 

5w
.5 , .z.
,.. Fa... . r>
. F»? but a:
3.. «.9
E
1.3. s.
. :3.

.Swmn 4

 

, , . V w .. ...
«Wk... WM.
5%. _

J:

m.

x

A .
$4.... a: a.

if}? 3
A...5.§«2.ﬂ 43...;

AIS V “23'4“... :23!

1...!

5.3.133; . «kn.
u. . ....«....:.

.15.? in
3:14.

 

_
.§
.§

sin. 4.

3...».
any? .
«I. wrap. ~
tr "than!
.. E.
a
damn.

. a E .. ..
:3, . .1» s
z a $4.” a?! .3.)an

.. h Dv $0. .n
9.0.. .n WJQJH: 1.... I ..
a N; _ . 3.- ._m~..m..u.n

 

aeoé

 

 

LIBRARY
Michigan State
University

 

 

 

This is to certify that the
dissertation entitled

THE INFLUENCE OF MOTIVATION ON COGNITIVE
MECHANISMS INOVLVED IN PROBLEM SOLVING

PhD.

 

presented by
Mareike Wieth

has been accepted towards fulfillment
of the requirements for the

degree in PsychologL

K». Kw

Major Professor's Signature

é/z 21/05“

Date

MSU is an Afﬁrmative Action/Equal Opportunity Institution

PLACE IN RETURN BOX to remove this checkout from your record.
To AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE

DATE DUE

DATE DUE

 

Elf-0.551082%?)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2’05 C'JClmoDueJﬁpjs'

 

THE INFLUENCE OF MOTIVATION ON COGNITIVE MECHANISMS
INOVLVED IN PROBLEM SOLVING

By

Mareike Wieth

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Psychology

2005

ABSTRACT

THE INFLUENCE OF MOTIVATION ON COGNITIVE MECHANISMS
INOVLVED IN PROBLEM SOLVING

By

Mareike Wieth

An increasing number of studies are showing a connection between emotion and
motivation, and cognitive mechanism. The exact relationship between motivation and
cognitive mechanisms however has not been explored. This work was designed to
investigate the relationship between motivation and cognitive mechanisms in problem
solving. To avoid the limitations of a correlational design, this work manipulated
motivation by giving participants an incentive. Five experiments showed an increase in
problem solving accuracy due to the incentive. Experiments 1a and 1b examined whether
the increase in performance was caused by an increase in persistence with one problem
solving approach. Participants completed incremental and insight problems, which should
react to persistence with one approach differently. Results showed that the incentive
increased problem solving for both types, indicating that the incentive does not inﬂuence
performance through persistence with one problem solving approach.

Experiments 2a and 2b investigated incentive effects on problem solving duration
and depth of processing. Participants in the incentive condition spent the same amount of
time solving problems as participants in the non-incentive condition. However,
participants in the incentive condition remembered more problems than participants in
the non-incentive condition. These ﬁndings indicate that incentives lead to deeper

processing of information without an increase in time spent on each problem.

Experiments 3 and 4 used a dual-task approach to examine how incentives
inﬂuence attention allocation during problem solving. A concurrent tone monitoring task
was designed to tax similar attentional resources as problem solving and performance
decrements were found in Experiment 3. In Experiment 4 problem solving performance
increased for participants given an incentive in the single task condition but not the dual-
task condition. Participants in the single task condition given an incentive engaged in
deeper processing of the underlying problem structures than participants not given an
incentive. In the dual-task condition participants given an incentive showed more surface
processing. These ﬁndings suggest that incentives lead to an increase in performance by
causing a shift of attentional resources to the rewarded task. However, when no
additional resources are available incentives lose their effectiveness and no increase in

problem solving performance is seen.

Cepyright by
Mareike Wieth

2005

To my family.

I

“Man mu/J’ das Unmb'gliche versuchen, um das Mo'gliche zu erreichen. '

- Hermann Hesse

ACKNOWLEDGMENTS

I would like to thank the many people that have contributed to this dissertation
either directly or through their friendship and support. First of all, I would like to thank
my advisors, Bruce Burns and Rose Zacks. Bruce and Rose have guided me throughout
my time in graduate school and have helped me develop as a researcher and teacher. The
lessons they have taught me will forever shape me and my career. In addition to my
advisors I would like to thank the rest of my doctoral guidance committee, Tom Carr and
Zach Hambrick, for challenging me to think about my work in new and different ways.

Before going off to graduate school my undergraduate advisor, Ellen Stoltzfus,
told me that in order to survive graduate school you must have friends. I now know how
right she was. Lisa Helder, Sian Beilock and Berkeley, Chris Velarde, Torn Wagner, and
Matt Husband — thank you for helping me survive graduate school. A special thank you
goes to Monica Castelhano - your friendship and support throughout the years has helped
me tackle countless obstacles. Outside of graduate school I would like to thank Betsy
Tietjen and Patrick Gampp for their friendship and all the conversations that have
inspired and encouraged me.

Most importantly I would like to thank my parents Hermann and Eleonore Wieth
for their unconditional support and my brother Marcel Wieth for helping me keep my
stick on the ice! Finally, I would like to thank Jonathan Nycz, who will soon be part of

my family, for always making me laugh!

vi

TABLE OF CONTENTS

LIST OF TABLES ........................................................................... ix
LIST OF FIGURES ......................................................................... x
1 INTRODUCTION ..................................................................... 1
1.1 Incentive Effects on Performance ................................................ 4
1.1.1 Incentive Effects on Problem Solving ................................... 6

1.2 Incentives and Cognitive Mechanisms ............................................ 7
1.2.1 Persistence with One Strategy ............................................. 12

1.2.2 Increased Time on Task ..................................................... 13
1.2.3 Deeper Processing ........................................................... 14
1.2.4 Attention and Information Processing .................................... 17

1.3 Summary of the Predictions ..................................................... 25
2 INCENTIVES AND PERSISTENCE WITH ONE STRATEGY ............ 26
2.1 Experiments 1a and 1b ............................................................ 26
2. 2 Method .............................................................................. 27
2.3 Results ............................................................................ 30
2.4 Discussion ........................................................................ 33

3 INCENTIVES, TIME ON TASK, AND DEEPER PROCESSING 37

3.1 Experiments 2a and 2b ............................................................. 37
3.2 Method ................................................................................ 39
3.3 Results ............................................................................... 42
3.4 Discussion ............................................................................ 51

4 INCENTIVES AND ATTENTION .................................................. 53
4.1 Experiment 3 ........................................................................ 55
4.1.1 Method ....................................................................... 57

4.1.2 Results ........................................................................ 61

4.1.3 Discussion ................................................................... 75

4.2 Experiment 4 ....................................................................... 79
4.2.1 Method ...................................................................... 81

4.2.2 Results ....................................................................... 82

4.2.3 Discussion .................................................................. 98
5 GENERAL DISCUSSION ........................................................... 103
5.1 Summary of Experimental Results ................................................ 103
5.2 Incentives and Attentional Resources ........................................... 107
5.3 Insight versus Incremental Problems ............................................. 111
5.4 Cognitive Psychology and Motivation ............................................ 113
5.5 Future Directions ................................................................... 114

vii

5.6 Conclusions ......................................................................... 118

APPENDIX A ............................................................................... 119
APPENDIX B ............................................................................... 126
REFERENCES .............................................................................. 1 30

viii

LIST OF TABLES

Table 1. Mean incremental and insight scores (standard deviations in parentheses)
for Experiments 1a andlb (two problem sets used) ......................................... 31

Table 2. Mean incremental and insight scores (standard deviations in parentheses)
for Experiments 2a and 2b .................................................................... 43

Table 3. Mean problem solving duration in seconds (standard deviations in
parentheses) for incremental problems, insight problems, and their totals across
both problem types and incentive condition in Experiments 2a & 2b .................. 44

Table 4. Mean memory scores (standard deviations in parentheses) for the coarse
and ﬁne measure for incremental problems, insight problems, and their totals
across both problem types in Experiments 2a & 2b ....................................... 51

Table 5. Mean incremental and insight scores (standard deviations in parentheses)
in the single and dual-task 2-tones and 3-tones conditions for Experiment 3 ......... 62

Table 6. Mean incremental and insight scores (standard deviations in parentheses)
for participants in the 2-tone condition across target for Experiment 3 ................ 65

Table 7. Mean incremental and insight scores (standard deviations in parentheses)
for participants in the 3-tone condition across target for Experiment 3 ................ 66

Table 8. Mean problem solving duration in seconds (standard deviations in
parentheses) for incremental and insight problems in the single task and dual-task
conditions divided by number of tones for Experiment 3 ................................ 67

Table 9. Mean incremental and insight scores (standard deviations in parentheses)
for participants in the single and dual-task conditions divided by incentive for
Experiment 4 ..................................................................................... 83

Table 10. Mean coarse memory scores for incremental and insight problems
(standard deviations in parentheses) in the single and dual-task divided by
incentive as well as the totals across conditions for Experiment 4 ....................... 92

Table 11. Mean ﬁne memory scores for incremental and insight problems (standard
deviations in parentheses) in the single and dual-task conditions divided by
incentive as well as the totals across conditions for Experiment 4 ..................... 94

Table 12. Mean irrelevant information scores for incremental and insight problems

(standard deviations in parentheses) in the single and dual-task condition divided
by incentive for Experiment 4 ............................................................... 96

ix

LIST OF FIGURES

Figure 1. Mean problem solving duration for participants in the non-incentive and
incentive condition for Experiments 2a and 2b. Error bars represent standard errors. 46

Figure 2. Proportion of problems recalled (coarse memory measure) for participants
in the non-incentive and incentive condition for Experiments 2a and 2b. Error bars
represent standard errors ....................................................................... 48

Figure 3. Mean amount of problem detail given (ﬁne memory measure) for
participants in the non-incentive and incentive condition for Experiments 2a and 2b.
Error bars represent standard errors ........................................................ 50

Figure 4. Mean solution rates for incremental and insight problems in the single
and dual-task conditions for Experiment 3. Error bars represent standard errors 64

Figure 5. Mean tone task accuracy in Experiment 3 for the tone task at the
beginning of the experiment, the tone task while solving incremental problems, the
tone task while solving insight problems and the tone task at the end of the
experiment. Error bars represent standard errors .......................................... 71

Figure 6. Mean tone task response time (in ms) in Experiment 3 for the tone task at
the beginning of the experiment, the tone task while solving incremental problems,
the tone task while solving insight problems and the tone task at the end of the
experiment. Error bars represent standard errors .......................................... 74

Figure 7. Mean solution rates for problems in Experiment 4 for the single and dual-
task conditions for participants either given an incentive or not. Error bars
represent standard errors ...................................................................... 84

Figure 8. Mean tone task accuracy in Experiment 4 for participants in the incentive
and non-incentive conditions performing the tone task alone, the tone task while
solving incremental problems, and the tone task while solving insight problems.
Error bars represent standard errors ......................................................... 88

Figure 9. Mean tone task response times (in ms) in Experiment 4 for participants in
the incentive and non-incentive condition while performing the tone task alone, the
tone task while solving incremental problems, and the tone task while solving
insight problems. Error bars represent standard errors .................................... 90

Figure 10. Mean irrelevant information score for problems in Experiment 4 for the
single and dual-task conditions for participants either given an incentive or not.
Error bars represent standard errors ......................................................... 98

1 INTRODUCTION

Motivation is generally seen as an important factor inﬂuencing performance (e.g.,
Deci, Koestner, & Ryan, 1999; Jenkins, Mitra, Gupta, & Shaw, 1998). Despite this,
motivation has largely been ignored in regard to its inﬂuence on cognitive processes. This
might be because the cognitive revolution has emphasized the passing of information
between perceptual, memory, and motor components. Usually left out of this view is a
role for motivation and emotion, which were issues that had been emphasized by the
behaviorist theories that the cognitive revolution overturned. Even when the effect of
motivation on cognition is considered, it is often done so to point out that it will not
inﬂuence cognitive processes much. For example, Simon (1994) suggested that:

". . when measuring problem solving skills, or the use of language or
visual imagery, we usually take motivation for granted, and not without good
reason. We have extensive experience with the fact that, within broad limits,
people are very obliging at doing what researchers ask of them. Provided they
direct their attention to the task and are not distracted, added increments of effort
would not greatly alter their performance. Within broad limits, trying harder
would not alter their performance much."(Simon, p. 10).

Simon does not appear to be alone in this assumption, since he pointed out that in most
descriptions of experiments conducted in cognitive psychology laboratories motivation is
only mentioned in terms of the amount of money participants were paid or the class credit
they received.

More recently, however, a variety of behavioral results have suggested that

cognitive psychologists should reconsider the importance of motivation and emotion.

