty in determining the exact number of students participating. This is because in some cases, a student was absent or not registered in the course on one of the two days that the evaluation was conducted. This did not occur frequently, however, and has little impact on the overall trend shown by the results. According to our data, it is about six students out of about 130 participants. Summary of Results The detailed listing of all of the students’ responses can be found in the Appendix. It should be referred to in order to note the creativity and variety that was produced by the students. Tables 1 Proceedings of the 2005 American Society for Engineering Education Annual Conference & Exposition Copyright © 2005, American Society for Engineering Education

and 2 summarize the results for each question. “Before” refers to the evaluation given towards the beginning of the class and “after” refers to the evaluation given near the end of the course. Where Are You? Average Number of Students

Total Number of Different Solutions (Before)

Total Number of Different Solutions (After)

Average Number of Solutions Per Student (Before)

63

79

166

5.742

Standard Deviation (Before) 1.78

Average Number of Solutions Per Student (After)

Standard Deviation (After)

12.781

2.23

Table 1: Overview of results from “Where Are You?” question

The Jumping Problem Average Number of Students

Total Number of Different Solutions (Before)

Total Number of Different Solutions (After)

Average Number of Solutions Per Student (Before)

64

94

220

4.969

Standard Deviation (Before) 1.34

Average Number of Solutions Per Student (After)

Standard Deviation (After)

12.25

1.63

Table 2: Overview of results from “The Jumping Problem” question

The following table depicts the number of students from each individual class that answered the given questions. The different numbers of students between “before” and “after” in a given class result from students being absent during one of the evaluation days. Number of Students From Each Class Class Before After Question ESP 2001 10 10 Where Are You? ESP 2001 10 10 The Jumping Problem AAI 2001 7 7 Where Are You? AAI 2001 6 6 The Jumping Problem ESP 2003 11 11 Where Are You? ESP 2003 12 11 The Jumping Problem AAI 2003 9 9 Where Are You? AAI 2003 9 8 The Jumping Problem College 2004 14 15 Where Are You? College 2004 15 17 The Jumping Problem ESP 2004 11 12 Where Are You? ESP 2004 12 12 The Jumping Problem Table 3: Breakdown of participants by question and class


Analysis of Results The data shows a definite trend of an increase in ideation. On average, students generate more than twice as many solutions after completing the course. The quality of the answers were not considered in this study. It was the case that some students produced fewer, but more thoughtful or elaborate answers, while others had many short solutions. Each student interpreted the questions individually. One interesting note about the resulting solution is that one student described the location of the man to the buildings given as the image on the handout. This means that the use of only text, only pictures, or both to present the problem could alter the number and type of results produced. All of the students involved here, however, where given identical sheets on the same color paper as shown previously. The increase in average number of solutions per student was 2.23 fold for the average number of solutions generated by the students for the “Where Are You?” problem. In addition, a total of 87 new solutions were generated by our classification. This means that the number of independent ideas doubled. There was a similar trend for “The Jumping Problem.” On average, 2.47 times more solutions per student were generated between the first and second evaluation periods. Similarly to the first problem, the number of new solutions doubled with an increase of 126 ideas. Even with somewhat of a large variance in deciding what is a “different” solution, there is clearly an increase in the number of different solutions produced as a whole. Overall, the results show a doubling in ideas generated.

Conclusion Although we can be certain that students create more solutions in general, what causes this change is only speculated. Many diverse factors including the exposure to idea-creation methods, increased confidence, reduction in the need to please the professor, possible increased cognitive reasoning due to hands-on activities, team and communication exercises and the particular classroom environment that the course creates are all possible reasons for this trend. We believe that the combination of these may be the main factor. This research shows a clear indication that it is possible to enhance ideation through some type of classroom instruction. The number of unique ideas produced as a whole doubled, and the number of ideas per student on average more than doubled. While the exact ingredients for such instruction that led to the meaningful increase can not be clearly determined by the evaluation conducted, we believe that the described environment was very beneficial. The atmosphere and freedom to think freely were likely conductive to this increase. At the start of class, students were focused on trying to please the teacher in order to obtain high marks. The students generally asked a lot of questions and looked for specific directions. In addition, they tried to “follow the rules” and looked for the “right” answer. When specific rules and directions were not provided in nearly all cases, they gradually began to think more openly and came up with ideas that they would have previously considered as “unacceptable” solutions.


