Creativity and problem solving skills as a function of learning transfer

CREATIVITY AND PROBLEM SOLVING SKILLS

AS A FUNCTION OF LEARNING TRANSFER

by

Benjamin Saltsman

Submitted to the System Design and Management Program in 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 Author

Benjamin Saltsman

Certified by _Of

Dan Ariely Thesis Supervisor Associate Professor, Sloan School of Management, MIT

Accepted by

Steven D. Eppinger Co-Director, LFM/SDM Co-Director, CIPD

GM LFM Professo Management Science and Engineering Systems

Accepted by

Paul A. Lagace Co-Director, LFM/SDM Professor of Aeronautics & Astronautics and Engineering Systems MASSACHUSETTS INSTITUTE

OF TECHNOLOGY

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.

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.

TABLE OF CONTENTS

CHAPTER 1...8

CREATIVITY...

8

DEFINING CREATIVITY ...

8

LEVELS OF INVENTION ... 9

Two MODELS OF INNOVATION AND INVENTION: INDIVIDUAL VS CULTURAL ... 10

CREATIVITY PROCESS... ₁₁

Can people be taught to be more creative? ...

11

Structured Creativity Techniques ...

12

TRIZ O verview ...

12

Structured Inventive Thinking Overview...

14

Summary of Structured Creativity Techniques...

16

Creativity Barrier

...

17

How 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?...

24

Effects 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

LIST OF REQUIREMENTS FOR THE SURVEY... 32

DESIGNING PROBLEMS FOR THE SURVEY...

33

Puzzle Answers and Explanations ...

36

Section 1 ...

36

Section 2 ... ₃₆

PROTOTYPE OF THE SURVEY ...

37

DEVELOPING THE INSTRUCTIONS ...

37

DATA ANALYSIS...40

TRANSFER FORMULA...

40

COMPARISON OF FORMULAS ...

43

SELECTING THE FORMULAS FOR THE DATA ANALYSIS...

43

CHAPTER 5...45

RESULTS ...

45

SUMMARY OF THE SURVEY RESULTS...45

EXPERIMENTAL LIMITATION ...

47

VARIABLE TEST CONDITIONS...

47

SELF-SELECTION ... ₄₈

CHAPTER 6...50

DISCUSSION...50

DISCUSSION OF THE SURVEY RESULTS...

50

EFFECT OF THE INSTRUCTIONS ON TIME ...

50

EFFECT OF INSTRUCTIONS ON THE RATE OF CORRECT ANSWERS...51

EFFECT OF THE INSTRUCTIONS ON NUMBER OF ATEMPTS ...

53

EFFECT OF THE INSTRUCTIONS ON NUMBER OF GIVE UPS...54

EFFECTS OF INSTRUCTIONAL TYPES ON LONG-TERM MEMORY RETENTION

54

CHAPTER 7...55

CONCLUSIONS...55

BIBLIOGRAPHY...58

LIST OF TABLES

Number Page

TABLE 1. ANTICIPATED EFFECTS OF INSTRUCTIONAL TYPES ON KEY

LEARNING TRANSFER PARAMTERS... 28

TABLE

2.

33

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

T YPE ... 48

Page 6 of 6

LIST OF FIGURES

FIGURE 1. LEVELS OF INVENTION ... 9 FIGURE 2. SIMPLIFIED ARIZ DIAGRAM ... 14 FIGURE 3. FLOWCHART OF THE SIT PROCESS [26] ... 15 FIGURE 4. TRIZ SOLUTION -GRIPPING COMPLEX PARTS WITH A VISE .... 16

FIGURE 5. EFFECT OF THE CREATIVITY BARRIER ON THE SOLUTION PATH 18

FIGURE 6. FUNCTIONAL DECOMPOSITION OF THE CREATIVITY BARRIER .. 20 FIGURE 7. DIAGRAM OF THE SURVEY PROCESS ... 31

FIGURE

8.