Kuhl and Kazén (1999) found that by manipulating participant’s emotion the Stroop
effect can be eliminated. When participants were given a word with positive affect as a
prime the amount of interference due to the Stroop effect was signiﬁcantly smaller than
when participants were presented with a neutral or negative prime. Vollmeyer and
Rheinberg (1998) found motivation affected performance in a complex problem solving
task such that participants with higher levels of motivation were more likely to persist
with a systematic strategy whereas participants with lower levels of motivation would
switch away from a systematic strategy adopting a guessing strategy. Similar inﬂuences
of motivation on leaming strategies and performance on geometry problems were found
by Pokay and Blumenfeld (1990). Geometry students with higher motivation were more
likely to use and persist with a variety of study strategies (general and geometry speciﬁc)
compared to less motivated students. Looking at problem solving, Wieth and Burns
(2000) found a correlation between motivation and problem solving performance.
Participants with higher motivation were more successful at solving incremental or
analytic problems than participants with lower motivation.

Advances in the study of the brain have also thrown into doubt the splitting of
cognitive processes from emotion and motivation (Lezak, 1994). Damasio (1994) has
found impaired decision making among patients with ventromedial prefrontal cortex
lesions which seems to stem from their lack of normal emotional responses to decision
making tasks (see Bechara, Tranel, & Damasio, 2000, for a summary). Gehring and
Willoughby (2002) found that a loss in a decision making task rather than a gain led to
riskier decisions on subsequent trials, and generated a larger negative-polarity event-

related potential in a medial-frontal region of the cortex. This sensitivity to losses was not

simply a reﬂection of detecting an error; gains did not elicit the medial-frontal activity
when the alternative choice would have yielded a greater gain, and losses elicited the
activity even when the alternative choice would have yielded a greater loss. Gehring and
Willoughby see these results as neurophysiological evidence for the motivational impact
of events guiding choice behavior.

Spaulding (1994) distinguished between motivation, emotion, and cognition,
where motivation refers to the meaning and purpose of behavior, emotion to the
experiential and psychophysiological phenomena that accompanies motivation processes,
and cognition to the organismic activity that translates motivation and emotion into
observable behavior. Thus, changes in motivation should change cognitive activity and
produce different results. This work was designed to investigate the connection between
motivation and cognitive activity by examining how motivation might inﬂuence
cognitive mechanisms involved in problem solving. Finding effects of motivation on
cognitive processes, however, has been notoriously hard (Rheinberg, Vollmeyer, &
Burns, 2001), and has often relied on correlational designs linking motivation and
performance. In order to avoid the limitations associated with correlational research,
motivation was manipulated through the use of an incentive. An incentive is reward that
is used to induce a desired type of performance or behavior from a person. Since
incentives can be manipulated a greater number of conclusions regarding the relationship
between motivation and problem solving performance can be drawn. Two major
questions were investigated in this work. One, do incentives, and therefore motivation,
inﬂuence problem solving performance? Two, what cognitive mechanisms involved in

problem solving are inﬂuenced by incentives?

1.1 Incentive Effects on Performance

Positive effects of incentives. The question of how incentives relate to
performance has been of special interest to those concerned with worker productivity.
Overall it has been shown that incentives have positive effects on productivity. For
example, Saari and Latham (1982) studied the performance of beaver trappers before the
implementation of an incentive plan and under the incentive plan. It was found that the
number of rodents trapped per hour increased signiﬁcantly under the incentive plan
(payment for each beaver trapped) compared to the base rate system of pay (a set hourly
wage), which was in place before the incentive plan. Similarly, LaMere, Dickinson,
Henry, Henry, and Poling (1996) found that truck drivers increased their productivity
after an incentive pay system was introduced which rewarded the drivers for
accomplishing each job they had to perform (e.g., delivering goods, loading and
unloading goods) compared to a base rate system of pay (a set hourly wage). This
increase in productivity was sustained over a period of nearly four years and was not
accompanied by worker dissatisfaction or increases in accidents. Looking at the
inﬂuences of incentives on productivity in a more controlled setting Riedel, Nebeker, and
Cooper (1988) asked participants to do a clerical task that involved transferring data from
handwritten questionnaires onto mark-sense forms. All participants earned a base rate of
pay however some were given the opportunity to earn incentive pay if they performed
above the standard of 5.75 questionnaires per hour. Participants earning incentive pay
transferred signiﬁcantly more data than participants in the non-incentive group. Overall
incentives seem to have a positive effect on worker productivity.

Negative eﬂects of incentives. Incentives, however, have also been shown to hurt

performance. A meta-analysis of 128 studies by Deci, Koester, and Ryan (1999)
examined the effects of incentives on motivation and found that incentives decrease a
persons’ inherent motivation and self-reported interest in the task which often leads to a
reduction in performance. More speciﬁcally, incentives are considered forms of external
motivation where participants’ desires to perform a task are due to an outside inﬂuence
(e. g., money) and not to their inherent interest in the task. External motivation has been
shown to decrease a person’s intrinsic motivation and once the external reward is
removed people spend less time on the previously rewarded task and show decreased task
interest (e.g., Deci, 1971, 1972a, 1972b; Lepper, Greene, & Nisbett, 1973).

Detrimental effects of incentives have also been seen on creativity. Kruglanski,
Friedman, and Zeevi (1971) asked participants to read a variety of passages while either
in the incentive or non-incentive condition. Participants in the incentive condition were
promised a monetary reward for their participation in the experiment while the reward
was not mentioned in the non-incentive condition. After reading the passages participants
were asked to create as many titles as they could for each passage. Results showed that
the titles produced by those participants that had been given an incentive were judged to
be less creative than the titles given by the students not given an incentive. Similarly,
Amabile, Hennessey, and Grossman (1986) had children tell a story based on a picture
book either in an incentive condition or a non-incentive condition. Children in the
incentive condition were promised the opportunity to take pictures with a Polaroid
camera at the end of the experiment. It was found that children who were given the
incentive (taking Polaroid pictures) told stories that were less creative than those children

in the non-incentive condition. Consequently, it seems that incentives can also lead to

negative effects on performance.

Based on the literature overall it is apparent that incentives have been shown to
have both positive and negative effects. A recent review by Camerer and Hogarth (1999)
of 74 experiments that manipulated incentives lends further support that incentives can
lead to mixed effects. Camerer and Hogarth found that the modal ﬁnding in these
experiments was no effect of incentives; however there were also studies that showed
positive and negative effects. The question then becomes how incentives might inﬂuence
problem solving?
1.1.1 Incentive Effects on Problem Solving

A few studies have examined the effects of incentives speciﬁcally on problem
solving performance. McGraw and McCullers (1979) examined the inﬂuences of an
incentive on performance of the water jar task. Participants were given nine set inducing
water jar tasks of the style used by Luchins (1942) that could all be solved in the same
way. Then participants were given the tenth problem that required breaking the mental set
established in the ﬁrst nine problems. Results showed that participants given an incentive
were much slower to break mental set than participants not given an incentive. McGraw
and McCullers concluded that their results were evidence for the detrimental effects of
incentives. Similarly, Glucksberg (1962) found that incentives increased problem solving
performance on an easy version of Duncker’s candle problem (the tacks had already been
removed from the tack box) but decreased problem solving on the regular version of the
problem. Looking at the Wason four card selection task (Wason, 1966), which is a
deductive reasoning task that asks participants to test the rule “If P then Q”,

Kemmelrneier, Bless, Schwartz, and Bohner (2004) found no effect of an incentive on the

correct solution. Participants given an incentive were no more likely to ﬁnd the correct
solution than participants not given an incentive. Looking at participants incorrect
answers however, results showed that participants given an incentive were less likely to
include the obvious and correct card (the solution to the Wason card selection task
requires testing two cards) than participants not given an incentive. Following Camerer
and Hogarth (1999) incentive effects on problem solving type tasks also seem to be
mixed.

1.2 Incentives and Cognitive Mechanisms

What might be the cause of these mixed ﬁndings? In order to understand how
things work one must understand what underlying mechanisms are involved in their
ﬁmctioning. In order to understand how incentives inﬂuence problem solving one must
understand how incentives might be inﬂuencing the cognitive mechanisms involved in
problem solving performance. Once the inﬂuence of incentives on the cognitive
mechanisms involved in problem solving is understood, the cause of the mixed incentive
effects seen in the literature might be explained. A goal of this work was to investigate
the underlying cognitive mechanisms that are inﬂuenced by an incentive. A variety of
cognitive mechanisms were investigated to try to better understand how incentives
inﬂuence problem solving performance.

Within the literature a variety of explanations have been put forth on how
incentives might inﬂuence problem solving. None of them, however, look at cognitive
mechanisms directly. For example, Eisenberger (1992), in his learned industriousness
theory proposed that the relationship between incentives and performance is mediated by

effort. Incentives ameliorate the aversive sensations associated with high effort and can

therefore lead to an increase in performance. However, if an incentive is given for low
effort tasks, performance will decrease as participants learn to associate low effort with
rewards. Eisenberger goes on to argue that incentives given for divergent thought by
encouraging a variety of approaches to a task will lead to increases in performance while
incentives given for more narrow thought will lead to decreases in performance.

Cognitive evaluation theory put forth by Deci (1971) places a heavy emphasis on
the person’s interpretation of the incentive. More speciﬁcally, incentives, which are
extrinsic forms of motivation, can be interpreted as controllers of behavior or as
indicators of competence. When incentives are seen as controlling they reduce
satisfaction of the need for autonomy, cause a more external perceived locus of control,
and undermine intrinsic motivation. On the other hand, if incentives are seen as indicators
of competence they provide satisfaction of the need for competence and enhance intrinsic
motivation. This can lead to differences in performance due to different interpretations of
the incentive.

Even though both of these theories are viable explanations of how incentives
might inﬂuence performance, neither provides a clear answer as to how incentives might
inﬂuence cognitive mechanisms involved in problem solving. Additionally, it is unclear
what predictions they would make regarding the involvement of cognitive mechanisms in
problem solving. One theory however does provide some guidance as to how incentives
might inﬂuence cognitive processes. Amabile (1987) proposes that incentives will have
different effects on performance depending on task characteristics. More speciﬁcally,
Amabile argues that incentives motivate individuals to achieve their goal in the most

direct or obvious manner. This direct approach is beneﬁcial for tasks that are

straightforward where the path to solution is clear and can be followed easily
(algorithmic tasks) but harmful for tasks involving creativity that are open-ended without
a clear path to the solution (heuristic tasks). Depending on task characteristics, incentives
will have different effects on performance. A similar proposal has been made by Camerer
and Hogarth (1999) in their review of incentive effects on performance. More
speciﬁcally, Camerer and Hogarth have argued that positive incentive effects tended to
be seen for "tasks where effort responds to incentives and where increased effort
improves performance" (Camerer & Hogarth, p. 8). Negative incentive effects tended to
be seen for tasks in which it was possible to exert too much effort, for example choking
or failing under pressure in sports, or in which people over-apply a heuristic, such as in
insight problem solving. Based on Amabile and Camerer and Hogarth it is possible then
that different types of problems might be inﬂuenced differently by an incentive
depending on their task characteristics.

Incremental and insight problems. Incremental problems or analytic problems
(Schooler & Melcher, 1995) require the solver to "grind out the solution" by taking a
series of steps. Reaching the solution might take time but the solver usually has a good
idea how to reach it early in the problem solving process. In contrast, insight problems
are often solved suddenly with a “ﬂash of illuminance” (Metclafe & Wiebe, 1987), or
what has also been called an “Aha” experience where the solution seems to just pop into
mind (Schooler & Melcher). Dominowski (1995) deﬁned insight problems as containing
three key features: (1) to reach the solution a change in view of the problem is required
(2) some form of a unique response is required (in contrast to a memorized procedure or

answer), and (3) no specialized knowledge is needed to solve the problem. More

speciﬁcally, insight problems often lead to an impasse where problem solving comes to a
halt because all possible solutions seem to be exhausted and the solver cannot think of a
way to proceed. Here the solver must break away from the current representation of the
problem and ﬁnd an alternative way of structuring the problem space (e.g., Smith, 1995,
Ohlsson, 1992). In contrast for incremental problem solving the solver usually has a good
idea how to reach the solution early in the problem solving process, reaching a solution is
usually just a matter of time. For a problem to be considered an insight problem its
solution requires some form of new answer. Participants must create an answer by
combining experience and not simply recall a memorized answer or habitual experience.
The experiences might all be familiar but the combination is new therefore leading to a
unique solution. Alternatively, incremental problems often require the solver to recall a
memorized procedure (setting up an algebraic equation) to reach the solution. Finally,
solving an insight problem does not require any specialized knowledge. Instead the
problem is well within the competence of the solver and reaching the solution does not
require any memorized procedures or equations. Incremental problems, on the other
hand, do often involve previous knowledge that must be retrieved from memory to solve
the problem.

