CREATIVITY AND PROBLEM SOLVING SKILLS AS A FUNCTION …

CREATIVITY AND PROBLEM SOLVING SKILLSAS A FUNCTION OF LEARNING TRANSFER

by

Benjamin Saltsman

Submitted to the System Design and Management Programin Partial Fulfillment of the Requirements for the Degree of

Master of Science in Engineering and Business Management

at the

Massachusetts Institute of Technology

February 2002

( Benjamin Saltsman. All rights reserved.The author hereby grants to MIT and Ford Motor Company permission to reproduce and to

distribute publicly paper and electronic copies of this document in whole or in part.

Signatures of AuthorBenjamin Saltsman

Certified by OfDan Ariely

Thesis SupervisorAssociate Professor, Sloan School of Management, MIT

Accepted bySteven D. Eppinger

Co-Director, LFM/SDMCo-Director, CIPD

GM LFM Professo Management Science and Engineering Systems

Accepted byPaul A. Lagace

Co-Director, LFM/SDMProfessor of Aeronautics & Astronautics and Engineering Systems

MASSACHUSETTS INSTITUTEOF TECHNOLOGY

JUL 1 8 2002

LIBRARIES

ACKNOWLEDGMENTS

The author wishes to thank Ford Motor Company for giving him the opportunity

to be part of this exciting program at MIT thus fulfilling a long-time dream. This

extraordinary learning experience has given me precious insights and allowed to

make new friends.

The author wishes to thank his thesis advisor, Professor Dan Ariely, for

suggesting this interesting topic, and his invaluable guidance and assistance

throughout this project.

The author would like to thank his classmates for providing a challenging,

stimulating and competitive environment and setting sky-high standards.

I would like to thank the SDM staff for their hard work and dedication.

Last, but not least, I would like to express my profound gratitude to my parents

for instilling in me the values of good education and providing the moral and

operational support throughout this journey.

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ABSTRACT

Processes of learning and the transfer of learning are central to understanding

how people develop important competencies. Since early childhood people are

exposed to various types of learning experiences: instruction, tutoring, self-

discovery, etc. Knowledge and skills acquired through these various types of

experiences lead to varying levels of proficiency.

The focus of this thesis is to answer the question which type of learning

experience not only provides adequate learning, but also positively affects

learning transfer, defined as the ability to extend what has been learned in one

context to new contexts. This positive learning transfer is the foundation of

effective problem solving skills highly sought out in today's environment. While

the topic of learning transfer is discussed extensively in the literature, the link

between learning transfer on the one hand and creativity and problem solving

ability on the other hand remains largely unexplored.

Experiment was conducted in which the data was analyzed from 84 engineers,

students and professionals. These individuals were randomly assigned to one of

the three groups. Each of the groups received varying levels of instructions and

asked to solve the same set of puzzles. The respondents were measured on

several parameters (speed, correctness, etc.). The results of this study show that

while the instructions help narrow the scope of the solution space by focusing the

effort and steering the respondents away from the erroneous directions, if the

instructions do not fit the problem formulation well, or are not transparent to the

respondent, they become a liability. Instructions stifled creativity in this

experiment and adversely affected the problem solving skills of the respondents.

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TABLE OF CONTENTS

CHAPTER 1.......................................................................................................8

CREATIVITY............................................................................................... 8

DEFINING CREATIVITY ......................................................................... 8

LEVELS OF INVENTION .................................................................................. 9Two MODELS OF INNOVATION AND INVENTION: INDIVIDUAL VS CULTURAL

........................................................................................................................ 10CREATIVITY PROCESS..................................................................................... 11

Can people be taught to be more creative? .......................................... 11Structured Creativity Techniques ........................................................ 12

TRIZ O verview ................................................................................ 12Structured Inventive Thinking Overview.......................................... 14Summary of Structured Creativity Techniques................................. 16

Creativity Barrier ................................................................................... 17How to reduce the creativity barrier ................................................. 21

CHAPTER 2.................................................................................................22

TRANSFER OF LEARNING.....................................................................22

WHAT IS LEARNING TRANSFER ......................... 22

PROMOTING POSITIVE LEARNING TRANSFER............................................. 24

What Affects Learning Transfer?......................................................... 24Effects of the Instructional Types on Learning Transfer...................... 25

CHAPTER 3.................................................................................................27

HYPOTHESES............................................................................................27

CHAPTER 4.................................................................................................29

EXPERIMENTAL APPROACH ............................................................. 29

BRIEF DESCRIPTION OF THE EXPERIMENT.................................29

SELECTION OF THE INDIVIDUALS FOR THE STUDY..................32

DEVELOPING THE SURVEY..................................................................32

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LIST OF REQUIREMENTS FOR THE SURVEY................................................. 32DESIGNING PROBLEMS FOR THE SURVEY................................................... 33

Puzzle Answers and Explanations ........................................................ 36Section 1 ............................................................................................ 36Section 2 ............................................................................................ 36

PROTOTYPE OF THE SURVEY ...................................................................... 37DEVELOPING THE INSTRUCTIONS ................................................................ 37

DATA ANALYSIS........................................................................................40

TRANSFER FORMULA................................................................................... 40COMPARISON OF FORMULAS ...................................................................... 43SELECTING THE FORMULAS FOR THE DATA ANALYSIS............................... 43

CHAPTER 5.................................................................................................45

RESULTS ..................................................................................................... 45

SUMMARY OF THE SURVEY RESULTS.............................................45

EXPERIMENTAL LIMITATION .......................................................... 47

VARIABLE TEST CONDITIONS..................................................................... 47SELF-SELECTION ........................................................................................ 48

CHAPTER 6.................................................................................................50

DISCUSSION...............................................................................................50

DISCUSSION OF THE SURVEY RESULTS........................................ 50

EFFECT OF THE INSTRUCTIONS ON TIME .................................................... 50EFFECT OF INSTRUCTIONS ON THE RATE OF CORRECT ANSWERS..............51EFFECT OF THE INSTRUCTIONS ON NUMBER OF ATEMPTS ........................ 53EFFECT OF THE INSTRUCTIONS ON NUMBER OF GIVE UPS.........................54EFFECTS OF INSTRUCTIONAL TYPES ON LONG-TERM MEMORY RETENTION 54

CHAPTER 7.....................................................................................................55

CONCLUSIONS..........................................................................................55

BIBLIOGRAPHY........................................................................................58

APPENDIX - COMPLETE RESULTS OF THE EXPERIMENT..........60

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LIST OF TABLES

Number PageTABLE 1. ANTICIPATED EFFECTS OF INSTRUCTIONAL TYPES ON KEY

LEARNING TRANSFER PARAMTERS.................................................... 28TABLE 2. PRIORITY OF THE REQUIREMENTS............................................... 33TABLE 3. COMPARISON OF PERCENTAGE TRANSFER OBTAINED BY THREE

TRANSFER FORMULAS.......................................................................... 44TABLE 4. SUMMARY OF SURVEY RESULTS................................................... 46TABLE 5. BREAKDOWN OF TIE ANALYZED OUTPUT FILES BY THE GROUP

T YPE ..................................................................................................... 48

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6

LIST OF FIGURES

FIGURE 1. LEVELS OF INVENTION .................................................................. 9FIGURE 2. SIMPLIFIED ARIZ DIAGRAM ...................................................... 14FIGURE 3. FLOWCHART OF THE SIT PROCESS [26] .................................. 15FIGURE 4. TRIZ SOLUTION - GRIPPING COMPLEX PARTS WITH A VISE .... 16FIGURE 5. EFFECT OF THE CREATIVITY BARRIER ON THE SOLUTION PATH 18FIGURE 6. FUNCTIONAL DECOMPOSITION OF THE CREATIVITY BARRIER .. 20FIGURE 7. DIAGRAM OF THE SURVEY PROCESS ........................................ 31FIGURE 8. FIRST PUZZLE OF THE NUMBER SERIES AS PRESENTED TO THE

C ONTROL G ROUP .................................................................................. 38FIGURE 9. FIRST PUZZLE OF THE NUMBER SERIES AS PRESENTED TO THE

GROUP 1 (GENERIC INSTRUCTIONS) .................................................... 39FIGURE 10. FIRST PUZZLE OF THE NUMBER SERIES AS PRESENTED TO THE

GROUP 2 (SPECIFIC INSTRUCTIONS) .................................................... 39FIGURE 11. EFFECT OF THE INSTRUCTIONS ON TIME, SECTION 1. .......... 50FIGURE 12. EFFECT OF THE INSTRUCTIONS ON TIME. SECTION 2 ............ 50FIGURE 13. EFFECT OF THE INSTRUCTIONS ON THE RATE OF CORRECT

A NSW ERS, SECTION 1........................................................................... 51FIGURE 14. EFFECT OF THE INSTRUCTIONS ON THE RATE OF CORRECT

A NSW ERS, SECTION 2 ............................................................................ 51FIGURE 15. EFFECT OF THE INSTRUCTIONS ON NUMBER OF ATTEMPTS,

SECTION 1.............................................................................................. 53FIGURE 16. EFFECT OF THE INSTRUCTIONS ON NUMBER OF CORRECT

ANSW ERS, SECTION 2........................................................................... 53FIGURE 17. EFFECT OF THE INSTRUCTIONS ON NUMBER OF GIVE UPS,

SECTION 1.............................................................................................. 54FIGURE 18. EFFECT OF THE INSTRUCTIONS ON NUMBER OF GIVE UPS,

SECTION 2.............................................................................................. 54FIGURE 19. SOLUTION PROCESS FOR SELF-DISCOVERY.............................56FIGURE 20. SOLUTION PROCESS WITH INSTRUCTIONS .............................. 56

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Chapter 1

CREATIVITY

DeEning Creativhit

Many definitions of the word "creativity" exist and are being used. The

Wordsmyth.net [30] dictionary gives the following definition for creativity: "the

capability of inventing or producing original or imaginative work". Roget's II [21]

definition is even briefer: "the power or ability to invent". Researchers often give

their own definition to this term. For example, D. Feldman, M. Csikszentmihalyi

and H. Gardner in their 1994 book Changing the World: A Framework for the Study of

Creafiti [10] produce the following definition: "creativity is the achievement of

something remarkable and new, something which transforms and changes a field

of endeavor in a significant way".