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

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

FIGURE 12. EFFECT OF THE INSTRUCTIONS ON TIME. SECTION 2 ... 50

FIGURE 13. EFFECT OF THE INSTRUCTIONS ON THE RATE OF CORRECT A NSW ERS, SECTION 1... 51 FIGURE 14. EFFECT OF THE INSTRUCTIONS ON THE RATE OF CORRECT

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

SECTION 1... ₅₃

FIGURE 16. EFFECT OF THE INSTRUCTIONS ON NUMBER OF CORRECT

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

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

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

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

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 3 - Invention inside Paradigm

45%

Level 5- Discovery

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.

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

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

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

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.

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 Method

Collect Draw Draw

Information _Closed-World Qualitative-Diagram Change Graphs

Select _Unique"

Objects Determine Draw ness

Detemine _{Apply Da}

Initial & Final pply And/Or States Particles Tree

Particles Method Dimensionality Solution _{- Pluralization} Concepts

Redistribution

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.

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.

Solution

0

4

|e

path

hindered by the Creativity Barrier

Figure 5. Effect of the

B) Solution path found around the Creativio Barrier

Creativity Barrier on the Solution Path

Page 18 of 79

C) Break through

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

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.

Creativity Barrier Individual Context Inhibitions Groove-in Setting Practice Pressure

Type of transfer Expectations Fear of failure Risk aversion

Other Other

Figure 6. Functional Decomposition of the Creativity Barrier

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.

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]:

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.

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

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

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.

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

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

Specific

Parameter

Discovery

Instructions

Instructions

Level of

understanding of

High

Medium

Low

the subject Matter

Thought flexibility

High

Medium

Low

Speed

Low

Medium

High

Table 1. Anticipated Effects of Instructional Types on Key Learning Transfer Paramters

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

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

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 is contacted by e-mail ---- --- + Opt out Individual runs the program Random assignment ---_{+ Opt out}

Control group Group 1 Group 2

(No

Instructions)

O---+ opt out Individual solve the puzzles ---+ Opt out

Individual

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.

Assessment of learning transfer

Gauge the effectiveness of learning transfer High Teach a skill in the course of the survey High Measure the effectiveness of the learning _High transfer of a somewhat different task

Repeat previous two steps for another set High of 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 High

Run 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.

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.

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

A2

2

2

2

A

3

A

6

A

5

9

3

5

A2

2

1

3

4

4

5A

G

D

AF

F

C

7

B)

4

2

D)

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.

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.

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. Apply

this 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 presented to the Control Group

Think at the misakig number in terms of a trend of numbers. Is the

trend bntre n or de"'Ing? Can you determlne anotlw p*tnm? If t etnd is kh", how apidty do the numbws incen? Now think of the mattwinaical functions tht can egain such a behavior. For example, i the trendnates a rapi 1inCRfse, It could te explned by muApltatot, pOer lvw, etc, while a slower nscxdIng trend could be explained by sumrntict Dedue thefvmula that

IkfS the numbers and determine the net number r the series. For exampte, coside the nqwnce of numnt beow

2, 5, 14, 41,7

This s a rapidy ascending trend; the diference between the

numbers repst* a P4*we srist Apply tis ormula to d m*W e the 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 presented to the Group 1 (Generic Instructions)

Consider the sequence of nurabets WeOW By COMdWC~ng

tna#t4&mAIc manopulatian" (addifion, wsbion, mutlilcatlwn, etcj deduce ttw- formula that links the numbers. Appty this tforula to determine te nrxA numbef In each of the wsft,

The dstmnoe bybwlen the numbeTs iM this series repsents a powe

series

between the last number ki the senes and 41 should equal 34 (3 to Ine

pownr 4) 0r81 lTau the

answr

to the put.l is z-41=41 or

=122

5, 14, 41, Piveae type the number t(nd press the return a ky)

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

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

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 transfer}

75

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*

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

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*

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

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

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

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

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 Transfer Obtained 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 Page 44 of 79

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

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% Section 1, Question 5 C El (G) E2 (S) Transfer 1 Transfer 2 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% Section 2, Question 1 C El (G) E2 (S) Transfer 1 Transfer 2 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% Section 2, Question 4 C El (G) E2 (S) Transfer 1 Transfer 2 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