Differences between these two types of problems have been demonstrated
empirically by studies comparing their problem solving performance. In a study by
Metcalfe and Wiebe (1987) participants were asked to rate how close they thought they
were to the solution every 15 seconds while solving incremental and insight problems.
The rating results showed that problem solvers had a good idea when they were close to

the solution for incremental problems, but were unable to perceive when they were close

10

to a solution for insight problems. Solutions for insight problems came suddenly and with
little awareness that the solution was about to be found. Additionally, it was discovered
that participants were more successful at predicting which incremental problems they
could solve than which insight problems they could solve. These results indicate that
there are distinct difference between incremental and insight problems, which could be
caused by qualitative differences in underlying processes used to solve these two
problems (Metcalfe & Wiebe). Further evidence that there are differences in the
processes used to solve these two types of problems has been provided by studies that
have had participants give verbal protocols while solving both incremental and insight
problems (Schooler & Melcher, 1995; Schooler, Ohlsson, & Brooks, 1993). Schooler et
al. found that participants asked to verbalize their problem solving strategies showed
signiﬁcantly impaired performance on insight problems but not on incremental problems.
Additionally, it was found that participants paused more and tended to have a harder time
articulating their thoughts while solving insight problems compared to incremental
problems. Furthermore, the nature of the protocols also differed in that incremental
problem protocols contained more logic or means-ends analysis statements than insight
problems (Schooler & Melcher). These ﬁndings have been attributed to differences in the
processes used to solve these two types of problems. Speciﬁcally, Schooler and Melcher
and Schooler, et a1. argued that the impairments during insight problem solving while
verbalizing are due to the disruption of non-reportable processes that are critical to
solving insight problems but are not necessary for solving incremental problems.
Additionally, Dominowski (1995) has argued that insight problems involve a

greater degree of creativity than incremental problems because the solver is required to

11

produce solutions that are less frequent than those that are more easily elicited.
Furthermore, insight problems require more creativity because the solver has to re-
represent the problem in order to reach the solution.

For the purpose of this dissertation insight problems will be deﬁned as problems
for which a change in view of the problem is required for solution, a unique response is
required, and no specialized knowledge is needed to solve the problem (Dominowski,
1995)

1.2.1 Persistence with One Strategy

The characteristics of incremental and insight problems can easily be mapped
onto the distinction Amabile (1987) draws between algorithmic and heuristic tasks. An
algorithmic task has a clear and often obvious path to the solution. Incremental problems
can be solved by sticking to a clear path to the solution. A heuristic task on the other hand
often involves more creativity and is open ended without a clear path to the solution.
Insight problems do not have a clear path to the solution and often require the solver to
re-represent the problem. Amabile has argued that incentives discourage participants
from exploring the problem space and encourage them to take the most straightforward
and obvious path to the solution. This would be advantageous for incremental problem
solving since the obvious path will often lead to the correct solution. However, the most
obvious path will often lead to a solution which is not plausible for insight problems
solving, therefore incentives may decrease insight problem solving performance.

These predictions also seem to ﬂow from Vollmeyer and Rheinberg (1998) who
found that motivation inﬂuenced performance via the use of a good strategy. More

speciﬁcally participants were asked to ﬁgure out the underlying links of a complex

12

system by changing one variable at a time. Volhneyer and Rheinberg found that
participants with higher motivation were more likely to stick with the instructed strategy
and solve the task correctly, while participants with lower motivation were more likely to
switch from the instructed strategy to a guessing strategy and therefore fail to solve the
complex task. Volhneyer and Rheinberg concluded that motivation leads to persistence
with one good strategy or approach. Again, this kind of persistence would help solve
incremental problems because it encourages solvers to stay on the obvious path even if
the path is long and difﬁcult. For insight problems, however, persistence with one
approach might be harmful due to the creation of mental set effects (Luchins, 1942)
where the solver cannot re-represent the problem. Persistence with one particular
approach would most likely lead to an implausible solution since exploration of problem
space is needed in order to solve insight problems successfully. It is possible then that
incentives inﬂuence persistence with one approach to the problem. In order to test this
possibility participants in Experiments 1a and 1b were asked to solve both incremental
and insight problems while either given an incentive or not. It was predicted that if
incentives lead to persistence with one problem solving approach then participants given
an incentive should show an increase in incremental problem solving but a decrease in
insight problem solving compared to participants not given an incentive. ’
1.2.2 Increased Time on Task

Another way incentives might inﬂuence problem solving is by increasing the
amount of time participants spend on a task. For example, Miller and Horn (1990) found
that participants given a monetary incentive for completing solvable and unsolvable

anagrams spend more time trying to solve the unsolvable anagrams compared to

13

participants not given an incentive. Similar effects have been seen in the worker
productivity literature where incentives increased the amount of time participants spent
with a task (e.g., Saari & Latham, 1982). In light of this, incentives may lead to an overall
increase in the amount of time participants spend on each problem. Perhaps incentives
lead participants to work on a problem longer increasing their chances of ﬁnding the
correct answer. It is possible that an incentive that encourages accuracy might also
encourage participants to spend more time on each problem to guarantee the correct
answer to the problem. In Experiments _2a and 2b this possibility was investigated by
measuring participants’ problem solving duration. If incentives cause an increase in
problem solving duration then participants given an incentive will spend more time
solving problems than participants not given an incentive.
1.2.3 Deeper Processing

Finding an increase in the amount of time spent solving problems alone would not
be remarkable. If incentives simply lead to an increase in time one could argue that
incentives do not actually change any cognitive mechanisms and can therefore be ignored
in certain circumstances (for example, building a model of task performance, and
constructing training programs). It is possible, however that incentives are not just
causing participants to do the same thing for a longer period of time, instead incentives
might be causing participants to do more during the same amount of time. Vansteenkiste,
Simons, Lens, Sheldon, and Deci (2004) have shown that motivation leads to a greater
amount of deep processing of material compared to surface processing. More
speciﬁcally, participants were asked to read a text passage after which they were asked to

ﬁll out a questionnaire assessing the degree to which they engaged the material in a

14

superﬁcial way (e. g., “I skipped parts of the text that I did not understand very well.”) or
a deep way (e.g., “I studied the text by associating the things I read with what I already
knew.”). Participants were also tested on the material in a written test and a group
discussion. Results showed that participants with greater motivation engaged in deep
processing much more frequently than superﬁcial processing and were therefore able to
remember more information they had read compared to participants with less motivation.
Looking at incentives, Eysenck and Eysenck (1982) found evidence for deeper
processing on word list recall due to monetary incentives. Participants were asked to
recall a mixed list of high and low monetary (10 pence and 2 pence, respectively)
incentive words. During recall participants where given weak and strong retrieval cues
(e.g., “TABLE associated with __”); determined by word association norms. Results
showed that high incentive words were recalled more than low incentive words with
weak retrieval cues but there was no effect with strong retrieval cues. Eysenck and
Eysenck argued that these ﬁndings indicate that low incentive words were processed
based only on their most obvious and easily accessible features whereas high incentive
words were processed in terms of both easily accessible and less accessible features. It is
possible then that incentives will also lead to deeper processing during problem solving.
Both of these studies indicate that motivation can lead to deeper processing of
information and therefore greater recall at test. What might deeper processing mean for
problem solving? Craik and Tulving (1975) argued that encoding information in a more
meaningful or semantic manner results in improved retention. Perhaps participants given
an incentive represent problems in a more meaningful way by drawing greater

connections between these problems and previous knowledge. This then may lead to

15

greater retention for the problems. Experiments 2a and 2b tested this possibility by giving
participants a surprise memory test after they had attempted several problems. In this
memory test participants were asked to recall as many of the problems that they had just
attempted in as much detail as possible. If incentives lead to deeper processing then
participants given an incentive should remember more problems in greater detail than
participants not given an incentive.

Deeper processing in problem solving could also lead to greater understanding of
the problem. Perhaps participants given an incentive are more likely to look at the
underlying structure of the problem than participants not given an incentive. Chi,
Feltovich, and Glaser (1981) found that physics experts were more likely to organize
each problem based on the underlying physics principles while novices organized
problems on the mentioned objects. One does not need to be a physics expert to solve
incremental and insight problems however this study can perhaps give some guidance as
to what exactly deeper processing means in the domain of problem solving. There are
two general approaches to solving problems. One approach would be to ﬁgure out the
underlying structure of the problem (e.g., setting up an equation) while another would be
to simply guess based on the conditions stated in the problem. For example, given the
following problem “Ann is twice as old as her son. Ten years ago Ann was three times as
old as her son. What are their present ages?” one could ﬁgure out the underlying structure
and set up an equations (e.g., 3X = 2X +10) to solve the problem. This type of approach
would require deeper processing of the problem as participants need to tie the current
problem to their previous knowledge in order to set up an equation. On the other hand,

one could simply guess the answer by picking two ages and seeing if they ﬁt the

16

conditions stated in the problem. For example, picking the ages 10 and 20 would satisfy
the condition that Ann is currently twice as old as her son but would not satisfy the
condition that ten years ago she was three times as old as her son. (Ten years ago the son
would have been zero [10 — 10] and Ann ten [20 -— 10].) A guessing approach would
involve much shallower processing as participants do not need to link the currently
problem to previous knowledge and only need to operate within the conditions given in
the problem. It is possible then that deeper processing for problem solving also refers to
greater processing of the underlying structure of the problem and less surface structure
processing. Incentive might not only lead to an increase in memory for the problems but
might also lead to greater recall of problem relevant information. In order to test this
possibility irrelevant information was added to the problems in Experiment 4. The
information added to each problem was not necessary for solving the problem; however
this was not readily apparent when ﬁrst encountering the problem. If incentives lead to
deeper processing by causing participants to focus on the underlying structure of the
problem then participants in the incentive condition should recall less irrelevant
information than participants not given an incentive (indicating more surface processing).
1.2.4 Attention and Information Processing

Attention is essential in determining what information is processed, encoded into
memory, and later retrieved (Broadbent, 1958; Cherry, 1953; Craik, Govoni, Naveh-
Benjarnin, & Anderson, 1996; Logan & Etherton, 1994; Logan, Taylor, & Etherton,
1996; Naveh-Benjarnin, Craik, Guez, & Dori, 1998; Treisman, 1964). In order to solve
problems successfully one must properly allocate attentional resources responsible for

information processing, encoding, and retrieval. When participants do not allocate the

17

appropriate amount of resources learning or in this case problem solving will not occur.
For example, in a study looking at word pair learning Logan and Etherton (1994) asked
participants to make a judgment on a series of consistently paired words. Some
participants were asked to look at both words in the pair to make the judgment while
others were asked to look only at the colored word in the word pair. Results showed that
those participants that looked at both words showed a performance advantage from the
consistent pairing but those participants that only looked at one word did not show an
advantage for the consistent pairing. These ﬁndings indicate that participants given the
color cue consistently ignored the second word and only devoted their attention to the
task relevant word. Perhaps this is also how incentives inﬂuence problem solving.
Incentives rrright serve the same function as the color cue and direct participants attention
to the rewarded task ensuring proper allocation of resources to complete the task.
Kahneman (1973) argued that an individual’s enduring dispositions, momentary
intentions, and evaluation of the capacity demands will inﬂuence the allocation of
attentional resources. Those tasks that are seen as more appealing, interesting, or
important will receive more attention than tasks seen as unappealing, boring, and
unimportant. It is possible then that incentives might lead to an increase in appeal,
interest, and importance and cause participants to allocate more attention to the rewarded
task.

This prediction also seems to follow from the goal setting literature which has
examined the effects of goals on resource allocation. Each incentive usually encompasses
a goal that speciﬁes the conditions under which someone will receive the incentive. For

example, giving participants the opportunity to leave the experiment early if four

18

problems are solved correctly encompasses both an incentive, the opportunity to leave the
experiment early, and a goal, solving four problems correctly. It is particularly useful
then to look at research looking at goal setting and attention allocation. Locke and
Latham (1990, 2002) have noted that one way goals inﬂuence performance is by
directing resources and effort towards goal relevant tasks and away from goal irrelevant
tasks. Rothkopf and Billington (1979) gave participants informational goals and tracked
their reading times and eye movements while reading several text passages. It was found
that goal-relevant sentences resulted in more and longer ﬁxations than goal-irrelevant
sentences. Additionally, participants recalled more goal-relevant information than goal-
irrelevant information. These ﬁndings indicate that participants direct more attention to
goal relevant information than goal-irrelevant information. Similarly, Locke and Bryan
(1969) found that feedback on an automobile driving task only led to improvement for
goal related tasks but not for non-goal related tasks (even when the feedback was about
non-goal related tasks). For example, participants’ instructed to keep their speed within a
certain range would adjust their speed when given feedback but ignored any feedback
regarding following distance between their car and other cars. It is possible then that
incentives like goals direct attention to the goal-relevant or rewarded task. Experiment 4
was designed to examine the effects of an incentive on the allocation of attention. It was
predicted that an incentive would increase the amount of attention devoted to the
rewarded task.