Under such a definition only "high" creativity is given consideration. Only when

something of a very high caliber, like a transistor, is created, the authors argue the

creativity is exercised. I would disagree with such a narrow definition. Creativity

is much more common is our society and, furthermore, it is even required of

"ordinary" people, like students, engineers, scientists, managers, etc. on a daily

basis. For example, students display their creativity in various contests (i.e. MIT

50K Entrepreneurship Competition, http://50k.mit.edu), coursework (i.e.

building race cars as part of the course 2.810, http://me.mit.edu/2.810),

infamous hacks (http://hacks.mit.edu/), and in many other ways. Creativity in

other areas of human activity is also quite common: creative ad campaigns are

often used in marketing to attract consumers and make the message more

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memorable. We will limit our discussion however to the realm of science and

engineering. In these disciplines, the patent database reflects the creative effort of

many thinkers.

Levels of Invention

Based on his patent research, G. Altshuller [1] differentiated between five levels

of inventions. According to his classification, Level 1 problems are the easiest

ones and Level 5 problems are the most difficult. He gives the following

explanation: "In problems of the first level the object (device or method) does

not change (for example, the heat insulation already present is strengthened). At

the second level, the object is changed but not substantially (high reflective

surface is added to the heat shielding device). At the third level the object is

changed essentially and at the fourth level the object is changed entirely; in the

fifth level the entire technical system is changed in which the object fits."

The study of the patent database points at the following breakdown of patents by

the levels of inventions.

4% 1%

Level 1 - Apparent Solution

18% 32% J Level 2 -Improvement

Level 3 - Invention inside Paradigm

45% Level 4- invention outside Paradigm

Level 5- Discovery

Figure 1. Levels of Invention

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Altshuller classifies creativeness by the type of the solution. This is a more open

and useful approach. Under Feldman et al definition of creativity only problems

of Levels 3 through 5 are being considered. This leaves out the vast majority of

problems (Levels 1 and 2 account for 77%) that most individuals encounter in

their lives.

Two Models of Innovation and Invention: Individual vs Cultural

Two different theories or explanations of the discovery process are often

discussed. One explanation is the "great inventive genius" model of discovery.

The proponents of this paradigm maintain that the inherent creative genius of

some individual's mind is responsible for the discoveries. The other theory relies

on the hypothesis that the discovery is "in the air" at that time - that the cultural

conditions are ripe for the discovery. These two explanations of discovery stem

from two opposing views of human behavior: an individualistic explanation

versus a group or social view.

Robert Haskell [15] compares the great inventive genius model to "the great

man" theory in history. According to this theory, it's the great individual who

changes history. The contrary view is that historical conditions create the "great

man". The sociocultural model of inventions includes such factors as economics,

opportunity, and support systems for promoting transfer.

There is little doubt that historical conditions are often responsible for great

innovations, but not always. One has only to examine the ideas of Leonardo da

Vinci (1452-1519), for example, his inventing the helicopter, to see that "the

times" often have little to do with creative genius. But often they probably do.

However, even when sociocultural or historical conditions are necessary, they are

not sufficient.

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R. Haskell quotes Stanford Ovshinsky, the inventor of amorphous

semiconductors: "There are a lot of people who may be smarter than I - so what

is it that makes me a successful inventor? It's got to be that I process my

information differently and draw upon my store, my environment, differently".

Let's examine the creativity process in more detail.

Creativity Process

While no one can draw an exact diagram of what is going in one's mind when

exercising creativity, the following approach may be useful in an attempt to frame

the issue. Consider an individual faced with a problem P. At some point in time,

a solution S may be developed.

P-S

This framework schematically represents that a certain stimulus P (problem)

yields a defined and expected solution S. However, it is often the case that many

individuals may come up with different solutions. This means that the "-"

represents the creative process within the individual. The "-" may also

characterize how well the individual knows the background information, how

extensive his/her knowledge it, how widely it spreads into the other domains,

what problem solving techniques are used, etc. Analysis of what is behind the

"-" may also help understand why some people seem to find the solution and

others don't.

Can people be taught to be more creative?

Ever since serious efforts to study creativity had begun the question of increasing

one's creativity was lingering in the air. Psychologists spent a great deal of effort

studying creative people (both deceased and alive) in an attempt to deduce

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common trends in their upbringing, education, habits, likes and dislikes, etc. as if

one can imitate a creative person's diet to stimulate his/her creativity. Over the

years many approaches have been proposed ranging from recommendations on

how to be more open-minded (Csikszentmihalyi) to detailed algorithms

advocated by the TRIZ [1, 29] and SIT practitioners [16, 23, 26].

Structured Creativi Techniques

TRIZ Overview

TRIZ (Russian acronym for Theory of Solving Inventive Problem) is a technique

that helps approach inventive problems in a structured manner [1]. Derived on

the basis of extensive analysis of the patent database, the TRIZ methodology

encompasses a set of tools useful for engineers and others dealing with problems

of technical nature. Attempts have been made to expand TRIZ principles into

management techniques, creativity education for the children [29], etc., but they

are less successful than the core discipline.

Several notions lie at the heart of TRIZ. The principle of idealiy (defined at the

sum of all useful functions of the system divided by the sum of all harmful

functions of the system) states that all systems evolve in the direction of increased

ideality. For example, today's automobiles have more useful functions (higher

reliability and durability, better comfort, more features, etc.) and fewer harmful

functions (cleaner emissions, lower noise, lower content of non-recyclable

materials, etc.) than the vehicles produced even 10-15 years ago. Taken to an

extreme, an ideal system from the TRIZ point of view performs the function, but

does not itself exist. This maybe difficult or impossible to achieve in real life, but

it is a good "stretch goal".

To help illustrate this point, the following example may be useful. Suppose a set

of samples of several alloys need to be tested for their resistance to a corrosive

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environment. The alloy samples are made into small cubes, deposited into vials

with acid solution and are subjected to heat and vibration to accelerate the test.

Unfortunately, the glass vials tend to crack. What can be done to test the

samples? Traditionally engineers will try to upgrade the vials to a higher

performing material so that they survive the test or may try to find an environemt

less aggressive to the vials. From the TRIZ point of view, however, the vial is

only needed to contain the acid solution. It does not help to test the alloy

samples. The actual test occurs at the interface of the alloy sample and the acid

solution. Ideally the vial needs to be absent, but the acid solution needs to be

retained in some manner. How can this be accomplished? A simple way to do

this is to drill a round hole in the alloy sample and fill it with the acid solution.

Now the vial is gone and the acid solution is retained right where it needs to be.

The notion of ideality is quite general and somewhat philosophical in nature, but

it can drive the system architect to closely evaluate each component in the system,

define their useful and harmful characteristics, attempt to combine components

in order to reduce complexity, increase system reliability, etc.

Several other tools are more prescriptive in nature. For example, ARIZ (Russian

acronym for the Algorithm of Solving Inventive Problems) provides a step-by

step guide to define the problem, the ultimate desirable outcome, describe the

contradictions' that prevent one from reaching the solution and, finally, resolve

them without violating the ideality principle.

1 A contradiction is such a situation in which improving a desired parameter leads to deteriorationof some other parameter. For example, one may want to make a certain part stronger, but thatmakes it heavier at the same time.

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Yes

ItNo

Figure 2. Simplified ARIZ diagram

The tools of resolving contradictions are probably the most useful. According to

the TRIZ methodology, contradictions can be resolved in one of the four

following ways: in time, in space, between the parts of the object and the object

in whole, and upon a condition. For example, resolution upon a condition would

suggest speed sensitive steering efforts in an automobile (steering effort is low

when the vehicle is moving with low speed and steering effort is higher when the

vehicle is moving faster).

Structured Inventive Thinking Overview

Developed on the basis of TRIZ methodology, Structured Inventive Thinking

(SIT), grew in its own methodology. A student of Altshuller brought the method

to Israel, where it was extensively revised and simplified, enabling the method to

be learned in a significantly shorter time, and with less reliance on external

databases.

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The SIT methodology deals with conceptual solutions to technological problems.

Its purpose is to focus the problem solver on the essence of the problem, to

enable the discovery of inventive solutions, and to make the process an efficient

one. It does this by guiding the user through either of two algorithms (see Figure

3) which structure the problem in such a way as to allow the user to bring to bear

various techniques that have been found to be helpful in inspiring creative

solutions.

SIT has been taught to over 3000 engineers in Israel, and is being used by a

number of companies there, including Motorola and Intel. Ford is the first

company to introduce the method in the U.S. It is currently being taught at Ford

Design Institute. The courses, 24 contact hours in length, have been given so far

to over 1000 Ford engineers and scientists in the U.S. and Europe.

Closed World MethodCollect Draw Draw

Information Closed-World Qualitative-Diagram Change Graphs

Select Unique"Objects Determine Draw ness

Detemine Apply DaInitial & Final pply And/OrStates Particles Tree

Particles Method

DimensionalitySolution - PluralizationConcepts

Redistribution

Figure 3. Flowchart of the SIT Process [26]

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Summary of Structured Creativit Techniques

Structured creativity techniques, are useful tools to help engineers and scientists

develop creative solutions. Commercially available software products simplify

database searches and provide pictorial examples of creative solutions to

problems similar in nature. For example, if someone is trying to solve the

problem of gripping parts of complex shape with a vise, the software tool called

Innovation WorkbenchTM distributed by Ideation International Inc, will suggest

the adding intermediary elements that can conform to the complex shapes, yet

effectively transfer the gripping force as illustrated in Figure 4.

Figure 4. TRIZ Solution - Gripping Complex Parts with a Vise

A product utilizing a similar principle appeared recently on the market. The

Gator-Grip@ socket (http://www.gator-grip.com) claims to grip "anything that

isn't round"!

Typically the user will benefit greatly from attending a course or workshop where

the basic principles of these methodologies are reviewed.

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Creativity Barrier

Problem solving is sometimes hindered by the Creatioiy Barrier, which prevents

the individuals from choosing the direct path to the solution. Figure 5A

illustrates the problem solving process influenced by such a creativity barrier: the

efforts of the individual to solve this problem are halted by the creativity barrier.

Depending on the difficulty of the problem, this can be a more or less permanent

position. Research shows that the more difficult the problem, the more attempts

are required in order to solve it. Often after many trials and failures, a solution

path is finally found. This is shown in Figure 5B where the solution path goes

around the creativity barrier. This process is characterized by extended time and

fruitless trials. If the individual is successful in breaking the creativity barrier,

he/she is able to attain the solution much more directly and faster (Figure 5C).

The difference between the approach in Figure 5B and Figure 5C is in the

fundamental level of understanding the challenge and in the ability to face the

root cause. The approach depicted in Figure 5B is usually referred to as trail-and-

error. Typically multiple solution attempts will be emanating in various directions

from the node P and one of them may eventually yield solution S. Figure 5C

shows the process of someone who can pinpoint the root cause of the problem

and attack it directly.