As the class progressed, students were observed to be more open-minded. They developed better teaming and communication skills. In addition, they began to think more independently, learned how to work at their own pace, and produced work pleasing to themselves rather than work to please the professor. Overall, the students were joyous and excited to see what would be next. Not only did they learn to develop more ideas, but they also developed important interpersonal skills and how to have fun in the process.

Bibliography 1. Grossman, Rodgers, Moore, Innovation, Inc. Unlocking Creativity in the Workplace, Woodware Publishing Inc., Texas, 1988, pp. 5-10. 2. Altshuller, G., And Suddenly the Inventor Appeared: TRIZ the Theory of Inventive Problem Solving, Trans. L. Shulyak, Technical Innovation Center, Worcester, MA, 1996. 3. ---, 40 Principles: TRIZ Keys to Technical Innovation, Trans. L. Shulyak and S. Rodman, Technical Innovation Center, Worcester MA, 1997. 4. de Bono, E., The Use of Lateral Thinking, Penguin Books, 1990. 5. Wycoff, J., Mind Mapping: Your Personal Guide to Exploring Creativity and Problem Solving, Berkeley Publishing Group, 1991. 6. Raviv, D., “Eight Dimensional Methodology for Innovative Thinking,” Cutting Ed (formerly, Creativity, Innovation, and Design (CID) Report), November 2003. 7. ---, “Do We Teach Them How to Think?,” Proceedings of the 2002 American Society for Engineering Education Annual Conference and Exposition, Montrel, CA, June 2002. 8. de Bono, E., Lateral and Parallel Thinking, 30 Dec. 2004 (http://www.edwdebono.com/debono/lateral.htm). 9. Raviv, D., “Eight-Dimensional Methodology for Innovative Thinking,” Proceedings of the 2002 American Society for Engineering Education Annual Conference and Exposition, Montrel, CA, June 2002. 10. Raviv, D., “Hands-on Activities for Innovative Problem Solving,” Proceedings of the 2004 American Society for Engineering Education Annual Conference and Exposition, Salt Lake City, UT, June 2004. 11. The Herrmann Group, “Diversity Game,” Applied Creativity, Inc., 1992. 12. Raviv, D., “Where Are You?”, 2001. 13. Adapted from: Vaner, G., “JJ Jumping, Thinking About Thinking Using Brainteasers”, Thinking Education, Publication of the Branco Weiss Institute for Development of Thinking, Sept. 1995, pp. 36-40, (in Hebrew). 14. Book, D.L., “Problems for Puzzlebusters”, Enigmatics Press, Washington DC, 1992.

Acknowledgments Appreciation is due to the teaching assistants, Mr. Allapon, Mr. Richard Viens and Mr. Liam Myron who helped in many ways during the classes, including in the collection of the data used in this paper.


Appendix There are eight detailed tables included in this appendix. The four large tables list the individual responses and how many students generated a specific response. There are two tables for each question – one for “before” and one for “after”. The “before” table of each question shows the responses from the students during the beginning of the class. The “after” tables show the responses to the questions towards the end of the class. Preceding each of these large tables is a small summary table showing pertinent numerical data.

Data from “Where Are You?” Question Given at the Beginning of the Course

Where Are You? (Before) Number of Students

Number of Solutions

62

356

Solutions per Student Standard Deviation (Mean) 5.742

Solutions 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Ask someone Look around for popular landmark Use GPS Listen to the accents and dialects Look for street signs Look at the newspaper Observe the weather Ask a policeman Look in the phone book Look at a map Look at the license plates on cars Ask the telephone operator Look around Look at the structure of the buildings around you Look for a national monument Look at the arrangement of the sun and stars Open a mailbox and look at the address Ask the navigation system in the car Observe the kinds of trees and vegetation Determine if rural or urban Look at name of shopping plaza / store Look at the type of clothing people are wearing Look for "Welcome to ..." sign