Attention and a dual-task approach. One way of studying the allocation of
attention is by using a dual-task approach. In a dual-task approach participants’ limited

resources are taxed by performing two tasks at once. Similarities between the two tasks

19

determine the performance decrements seen. More speciﬁcally, Navon and Gopher
(1979) argued that performance decrements can be seen for tasks that have the same
“demand compositions” or resource requirements. Wickens (1980, 1984) expanded on
this by proposing a three-dimensional space of task characteristics (stages of processing,
codes, and modalities) that determines interference between tasks. Greater overlap in
resource requirements between two tasks leads to performance decrements in both tasks
if participants are performing the tasks simultaneously. In the context of this research if
participants are performing a secondary task that has the same resource requirements as
problem solving, performance decrements should be seen in both tasks. A dual-task
approach however can also be used to investigate if participants are preferentially
allocating their resources to one or the other task. Given that the two tasks tax the same
resources, if participants’ problem solving performance increases while their secondary
task performance decreases, one can argue that participants are shifting their limited
attentional resources to the problem solving task (and ignoring the secondary task). This
makes a dual-task approach particularly useful in investigating incentive effects on
attention allocation during problem solving. More speciﬁcally, if an incentive is similar
to a goal and causes participants to shift their attentional resources to the rewarded task
and away from the non-rewarded task then participants given an incentive in the dual-
task condition should show greater problem solving performance but lower secondary
task performance compared to participants not given an incentive. On the other hand, if
participants are performing both tasks at the same time then very few additional resources
will be available to devote to the rewarded task and the incentive should have no effect

on problem solving performance.

20

Secondary task effects and higher order cognition. As noted a key to using the
dual-task approach to investigate attention allocation is to ﬁnd a secondary task that taxes
the same resource requirements as problem solving. Very little research has investigated
the inﬂuences of secondary tasks on problem solving. One exception is a study by Lavric,
Forstrneier, and Rippon (2000) that asked participants listen to a concurrent tone task and
count the number of target tones that occurred while solving Duncker’s candle problem
and the Wason card selection task. Results showed decreased performance on the Wason
card selection task but not Duncker’s candle problem when participants were asked to
solve the problems and perform the concurrent counting task at the same time. Perhaps
this indicates that the resource requirements for the concurrent counting task were not
similar enough to the resource requirements of Duncker’s candle problem and therefore
the secondary task did not inﬂuence problem solving performance.

Further research that highlights the importance of overlapping resource
requirements comes from a ﬁeld that is closely related to problem solving, reasoning.
Early studies by Baddeley and Hitch (1974; Hitch & Baddeley, 1976) asked participants
to judge as quickly as possible whether a description of a sequence of letters matched the
actual sequence of two letters presented while trying to either remember a digit preload or
perform a concurrent articulation task. It was found that a six digit preload (but not a one
digit or two digits preload) as well as a concurrent articulation tasks increased mean
reasoning times signiﬁcantly compared to single task reasoning performance. More
speciﬁcally, the greatest increase in reasoning time was seen in the concurrent
articulation task that required participants to repeat cyclically a random six digit sequence

given to them. Similarly, Farmer, Bennan, and Fletcher (1986) found small disruptive

21

effects of concurrent articulation on simple grammatical reasoning tasks but not on
simple visuospatial reasoning tasks. A concurrent spatial task produced the opposite
results. Gilhooly, Logic, Wetherick, and Wynn (1993) examined the impact of concurrent
articulation, articulatory suppression and a visuospatial secondary task on syllogistic
reasoning tasks. It was found that syllogistic reasoning was disrupted by concurrent
articulation and to a lesser extent by articulatory suppression, but not at all by the
visuospatial task that involved tapping a visual pattern. Similar results were found by
Toms, Morris, and Ward (1993) for conditional reasoning. Klauer, Stegrnaier, and Meiser
(1997) also found that a spatial tracking task only disrupted spatial reasoning and not
propositional reasoning while a random number generation task and an articulatory
suppression task led to inference for both spatial and propositional reasoning.
Extrapolating from this research it can be seen that a secondary task that taxes the same
resources as the primary reasoning task interferes with reasoning performance (a
concurrent articulation task interferes with syllogistic reasoning) while a secondary task
that used different resources as the primary task does not (a visuospatial tapping task does
not interfere with syllogistic reasoning).

One can then look at the task characteristics of problem solving to determine what
type of secondary task might lead to interference. Successful problem solving involves
the active maintenance of goals and other relevant task information in memory (e. g.,
information given in the problem, intermediate problem states), comparing relevant
information to information in memory to develop solution strategies, inhibiting irrelevant
or distracting information, monitoring and evaluating progress towards goals, and

planning and executing response actions (Hambrick & Engle, 2003). These problem

22

solving components involve different processes (based on Baddeley & Hitch, 1974;
Baddeley, 2002; Smith & Jonides, 1999). The maintenance of goals and task relevant
information in problem solving involves executive processes for the continued
maintenance of information. The phonological loop might also be involved as
participants might store intermediate problem states in verbal form. There might also be
involvement of the visuospatial Sketchpad for those problems involving a visual/spatial
component. Comparing relevant information to information in memory to develop a
solution strategy again involves executive processes responsible for comparing
information and planning a sequence of tasks to accomplish a goal. The process of
inhibiting irrelevant or distracting information in problem solving depends on executive
processes responsible for controlling inhibition and attention. Monitoring and evaluating
progress towards a goal are important aspects of problem solving that involve executive
processes responsible for updating and checking information in working memory to
determine the next step. Lastly, planning and executing a response action during problem
solving is controlled by executive processes involved in planning and task management.
Following the above presented research and Navon and Gopher (1979) as well as
Wickens (1980, 1984), a task that has the same resource requirements (working memory
and executive processes) should then lead to problem solving performance decrements.
Concurrent tone monitoring tasks seem to tax much of the same executive
processes involved in problem solving. A concurrent tone task requires the maintenance
of a target tone in memory which involves executive processes for the continued
maintenance of the tone. Perceiving each test tone involves the echoic store and

comparing each test tone to the target tone held in memory involves executive processes

23

involved in checking and comparing the presented tone with the target tone. Withholding
or inhibiting responses to distracter tones relies on executive processes involved in
inhibition and monitoring. Finally, planning and executing a response action also
involves executive processes responsible for planning and task management. Both
problem solving and a concurrent tone task involve executive processes responsible for
maintenance, planning, checking and comparing, task management, monitoring, and
inhibiting. These similarities in the two tasks’ resource requirements should lead to a
competition for resources which may lead to decrements in task performance when both
tasks are performed at the same time (N avon & Gopher, 1979; Wickens, 1980, 1984).

A concurrent tone-monitoring task has been used by Beilock, Bertenthal, McCoy,
and Carr (2004) and Beilock, Carr, MacMahon, and Starkes (2002) has shown
decrements in primary task performance, namely golf putting. More speciﬁcally, it has
been shown that the putting performance of novice golfers, which is under attentional
control, is negatively inﬂuenced by the addition of the secondary tone-monitoring task
while expert’s putting performance, which is under proceduralized control that does not
require constant attention, is not. However requiring experts to perform the secondary
tone-monitoring task while performing puts with an unfamiliar putter (requiring non-
proceduralized processes) also caused decrements in putting performance. These ﬁndings
indicate that when the tone task is paired with a task that requires similar processes
decrements are seen.

Golf putting and problem solving might seem very different on the surface,
however, for novices performing the golf putting tasks there are similar demands on

executive processes as in problem solving. More speciﬁcally, Beilock and Carr (2002) (as

24

well as Anderson, 1987; F itts & Posner, 1967) have argued that novices’ performance is
controlled by declarative knowledge that is held in working memory and attended to in a
step by step fashion during performance. This indicates that during putt execution novice
participants, just as in problem solving, are maintaining goals and task relevant
information in memory (the distance of the hole, the weight of the putter etc.), comparing
relevant information to information in memory (the declarative knowledge of the steps
involved in performing a putt), and planning and executing response actions- These
common resource requirements make it feasible to compare golf putting and problem
solving and to therefore expect similar effects of a concurrent tone monitoring task on
problem solving performance. If incentives inﬂuence attention then taxing attention with
both a problem solving task and a concurrent tone monitoring task should elucidate a
possible connection between incentives and attention allocation. If participants in the
dual-task condition given an incentive show an increase in problem solving and a
decrease in the concurrent tone monitoring performance then it would indicate that
incentives cause a shift of all attentional resources to the rewarded task. On the other
hand, if participants in the dual-task condition given an incentive show a decrease in both
the problem solving and tone monitoring performance then it would indicate that
incentives cause a shift of additional attentional resources. In other words, incentives only
inﬂuence performance when spare attentional resources can be recruited for the rewarded
task. Experiment 4 tested these two possibilities.
1.3 Summary of the Predictions

Experiment 1a and 1b were designed to show incentive effects on problem

solving and test whether incentives lead to persistence with one problem solving

25

approach. If incentives lead to an increase in persistence with one problem solving
approach then incremental problem solving will increase while insight problem solving
will decrease. Experiments 2a and 2b were designed to test whether incentives lead to an
increase in problem solving duration or deeper processing. If incentives lead to an
increase in problem solving duration then participants given an incentive would show
longer problem solving durations than participants not given an incentive. If incentives
lead to deeper processing of information then participants given an incentive should
remember more problems in more detail than participants not given an incentive.
Experiments 3 and Experiment 4 were designed to investigate incentive effects on
attention allocation using a dual-task approach. Two possible predictions were tested:
participants given an incentive shift all their attentional resources to the problem solving
task at the expense of the secondary task, or participants given an incentive only shift
resources to the problem solving task when additional resources are available.
Additionally, Experiment 4 tested whether participants given an incentive engage in
greater processing of the underlying structures of the problem compared to participants
not given an incentive. If incentives lead to greater processing of the underlying
structures of the problem then participants in the incentive condition will recall less
problem irrelevant information than participants in the non-incentive condition.
2 INCENTIVES AND PERSISTENCE WITH ONE STRATEGY
2.1 Experiments la and 1b

Experiments 1a and lb tested the prediction that an incentive will inﬂuence
problem solving despite the widespread assumption that motivation can be ignored when

examining cognitive processes. Moreover, Experiments 1a and 1b were designed to test

26

whether an incentive differentially affects participants' performance on incremental and
insight problems. If an incentive increases persistence with one approach then, based on
the assumptions supported in the introduction, persistence should help incremental
problem solving and hinder insight problem solving (due to possible mental set effects).

Half of the participants were given an incentive and half were not. The incentive
was the opportunity to leave the experiment early if the participant solved a certain
number of problems correctly. Money was not used as an incentive due to the possible
contrary and often convoluted effects money can have on performance (Crano, 1991).
Instead a leave early incentive was used because it was assumed to be particularly
attractive to the undergraduate participant pool and it is cost efﬁcient.

2.2 Method

Design. A 2x2 mixed design was used with a between-subjects factor of incentive
(given or not) and a within-subj ects factor of problem type (incremental and insight).

Participants. Two hundred and twenty-three Michigan State University students
participated for course credit in Experiment 1a (mean age 19.3) and 206 in Experiment
lb (mean age 19.4). The majority of the sample was female (169 female, 53 male in
Experiment la; 144 female, 62 male in Experiment 1b) reﬂecting the nature of the
participant pool. In both Experiments 1a and lb no gender effects were found.

Procedure. Participants were randomly assigned to either the incentive or non-
incentive condition. At the beginning of the experiment participants completed a
background questionnaire assessing their gender, age, year in school, and college
entrance exam test scores. They were then given an easy incremental practice problem

used to familiarize them with the procedure and the types of problems they would be

27

solving. After completion of the practice problem participants were told that they would
be solving a similar series of problems that would take until the end of the session to
complete. Participants were informed that they would have six minutes for each problem
and that once the time was up the problems would be collected regardless if they were
completed or not. Participants in the incentive condition were then told about the
incentive: the opportunity to leave the experiment early if they solved four of the
problems correctly. In neither condition were participants told the total number of
problems. After the instructions, problems were presented one at a time, alternating
between insight and incremental problems. During the experiment participants in the
incentive condition were given anonymous feedback after each problem by marking
whether a person got a problem correct on a board visible to everyone in the experiment.
Anonymous identiﬁcation numbers were used and participants were allowed to leave
once they had solved four problems correctly. If participants in the incentive condition
did not solve four problems they left after attempting all the problems. Participants in the
non-incentive condition always attempted all the problems. The experiment took about 50
minutes to complete.