We will attempt to measure this process. In the experiment described in more

detail in Chapter 4, we will ask a group of individuals to solve a series of puzzles,

while taking measurements of time, the number of attempts, the rate of give ups,

and, of course, the success rate.

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Solution

0Creafivi_*

Barrier 4 .|e Solution

pathattempt

Problem

Solution Solution

Q~r Solution0

Creativiy -. u t

Barrier 4

0

Problem Problem

A) Creativity processhindered by the Creativity

BarrierFigure 5. Effect of the

B) Solution path found aroundthe Creativio Barrier

Creativity Barrier on the Solution Path

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C) Break throughthe Creativio Barrier

The notion of the Creativity Barrier can be illustrated with the help of this

familiar example. The task is to connect all the nine dots with four straight lines,

without lifting the pen from the paper.

* 0 0

* 0 0

Zander [31] describes the experience of someone solving this puzzle for the first

time: "...you will most likely find yourself struggling to solve the puzzle inside the

space of the dots, as though the outer dots constituted the outer limit of the

puzzle." We look at the dots and all we can see is a square. We then make a

typical mistake.

This situation is similar to the one shown graphically in Figure 1A. Of course,

this is not the right solution. What's needed to solve this puzzle is to abstract

from the outer dots and expand the solution space. We need to move ourselves

from the hopeless situation in Figure 1A to a desirable situation in Figure 1C. As

soon as one realizes that the instructions did not contain anything about fitting

the lines nithin the area staked out by the outer dots, and the entire white sheet

can be used, the creativity barrier begins to crumble. The reader is encouraged to

attempt to solve this puzzle before proceeding to the next page, where one of the

possible solutions is shown.

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It is thought that creative people are less affected by the creativity barrier and,

therefore, are capable of arriving at the solutions faster and more reliably than

others. Of course, the other way to look at the so-called "creative" people is to

say that they are more capable of expanding their solution space. So, it follows

that the lower one's creativity barrier or the more one is capable of consciously

destroying it, the more creative the person is. But what affects one's creativity

barrier and how does one go about lowering it?

The creativity barrier can be viewed as composed of two primary ingredients:

personal inhibiions and the context.

CreativityBarrier

Individual ContextInhibitions

Groove-in Setting

Practice Pressure

Type of transfer Expectations

Fear of failure Risk aversion

Other Other

Figure 6. Functional Decomposition of the Creativity Barrier

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To enhance the understanding of the notion of the creativity barrier it is

important to figure out how the two building blocks interact, what is the balance

between them, does this balance have a dynamic nature, what may be the

circumstances that cause this balance to shift in one direction or another.

The individual inhibition is a function of one's prior experience (groove-in),

practice with similar type of problems, type of knowledge transfer, fear of failure

or its consequences, etc. The context has to do with the environment, the setting

and pressure that may come from the desire to fulfill the expectations of others,

fear of saying or doing something that may cause others to not accept it or, even

worse, judge or make fun of you, etc.

In this thesis I will focus on the individual inhibitors and, in particular, on what

can be done to improve the knowledge transfer. I will use the terms "knowledge

transfer" and "learning transfer" interchangeably.

How to reduce the creativity barrier

While many ways to address each and every one of the elements shown in Figure

6 may be devised, this thesis centers on the investigation on how the creativity

barrier can be lower by influencing just a single factor - the transfer of learning.

From that point of view, I will examine how the three primary mechanisms of

learning transfer, namely self-discovery, instruction and tutoring, affect creativity

and problem solving skills.

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Chapter 2

TRANSFER OF LEARNING

Processes of learning and the transfer of learning are central to understanding of

the development of important competencies. Since early childhood people are

exposed to various types of learning experiences: instruction, tutoring, self-

discovery, etc. Knowledge and skills acquired through these various types of

experiences leads to varying levels of proficiency.

What is Learning Transfer?

Transfer of learning means that experience or performance on one task

influences performance on some subsequent task. Transfer of learning may take

three different forms: (1) performance on one task may aid or facilitate

performance on a second task, which represents positive transfer, (2) performance

on one task may inhibit or disrupt performance on a second task, which

represents negative transffer, and (3) finally, there may be no effect of one task on

another, in which case we have an instance of Zero transffer [9]. His study showed

that "students who have thoroughly mastered the principles of algebra find it

easier to grasp advanced work in mathematics such as calculus." Another study

[2], compared students learning LISP as a first programming language to students

learning LISP after having learned Pascal. The Pascal students learned LISP much

more effectively, in part because the appreciated the semantics of various

programming concepts.

For effective positive transfer to take place [19]:

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1. The student must understand that the learned behavior can be generalized to

other domains

2. It is necessary for the student to mindfully abstract or decontextualize the

schema from the learned behavior so that it can be modified and applied

3. The student needs to recognize the relevant sameness between the

instructional situation and a transfer situation.

Ability for abstract thinking as an important ingredient for problem solving and

creativity.

Negative transfer may also take place. In the case of the negative learning

transfer the previously acquired skill will prevent the individual from performing

well on the new task. This may be a result of overleaming leading to lack of

flexibility in thinking. Extensive experience in a certain field may give rise to such

a dichotomy. For example, those visiting the U.K. for the first time often have

difficulty navigating through traffic. The power of habit of first looking to the

left and then to the right when crossing the street does not work well when the

traffic moves in the opposite direction than one is used to coming from the U.S.

or continental Europe. In psychology this is referred to as automaticity.

Even though in problem solving we are dealing with a higher order cognitive

functions, the basic principle still applies. On the one hand deep expertise may be

required to perform the task well, but on the other hand, the same experience

may tend to lock the individual in a particular frame of mind, thus contributing to

negative transfer. To counter this, the "fresh eyes look" approach is often called

into action, which entails bringing a less experienced person to analyze the same

problem. In this case the less experienced person, who is not as constrained by

conventional wisdom, may offer new perspectives and help the situation.

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Promoting Positive Learning Transfer

What Affects Learning Transfer?

Leaming transfer has been studied extensively since early 1900's. Here I present

a very brief summary of the key points. Much of this is based on [4].

Several critical features of learning affect people's abilities to transfer what they

have learned. The amount and kind of initial learning is a key determinant of the

development of expertise and the ability to transfer knowledge.

While time on task is necessary for learning, it is not sufficient for effective

learning. Time spent learning for understanding has different consequences for

transfer than time spent simply memorizing facts or procedures from textbooks

or lectures.

The context in which one learns is also important for promoting transfer.

Knowledge that is taught in only a single context is less likely to support flexible

transfer than knowledge that is taught in multiple contexts. With multiple

contexts, students are more likely to abstract the relevant features of concepts

and develop a more flexible representation of knowledge. The use of well-chosen

contrasting cases can help students learn the conditions under which new

knowledge is applicable. Abstract representations of problems can also facilitate

transfer. Transfer between tasks is related to the degree to which they share

common elements, although the concept of elements must be defined

cognitively.

All new learning involves transfer. Previous knowledge can help or hinder the

understanding of new information. For example, knowledge of everyday

counting-based arithmetic can make it difficult to deal with rational numbers;

assumptions based on everyday physical experiences (e.g., walking upright on a

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seemingly flat earth) can make it difficult for learners to understand concepts in

astronomy and physics and so forth.

Effects of the Instructional Types on Learning Transfer

In this thesis we will demonstrate that the knowledge transfer is also affected by

the instructional type. Specifically, three various approaches will be considered.

1. Generic instructions. If the individuals are instructed to apply certain

knowledge in a hypothetical situation, it is hopeful that when they encounter the

situation similar to the "designated" one, they will apply the knowledge and

achieve a successful result. To achieve the successful outcome however, the

individuals must: 1) recognize that the situation is of the type when this particular

knowledge must be applied; 2) invoke the particular instructions in their mind

that relate to this situation; and 3) apply knowledge in the correct way. The

likelihood of the success depends on how well the instructions were received,

how explicit they were, how extensive the knowledge is (this is particularly

important if the encountered situation is somewhat different from the 'textbook'

version and a certain amount of knowledge manipulation is required) and how

proficient the individual is with the actual knowledge application. It is possible

the individuals will generate creative solutions in this situation, however,

following specific instructions is likely to yield a predictable result.

2. Specific Instructions (Tool). Another method of invoking knowledge

transfer is through the use of a specialized tool. Such a tool could be in the form

of detailed, step-by-step instructions or a software product, cue cards, etc.

Evidence suggests that a tool can be highly effective in the hands of a well trained

individual and will allow him or her to produce a large number of solutions in a

quick manner. The tool is much less effective for individuals lacking training. In

both instances, however, over reliance on the tool is possible. Another drawback

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of using a tool is for non-standard type situations when the effectiveness of the

tool is substantially diminished.

3. Self-discovery will require the most creativity from the individual and it is,

probably, the least certain method. Success in self-discovery stems from the most

in depth understanding of the subject matter, an insight and/or discovery of an

underlying trend. This in depth understanding is achieved through

experimentation with a wide range of solution directions and a deeper dive into

them. If the individual is successful in achieving the solution, it is likely to

remain in memory the longest. Even if the individual forgets the solution after a

period of time, he/she is likely to develop this solution once again if required as

long as the knowledge of the subject matter remains active.

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Chapter 3

HYPOTHESES

1. It is hypothesized that the learning transfer is affected by the method by which

the individuals acquire the skills needed to solve the problem. Three

distinctive methods are identified and compared in this study: 1) self-

discovery, 2) generic or process level instructions and 3) a tool or very

narrow and specific level instructions.

2. It is hypothesized that the quality of learning transfer can be measured by

the speed and the correctness of the responses.

a. The individuals using the self-discovery approach will require more

time initially, but as they acquire the fundamental understanding of

the subject matter through a more thorough investigation of a wider

range of appraoches, will take progressively less time. When

presented with a problem of a slightly different nature, but utilizing

the same underlying principle, they will recognize the fundamental

similarity and will be well poised to apply their knowledge to solve

this problem. These individuals will solve the non-standard

problem faster and with a higher percentage of correct answers than

those using methods 2 and 3, described above.

b. The individuals using generic instructions will take less time initially

than those using the self-discovery approach as the fundamental

principle is already extracted for them. If the application of this

distilled and readily available fundamental principle is clear to them,

they solve the initial problem faster than those practicing the self-

discovery approach. They are also likely to get a higher percentage

of the correct answers on the first attempt. When presented with a

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problem of a different nature, but utilizing the same fundamental

principle, these individuals will be less likely to apply their

knowledge than those using the self-discovery approach since the

creative step needed for this exercise was not practiced by them with

the previous problems.

c. The individuals using the tool, or specific instructions, will perform

well when the application of the tool is transparent. They will

exhibit the fastest time on the first problem and the highest

percentage of the correct answers on the first problem. However,

their performance on the problem of a different nature, but utilizing

the same fundamental principle, will be markedly worse than of

those practicing the self-discovery or those receiving the specific

instructions. The creativity of the individuals using the tool will be

hindered by the excessive reliance on the tool.