1.78 Number of Students With This Solution 45 19 19 17 17 14 12 11 11 10 10 8 8 8 8 7 7 5 5 4 4 4 4


24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Look for any signs Observe local wildlife Observe the weather Ask for the area code Ask the post office Find the border / ocean and determine how far you traveled Identify latitude and longitude Look at a compass Look for local business Look for police car / school bus with location on side Observe landforms Remember where you are going Use a computer to find out where you are Watch the news on TV Ask a government official Call 911 Look at the culture around you Look at the different types of festivals or parties that people throw Look for a "You are here" sign Look for a billboard Look for a public building for a "City of ..." sign Look for a state flag Look for the closest airport Look for the zip code Look in a local magazine Use phone to call friend and ask for area code on caller ID Ask a real estate agent Ask a taxi driver Describe the location to other people Eat at a local restaurant Find out what time zone it is Go back in time and see the founder Guess Identify from a relative place Know where you are Listen to the radio Look around Look at a directory Look at an emergency vehicle sign Look at the kind of money people are carrying Look at the library Look for a national park

4 4 4 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


66 67 68 69 70 71 72 73 74 75 76 77 78 79

Look for religious symbols Look for saltwater or freshwater Look for the social security number of people Look for tourism item for the name of city Observe the driving behavior Observe the wind direction Report yourself as a missing person and watch the news for the last known location Sacrifice an animal for an answer from the gods See what people eat See what type of industry is going on Start a fire so the firemen can tell you where you are Threaten people until a sheriff comes and ask him/her Use a spy satellite Use boyscout/girlscout survival skills

1 1 1 1 1 1 1 1 1 1 1 1 1 1


Data from “Where Are You?” Question Given Towards the End of the Course

Where Are You? (After) Number of Students

Number of Solutions

64

818


Solutions 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

Ask someone Look at any street signs Look for any familiar monuments or buildings Buy a map Look at the license plates of cars Use GPS Watch television Listen to the peoples' accent around you Call someone and have them look at your area code on caller ID Look at the temperature / climate Look for a police car that displays the name of the city Look in a phonebook Open a mailbox and look for the address Look for the closest airport Check the Internet to see where you are Listen to the radio Look at a newspaper Look at the wildlife and vegetation Look around for popular landmarks Call the information center Find the border or ocean and trace back how far you went Look at the scenery / landscapes See what type of clothing people are wearing Explore until you know where you are and recognize things Go up high in plane or helicopter to determine the type of land around you Look at the stars Look in an atlas Use the Onstar system Look at the telephone area code Look at your plane ticket Use a compass Call the operator Eat at a restaurant to see what food the city is known for Get arrested and go to the county jail Guess Look for a "You are here" sign Look for a highway or interstate

2.23 Number of Students With This Solution 64 40 38 34 26 26 26 24 20 20 20 18 16 15 14 13 13 13 12 11 11 11 9 8 8 8 7 7 6 6 6 5 5 5 5 5 5


38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

Look for a local taxi Look for a post office Look for a public building for a "City of ..." sign Look for a satellite image of the area Look for saltwater or freshwater (Water characteristics) Send a letter to your home and check the postmark Take the local public transportation to be able to recognize certain areas Watch the weather channels Cross into a new state and look at the sign Find out the zip code Find the city limit sign and read it Look at local businesses Look for a "Welcome to ..." sign Look for a billboard Look for the state flag Retrace your steps Compare the time difference from home Look at how people drive Look at the names of shopping centers and stores Look at the sun positions Look at the tourist information at a hotel Look for business cards Look for someone's ID Look for state colleges Look for tourism item for name of city Observe local crops Observe technology usage Observe the other side of the earth Observe the season and sun location Start a fire and ask fire rescue Use dog senses Wake up from dream Ask an alien Buy a house an look at the papers Buy something from a store that indicates the address Call the FBI Determine if the area is rural or a city Do something crazy - then watch the news and find out where you did it Find the nearest hospital Fly to outer space and observe Go to the next town Locate the latitude and longitude of the area Look for a national park Look for a police or fire department Look for a sport logo Look for a train station Look in a local magazine Observe anthropology threats