Note that problems were collected only after six minutes were up, even if
participants ﬁnished a problem earlier. This manipulation was critical to the success of
the experiment, because it prevented participants in the incentive condition from
employing the strategy of handing back problems they did not think they could solve and
only working on easy problems. Had participants in the incentive condition been allowed
to use this strategy it would ahnost certainly have resulted in the incentive and non-

incentive groups attempting different sets of problems, and thus make them impossible to

28

compare.

Materials. For Experiment 1a ﬁve problems were selected; three incremental and
two insight problems (see Appendix A for the text of the problems). The problems were
selected from Metcalfe and Wiebe (1987) and Schooler, Ohlsson, and Brooks (1993) and
were chosen based on their difﬁculty level and solution rates from previous experiments
(Wieth & Burns, 2000). Problems were presented in two different orders. An “easy”
order that presented the problems in increasing difﬁculty and a “hard” order that
presented the problems in decreasing difﬁculty. This allowed us to investigate whether
our methodology was vulnerable to problem solving order effects, as well as whether the
difﬁculty of the problems may interacted with the incentive we used. More speciﬁcally,
we were concerned that the incentive may have a smaller inﬂuence on problem solving if
participants initially did the harder problems, because failing to solve a problem may lead
them to think they had little chance of obtaining the "leave early" incentive and thus
render our incentive manipulation moot. In the easy order participants were ﬁrst given the
easy Dinner Party (incremental) problem, the Water Lilies (insight) problem, the medium
Store (incremental) problem, the Checker Game (insight) problem, and then the hard
Stakes (incremental) problem. The hard order was almost identical except that the Dinner
Party and the Stakes problem were switched such that participants in the hard order
started with the Stakes problem and ended with the Dinner Party problem. Both insight
problems (Water Lilies problem and Checker Game problem), on the other hand, were
chosen to have a medium solution rate (about 50%).

Experiment 1b did not manipulate order but two new sets of insight and

incremental problems were given in order to generalize the results. Each set contained

29

four different problems, two incremental problems (Set 1: Card problem, Bachelor
problem; Set 2: Store problem, Flower problem) and two insight problems (Set 1: Horse
problem, Marriage problem; Set 2: Sock problem, Policeman problem). The problems in
each set were chosen to have a solution rate at or slightly above 50 percent. Solution rates
for some of these problems were taken from Maier and Cassehnan (1970) or were
determined from our own previous experiments (Wieth & Burns, 2000). The text of the
problems can be found in Appendix A. A ﬁfth problem (the Job problem) was presented
to all participants that did not leave early to ensure that participants that met the incentive
would actually leave before those that did not meet the incentive. This problem, however,
was not included in any analyses.
2.3 Results

The incremental and insight problems were scored as either right or wrong. An
insight score was calculated for each participant by summing the two insight problems of
each experimental set and then dividing by two. The same procedure was used to
calculate participant’s incremental score, however in Experiment 1a only the Dinner
Party and the Store incremental problems contributed to the incremental score. The
hardest incremental problem (the Stakes problem) in Experiment la was not included in
the incremental composite score because so few participants solved it correctly (4%),
though all those that solved it were in the incentive condition. Additionally, our best
incentive group participants never attempted the Stakes problem if given the easy
condition, because they were able to solve the ﬁrst four problems correctly and then leave
without being given the last and most difﬁcult problem. So we simply dropped the Stakes

problem rather than analyzing it with a biased sample.

30

Experiment 1 a. Based on four problems (excluding Stakes), the mean incremental

and insight scores are presented in Table 1.

 

 

Incremental Insight

Experiment la

Non-incentive (n = 111) .75 (.30) .47 (.39)

Incentive (n = 112) .84 (.24) .58 (.38)
Experiment lb
Set 1

Non-incentive (n = 50) .47 (.33) .51 (.38)

Incentive (n = 52) .61 (.39) .56 (.35)
Set 2

Non—incentive (n = 53) .74 (.32) .46 (.35)

Incentive (n = 51) .80 (.27) .64(.36)

 

Table 1. Mean incremental and insight scores (standard deviations in parentheses) for
Experiments 1a andlb (two problem sets used).

A 2x2x2 mixed analysis of variance was performed on participants' insight and
incremental problem solving scores with between-subject factors of order (hard ﬁrst or
easy ﬁrst) and incentive (present or not), and a within-subject factor of problem type.
Results showed that there was no evidence of an effect of order (F[1, 219] = .65, p = .42,
MS, = .13) or an interaction between order and type of problem (1‘11, 219] = .62, p = .43,

MS. = .10) . Therefore all further analyses in these experiments will be presented pooled

31

over the order factor. Note that although the data was categorical an analysis of variance
rather than a loglinear modeling analysis was used. Lunney's (1970) simulations show
that ANOVA is a valid analysis for categorical data with large sample sizes and an equal
number of participants in each condition. Using an analysis of variance one can take
advantage of the fact that participants did more than one problem, which is more
problematic for loglinear analysis with its strong assumption of independence.

As Table 1 shows there was a signiﬁcant effect of incentive (F[1, 219] = 9.01, p <
.01, MS, = .13) and problem type (F[l, 219] = 81.84, p < .01, MS, = .10). All other
effects and interactions with problem type were not signiﬁcant. Of special interest was
the interaction between incentive and type of problem, which was found not to be
signiﬁcant, F(1, 219) = .11, p = .74, MS, = .10, indicating that the incentive inﬂuenced
both insight and incremental problem solving in the same way (see Table 1). The solution
rates for the four individual problems were also examined and it was found that
participants in the incentive condition out-performed participants in the non-incentive
condition on each of them.

Experiment I b. Based on the four problems everyone attempted, Table 1 presents
the mean incremental and insight scores separately for the two problem sets.

A 2x2x2 mixed analysis of variance was performed on participants' insight and
incremental problem solving scores with between-subj ect factors of problem set (Set 1 or
Set 2) and incentive (present or not), and a within-subject factor of problem type (insight
or incremental). As in Experiment la, a signiﬁcant effect of incentive was found, F (1,
202) = 8.17, p < .01, MS, = .14, but no signiﬁcant interaction between incentive and

problem type, F (1, 202) = .05, p = .82, MS, = .10. These ﬁndings, again, indicate that the

32

incentive inﬂuenced both insight and incremental problem solving. Table 1 shows that
the incentive increased the mean solution rates for all incremental and insight problems in
both sets.

There was again a signiﬁcant difference between the two problem types, F(1,
202) = 13.24, p < .01, MS, = .10 and also a signiﬁcant difference between the two sets
F(1, 202) = 11.98, p < .01, MS, = .14. This is not surprising given that the sets contained
different problems with different underlying levels of difﬁculty. Of more interest
however was that there was no interaction between incentive and either problem type (as
shown above) or set, F(1, 202) = .12, p = .73, MS, = .14. Additionally, there were no
hi gher-order interactions with incentive.
2.4 Discussion

Experiments la and 1b showed that participants given an incentive outperformed
participants not given an incentive on all problems regardless of problem type. These
ﬁndings provide evidence that incentives do inﬂuence problem solving processes and
more speciﬁcally that incentives inﬂuence problem solving positively. In neither
experiment was there an interaction between the incentive and problem type, indicating
that the incentive did not inﬂuence performance on insight and incremental problem
solving differently. This was contrary to the prediction that the incentive would help
incremental problem solving and hinder insight problem solving.

Previous studies examining incentive effects on problem solving have shown
mixed effects of incentives on performance (e.g., Glucksberg, 1962, McGraw &
McCullers, 1979). Why then did the incentive consistently increase problem solving

across four different problem sets in Experiments 1a and 1b? It is possible that different

33

incentive structures led to these differences in problem solving performance. For
example, Glucksberg found evidence of incentives slowing solution to Duncker's candle
problem when participants were paid on the basis of how fast they solved the problem.
Rewarding participants as a function of speed of solutions (as opposed to simply solution
accuracy, as in Experiments la and 1b) may encourage a strategy that is normally
adaptive but happens to fail in the given context. Bruner, Goodnow and Austin (1956)
found that when participants were given only a few trials to discover a concept they
varied multiple aspects of the stimuli at a time. This strategy was not optimal for a
guaranteed discovery of the concept, but gave participants the best chance to ﬁnd it
quickly. Similarly, the best chance of solving a problem quickly is to hope that the
obvious solution works, and try it. For Duncker’s candle problem which is an insight
problem this is a poor strategy, but Glucksberg's participants did not know that they were
faced with an insight problem. Thus Glucksberg's ﬁndings may have been due to his
particular incentive structure, rather than because incentives are inherently harmful to
insight problem solving.

McGraw and McCullers (1979) also found detrimental effects of incentives on 10
water-jar problems of the style used by Luchins (1942). They found that participants in
the incentive group were slower than participants in the non-incentive group at solving
the tenth problem that required breaking the mental set established in the ﬁrst nine
problems. McGraw and McCullers concluded that their results were evidence for the
detrimental effects of incentives; however, as in the study by Glucksberg (1962) the
measure of problem solving performance was confounded by the incentive structure.

More speciﬁcally, in McGraw and McCullers the incentives were based on getting the

34

problems correct, the measure of performance however was time on task. In fact,
participants were speciﬁcally instructed that "they could take as long as they needed to
ﬁnd the correct answer to each of the problems, because time was not crucia " (McGraw
& McCullers, p. 287). Furthermore the incentive scheme paid a bonus that tripled the
maximum payoff if all ten problems were correct, so getting the tenth problem right was
especially important for the incentive group as they were risking their bonus. Given the
special status of the tenth problem for the incentive group, and the instructed irrelevance
of time, it would be surprising if participants did not take longer to turn in a solution than
the non-incentive group even if there was no mental set to break. Thus it is not clear what
McGraw and McCullers’ results say about the effects of incentives on insight problem
solving. Experiments la and 1b represent a much cleaner test of the effects of incentives
on problem solving because the dependent measure was solution rate and the incentive
only related to solutions.

Experiments 1a and 1b, despite strong suggestions in the literatures, also showed
no evidence for an interaction between incentive condition and problem type
(incremental vs. insight). Amabile (1987) suggested that incentives should lead to
negative effects on tasks involving creativity that are more open ended without a obvious
path to the solution. Insight problem solving has been argued to involve more creativity
than incremental problem solving because participants must re-represent each problem in
order to solve it (e.g., see Stemberg & Davidson, 1995). Since research has shown that
under some circumstances creativity can be hurt by incentives (Eisenberger & Cameron,
1996; Eisenberger & Selbst, 1994; Hennessey & Zbikowski, 1993) it seems natural to

extrapolate the results of creativity research to insight problem solving. However, insight

35

problem solving and creativity do differ in an important way; measures of creativity often
rely on participants showing a divergence of solution (e.g., Amabile) whereas problem
solving ultimately requires a single, correct, solution. Perhaps the ﬁndings of
Experiments 1a and 1b, that incentives also help insight problem solving, suggest that the
proposed link between insight and creativity needs to be treated with a little more
skepticism.

The results of Experiments la and 1b that the incentive increases both incremental
and insight problem solving indicate that there does not seem to be any evidence in these
particular experiments that the incentive leads to an increase in persistence with one
problem solving approach. It should be noted that Experiments 1a and 1b did not assess
participants’ problem solving approaches directly. It is therefore possible that the
manipulation used in these experiments to assess persistence with one problem solving
approach was too indirect and therefore did not reveal more subtle strategy changes due
to an incentive. In order to more directly assess participant problem solving approaches a
talk aloud methodology could be used where participants given an incentive are solving
incremental and insight problems while talking about their problem solving processes out
loud. This type of study would be a more direct measure of participants’ problem solving
approaches. A study such as this however is outside of the scope of this dissertation. The
results of Experiments 1a and 1b however are clear in showing a consistent increase
across incremental and insight problems indicating that the incentive inﬂuences a process
that is helpful to both types of problem solving. The next experiment was designed to
look more closely at what cognitive mechanisms might be inﬂuenced by an incentive in

incremental and insight problem solving.

36

3 INCENTIVES, TIME ON TASK, AND DEEPER PROCESSING
3.1 Experiments 2a and 2b

Experiments 1a and 1b were able to demonstrate that an incentive does inﬂuence
problem solving accuracy, however they did not provide any direct evidence about the
mechanism by which the incentive had an effect. Experiments 2a and 2b were designed
to test two possible mechanisms.