3. It is hypothesized that the method of skill acquisition also affects the long-

term memory retention. Those practicing the self-discovery will have better

long-term memory retention than those receiving specific instructions, with

those receiving generic instructions falling between the other two categories.

However, this aspect of learning transfer is not a subject of this thesis.

The following table will help summarize the hypotheses described above.

Learning Transfer Self- Generic SpecificParameter Discovery Instructions InstructionsLevel ofunderstanding of High Medium Lowthe subject MatterThought flexibility High Medium Low

Speed Low Medium High

Table 1. Anticipated Effects of Instructional Types on KeyLearning Transfer Paramters

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Chapter 4

EXPERIMENTAL APPROACH

BriefDesciption of the Experiment

The experiment was devised to quantify the effect of the method by which the

learning skills are acquired. This experiment involved three groups of

respondents:

1) Control group. The individuals in this group received no instructions on

how to solve the problems. These individuals were forced to use the self-

discovery approach, although it was not communicated to them.

2) Test Group 1. The individuals in this group received generic instructions

on how to solve the first problem in each of the series.

3) Test Group 2. The individuals in this group received spedfic instructions

on how to solve the first problem in each of the series.

It is important to note that in the Groups 2 and 3 the respondents received

instructions for only the first problem in each of the two series.

The performance of each of the respondents was measured using several key

parameters for each of the puzzles (a total of 9 puzzles arranged in two series

were presented to each of the respondent):

1) Time. The time to solve the puzzle was measured and recorded to the

output file based on the computer internal clock.

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2) Success rate on the first attempt. If the respondent was able to

develop the correct answer on the first attempt, the value of 1 was

recorded to the output file. If the respondent entered a wrong answer

on the first attempt the value of 0 was recorded to the output file.

3) Ultimate success rate. If the respondent was able to develop and

enter the correct answer the value of 1 was recorded to the output file.

If the respondent was not able to develop the correct answer and gave

up the value of 0 was recorded to the output file.

4) Number of attempts undertaken in a quest to develop the final correct

answer.

5) Give up rate. If the respondent opted out of solving the problem and

hit the "Give Up" button, the value of 1 was recorded to the output file.

The individuals were contacted via e-mail. The e-mail contained a request to

download the attached file, run the program and e-mail the results back for

compilation of the data and analysis. The flowchart of the process is shown on

page 31.

The individuals had several opportunities to opt out of the survey. For example,

they may have disregarded the initial e-mail all together. A variety of reasons may

have led the person to this decision: too busy, not interested in helping out, etc.

The next opportunity to drop out was after the start of the program. When the

respondents got the first glimpse of the puzzles, they made a decision on whether

to proceed or quit. Some people found the puzzles of mathematical nature of

little interest or they may have disliked them based on the prior experience. Yet

another opportunity to opt out was any time throughout the survey process. The

respondents may have thought that the problems were too difficult, or they have

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already spent enough time, or it simply required more time commitment from

them than they originally anticipated. The last decision point on whether to go

through with the survey or to opt out arose upon completion of the survey. The

respondents had an opportunity to view their output file and make a decision on

whether to send this file for analysis or not.

Individual iscontacted by

e-mail

---- ------------ + Opt out

Individual runsthe program

Randomassignment

-----------------+ Opt out

Control group Group 1 Group 2(No Instructions) (Generic (Specific

Instructions) Instructions)

O---------------+ opt out

Individualsolve thepuzzles

-------------------+ Opt out

Individual e-mails results

file for analysis

Figure 7. Diagram of the Survey Process

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Selection of the Individuals for the Study

Since the goal of the study was to teach the participants a certain skill using three

distinctive methods and then to gauge how effectively they learned this skill, it

was important to select the individuals open to learning. At the same time, it was

important to select a relatively homogeneous group of people, so that no

significant advantage can be gained from having prior knowledge and or skill.

Based on these considerations, it was decided that graduate students at MIT

Sloan and Engineering Schools, Haas Business School at University of California

at Berkeley, and engineering professional at Ford Motor Company and a several

other organizations, would be targeted. It was decided that approximately 100

output files need to be collected and analyzed to ensure statistical power of the

data.

Developing the Survey

Applying the principles learned in System and Project Management as well as in

Systems Engineering, the first item of priority was to define the requirements for

the survey.

List of Requirements for the Survey

The following set of the requirements was identified and prioritized based on the

available resources, timing and expected level of commitment on the part of the

respondents.

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Assessment of learning transfer

Gauge the effectiveness of learning transfer HighTeach a skill in the course of the survey HighMeasure the effectiveness of the learning Hightransfer of a somewhat different taskRepeat previous two steps for another set Highof problems

Measure respondent on at least two scales High

Time High

Correctness of the response High

Ease of use

Provide fun and excitement for the respondent High

Takes no more than 10 minutes to complete Medium

Save data for analysis HighRun on PC, Mac or Unix platform High

Provide information about the respondents

Demographics Low

Education level Low

Educational background Low

Table 2. Priority of the Requirements

Designing Problems for the Survey

Selecting the problems for the study was the crucial task. The problems have to

have a certain amount of commonality between them so that the respondents

could practice with them while acquiring the skill, and, at the same time one of

the problems needs to be of a similar type, yet different enough to allow the

respondents a chance to transfer the learning. So, the series of the such problems

was represented as follows: A, A', A", A', B. In this series the problems A, A',

A", and A"' share common features, while the problem B although based upon

the same underlying principle, is substantially different.

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A number of various problems were considered. In the end, it was decided that a

the first set of problems will comprise of a number series and the second set of

problems will be more graphical and involve a series of triangles with numbers

forming a certain pattern arranged at the peaks of the triangle and in the center.

In the number series of the puzzles the respondents were asked to determine the

next number in each of the strings. The following puzzles were used (Part 1 of

the survey):

A) What is the next number in this series?

2, 5, 14, 41

B) What is the next number in this series?

84, 80, 72, 60

C) What is the next number in this series?

39, 50, 63, 78

D) What is the next number in this series?

55, 74, 57, 72, 59

E) What is the next number in this series?

144, 12, 120, 10

Puzzles were presented one by one to the respondents so that they couldn't easily

cross-reference them. The respondents were informed whether the entered

solution was either correct or wrong; they were not allowed to go back to a

particular puzzle once they either entered the correct answer or gave up.

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In the triangle series of the puzzles the respondents were asked to determine the

value in the center of the last triangle in each of the strings (Part 2 of the survey):

A)

3

A22 2

2

A3 2

4

A

6

A

5 9

3 5

3

A22

1

3

3

4 4

5A

3

GD

AFF C

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7B)

4

C)

2D)

2

2 7

D

E A E G

PuZZle Answers and Explanations

Section 1

A) The difference between the numbers in this series represents a power series of

3 (5-2=3; 14-5=9, 41-14=27 or 31, 32, 3). So, the difference between 41 and the

last number in the series should be 34=81, making the last number 41+81= 122

B) The difference between the numbers in this series is: 4, 8, 12. Clearly, this a

arithmetic progression, increasing by 4. So, the next delta should equal 16. This

makes the last number in the series: 60-16=44.

C) Similarly to B, the delta between the numbers in the series is 11, 13, 15. The

next odd number is 17, making the last number in the series 78+17=95.

D) There are two series embedded into this string of numbers. One series is 55,

57, 59 which is increasing by 2. The other series is: 74, 72, ?, which is decreasing

by 2. So, the last number in the series is 72-2=70.

E) This series can be solved in the following manner: 144 divided by 12 (a

constant) is 12, which is the next number in the series after 144. If the result of

the division operation is then multiplied by 10, it yields 120, which is the next

number in the series. Similarly, 120 divided by 12 (same constant) yields 10 - next

number in the series. 10 multiplied by 10 (equals 100) produces the answer to the

puzzle.

Section 2

A) Adding the numbers at the comers of the triangle yields the solution: 14.

B) Multiplying the numbers at the corners of the triangle yields the solution: 15.

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C) Multiplying the number at the top of the triangle by the number at the bottom

right hand comer and subtracting the number at the lower left comer yields the

solution: 12.

D) Converting the letters into numbers and manipulating the numbers as

described in C), yields the answer: W.

Prototype of the Survey

Two main platforms for conducting the survey were considered: the web-based

and a stand alone program. Each has its own advantages and disadvantages. For

example, the web-based survey is easy to create, easy access and it allows

automatic data compilation. The main challenge with the web-based approach,

however, is that the variations in network traffic density can substantially affect

the time calculation. Since the time is one of the main measures of the learning

transfer, it was decided to use the stand alone program to ensure the high quality

of the time data, even though this approach does not allow for as easy of an

access or automatic data compilation.

The web-based prototype was used early in the development (beta testing 1). The

goal was to ensure that the respondents can solve the puzzles in the reasonable

amount of time and that the instructions were clear.

Developing the Instructions

The importance of this step should not be underestimated. The instructions for

Group 2 should be such that they convey the general principle useful to solve any

of the problems in the given series. On the other hand they can't be specific too

specific because then the difference between the Groups 2 and 3 will disappear.

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The following screen captures illustrate the varying levels of instructions used for

the Control Group and Groups 2 and 3.

Conskier the sequence of numbers below-

By conducting mathematical manipulations (addition, subtractin,multiplication, etc.) deduce the formula that links the numbers. Applythis formula to determine the next number in each of the series

Please type In the number (and press the return key)

Figure 8. First puzzle of the number series as presentedto the Control Group

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Think at the misakig number in terms of a trend of numbers. Is thetrend bntre n or de"'Ing? Can you determlne anotlw p*tnm?If t etnd is kh", how apidty do the numbws incen? Nowthink of the mattwinaical functions tht can egain such a behavior.For example, i the trendnates a rapi 1inCRfse, It could teexplned by muApltatot, pOer lvw, etc, while a slower nscxdIngtrend could be explained by sumrntict Dedue thefvmula thatIkfS the numbers and determine the net number r the series.