5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2


86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133

Observe the local culture See how many casinos there are Use time machine to back a few days before Wait for someone to look for you Walk along the railroad track Ask a bus driver Ask someone in a local house Ask someone on a CB radio Ask someone on a HAM radio Ask the children Ask the friend who drove you Attach a sign "Remind me where am I" on your back Be smarter and realize by yourself Become a secretary and look at addresses in files Become a taxi driver Become telepathic / psychic Call 911 Call a movie theater and get directions Compare the similarities and differences from your hometown Determine the types of local industries Find a congressman name to indicate district Find a friend Find out where you are not Find the state capital Flush the toilet Follow clues like a scavenger hunt Get a ticket and look at that Go home Go to a gathering Go to concert and let singer tell you Have Homeland Security pick you up - they will tell you during the interrogation Hold up a sign "where am I?" until someone tells you Hurt yourself and go the hospital Identify from the unique characteristics Just stay (Don’t worry about where you are) Knock on someone's door and ask Know where you are going Let local people known that you don’t know where are you Listen the local music Listen to zip-code at store cash register Look at the economic status of the city Look at the power on the wall outlet Look at the state lottery in gas station Look at the type of people that are around you Look at your feet Look for a car dealership Look for a city park Look for a sports stadium

2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166

Look for a state dog tag Look for a subway station Look for a tourist attraction Look for farm animals Look for local ads Look for pay-phone booths Look for the county that you are in Look for the school district Look for theme parks Look in gift shops that might attract tourists Look when someone fills out an application form No Solution Observe structures Observe the distance between two cities Observe the hobbies of local people Observe the kinds of cars Observe the local history Observe the local law Observe the population density Observe the soil Observe the wind Pray Report yourself as a missing person Send a signal to ask Shoot a laser and observe the angle of reflection Take a train and look at the map inside Trade something for someone to tell you where you are Use a hot-air balloon Use a pedometer and walk to Canada - find your location Use a satellite phone Walk around until you figure it out Wave down a car You know you are in the USA

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


Data from “The Jumping Problem” Question Given at the Beginning of the Course

The Jumping Problem (Before) Number of Students

Number of Solutions

64

318


Solutions

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

JJ was a stuntman and jumped on something soft JJ jumped down with a parachute JJ landed in his pool that was very deep JJ didn't stay in his apartment JJ jumped from inside and landed on his balcony JJ landed on a trampoline JJ jumped onto the fire escape JJ was bungee jumping JJ jumped from someone else's apartment JJ jumped up and landed in his apartment JJ was a bird JJ was a cat JJ was able to safely land on his feet JJ was caught by a fireman JJ didn't open the window The building was on the moon JJ didn't jump out of window JJ jumped down to the trees JJ jumped from the first floor JJ landed on ZZ and ZZ is dead No Solution The building was an underground building JJ fell on an overhang JJ jumped in place JJ jumped to a rope or ladder and slid down JJ landed in a garbage dumpster JJ landed on a bush JJ thought he was superman and could fly JJ had a hang-glider JJ jumped to an awning JJ was caught by superman The floor numbers were reversed There was no gravity, so he could not be hurt Gravity in that area was very low JJ grabbed the window JJ jumped back into the apartment JJ jumped on another building

1.34 Number of Students With This Solution 27 21 15 13 13 13 12 9 7 7 7 7 7 7 6 6 5 5 5 5 5 5 4 4 4 4 4 4 3 3 3 3 3 2 2 2 2