A possibility not explored in Experiments 1a and lb is that an incentive leads to
an increase in the overall time participants spend on a task. More speciﬁcally, it is
possible that an incentive leads participants to increase the amount of time they spend
solving each problem to ensure that they get the problem right. Research interested in
worker productivity has often shown an increase in the amount of time workers spend at
their task when they are given an incentive. For example, Saari and Latham (1982) found
that in response to an incentive beaver trappers reduced their breaks and spent more time
trapping beavers. Similarly, LaMere, et al. (1996) found that truck drivers’ increased the
amount of time they spent on the job. It is possible then that the increase in problem
solving due to the incentive seen in Experiments 1a and 1b is due to an overall increase
of time spent on each problem solving task. Note that although in Experiments 1a and lb
participants were given six minutes to solve each problem, it was often observed that
participants would not spend all six rrrinutes working on the problem (e.g., they would
turn over their sheet indicating that they were ﬁnished). Thus although all participants
had the same amount of time available to work on a problem, they appeared to choose
how much of the available time they spent actually working on the problem. The group

format of Experiments 1a and 1b, however, made it difﬁcult to measure individual

37

participants’ problem solving duration. In order then to assess whether the incentive
might lead to an increase in time spent, problem solving duration was directly measured
in Experiments 2a and 2b.

An alternative possible mechanism by which incentives may improve problem
solving is that they may encourage a change in thoroughness of processing, rather than a
change in time on task. Evidence for deeper processing due to an incentive can be seen in
Eysenck and Eysenck (1982). Participants were asked to recall a mixed list of high and
low monetary (10 pence and 2 pence, respectively) incentive words. During recall
participants where given weak and strong retrieval cues (e.g., “TABLE associated with

”); determined by word association norms. Results showed that high incentive
words were recalled more than low incentive words with weak retrieval cues but there
was no effect with strong retrieval cues. Eysenck and Eysenck argued that these ﬁndings
indicate that low incentive words were processed based only on their most obvious and
easily accessible features whereas high incentive words were processed in terms of both
easily accessible and less accessible features. It is possible then that the incentive might
lead to deeper processing of the problems and results in better memory for the problems
for participants in the incentive condition. This was investigated by giving participants a
surprise memory test which asked participants to recall all the problems they had
attempted so far.

In summary, if the incentive leads to an increase in time spent on each problem
solving task then participants in the incentive condition would have longer problem
solving durations than participants in the non-incentive condition. It is also possible

however that the incentive leads to deeper processing without an increase in time on task

38

which would lead to greater memory for the problems for participants in the incentive
condition compared to participants in the non-incentive condition. Experiments 23 and 2b
were designed to test these predictions.

Additionally, Experiments 2a and 2b addressed a possible confound in
Experiments la and 1b. In Experiments 1a and 1b participants in the incentive condition
were not only given the opportunity to leave the experiment early but also given feedback
regarding their own and other participants’ performance on each problem. Participants in
the non-incentive condition were given neither the incentive nor any feedback on their
problem solving performance. It was possible that the increase in problem solving
performance in the incentive condition was not only due to the incentive but also due to
the potentially motivating feedback participants received. This potential confound was
addressed by eliminating any feedback during the experiment. Participants in the
incentive condition were simply told when they could leave the experiment.

3.2 Method

Design. A 2x2 mixed design was used with a between-subjects factor of incentive
(given or not) and a within-subj ects factor of problem type (incremental and insight).

Participants. Two hundred and eight Michigan State University students
participated for course credit in Experiment 2a (mean age 19.2) and 200 in Experiment
2b (mean age 19.1). Again, the majority of the sample was female (154 female, 54 male
in Experiment 2a; 151 female, 49 male in Experiment 2b) reﬂecting the participant pool.
No gender effects were found.

Procedure. Participants were randomly assigned to either the incentive or non-

incentive condition. They were ﬁrst given the background questionnaire from the

39

previous experiments, then up to six problems alternating between incremental and
insight problems. Since results from Experiment 1a showed no order effects (easy versus
hard) we did not investigate this variable in Experiment 2. Unlike in Experiments la and
1b, the problems were presented by a computer (as web pages controlled by J avaScript,
see Bums & McFarlane, 2003) that recorded participants’ solutions (typed into a text
box, though scratch paper was available for participants to use throughout the
experiment) and the time they submitted them. Participants were given instructions on
how to use the computer program and the experimenter took participants step by step
through an example problem illustrating the procedure.

Participants were told they would be solving a series of problems and that they
would have four minutes to solve each problem. The amount of time given was reduced
from the previous experiments because in a pilot study it was found that participants
could solve these particular problems in a much shorter time span than some of the
problems presented in previous experiments. Participants were instructed to click a button
to submit their answer after writing the answer in a textbox. If they wanted to change
their answer before the four minutes were up, they could edit their text and resubmit.
Pressing a button to submit their answers allowed us to measure the amount of time it
took participants to provide an answer. After four minutes the computer automatically
moved the participants on to the next screen, recording the last thing that had been
written in the text box.

In order to address a potential confound in Experiments 1a and 1b participants in
both conditions were not given any feedback regarding their performance after

submitting an answer. Participants in the incentive condition were simply told by the

40

experimenter when they could leave the experiment. Problems were presented in the
same order to all participants alternating between incremental and insight problems.
Participants were told that the experiment would take approximately one hour to
complete. In addition, participants in the incentive condition were told that there was a
special incentive for their group in that they would be able to leave early if they got four
problems correct. After solving the appropriate number of problems, participants were
asked to complete a surprise memory question that asked them to write down as many
details of each problem as they could remember. There was no time limit for the memory
question. Before starting the memory question the experimenter removed any scratch
paper the participants might have used.

In Experiment 2a participants were given the memory question at the end of the
experiment after completing all of their problems. This created a possible confound given
that participants in the incentive condition potentially needed to recall only four problems
to receive a perfect recall score (although few actually did get to leave early) whereas
participants in the non-incentive condition always had six problems to recall. In
Experiment 2b the memory question was always presented after the ﬁrst four problems,
thus all participants then had to try to remember the same number of problems for the
memory question. Apart ﬁ'om this change, Experiment 2b was identical to Experiment
2a. Both Experiment 2a and 2b took about 45 minutes to complete.

Materials. A new set of insight and incremental problems were given in
Experiments 2a and 2b, the text of which (plus solution rates) can be found in the
Appendix A. For both experiments participants received the same two incremental (Age

problem and Water problem) and two insight problems (Month problem and Matchstick

41

problem) in the same order (Age problem, Month problem, Water problem, and
Matchstick problem). Participants that did not solve the ﬁrst four problems correctly and
participants in the non-incentive condition completed up to two additional problems (Job
problem and Prisoner problem). Problems were taken from Ash and Wiley (2002),
Knoblich, Ohlsson, and Raney (2001), and Metcalfe and Wiebe (1987) and were chosen
to match each other in difﬁculty such that each incremental problem would
approximately match an insight problem in difﬁculty. To conﬁrm this, the solution rate
for each problem was ﬁrst checked in a paper and pencil pilot study (non-incentive) with
64 participants.

3.3 Results

The insight and incremental problems were scored as either right or wrong.
Solution rates were similar to the rates found in the paper and pencil pilot study. As in
Experiment 1a and 1b participants’ insight and incremental scores were calculated using
the ﬁrst four problems presented in the experiment, since participants in the incentive
condition might never have attempted the last two problems. As in the previous
experiments, most participants attempted all 6 problems (32 participants in the incentive
condition got to leave early).

Incentive eﬂects on solution. Table 2 presents the means and standard deviations
for insight and incremental scores. A 2x2 analysis of variance was performed on these
scores with a between-subjects factor of incentive (present or not) and a within-subjects
factor of problem type (insight or incremental). As in the previous experiments there was
a signiﬁcant effect of the incentive (Experiment 2a, F[1, 206] = 6.96, p < .01, MS, = .17;

Experiment 2b, PH, 198] = 8.53, p < .01, MS, = .19) and a signiﬁcant difference between

42

the two problem types, insight and incremental but only in Experiment 2b (Experiment
2a, H1, 206] = .03, p < .87, MS, = .01; Experiment 2b, F[1, 198] = 4.28, p < .01, MS, =
.39). However there again was no interaction between problem type and incentive
(Experiment 2a, F[1, 206] = .23, p = .63, MS, = .09; Experiment 2b, F[1, 198] = 1.98, p =

.16, MS, = .09) and all other effects and interactions with problem type were not

 

signiﬁcant.
Incremental Insight

Experiment 2a

Non-incentive (n = 104) .51 (.37) .52 (.37)

Incentive (n = 104) .63 (.35) .61 (.35)
Experiment 2b

Non-incentive (n = 100) .44 (.36) .55 (.38)

Incentive (n = 100) .61 (.39) .63 (.36)

 

Table 2. Mean incremental and insight scores (standard deviations in parentheses) for
Experiments 2a and 2b.

Problem solving duration. In order to further investigate the effects of the
incentive participants’ problem solving duration was recorded. Problem solving duration
for correct answers was determined by analyzing the ﬁrst time that participants answered
the problem correctly. If an incorrect solution was submitted, then problem solving
duration was determined by taking the time for the last unique answer provided.
(Participants would often submit their ﬁnal answer several times because pressing the

submit button gave them an indication of how much time was left before the computer

43

would move them on to the next problem). If participants did not submit an answer
before the four rrrinutes were up, their answer was scored as incorrect and a time of four
minutes was assigned. Table 3 presents mean durations for each incentive condition both
across and broken down by problem type. Only the durations of the ﬁrst four problems

were analyzed.

 

Incremental Insight
Experiment 2a
Non-incentive 175.1 (58.4) 145.9 (79.5)
Incentive 180.3 (60.1) 144.7 (78.2)
Experiment 2b
Non-incentive 173.8 (59.5) 146.2 (76.9)
Incentive 177.4 (61.7) 151.6 (77.1)

 

Table 3. Mean problem solving duration in seconds (standard deviations in parentheses)
for incremental and insight problems in the non-incentive and incentive conditions for
Experiments 2a & 2b.

In order to investigate whether participants’ problem solving duration differed for
problems they got correct compared to problems they got incorrect a 2x2x2 analysis of
variance on problem solving duration was performed with incentive (given or not),
problem type (insight or incremental), and whether or not the problem was solved
correctly (correct or incorrect). An analysis that includes correctness is important because

correctness could have a complex relationship with duration. However, in order to

analyze the correct/incorrect factor each problem for each participant has to be treated as

44

a single case. This is not an ideal way of analyzing the problem solving data because it
creates a large number of cases that could lead to signiﬁcant differences that are in reality
very small. Unfortunately, there are no other analyses that can be used to look at the
connection between problem solving duration and problem correctness as they are
directly linked. In both experiments participants in the incentive condition had
statistically signiﬁcantly greater problem solving durations than participants in the non-
incentive condition (Experiment 23, PI], 824] = 6.6, p < .05, MS, = 3332.05; Experiment
2b, F[1, 792] = 9.75, p < .01, MS, = 3545.27). However as Figure 1 shows, these
difference were only a few seconds out of a total possible time of 2408. The smallness of
these effects is illustrated by the effect sizes: d = .03 for Experiment 2a, d = .06 for
Experiment 2b. Despite the statistically signiﬁcant effects of incentive on duration, they
seem too small to explain the large (averaging 21.6% across all experiments) increases in

problem solving when an incentive was given.

45

 

ll, Non-incentive El Incentiﬁj

 

 

 

 

_L
(J!
0

Solving Duration
(In seconds)
:8; _ .

 

8

o l l I

 

 

 

 

 

 

 

 

 

Experiment 2A Experiment 28

Figure 1. Mean problem solving duration for participants in the non-incentive and
incentive condition for Experiments 2a and 2b. Error bars represent standard errors.

Participants consistently spent more time on incremental problems than insight
problems and on problems they got correct. However, there were no statistically
signiﬁcant interactions between incentive and problem type or problem correctness.
There was a signiﬁcant interaction between problem type and correctness (Experiment
2a: F[1, 824] = 8.67,p < .01, MS, = 3332.05, Experiment 2b: F[1, 792] = 8.16, p < .01,
MS, = 3545.27) indicating that participants spent less time on insight problems when they
got them correct. This is consistent with the nature of insight problem solving as duration
depends on when the insight occ'urs, rather than requiring time to work through a
procedure for arriving at the solution.

Memory. The memory question was a free recall measure designed to investigate

participants’ memory for the problems that they had just attempted. Several analyses

46

were run using the information obtained from the memory measure.

First a coarse memory measure was created that was the proportion of all the
problems that participants had any memory of. All problems were scored blind to
condition, and a problem was counted as remembered if the participant mentioned any
unique, identifying aspect of the problem. A response that only mentioned that the
problem was a math problem or an equation problem was not counted as remembered.
The number of problems was then divided by the number of problems the participant
attempted in the experiment. In Experiment 2a the number attempted was always six for
participants in the non-incentive condition but could vary between four and six for those
in the incentive condition depending on whether they solved enough problems to leave
early (35% did less than six). In Experiment 2b the memory question was given to all
participants after their fourth problem, thus all had attempted the same number of
problems when their memory was tested, regardless of condition.