For exampte, coside the nqwnce of numnt beow2, 5, 14, 41,7

This s a rapidy ascending trend; the diference between thenumbers repst* a P4*we srist Apply tis ormula to d m*W ethe net number wi each o# the senws

Please type in the number (anid pre the return key)

Figure 9. First puzzle of the number series as presentedto the Group 1 (Generic Instructions)

Consider the sequence of nurabets WeOW By COMdWC~ngtna#t4&mAIc manopulatian" (addifion, wsbion, mutlilcatlwn, etcjdeduce ttw- formula that links the numbers. Appty this tforula todetermine te nrxA numbef In each of the wsft,

The dstmnoe bybwlen the numbeTs iM this series repsents a poweseries of 3 (5-2=3=; 14-5=9=32 41-14=27=3J So the dfrencebetween the last number ki the senes and 41 should equal 34 (3 toIne pownr 4) 0r81 lTau the answr to the put.l is z-41=41 or

=122

5, 14, 41,

Piveae type a the number t(nd press the return ky)

Figure 10. First puzzle of the number series as presentedto the Group 2 (Specific Instructions)

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Data Analysis

Approximately 250 individuals were contacted by e-mail and 90 output files were

collected.

Transfer Formula

The amount and direction (positive or negative) of transfer is determined by

employing one of several formulas. The three transfer formulas described below

are similar in that they involve making comparisons between the experimental

and control groups on performance on the transfer task.

In order to apply a transfer formula to a given set of data, some measure of

performance must have been taken. Measures frequently used include: (1) the

number of trials required to reach a given level of mastery; (2) the amount of time

required to reach a given level of mastery; (3) the level of mastery reached after a

given mount of time or number of trials, such as the number of correct

responses; and (4) the number of errors made in reaching a given criterion of

mastery.

A simple transfer formula is described below. Let E represent the mean

performance of the experimental group on the transfer task (Task B) and let C

represent the mean performance of the control group on the transfer task (Task

B). By comparing the difference between E and C groups with C itself a

percentage transfer formula can be expressed as follows:

Percentage of Transfer = * 100 (1a)C

This formula is appropriate if the measure of performance is such that the larger

the value of the measure, the better the performance. For example, if the measure

of performance is the number of correct responses, then the formula is

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appropriate because the number of correct responses becomes larger with better

performance.

Formula (1a) will be illustrated with a simple example. Suppose we conduct a

transfer experiment in which we measure the effect of taking French this year on

the taking of German next year. In other words, we want to know if taking

French will aid or interfere in the subsequent learning of German. We employ

two groups: an experimental group that studies French for a year and then takes

German the following year and a control group that studies only German. In this

instance, Design I is employed. A measure of performance is taken on the first

test on German and we discover that the E group averages ninety correct

responses whereas the C group averages only seventy-five correct responses on

the test. Applying Formula (1a) and substituting the values for E and C, we

obtain:

9075* 100 = * 100 = 20percent transfer75 75

The E group shows 20 per cent transfer, which means that the E group performs

20 per cent better in German compared with the C group. Of course, we do not

know if the positive transfer is a result of the specific features of French or of

learning to learn; it is likely a mixture of both.

Formula (1a) must be modified by reversing the numerator to C - E if the

measure of performance is such that the smaller the value of the measure, the

better the performance. In this case, the formula becomes:

Percentage of transfer = CE* 10 0 (1b)C

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This formula is appropriate with such measures as errors, trials to reach some

criterion, or time. It is obvious that as errors, trials, or time are reduced in value,

performance improves.

A second type of transfer formula was proposed by Gagne et al. (1948). This

procedure compares the difference between the E and C groups with the

maximum amount of improvement possible on the transfer task. The maximum

improvement possible is indicated by the difference between the total possible

score on Task B and the performance of the C group on Task B. If the measure

of learning is one such as number of correct responses, as in Formula (la) , and T

stands for the total possible score, the formula is

Percentage of transfer = E-C * 100 (2a)T-C

The denominator and numerator are reversed if the measure of learning is one

such as time, trials or errors, as in Formula (1b).

Percentage of transfer = CE* 100 (2b)C-T

A chief difficulty with using either Formula (2a) or Formula (2b) is that we do not

always know the total possible score T, and its determination may be difficult or

impossible.

Murdock (1957) has suggested a third type of transfer formula which has a

distinct advantage over the first two described. The maximum amount of

positive transfer which can be obtained is 100 per cent transfer and the maximum

amount of negative transfer is -100 per cent; in other words, the upper and lower

limits are equal, and positive and negative transfer are symmetrical. This is

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accomplished by making the denominator of the formula include the

performance of the E group as well as the G group. The formula is:

Percentage of transfer = F-C * 100 (3a)E+C

Like Formula (1a), Formula (3a) is appropriate if the measure of performance is

such that the larger the value of the measure, the better the performance. If the

measure of performance is such that the smaller the value of the measure, the

better the performance, the formula must be modified to read:

Percentage of transfer = CF *10 0 (3b)E+C

Comparison of Formulas

A comparison of Formulas (la), (2a), and (3a) is shown in Table 3, p. 44.

Hypothetical values for E, G, and T are listed along with the percentage transfer

obtained with each formula. Because different percentages of transfer are

obtained with each formula, the importance of knowing what transfer formula

was used in a particular study becomes obvious, especially if one wishes to

compare the magnitude and direction of transfer obtained in different studies.

This latter point has been strongly emphasized by both Gagne et, al. (1948) and

Murdock (1957).

Selecting the Formulas for the Data Analysis

Since the total possible score (T) is unknown in the types of problems used for

the study in this thesis, the application of formulas 2(a) and 2(b) is not possible.

Also, since we are interested in determining the relative performance of the three

groups (Control Group and Groups 1 and 2), and not in establishing the upper

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and lower control limits, the choice of formula becomes quite obvious. The

Formulas 1(a) and 1(b) will help us quantify the effect of learning transfer.

Table 3. Comparison of Percentage TransferObtained by Three Transfer Formulas

Number of Correct Responses Percentage Transfer from Formula

E C T (1a) (24) (3a)

50 0 50 +Infinity +100 +100

25 15 50 +67 +29 +25

15 15 50 0 0 0

15 25 50 -40 -40 -25

0 50 50 -100 -Infinity -100

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Chapter 5

RESULTS

Summary of the Survey Results

The complete set of survey results can be found in Appendix.

The survey output files were received from 90 respondents. Individual output

files were examined and the outliers excluded from the analysis (see Experimental

Limitation section, p. 47). After the outliers were excluded, 84 "good" output

files were analyzed. The tables below summarize the learning transfer for the first

and the last puzzles in Sections 1 and 2. The learning transfer values for time,

number of attempts and give ups were calculated according to the formulas 1(b)

since the lower value points at a better outcome. The values for number of

correct answers on the first trial and the ultimate number of correct responses

were calculated using formula 1(a).

The following abbreviations are used in the tables below:

C - Control Group using self-discovery

El (G) - Experimental Group 1, using Generic instruction

E2 (S) - Experimental Group 2, using Specific instruction

Transfer 1 - Learning transfer for El

Transfer 2 - Learning transfer for E2.

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Section 1, Question 1

C El (G) E2 (S) Transfer 1 Transfer 2

Time, sec 93.000 121.000 91.000 -30% 2%

Correct 1 0.818 0.625 0.778 -24% -5%

Correct 0.909 0.667 0.926 -27% 2%

# attempts 1.152 1.333 1.185 -16% -3%

Give ups 0.030 0.042 0.000 -40% 100%



Time, sec 98.456 59.653 47.043 39% 52%

Correct 1 0.545 0.333 0.407 -39% -25%

Correct 0.848 0.625 0.667 -26% -21%

# attempts 1.545 1.958 2.000 -27% -29%

Give ups 0.121 0.250 0.296 -107% -145%



Time, sec 24.157 65.007 30.227 -169% -25%

Correct 1 0.970 0.958 0.963 -1% -1%

Correct 1.000 0.958 0.963 -4% -4%

# attempts 1.061 1.000 1.000 6% 6%

Give ups 0.042 0.000 0.000 100% 100%



Time, sec 95.673 121.099 123.115 -27% -29%

Correct 1 0.273 0.250 0.296 -8% 8%

Correct 0.515 0.417 0.667 -19% 30%

# attempts 1.788 3.542 2.519 -98% -41%

Give ups 0.364 0.458 0.148 -26% 59%

Table 4. Summary of Survey Results

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The values in the columns C, El and E2 represent the mean values based on the

analysis of output files falling into the respective categories.

Learning transfer for experimental Group 1 (Transfer 1) - those using Generic

instructions - is mostly negative with the single exception of time (speed) for the

last puzzle in Section 1 (negative transfer for number of attempts and give ups

indicates more attempts and give ups respectively).

Learning transfer for the experimental Group 2 (Transfer 2) - those using specific

instructions - appears to be more ambiguous. The instructions helped the Group

2 solve the puzzles faster than the control group in the first section, but served as

a detriment in other measured attributes (time, number of correct responses on

the first trail, ultimate number of correct responses, number of attempts and

number of give ups). The situation changed for the second section where the

instructions adversely affected the speed and number of attempts, but improved

the rate of correct responses and allowed for fewer give ups.

Expermental Limitation

Variable Test Conditions

The nature of the experiment required that the respondents take the survey at in

the environment of their choice. Varying ambient noise level, and other

conditions may have affected the level of focus on the part of the respondents.

Among the outliers were those output files in which the time for a particular

question was substantially longer than anticipated or than it took this respondent

to answer a similar question in the survey. For example, in one of the files it took

the responded nearly 27 minutes to answer question number 3 in part 1. Such an

extended time may be explained by a distraction on the part of the respondent.

In fact, one of the respondents mentioned to me that as he was taking the survey

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in his office, he received a visitor who engaged him in a conversation, thus

distracting the respondent from the survey. This particular respondent did not

read the instruction carefully enough to realize that he was being timed.

Self-Selection

As indicated in Figure 7, the respondents had several opportunities in the course

of the survey to opt out. Every decision point contributed to the self-selection.

The last decision point was probably the most critical. Looking at their results,

the individuals assessed their own performance on the survey. Their self-

assessment at this point was very subjective as they had no reference point and

didn't know the average results or results of others who tool the survey.

Nevertheless some respondents may have decided that their results are not

adequate and may have elected not to send them in for analysis. The fact the

author of the thesis personally knew most of the respondents exerted further

pressure on them. Those who decided to refrain from returning the surveys, may

have felt embarrassed about their performance and preferred not to reveal it so

that the author of this thesis does not think negatively of them. This type of self-

selection may have affected the data set, decreasing the population of poor

performers. It is hard to tell now which one of the three groups had the largest

number of the dropouts.