38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

JJ jumped to the next window across from him JJ landed onto a fire blanket JJ lives in the matrix and there is no apartment JJ was a superhero JJ was killed The building was on a hill and he did not have far to fall ZZ caught him He jumped to a flag pole JJ fell on a truck of marshmallows JJ fell to a painters stand JJ fell to a pile of leaves JJ flew down to the ground JJ had a cable to hold him JJ had a miracle happened to him JJ had an experience to protect himself JJ had internal bleeding JJ had on loose fitted clothes which guided him to the ground JJ is a hologram JJ jumped but he felt no pain JJ jumped closer to the window JJ jumped from the sixth floor to the fifth floor JJ jumped in his imagination JJ jumped in spirit JJ jumped next door JJ jumped out 1 floor, but climbed down the rest JJ jumped sideways JJ jumped to his patio JJ jumped to the outside of the door JJ just acted like he was going to jump JJ landed on a giant eagle JJ landed on a thick layer of grass JJ landed on bail or straw JJ landed on open truck full of feathers JJ landed on people JJ landed on someone JJ landed on ZZ JJ lived on a midget apartment so he was not hurt when he jumped JJ opened a different window JJ used bed-sheet as parachute JJ was a ball of energy JJ was a flying squirrel JJ was a freak of nature JJ was a kangaroo JJ was a toy and cannot get hurt JJ was an ant JJ was an exoskeleton man JJ was an orangutang JJ was caught by a big balloon

2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


86 87 88 89 90 91 92 93 94

JJ was wearing clothing that protected him from the fall JJ who jumped was not the same JJ that ZZ knew JJ wore spring shoes JJ's building sucked him back in JJ's room is connected to a lower level window Someone caught JJ before he fell ZZ thought JJ jumped but he did not ZZ was dreaming ZZ was hallucinating

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Data from “The Jumping Problem” Question Given Towards the End of the Course

The Jumping Problem (After) Number of Students

Number of Solutions

64

784


1.63

Solutions

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

JJ used a parachute JJ landed in water JJ landed in something soft JJ was lying and didn’t really jump JJ was bungee jumping JJ jumped to a lower floor JJ landed on a trampoline JJ was a bird JJ was a cat and landed safely on his feet JJ was a stunt man The window was a fire escape JJ could fly JJ had a jet pack or rocket JJ tied a rope around himself and lowered himself to the ground The building was underground so the sixth floor was at ground level JJ was a superhero JJ was already dead JJ landed on a garbage truck JJ landed in a net JJ lived in a midget/dwarf apartment that was half the size as a normal building JJ had a hang-glider JJ used a ladder to climb down JJ grabbed onto the water drain pipe JJ jumped to helicopter JJ jumped to next building JJ was on the first floor and jumped JJ caught his shoe lace on the side of the window JJ jumped backwards JJ landed on trees JJ landed on ZZ JJ was Spiderman and climbed down safely There was a slide on the side of the building and JJ went down it ZZ thought he saw JJ jump out of the window JJ jumped in his own apartment JJ jumped out of an indoor window JJ landed on a window on a lower floor JJ was immune to gravity

Number of Students With This Solution 47 29 25 25 21 17 17 17 17 17 16 14 14 14 14 13 13 12 10 10 9 9 8 8 8 8 7 7 7 7 7 7 7 6 6 6 6


38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

Someone caught JJ Superman saved JJ The building was on the moon A fireman caught JJ Each floor was only one foot high JJ fell in the bushes JJ is invincible JJ was a set of twins JJ believed he was a god and could not get hurt JJ held onto the ledge JJ jumped back inside JJ jumped down onto the balcony below one by one JJ jumped to a flying car JJ jumped to helium balloon JJ landed on someone JJ was a cartoon character JJ was using suction cups to walk down the side of the building JJ was ZZ's imaginary friend The building was built on a hill and JJ did not have far to fall JJ had an experience to protect himself JJ jumped into a pile of clothes JJ jumped into his spaceship JJ jumped to scuffling JJ landed on an open truck full of features JJ was hurt, but by the time ZZ got there he was OK JJ was in a bubble and bounced back up JJ's building is a dollhouse and JJ is a doll made of plastic ZZ caught JJ Angel saved JJ Doctor on the ground fixed JJ immediately It was a video game and JJ was an animated character JJ fell onto a tent JJ had a blast of air so strong it blew him back into his apartment JJ had an anti-gravity belt JJ had something to slow his descent JJ had wings JJ is a robot that cannot be hurt JJ is in a movie and there is no such thing as a 6th floor apartment JJ jumped onto large construction equipment JJ landed in an ocean JJ landed in an opened sewer JJ landed in the arms of some cheerleaders JJ landed on a carnival moonwalk JJ landed on a flying carpet JJ landed on a giant eagle JJ landed on a hay stack JJ landed on a pile of feathers JJ landed on an open truck with full of hay