A 2x2 analysis of variance was run on the coarse memory measure with incentive
(given or not) and problem type (incremental and insight) as factors (see Table 4). For
both Experiment 2a and Experiment 2b a signiﬁcant effect for incentive was found
(Experiment 2a: F (1, 206) = 7.15,p < .01, MS, = .04, Experiment 2b: F(1, 198) = 6.31,p
< .05, MS, = .03). There was no effect of problem type (Experiment 2a: F (1, 206) = 1.36,
p = .24, MS, = .06, Experiment 2b: F[1, 198] = .40, p = .53, MS, = .03) nor an interaction
between problem type and incentive (Experiment 2a: F (1, 206) = .80, p = .37, MS, = .06,
Experiment 2b: F[1, 198] = .90, p = .35, MS, = .03). As Figure 2 shows participants in
the incentive condition remembered a greater proportion of the problems than

participants in the non-incentive condition regardless of problem type. In order to be able

47

to compare the effect of incentives on problem solving duration and the memory
measure, effect size was again calculated. In both Experiment 2a and 2b the incentive had
a small to medium effect on the coarse memory measure (Experiment 2a: d = .37,
Experiment 2b: d = .36), indicating that the incentive had a greater effect on memory than

on problem solving duration.

 

i El Non-incentive 7E1 Incentive]

 

 

 

Proportion recalled
o
o:

 

   

 

 

 

 

 

 

0.2 i:_1 -

0.1 if I

0 V :
Experiment 2a Experiment 2b

Figure 2. Proportion of problems recalled (coarse memory measure) for participants in
the non-incentive and incentive condition for Experiments 2a and 2b. Error bars represent
standard errors.

For the coarse memory measure participants only had to refer to a problem for it
to be counted as remembered, however, participants' responses would often be much
more elaborate. In order to get a better sense of participants' responses, a ﬁne memory
measure was also created by scoring the participants’ responses to the memory questions

for the amount of detail or descriptiveness, of each problem. Two raters, blind to

48

condition, independently scored each of the problem responses on a rating scale ranging
from 1 to 4 designed to differentiate between the amounts of detail participants provided.
A score of 1 was assigned to responses with very little or no detail about a problem, while
a score of 4 was given to responses that had all or almost all the details of a problem (see
Appendix B for details). If participants did not mention a problem at all a score of 0 was
assigned for that particular problem. Scoring of the ﬁne measure is more subjective than
the coarse measure, but inter-rater reliability was found to be satisfactory for both
experiments (Experiment 2a: K = .88, Experiment 2b: K = .86). A 2x2 analysis of
variance of the ﬁne memory measure using incentive and problem type as factors found
that in both experiments participants in the incentive condition provided more detailed
descriptions of the problems than participants in the non-incentive condition (see Figure
3), Experiment 2a: F(1, 206) = 5.85,p < .05, MS, = 1.5, Experiment 2b: F(1, 198) = 4.11,
p < .05, MS, = '1.4 (see Table 3 for means and standard deviations). There was no effect
for problem type (F[1, 206] = .95, p =.33, MS, = .62, Experiment 2b: F[1, 198] = .06, p =
.81, MS, = .40) and no interaction between problem type and incentive (F[1, 206] = .41, p

= .52, MS, = .62, Experiment 2b: F[1, 198] = .01, p = .99, MS, = .40).

49

 

r . " "7’ .
‘El Non-Incentive Cl Incentive;J

 

3.5 -

 

F-l

 

 

41*
H
r——r

2.5

 

Detail score

 

 

 

 

 

 

 

 

Experiment 2a Experiment 2b

Figure 3. Mean amount of problem detail given (ﬁne memory measure) for participants in
the non-incentive and incentive condition for Experiments 2a and 2b. Error bars represent
standard errors.

Again, effect size was calculated and was found to be a small to medium effect
(Experiment 2a: d = .29, Experiment 2b: d = .29). Thus, across the two experiments,
participants in the incentive condition displayed better memory for the problems whether
their memories were scored using a loose criterion (coarse memory measure) or a strict
criterion (ﬁne memory measure) than participants in the non-incentive condition. Most
importantly, both of these problem memory measures showed substantially larger effect

sizes than problem solving duration.

50

 

Incremental Insight
Experiment 2a
Coarse
Non-incentive .83 (.21) .78 (.21)
Incentive .86 (.25) .85 (.21)
Fine
Non-incentive 2.38 (1.01) 2.40 (.94)
Incentive 2.62 (1.12) 2.75 (1.08)
Experiment 2b
Coarse
Non-incentive .93 (.19) .92 (.17)
Incentive .95 (.15) .98 (.11)
Fine
Non-incentive 3.08 (.99) 3.10 (.94)
Incentive 3.32 (.96) 3.34 (.89)

 

Table 4. Mean memory scores (standard deviations in parentheses) for the coarse and ﬁne
measure for incremental problems, insight problems, and their totals across both problem

types in Experiments 2a & 2b.

3.4 Discussion

Experiments 2a and 2b were designed to investigate the mechanisms by which

incentives inﬂuence problem solving. Results replicated the ﬁndings from Experiments

51

1a and 1b, showing that the "leave early" incentive increased problem solving
performance, and provided further evidence that incentives do inﬂuence cognitive
processes. Additionally, Experiments 2a and 2b replicated the ﬁnding that the incentive
inﬂuenced incremental and insight problems equally, as performance on both problem
types increased in the incentive condition. These results provide evidence that ﬁndings
from Experiments 1a and lb were not simply caused by a confound in the incentive
condition (participants receiving feedback), instead it shows that the incentive (the
opportunity to leave the experiment early) alone is a strong motivator.

Critically, Experiments 2a and 2b produced evidence for incentives leading to an
increase in performance via deeper processing of information. It was found that
participants in the incentive condition had greater memory for each of the problems they
attempted than participants in the non-incentive condition. Yet the incentive had only a
very small effect on a measure of how much time participants spent trying to solve each
problem. This suggests that incentives affect problem solving by leading to more though

processing of information rather than simply by increasing time spent on the task.

52

4 INCENTIVES AND ATTENTION

Experiments 2a and 2b provided evidence that participants in the incentive
condition engaged in deeper processing of the problems than participants in the non-
incentive condition. The question then becomes what is the cognitive mechanism behind
this increase in processing? Attention has been shown to be an important factor for recall
performance (Craik, Govoni, Naveh-Benj amin, & Anderson, 1996; Logan & Etherton,
1994; Logan, Taylor, & Etherton, 1996; Naveh-Benjamin, Craik, Guez, & Dori, 1998).
More speciﬁcally, it has been shown that attention during encoding is essential for
successﬁrl processing and retrieval as large decrements in retrieval can be seen when
attention is divided during encoding (e. g., Craik, Govoni, Naveh-Benj amin, & Anderson,
1996; Naveh-Benjamin, Craik, Guez, & Dori, 1998). Perhaps the increase in memory for
participants in the incentive condition in Experiments 2a and 2b was due to an increase in
attention to the problem solving task. Research on goal setting has shown that
participants shift their resources and attention to goal relevant information and away from
goal irrelevant information (e. g., Rothkopf & Billington, 1979). Since incentives usually
encompass a goal, as well as a reward, it is possible that incentives also lead to an
increase in attention to the rewarded task. In Experiments 2a and 2b participants in the
incentive condition recalled more problems in more detail, indicating deeper processing.
Given the importance of attention during encoding it is possible then that participants
given an incentive allocated more attention to the problem solving task compared to
participants not given an incentive.

In order to test this possibility a dual-task approach was tested in Experiment 3. It

has been shown that performing two tasks with similar resource requirements

53

simultaneously will lead to decrements in task performance (N avon & GOpher, 1979;
Wickens, 1980, 1984). Giving participants a task that taxes the same cognitive resources
as problem solving should therefore affect performance. A dual-task approach then can
be used to investigate if incentives lead to an increase in attention to the rewarded task. If
incentives during single task performance normally lead to an increase in attention to the
rewarded task then taxing participants’ attentional resources with a problem solving task
and a secondary task at the same time may lead to two possible outcomes. Participants
may shift all their attention to the problem solving task and ignore the concurrent tone
monitoring task, as suggested by the goal setting literature. On the other hand, it is
possible that incentives only cause a shift of additional or spare attentional resources to
the rewarded task. This then would lead to the elimination of the problem solving
advantage seen for participants in the incentive condition.

There has been virtually no research investigating secondary task effects on
problem solving. One exception however is a study by Lavric, et a1. (2000) that recorded
ERP responses while participants solved what the authors referred to as an incremental
problem (a version of the Wason card selection task) and an insight problem (Duncker’s
candle problem) while concurrently counting auditory stimuli. It was found that
incremental problem solving performance was impaired by the concurrent counting task
however insight problem solving was not. Additionally, at the electrophysiological level
peak and time-window average P300 (a measure sensitive to working memory function)
showed greater amplitude in the frontal region in response to counting tones during
incremental problem solving compared to insight problem solving and the counting task

alone. Since P300 is a measure reﬂecting working memory, Lavric, et a1. believe that

54

these ﬁndings show greater competition for working memory resources between the
concurrent counting task and the incremental problem task than the insight problem task.
It is possible then that a secondary task might tax incremental and insight problems
differently. In order to investigate this possibility Experiment 3 retained both incremental
and insight problems despite the null problem type effects found in Experiments 1a and
1b as well as Experiments 2a and 2b.

Even though there has been very little research on secondary task effects in
problem solving there has been research looking at secondary task effects on reasoning.
Overall ﬁndings in this literature are consistent with Navon and Gopher (1979) and
Wickens (1980, 1984) that performance decrements are seen when the two tasks have the
same resource requirements and therefore tax the same resources. For example Farmer, et
al. (1986) found small disruptive effects of concurrent articulation on simple grammatical
reasoning tasks but not on simple visuospatial reasoning tasks. A concurrent spatial task
on the other hand led to disruptive effects on a visuospatial task but not on a grarmnatical
reasoning task. Similarly, Gilhooly, et al. (1993) found that syllogistic reasoning was
disrupted by concurrent random number generation and to a lesser extent articulatory
suppression, but not at all by the visuospatial task that involved tapping.

4.1 Experiment 3

If a dual-task approach is going to be used to investigate incentive effects on
attention in problem solving, then it is important to ﬁnd a secondary task that will tax the
same attentional resources as the incremental and insight problem used in Experiments 2a
and 2b. Problem solving involves maintaining information and goals in memory,

comparing new information to stored information, inhibiting irrelevant pieces of

55

information, monitoring and evaluating ones progress towards goals, and planning and
executing responses (Hambrick & Eagle, 2003). These problem solving components
involve executive processes responsible for maintenance of information, monitoring,
updating and checking, inhibiting irrelevant information, and planning responses and
actions (based on Baddeley & Hitch, 1974; Baddeley, 2002; Srrrith & Jonides, 1999). In
this experiment a concurrent tone monitoring task was used because of its similar task
requirements to problem solving. More speciﬁcally, participants were asked to listen to a
series of tones and respond by pressing a foot pedal every time they heard a target tone.
This concurrent tone task requires the maintenance of a target tone in memory which like
problem solving involves executive processes for the continued maintenance of the tone.
Comparing each test tone to the target tone held in memory involves executive processes
involved in checking and comparing while withholding or inhibiting responses to
distracter tones relies on executive processes involved in inhibition and monitoring.
Finally, as in problem solving, planning and executing a response to a target tone also
involves executive processes responsible for planning and task management. These
similarities in the two tasks’ resource requirements should lead to decrements in task
performance in both the problem solving tasks and the concurrent tone monitoring task.
Experiment 3 was designed to investigate the impact of the concurrent tone
monitoring task on problem solving. It was predicted that if the concurrent tone
monitoring task has similar resource requirements as problem solving then decrements in
problem solving performance should be seen. Additionally, if this is the case decrements
in tone monitoring performance should also be seen when participants are performing the

tone monitoring task while solving problems compared to participants performing the

56

tone monitoring task alone. Since there has been very little work looking at secondary
task effects on problem solving Experiment 3 was also designed to test different
parameters for the concurrent tone task. Participants were presented with either a 2-tone
monitoring task (their target tone and another tone) or a 3-tone monitoring task (their
target tone and two other tones) to determine whether or not difﬁculty of the concurrent
tone monitoring task varied across these two conditions. Additionally, participants’ target
tone was varied such that some participants in the 2—tone condition could be given either
the low tone or the high tone as their target. In the 3-tone condition participants could be
given either the low, medium, or high tone as their target. Target tone was varied in order
to determine if any of the tones used in the task were more or less distinguishable from
each other; potentially causing performance differences across target tone.
4.1.1 Method

Design. A 2x2x2 mixed design was used with between-subjects factors of task
(single task or dual-task) and number of tones (two or three), and a within-subjects factor
of problem type (incremental and insight). Participants in the single task condition only
solved incremental and insight problems while participants in the dual-task condition
solved incremental and insight problems and performed the tone task with either two or
three tones simultaneously. All participants completed the tone task (either two or three
tones) by itself before and after the problems. Additionally, participants’ target tone was
manipulated. Participants in the 2-tone condition received either the low tone or the high
tone as their target. Participants in the 3-tone condition received either the low tone,
medium tone, or high tone as their target.