The table below provides the breakdown of the 84 analyzed output files by the

Group type.

Group Control Group Experimental ExperimentalGroup 1 Group 2

Count 33 24 27

Table 5. Breakdown of the Analyzed Output Files by the Group Type

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Curiously enough, the most surveys returned came from the Control Group. The

obvious question arises: is such an outcome a result of the random nature of the

process of assigning the respondents to one of the three groups or is this

distribution affected by the self-selection? In other words, assuming that equal

number of people got assigned to each of the three groups, it is possible that the

individuals in the Control Group are more likely to return their output files than

those in the experimental groups? To answer this question from the statistical

point of view, one needs to compare the actual count numbers to the expected

value. If a total of 84 surveys were assigned randomly to three groups, one would

expect to see 28 surveys in each of the groups. However, in our case, we end up

with a distribution of 33, 24 and 27. So, what is the probability of getting 33

when 28 is expected? The analysis shows that such a probability is approximately

10%. Similarly, the probability of getting 24 when expecting 28, is approximately

15% (probability of getting 28 is 50%).

Although the probability of such a distribution is still within the random nature

of the process, the slight shift in favor of the control group is obvious. This leads

to the conclusion that the individuals in the control group feel somewhat better

about their result and are more likely to return their output files. One possible

explanation to this is that the expectations of solving the puzzles among the

respondents in this group are closer to the reality than for those in the

experimental groups, even though the latter ones were not told that they belong

to the experimental groups. The only way to get around this issue is to conduct

the experiment in the controlled environment, were all the respondents must

return their output files.

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Chapter 6

DISCUSSION

Discussion of the Survey Results

The survey results once again demonstrate that the problem solving activity is a

multidimensional process.

Effect of the Instructions on Time

The two plots below show time normalized with respect to the control group.

3.0-

2.5 - - - - - - - - - - - - - - - - - - --4-Control Group

j: 2.0 -- Group 1 (Generic Instructions)

-*- Group 2 (Specific Instructions). 1.5

0.5 - - - - - -

0.01Puzzle 1 Puzzle 5

Figure 11. Effect of theInstructions on Time, Section 1.

3.0

2.5- - - - - - - - - -

i 2.0 - - - - - - - -

. 1.5 - - - - - - - - - - - - -

1.0 -----4- Control Group

0.5 -U-w-Group 1 (Generic Instructions) ---- Group 2 (Specific Instructions)


Figure 12. Effect of theInstructions on Time. Section 2

It can be seen that respondents in the Experimental Groups spend more time

thinking about the puzzles initially. However, when they get to the last puzzle in

the series, they spend much less time than before. In fact, in Section 1 they

spend less time than those on the Control Group and the Section 2, even though

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they spend more time than the Control Group, they have cut down very

significantly on their time allocation.

NOTE: The time data may be confounded by the fact that the respondent in the

Experimental Groups had to spend the time on reading the instructions, while

the respondents in the Control Group did not have to do that. Since it is unclear

how much time on average the respondents in the Experimental Groups spent

reading and thinking over the instructions, the actual solution time cannot be

extracted from this data set. To get around this, a more detailed analysis of time

spent on each of the problems in series may be required.

Effect of Instructions on the Rate of Correct Answers

1.4

1.2 - - - - - - - - - - - - --0 1

00

s0.8----

0 .6 - - - - - - - - - - - -S4 -4- Control Group0.2 - Group 1 (Generic Instructions)

-- Group 2 (Specific Instructions)Z 0.0 l

Puzzle 1 Puzzle 5

Figure 13. Effect of the Figure 14. Effect of theInstructions on the Rate of Instructions on the Rate ofCorrect Answers, Section 1 Correct Answers, Section 2.

Here we present the effect of the instructions on the rate of the ultimate correct

answers. The data is very similar to the effect of the instructions on the rate of

correct answers achieved on the first attempt. This says that the respondents are

equally likely to produce the ultimate correct answer as the correct answer on the

first attempt.

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1.4

02 1.20S 1.0- - - - - - -

0 0. -4- Control Group-0.4- - Group 1 (Generic Instructions)

0.2 -*- Group 2 (Specific Instructions)


The general instructions had a neutral effect on the performance of Group 1 in

Section 1 and hindered the performance of the same group in Section 2. The

negative effect of the Generic instructions in the Section 2 may be explained by

the fact that the Puzzle 4 was more difficult than the previous puzzles in this

series and the instructions were not readily available. So, the respondents in this

group found themselves in a situation when they had to resort to the self-

discovery mode, which they have not practiced.

The effect of the instructions on Group 2 is more complex. While the specific

instructions hindered the performance of this group in Section 1, they turned out

beneficial in Section 2.

One of the reasons why the respondents practicing self-discovery were able to

outperform those who received instructions, could be due to the fact that they

developed a better thinking flexibility. In the first puzzle the respondents in the

control group had to examine multiple solution paths before finding the one that

yielded the correct result. This more extended search served two purposes: open

the scope of potential solutions and increase the expertise by trying the approach

on other solution paths.

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Effect of the Instructions on Number of Attempts

( 2.5 -- - - - - - --E -4- Control Group

2.0 -1U-- Group 1 (Generic Instructions) -1. -ar- Group 2 (Specific Instructions)0 1.5

0 .5 -- - - - - - - - - - - - _ _ _ _ _-

0Z 0 .0 P

Puzzle 1 Puzzle 5

j2.5E0 2.0 - - - - - - - - - - - - -

1 1.5 - - - - - - - - - - - -

1.0 - - - - --

:N --- Control Group0.5 -- Group 1 (Generic Instructions)

-*- Group 2 (Specific Instructions)

Puzzle 1 Puzzle 4

Figure 15. Effect of the Figure 16. Effect of theInstructions on Number of Instructions on Number ofAttempts, Section 1 Correct Answers, Section 2

If the number of attempts is considered together with the time, it can be seen that

the respondents in the experimental Groups 1 and 2 spend progressively less time

on generating a solution and trying it out. Unfortunately for them, their rate of

finding the correct solution is not as high as for those in the Control Group and

they need to try again. It appears that the instructions promote the trail and error

mode of operation, while the respondents in the Control Group "aim and shoot"

more precisely.

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Effect of the Instructions on Number of Give Ups

3.0-

CL 2.5 -- - - - - - - - - - - -A - - -

2.0 -- - - - - - - - - -~1.5-- 1.0 - -- _ _ _ _ _ _ _ ---

-4- Control Group0 0.5- -- Group 1 (Generic Instructions)

-A-- Group 2 (Specific Instructions)0.0

Puzzle 1 Puzzle 5

3.0-

2.5 - -4-Control Group* -a- Group 1 (Generic Instructions)2~ 2.0-0 *, Group 2 (Specific Instructions)

~1.51.5 - --------------

N

0 0.5--------- --


Figure 17. Effect of the Figure 18. Effect of theInstructions on Number of Instructions on Number of GiveGive Ups, Section 1 Ups, Section 2

The respondents in the Groups 1 and 2 are also more likely to give up. It

suggests that the reliance on the tool adversely affects the persistence of the

respondents.

May need a button to invoke the instructions and stop time or provide a hard

copy of the instructions for continuous reference in the course of the experiment.

Effects of Instructional Types on Long-Term Memory Retention

Another effect of instructional type - retention in memory - was not examined in

this thesis. Although hypothesis can be made that the self-discovery will lead to a

better retention in memory since those practicing it discover the underlying

principle of the puzzle, the time frame of the thesis project is not sufficient to

conduct a time-delayed experiment to assess the long-term memory retention.

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Chapter 7

CONCLUSIONS

As hypothesized in Chapter 3, the instructions clearly affected the performance

of the two Experimental Groups with respect to the Control Group. While the

trends are not entirely consistent for all the experiments, some important

conclusions can still be drawn from this experiment.

Parameters measured in the experiment, such as time and rate of correct answers

give a good indication of the quality of learning transfer, while the other

parameters - namely the number of attempts and give ups - are good indicators

of the persistency and determination on the part of the respondents. Instructions

clearly affected the respondents on both dimensions.

Close examination of the measured parameters reveals that not all the variables

are truly independent. In fact, the rate of correct answers (ROC) is proportional

to time spent and inversely proportional to the number of attempts and give ups.

ROC - TimeNumber of Attempts * Give ups

The individuals in the Control Group, who received no instructions and thus

were forced to practice self-discovery, on the average spent more time, exercised

fewer attempts and gave up less. This demonstrates a higher level of commitment

and the drive to deliver the correct solution on the first attempt (drive for quality

of result).

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The individuals receiving instructions, spent less time developing the solutions,

but tried more. Unfortunately, their level of commitment suffered as well (more

give ups), leading to worse overall result.

Instructions narrow the scope of the solution space by focusing the effort and

steering the respondents away from the erroneous directions.

Solution Solution

0 0

Instructions

ProblemProblem

Figure 19. Solution Process Figure 20. Solution Processfor Self-Discovery with Instructions

However, instead of thinking about how to solve the problem, the respondents

think about how to apply the instructions. The respondent engages in the

iterative process of understanding the instructions and figuring out how the

instructions relate to the problem at hand. In the case of generic instructions,

more iterations (solution attempts) may be required to connect the consolidated

and more abstract knowledge in the instructions to the problem than in the case

of specific instructions, where the instructions are so simple that they serve to

provide a quick glimpse or insight into the problem. For the relatively simple

puzzles presented in the survey, the simple and quick specific instructions may be

a better approach. However, for a more difficult problem, generic instruction will

of 79

probably be a better method, as they will serve to both educate the user and assist

with finding the solution.

If the instructions do not fit the problem formulation well, or are not transparent

to the respondent, they become a liability. The respondent tries applying the

instructions, giving it less thought then probably needed, receives an incorrect

result and gives up. He or she might be thinking: "I was given this tool and told

that it should work. I tried it several times and it obviously does not work. I give

up". The respondents in the Experimental Groups are not conditioned to think

through the puzzles in the same way as those in the Control Group, who received

no instructions and were required to deduce the solutions from the very

beginning.

Instructions stifled creativity in this experiment and adversely affected the

problem solving skills of the respondents.