6 6 6 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2


86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133

JJ opened the window in the corridor JJ threw a dummy out of window JJ used an umbrella to hover down JJ was lucky JJ was wearing a special suit that not let him get hurt JJ wore spring shoes JJ's building had burned to the ground so the 6th floor was the first The building was sideways and all the floors were at ground level The story is not complete Wind helped him to fall slowly Both JJ and ZZ were in virtual reality game Both JJ and ZZ were insane people Building had a lot of snow to 5th floor Building had only one floor Building was an underwater building Building was flooded Building was in space station Building was not very high Demon saved JJ Ground was bounding rubber His apartment was 6 stories high It was a dream It was not time for JJ to die JJ can walk on air JJ changed the charge of his body JJ didn't hit the ground yet JJ dove into a glass water cup JJ drank a "Red-Bull" and it gave him "wings" JJ fell just right JJ floated down JJ glided his way down JJ grabbed an overhang JJ had a blimp JJ had a cushion JJ had a mutant power JJ had a new flying machine JJ had a super watch JJ had bouncing shoes JJ had on anti-gravity boots JJ had on special gear JJ had strong bones JJ had telekinetic power JJ hovered in air JJ is a ghost JJ is a gymnast JJ is an electronic airplane JJ is like Rudolph the Red Nosed Reindeer JJ jumped and grabbed 2nd floor escape

2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181

JJ jumped from a tied blanket to ground JJ jumped in freight JJ jumped in the room JJ jumped into a hot air balloon JJ jumped into the stairwell JJ jumped on a windowsill JJ jumped onto a crane JJ jumped onto an elevator and rode it all the way down JJ jumped sideways JJ jumped to a cherry picker JJ jumped to clothesline JJ jumped to flagpole JJ jumped to light-post JJ jumped to log JJ jumped to pipe and slide down JJ landed in a manhole full of water JJ landed in a pile of dirt JJ landed in a river JJ landed in snow JJ landed in the arm of person JJ landed on a baby carriage JJ landed on a bed JJ landed on a big bird JJ landed on a big bird nest JJ landed on a big pile of dust JJ landed on a big umbrella JJ landed on a car JJ landed on a cart of pillows JJ landed on a cloud JJ landed on a convertible car JJ landed on a group of cats JJ landed on a group of chickens JJ landed on a horse carriage JJ landed on a jello pool JJ landed on a laundry cart JJ landed on a mayonnaise pool JJ landed on a pile of boxes JJ landed on a pile of dead people JJ landed on a pile of wigs JJ landed on a plane JJ landed on a sandbox JJ landed on a soft sofa JJ landed on a soft spot JJ landed on a some balloons JJ landed on a tank of water JJ landed on an open truck full of lettuce JJ landed on Dumbo (flying elephant) JJ landed on fish underwater

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182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220

JJ landed on fuzzy fertilizer JJ landed on giveaway JJ landed on his feet JJ landed on his friend JJ landed on street dogs JJ landed on tarps JJ landed on the back of an elephant JJ landed on the back of horse JJ looked like he was alive JJ opened the car window JJ played a game JJ slowed down time and was not hurt JJ trained himself to jump out of 6th story buildings JJ tried to clean the window JJ was a Batman JJ was a computer graphic JJ was a doll JJ was a flying squirrel JJ was a kangaroo JJ was a lizard JJ was a monkey and swung down JJ was a pain-free person JJ was a stuffed animal that came to life and landed without getting hurt JJ was an alien JJ was blind JJ was committing suicide JJ was deep sea diving JJ was disabled and could not jump JJ was grabbed by alien JJ was jumping in bed JJ was on a pogo stick JJ was six stories tall JJ was stuck at the window Someone else was disguised as JJ The numbers on the floors were backwards: Biggest to Smallest There were two JJs ZZ called for help ZZ did not think JJ was hurt ZZ misidentified JJ

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