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BIBLIOGRAPHY

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2. Anderson J.R., Farrell R., Sauer R., Learning to Program in LISP, CognitiveScience, Vol., pp. 87-129, 1984

3. Blissett S.E., McGrath R.E., The relationship belween creativit and interpersonalproblem-solving skills in adults, Journal of Creative Behavior, 1996, pp 173-182

4. Bransford J.D., Brown A.L., Cocking R.R., How People Learn, NationalResearch Council, 1999

5. Cohen W.M., Levinthal D.A., Absorptive Capacit: A New Perspective onLearning and Innovation, Administrative Science Quarterly, Vol. 2, pp. 128-152, 1990

6. Cormier, S. & Hagman, J., Transfer ofLearning. San Diego, CA: AcademicPress, 1987.

7. Csikszentmihalyi M., Creativio: Flow and the Psychology of Discovery andInvention, HarperCollins, New York, NY 1996

8. Drabkin S., Enhancing creativit when solving contradictog technicalproblem,Journal of Professional Issues In Engineering Education and Practice,Apr 1996, pp 78-82

9. Ellis H.C., The Transfer ofLearning, The Macmillan Company, NY, 1965

10. Feldman D.H., Csikszentmihalyi M., Gardner H., Changing the World: AFrameworkfor the Study of Creativiy, Praeger, Westport, CT, 1994

11. Fontenot N.A., Effects of training in creativit and creative problemfinding uponbusinesspeople, Journal of Social Psychology, Feb 1993, pp 11-22

12. Fulton J., MENSA The Genius Test, Carlton Books, London, UK, 1999

13. Gardner H., Creating Minds

14. Grose, R. & Bimey, R., Transfer Of Learning. Princeton, NJ: Van Nostrand,1963

15. Haskell, R., Reengineering Corporate Training Intellectual Capital and Trans/er ofIearning, Quorum Books, Westport, CT, 1998

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16. Horowitz, R., Maimon, 0., Creative Design Methodology and the SIT Metohd,ASME Design Engineering Technical Conference, Sacramento, CA, 1997

17. Leonard D, Sensiper S, The Role of Tacit Knowledge in group innovation,California Management Review, 40 (3): 112-+, Spr 1998

18. Marakas G.M., Elam J.J., Creativit enhancement in problem solving: Throughsoftware orprocess?, Management Science, Aug 1997, pp 1136-1146

19. Niedelman, M., Problem Solving and Transfer, Journal of LearningDisabilities, Vol. 24, 1991

20. Pinker S., How the Mind Works, W.W. Norton & Company, New York,NY, 1997

21. Roget's IH: The New Thesaurus, Third Edition by the Editors of theAmerican Heritage® Dictionary, Houghton Mifflin Company, 1995

22. Ruscio A.M., Amabile T.M., Effects of instructional syle on problem-solvingcreativity, Creativity Research Journal, 1999, pp 251-266

23. Sickafus, E., Unfied Structured Inventive Thinking, Ntelleck, LLC, 1998

24. Simon H.A., The Sciences oftheArtzficial, The MIT Press, Cambridge, MA,1996

25. Smith P.G., Reinertsen D. G., Developing Products in Haf the Time, JohnWiley & Sons, 1998

26. Stefan, C., Structured Inventive Thinking,http://www.srl.ford.com/sitteam/sit.htm

27. Steiner C, A rolefor individuality and mysteg in "managing" change, Journal ofOrganizational Change, 14(2): 150-167, 2001

28. Treffinger D.J., Creative problem-solving - overview and educational imp lication,Educational Psychology Review, Sep 1995, pp 301-312

29. TRIZ Journal, www.triz-journal.com

30. www.Wordsmyth.net

31. Zander, Rosamund Stone and Zander, Benjamin. The Art ofPossibiliy,Harvard Business School Press, Boston, MA, 2000

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Appendix - Complete Results of the Experiment

ANOVA Table for RTInclusion criteria: Question IS 'Typel Q1" from Ben.Stat

DF Sum of Squares Mean Square F-Value P-Value Lambda PowerCond 2 14756.813 7378.406 .797 .4543 1.594 .176Residual 181 750102.500 9260.525

Means Table for RTEffect: CondInclusion criteria: Question IS "Type1Q1" from Ben.Stat

Count Mean Std. Dev. Std. Err.Generic 24 121.583 144.144 29.423Self-discovery 33 93.298 76.443 13.307Specific 27 91.111 57.253 11.018

Fisher's PLSD for RTEffect: CondSignificance Level: 5 %Inclusion criteria: Question IS "Type1Q1" from Ben.Stat

Mean Diff. Crit. Diff. P-ValueGeneric, Self-discovery 28.285 51.366 .2765Generic, Specific 30.472 53.716 .2623Self-discovery, Specific 2.187 49.687 .9304

Interaction Bar Plot for RTEffect: CondInclusion criteria: Question IS "Typel Q1" from Ben.Stat

140

120

100

CeU

(D 80

~'60

40

20

0Generic Self-discovery Specific

Cell

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ANOVA Table for Correct1?Inclusion criteria: Question IS "Type1Q1" from Ben.Stat

DF Sum of Squares Mean Square F-Value P-Value Lambda PowerCond 2

Residual 1811.549 1

15.201 1

.275 1 1.463 1 .2375 1 2.927 1 .293

.188 1 I I I

Means Table for Correcti?Effect: CondInclusion criteria: Question IS "Type1Q1" from Ben.Stat

Count Mean Std. Dev. Std. Err.

Generic 24 .625

Self-discovery 33 .818

Specific 27 .7781

.495 .101

.392 .068

.424 .082

Fisher's PLSD for Correcti?Effect: CondSignificance Level: 5 %Inclusion criteria: Question IS "Type1Q1" from Ben.Stat

Mean Diff. Crit. Diff. P-Value

Generic, Self-discovery

Generic, Specific

Self-discovery, Specific

-.193 .231 .1003

-.153 .242 .2123

.040 .224 .7202

Interaction Bar Plot for Correct1?Effect: CondInclusion criteria: Question IS "Type1Q1" from Ben.Stat

.9

.8

.7

.6

.5

( .4

.3

.2

.1

0Generic Self-discovery

CellSpecific

of 79

I

ANOVA Table for Giveup?Inclusion criteria: Question IS 'ypelQl" from Ben.Stat

DF Sum of Squares Mean Square F-Value

Cond 2

Residual 1 81 1.024 1

1.928 1

P-Value Lambda Power

.012 1 .512 1 .6015 1 1.023 1

.024 1

Means Table for Giveup?Effect: CondInclusion criteria: Question IS "Type1Q1" from Ben.Stat


Generic

Self-discovery

Specific

24 .042 .204 .04233 .030 .174 .03027 0.000 0.000 0.000

Fisher's PLSD for Giveup?Effect: CondSignificance Level: 5 %Inclusion criteria: Question IS "Type1Q1" from Ben.Stat



Generic, Specific


.045

.04 -

.035 -

.03 -

.025 -

> .02 -U

.015 -

.01 -

.005 -

0 -

.011 .082 .7844

.042 .086 .3386

.030 .080 .4513

Interaction Bar Plot for Giveup?Effect: CondInclusion criteria: Question IS 'ype1Q1" from Ben.Stat

Generic Self-discoveryCell

Specific

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I I I I.128I.128 1

I I I I

ANOVA Table for # of attemptInclusion criteria: Question IS "Type1Q1" from Ben.Stat


Cond 1 2

Residual 1811.493

41.650 1

P-Value Lambda Power.247 .479 1 .6209 1 .959 1 .123 1

.514 1 I I I

Means Table for # of attemptEffect: CondInclusion criteria: Question IS "Type1Q1" from Ben.Stat


Generic

Self-discovery

Specific

24 1.333 1.049 .214

33 1.152 .566 .098

27 1.185 .483 .093

Fisher's PLSD for # of attemptEffect: CondSignificance Level: 5 %Inclusion criteria: Question IS "Type1Q1" from Ben.Stat



Generic, Specific


1.4

1.2

1

0

.8

.6

.4

.2

0

.182 .383 .3474

.148 .400 .4636

-.034 .370 .8569

Interaction Bar Plot for # of attemptEffect: CondInclusion criteria: Question IS "Type1Qi" from Ben.Stat


Specific

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I

ANOVA Table for Final Correct?Inclusion criteria: Question IS "Type1Q1" from Ben.Stat

DF Sum of Squares Mean Square F-Value P-Value Lambda Power

Cond

ResidualI 2 I1.076 I .538 I 4.395 I .0154 8.790 .7481 19.912 1.122 1 11

Means Table for Final Correct?Effect: CondInclusion criteria: Question IS "Type1Q1" from Ben.Stat


Generic

Self-discovery

Specific

24 .667 .482 .098

33 .909 .292 .051

27 .926 .267 .051

Fisher's PLSD for Final Correct?Effect: CondSignificance Level: 5 %Inclusion criteria: Question IS "Type1Q1" from Ben.Stat


Generic, Self-discoveryGeneric, SpecificSelf-discovery, Specific

1-.9 -

.8 -

.7 -

Q .6 -2.5 -

o .4 -.3 -.2 -

.1 -

0-

-.242 .187 .0116 S

-.259 .195 .0099

-.017 .181 .8533

S

Interaction Bar Plot for Final Correct?Effect: CondInclusion criteria: Question IS "Type1Q1" from Ben.Stat

Generic Specific

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ANOVA Table for RTInclusion criteria: Question IS "TypelQ5" from Ben.Stat

DF Sum of Squares Mean Square F-Value P-Value Lambda PowerI2 I 43460.505 I21730.253 I1.831 I.1668 I3.662 I.35981 961258.279 11867.386

Means Table for RTEffect: CondInclusion criteria: Question IS 'ypelQ5" from Ben.Stat


24 59.653 57.867 11.812

33 98.456 162.261 28.246

27 47.043 40.061 7.710

Fisher's PLSD for RTEffect: CondSignificance Level: 5 %Inclusion criteria: Question IS 'ypelQ5" from Ben.Stat

Mean Diff. Crit. Diff.


Generic, Specific


P-Value

-38.803 58.148 .1880

12.610 60.808 .681051.413 56.247 .0727

Interaction Bar Plot for RTEffect: CondInclusion criteria: Question IS "TypelQ5" from Ben.Stat


Specific

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CondResidual

Generic

Self-discovery

Specific

120

2

100 -

80 -

60 -

40 -

20 -

0-

ANOVA Table for Correct1?Inclusion criteria: Question IS "TypelQ5" from Ben.Stat


Cond 2

Residual 1811.669 1

20.034 1

.334 1 1.352 1

.247 1

.2645 1 2.704 .273

I I I I

Means Table for Correct1?Effect: CondInclusion criteria: Question IS "TypelQ5" from Ben.Stat


Generic

Self-discovery

Specific

I..24 1.3331 .482 1 .0981

33 .545 .506 .088

27 .407 .501 .096

Fisher's PLSD for Correct1?Effect: CondSignificance Level: 5 %Inclusion criteria: Question IS "Type1Q5" from Ben.Stat



Generic, Specific


.6

.5 -

S.4-

2.3-

.2 -

.1 -

0 -

-.212 .265 .1158

-.074 .278 .5969

.138 .257 .2879

Interaction Bar Plot for Correct1?Effect: CondInclusion criteria: Question IS 'ypelQ5" from Ben.Stat


Specific

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ANOVA Table for Giveup?Inclusion criteria: Question IS "TypelQ5" from Ben.Stat


Cond 2

Residual 1811.498 1

13.645 1

.249 1 .478 .2341 1 2.957 1 .296 1

.168 1 I I I I

Means Table for Giveup?Effect: CondInclusion criteria: Question IS "TypelQ5" from Ben.Stat


Generic

Self-discovery

Specific

24 .250 .442 .090

33 .121 .331 .058

27 .296 .465 .090

Fisher's PLSD for Giveup?Effect: CondSignificance Level: 5 %Inclusion criteria: Question IS "TypelQ5" from Ben.Stat



Generic, Specific


.129 .219 .2456

-.046 .229 .6887

-.175 .212 .1041

Interaction Bar Plot for Giveup?Effect: CondInclusion criteria: Question IS "TypelQ5" from Ben.Stat


Specific

of 79

.35

.3 -

.25 -

a) .15

.1

.05

0-

ANOVA Table for # of attemptInclusion criteria: Question IS "TypelQ5" from Ben.Stat


Residual 18113.812

169.140 1

1.906 .913 .4055 1.826

2.088

Means Table for # of attemptEffect: CondInclusion criteria: Question IS "TypelQ5" from Ben.Stat

Count Mean Std. Dev. Std. Err.Generic

Self-discovery

Specific

24 1.958 2.010 .41033 1.545 .754 .131

27 2.000 1.494 .287

Fisher's PLSD for # of attemptEffect: CondSignificance Level: 5 %Inclusion criteria: Question IS "TypelQ5" from Ben.Stat

Mean Diff. Crit. Diff. P-ValueGeneric, Self-discovery

Generic, Specific


2.25

2

1.75

1.5 -

1.25 -

1-

.75 -

.5 -

.25 -

0-

.413 .771 .2900

-.042 .807 .9184

-.455 .746 .2290

Interaction Bar Plot for # of attemptEffect: CondInclusion criteria: Question IS "TypelQ5" from Ben.Stat


Specific

of 79

I I.196

2.088

ANOVA Table for Final Correct?Inclusion criteria: Question IS "TypelQ5" from Ben.Stat


Residual 811.835 I

15.867 I.417 I 2 131 I. . . .. A I 1 I

.196 112F,~ I 42~i2 I 412 I

I-I--I

Means Table for Final Correct?Effect: CondInclusion criteria: Question IS "TypelQ5" from Ben.Stat


Self-discovery

Specific

24 .625 .495 .101

33 .848 .364 .063

27 .667 .480 .092


Mean Diff. Crit. Diff. P-ValueGeneric, Self-discovery -.223 .236 .0634Generic, Specific -.042 .247 .7381Self-discovery, Specific .182 .229 .1173


.9

.8

.7

c .6

~ 5a).4U.3

.2

.1

0Generic Self-discovery

CellSpecific

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I

ANOVA Table for RTInclusion criteria: Question IS "Type2Q1" from Ben.Stat

DF Sum of Squares Mean Square F-Value P-Value Lambda PowerI2 I 25456.488 I12728.244 I1.178 I.3131 I2.356 I.24281 875054.624 10803.144

Means Table for RTEffect: CondInclusion criteria: Question IS "Type2Q1" from Ben.Stat


24 65.007 192.719 39.339

33 24.157 18.589 3.236

27 30.227 19.381 3.730




Generic, Specific


0D

70

60

50

40

30

20

10

0

40.850 55.480 .146834.781 58.017 .2364

-6.070 53.666 .8225

Interaction Bar Plot for RTEffect: CondInclusion criteria: Question IS 'Type2Q1" from Ben.Stat


Specific

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Cond

Residual

Generic

Self-discovery

Specific



Cond 2 .002 .001 .026Residual 1 81 1 2.891 .0361 1


~.72 52 .054



Generic 24 .958 .204 .042

Self-discovery 33 .970 .174 .030Specific 27 .963 .192 .037

Fisher's PLSD for Correct1?Effect: CondSignificance Level: 5 %Inclusion criteria: Question IS 'ype2Q1" from Ben.Stat

Mean Diff. Crit. Diff. P-ValueGeneric, Self-discovery -.011 .101 .8232Generic, Specific -.005 .105 .9306Self-discovery, Specific .007 .098 .8911

.8 -

( .6 -

o 4-

.2 -

0 -

Interaction Bar Plot for Correcti?Effect: CondInclusion criteria: Question IS "Type2Q1" from Ben.Stat


Specific

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,

ANOVA Table for Giveup?Inclusion criteria: Question IS "Type2Q1" from Ben.Stat


Cond 2

Residual 181 1.030 I.958 |

.015 I1.258 I.012I


.2898 I2516 256

I I I I



Generic

Self-discovery

Specific [24 .042 .204 .04233 0.000 0.000 0.00027 10.000 1 0.000 1 0.000



Generic, Specific


.042 .058 .1572

.042 .061 .1759

0.000 .056

Interaction Bar Plot for Giveup?Effect: CondInclusion criteria: Question IS "Type2Q1" from Ben.Stat


Specific

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. .i .1 2

.045

.04 -

.035 -

.03 -

.025 -& .02 -

.015 -

.005 -

0

.012 I I I I



Cond 2

Residual 181 1.074

3.879 1

.037 .768 .4671 1.537 .171

.048 I I I



Generic

Self-discovery

Specific

I. 24 1.000 0.000 0.000 133 1.061 .348 .061

27 1.000 0.000 0.000




Generic, Specific


1.2

.8

.6

.4

.2

0

L -.061 .117 .3050

0.000 .122 2

.061 .113 .2890

Interaction Bar Plot for # of attemptEffect: CondInclusion criteria: Question IS 'Type2Q1" from Ben.Stat


Specific

of 79

a0)

U

I

I I I

ANOVA Table for Final Correct?Inclusion criteria: Question IS "Type2Q" from Ben.Stat


Cond 2

Residual 181 1

.0311.921 1

.016 .655 .5220 1 1.310 .152

.024 1



Generic

Self-discovery

Specific

L 241 .958 .204 .042 1

33 1.000 0.000 0.00027 .963 .192 .037




Generic, Specific


1.2

-.042 .082 .3162

-.005 .086 .9149.037 .080 .3568


1 -

.8 -

.6-

.4-

.2-

0-Generic Self-discovery

CellSpecific

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.I I I I

U-

ANOVA Table for RTInclusion criteria: Question IS "Type2Q4" from Ben.Stat


Cond 2 14114.446 7057.223

Residual 1 81 1 1018775.104 12577.470

.561 1 .5728 1 1.122 .137

I I I I

Means Table for RTEffect: CondInclusion criteria: Question IS 'ype2Q4" from Ben.Stat


Generic

Self-discovery

Specific

24 121.099 134.434 1 27.441

33 95.673 97.965 1 17.053

27 1 123.115 1 106.699 1 20.534




Generic, Specific


25.426 59.863 .4006

-2.016 62.601 .9491

-27.442 57.905 .3485

Interaction Bar Plot for RTEffect: CondInclusion criteria: Question IS "Type2Q4" from Ben.Stat


Specific

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C

CO)

140

120

100

80

60

40

20

0

,



Cond 2

Residual 181 1.027

16.675 1

.014 .066 .9359 1

.206 1

.133 1 .060 1

I I II



Generic

Self-discovery

Specific

24 .250 .442 .090

33 .273 .452 .079

27 .296 .465 .090

Fisher's PLSD for Correct1?Effect: CondSignificance Level: 5 %Inclusion criteria: Question IS "Type2Q4" from Ben.Stat



Generic, Specific


-.023 .242 .8524

-.046 .253 .7170

-.024 .234 .8418

Interaction Bar Plot for Correcti?Effect: CondInclusion criteria: Question IS "Type2Q4" from Ben.Stat


Specific

of 79

.35

.3 -

.25 -

.~2

Q .15

.1-

.05 -

0-

ANOVA Table for Giveup?Inclusion criteria: Question IS "Type2Q4" from Ben.Stat

DF Sum of Squares Mean Square F-Value P-Value Lambda PowerCond 1 2

Residual 18111.319 1

17.002 1.660 1 3.143 1 .0485 1 6.285 1 .581 1

.210 I



Self-discovery

Specific

24 .458 .509 .104

33 .364 .489 .08527 .148 .362 .070



Generic, Specific


.095 .245 .4433

.310 .256 .0181 S

.215 .237 .0736

Interaction Bar Plot for Giveup?Effect: CondInclusion criteria: Question IS "Type2Q4" from Ben.Stat


Specific

of 79

I I I _j

.5.45

.4

.35

( .32.25

o .2.15

.1

.050


DF Sum of Squares Mean Sauare F-Value

Cond 2

Residual 181 1

P-Value Lambda Power42.738 1 21.369 1.115 .3329 2.230 .231

1552.214 19.163



24 3.542 6.467 1.32033 1.788 1.139 .19827 2.519 4.594 .884



Generic, Specific


1.754 2.337 .1392

1.023 2.444 .4072

-.731 2.260 .5219

Interaction Bar Plot for # of attemptEffect: CondInclusion criteria: Question IS "Type2Q4" from Ben.Stat


Specific

of 79

Generic

Self-discoverySpecific

4

3.5

3

2.5

2

U1.5

1

.5

0


I

ANOVA Table for Final Correct?Inclusion criteria: Question IS "Type2Q4" from Ben.Stat


Cond 2

Residual 181 1.817 1

20.076 1

.409 1 1.648 I

.248 1


II.1987 3.297 1 .326



24 .417 .504 .10333 .515 .508 .08827 .667 .480 .092


Mean Diff. Crit. Diff. P-ValueGeneric, Self-discoveryGeneric, Specific


-.098 .266 .4630

-.250 .278 .0772

-.152 .257 .2443


.7

.6

.5

(D .

.2

0Generic Specific

of 79

Generic

Self-discovery

Specific

CREATIVITY AND PROBLEM SOLVING SKILLS AS A FUNCTION …

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