Participants. One hundred and thirty Michigan State University students

57

participate in Experiment 3 for course credit (mean age 19.38). The majority of the
sample was female (103 female, 27 male). No gender effects were found.

Procedure. Participants were randomly assigned to either the single task (n = 65)
or dual task condition (n = 65). After obtaining consent participants completed the
background questionnaire used in the previous experiments. Participants were given an
overview of the experiment and then instructed on how to use the computer program. The
computer program used in this experiment was the same as in Experiments 2a & 2b
except that it was modiﬁed to accommodate the dual-task aspect of this study. The
experimenter took participants step by step through an example problem solving task
illustrating the procedure. Participants were told they would be solving a series of
problems and that they would have four minutes to solve each problem. Participants were
instructed to click a button to submit their answer after writing the answer in a textbox. If
they wanted to change their answer before the four minutes were up, they could edit their
text and re-subrrrit. As in Experiments 2a & 2b, after four minutes the computer
automatically moved the participants on to the next screen, recording the last thing that
had been written in the text box.

After explaining the problem solving procedure, the experimenter explained the
tone monitoring task. Each participant put on headphones and the target tone was played
three times at an interval of one tone every two seconds. Participants then completed a
practice tone monitoring task where they were asked to press a foot pedal every time they
heard the target tone. Participants would be presented with one tone every two seconds
and were either given two different tones (their target tone and another tone) or three

different tones (their target tone and two other tones). The target tone was either one of

58

the two or three tones presented and was determined randomly. Similarly, whether
participants were in the 2-tone or 3-tone condition was determined randomly. The
computer randomly generated the sequence of tones presented to each participant. The
practice tone monitoring task lasted for two minutes. After the practice task the
experimenter checked each participants hit rate. If the hit rate was less than ninety
percent participants were asked to listen to the target tone again and repeat the practice
task. After everyone successfully completed the practice tone monitoring task,
participants were presented with the actual tone monitoring task. The tone monitoring
task was exactly the same as the practice task except that participants were presented with
tones for four minutes. Again participants were reminded to hit the foot pedal every time
they hear the target tone.

After the tone monitoring task participants were given an easy incremental
practice problem and were reminded of the problem solving instructions. Participants in
the dual-task condition were told that they would have to solve the problem and do the
tone monitoring task concurrently. Participants in the single task condition were simply
told to solve the problem. After completing the practice problems participants were asked
if they had any more questions, then they were presented with an additional four
problems (two incremental and two insight) in four different orders. Note all participants
in this experiment attempted only four problems, unlike in the previous experiments
where participants could potentially attempt up to six problems. Each order ensured that
participants would be presented with incremental and insight problems in an alternating
fashion. Participants in the dual-task condition engaged in the tone monitoring task at the

same time as solving all four problems. Participants in the single task solved all the

59

problems without hearing tones. Between each problem participants were presented with
a screen that gave them the opportunity to listen to their target tone again. Participants
clicked on a link to move on to the next problem whenever they were ready.

After ﬁnishing all the problems participants were asked to complete the surprise
memory question that asked them to write down as many details of each problem as they
could remember. As in the previous experiments, there was no time limit for this
particular question and participants were not presented with tones. If participants had
used any scratch paper while solving the problems the experimenter removed it before
the participant started the memory question.

To test for possible tone task practice effects, participants then completed the tone
monitoring task again. Each participant regardless of condition was asked to listen to
their target tone one more time and then they completed the tone task. The tone
monitoring task lasted four minutes and the characteristics of the task (but not the actual
series of tones) were identical to the tone task participants completed earlier. Once
participants were done with the ﬁnal tone monitoring task they were debriefed and sent
on their way. The experiment lasted about 60 minutes.

Materials. The ﬁrst four problems from Experiments 2a and 2b were used, the
text of which can be found in the Appendix A. Since a new methodology was used,
problem order was manipulated to ensure that there are no order effects in a dual-task
context. Problems were presented in four different orders such that participants received
the two incremental (Age problem and Water problem) and two insight problems (Month
problem and Matchstick problem) in an alternating fashion.

A concurrent auditory tone monitoring task was used as a secondary task while

60

problem solving. The tone monitoring task was based on work by Beilock, et al. (2004)
and Beilock, et al. (2002) which have shown decrements in primary task performance due
to a similar tone monitoring task. The tone task in this experiment asked participants to
listen to a series of tones and press a foot pedal every time they heard a target tone. The
series of tones was randomly generated by the computer program that also presented
participants with the problem solving tasks. The tones (500 ms each) occurred once every
two seconds. The series of tones was composed of either two tones (a low tone and a high
tone) or three tones (a low tone, a medium tone, and a high tone). The tones chosen were
300 hertz, 900 hertz, and 1500 hertz. Participants were randomly assigned to one of these
tones as their target tone.
4.1.2 Results

The insight and incremental problems were again scored as either right or wrong.
As in the previous experiments participants’ insight and incremental scores were
calculated using the four problems presented in the experiment.

Dual-task eﬂects on solution. Table 5 presents the means and standard deviations

for insight and incremental scores.

61

Incremental Insight

 

Single task
2-tones (n = 29) .55 (.39) .41 (.33)
3-tones (n = 36) .65 (.33) .50 (.38)
Dual-task
2-tones (n = 25) .40 (.32) .36 (.37)
3-tones (n = 40) .50 (.39) . .35 (.30)

 

Table 5. Mean incremental and insight scores (standard deviations in parentheses) in the
single and dual-task 2-tones and 3-tones conditions for Experiment 3.

A 2x2x2 analysis of variance was performed on the incremental and insight scores with a
between-subj ect factors of task (single or dual), and number of tones (two or three), and a
within-subj ects factor of problem type (insight and incremental). Results showed that
there was no evidence of an effect of order (F[3, 126] = .15, p = .21, MS, = .22) nor any
interactions with order. Therefore all ﬁrrther analyses in this experiment will be presented
pooled over this factor. There was a signiﬁcant effect of the task (F[1, 126] = 7.00, p =
.009, MS, = 1.02) such that performance under dual-task conditions decreased for both
incremental and insight problem solving (see Figure 4). These ﬁndings indicate that the
concurrent tone monitoring task has similar resource requirements as problem solving
which led to the decrease in solution rate. There was also a signiﬁcant difference between
the two problem types, insight and incremental (F[1, 1268] = 8.66, p = .004, MS, = .91)
where incremental problems had a higher solve rate than insight problems. It was

attempted to match problem difﬁculty between incremental and insight problems,

62

however, solution rates of problems often differ between samples and can therefore be
difﬁcult to match perfectly. There was a slight trend for the number of tones (F[1, 126] =
2.08, p = .15, MS, = .30) such that participants’ solve rate in the 2-tone condition was
lower than in the 3-tone condition (see Table 5). This may indicate that the 2-tone
condition is more similar to the concurrent tone monitoring task and therefore causes a
greater decrease in problem solving than the 3-tone condition. This possibility will be
discussed ﬁrrther in the discussion section of this study. Unlike Lavric, et al. (2000) there
was no interaction between task and problem type (F[1, 126] = .38, p = .54, MS, = .04),
indicating that the secondary task did not inﬂuence incremental and insight problem
solving differently. Reasons why Lavric, et al.’s results were not replicated in this study
will be discussed in the discussion section following this experiment. All other
interactions were also not signiﬁcant. Overall the decrease in problem solving seen for
both incremental and insight problems indicates that the concurrent tone monitoring task

seems to have similar resource requirements as problems solving.

63

 

[El Single 13 Dual-task]

 

 

 

 

 

 

 

 

 

 

 

 

 

1 -
0.9 -
0.8 ~
0.7 i
T
g 0.6 t §2};g:§sigi15:sﬁ~.;;;g-;
é 0-5 7 I m}: .
_ {3:5} v Iii-.37 5:153- j
3 0.4 - 32:23?“ I
0.3 - g j ..... .
0.2 .
0.1 i figsfiif‘fi5‘257-igf iii}?.iéiifliii:
Eﬂfqifu‘lffﬂufi‘glfi UNIV-“Afﬂitﬁi‘
:ggrs . .1233“ .35. ‘Tif.:.:.§;.l9i§f;i'i35
O .. T H 1
Incremental Inslght

Figure 4. Mean solution rates for incremental and insight problems in the single and dual-
task conditions for Experiment 3. Error bars represent standard errors.

In order to investigate whether the target tone inﬂuenced solution rate two
analyses were run, one analysis for participants in the 2-tone condition and one for
participants in the 3-tone condition. One large analysis obviously could not be run as
there would be a missing cell in the 2 tone condition since participants could never have
gotten the medium target tone. A 2x2x2 analysis of variance was performed on the
incremental and insight scores for participants in the 2-tone condition with between-
subjects factors of task (single or dual) and target (low or high), and a within-subjects
factor of problem type (insight and incremental). Results showed that there was no effect
of target (F[1, 50] = 1.13, p = .30, MS, = .14) nor any signiﬁcant interactions with target.

These ﬁndings indicate that problem solving performance did not differ across target for

64

participants in the 2-tone condition (see Table 6).

 

Incremental Insight
Single task
low target (n = 16) .50 (.45) .34 (.24)
high target (n = 13) .62 (.30) .50 (.41)
Dual-task
low target (n = 12) .29 (.26) .46 (.40)
high target (11 = 13) .50 (.35) .27 (.33)

 

Table 6. Mean incremental and insight scores (standard deviations in parentheses) for
participants in the 2-tone condition across target for Experiment 3.

Looking at participants in the 3-tone condition, a 2x3x2 analysis of variance was
performed on incremental and insight scores with between-subj ects factors of task (single
or dual) and target (low, medium, or high), and a within-subjects factor of problem type
(insight or incremental). In this condition there again, was no effect of target (F[2, 70] =
1.23, p = .30, MS, = .19). However there was a trend for the interaction between task and
target (F[2, 70] = 2.62, p = .08, MS, = .40) such that solution rates for participants in the
dual-task condition were lower when they were given the medium or high target tone
than the low target tone (see Table 7). These ﬁndings might be due to the confusability of
the medium and high tone. Whereas the tones chosen for the tone task were equally
spaced in terms of frequency, subjectively the medium and high tone sounded much more
similar to each other than the low tone. It should also be noted that the power for this

analysis is very low and therefore the results should be interpreted with caution.

65

 

Incremental Insight

Single task

low target (n = 13) .65 (.32) .50 (.41)

medium target (n = 13) .69 (.38) .58 (.34)

high target (n = 10) .60 (.32) .40 (.39)
Dual-task

low target (n = 13) .69 (.33) .42 (.28)

medium target (n = 13) .35 (.43) .23 (.26)

high target (n = 14) .46 (.37) .39 (.35)

 

Table 7. Mean incremental and insight scores (standard deviations in parentheses) for
participants in the 3-tone condition across target for Experiment 3.

Problem solving duration. As in Experiments 2a and 2b problem solving duration
was again determined for the last unique answer provided. A 2x2x2x2 analysis of
variance on problem solving duration (in seconds) was performed with between-subj ects
factors of task (single or dual), problem type (insight or incremental), number of tones (2
or 3), and whether the problem was solved correctly (correct or incorrect). In order to
analyze the correct/incorrect factor each problem for each participant was again treated as

a single case (for means and standard deviations see Table 8).

66

Incremental Insight

 

Single task
2-tones (n = 58) 168.88 (67.65) 165.36 (84.56)
3-tones (n = 72) 161.27 (66.16) 152.47 (77.10)
Total (n = 130) 164.67 (66.68) 158.22 (80.45)
Dual-task
2-tones (n = 50) 183.08 (54.53) 171.59 (98.57)
3-tones (n = 80) 170.88 (63.17) 163.34 (75.51)
Total (n = 130) 175.57 (60.07) 166.51 (84.85)

 

Table 8. Mean problem solving duration in seconds (standard deviations in parentheses)
for incremental and insight problems in the single task and dual—task conditions divided
by number of tones for Experiment 3.

Examining the effect of the concurrent tone monitoring task on problem solving duration
it was found that there was no effect of task (F[1, 504] = .01, p = .93, MS, = 31.69).
Participants’ problem solving duration did not increase in the dual-task condition (M =
171.04, SD = 73.51) compared to the single task condition (M = 161.44, SD = 73.81).
These ﬁndings indicate that the concurrent tone monitoring task did not inﬂuence
problem solving duration. There was a signiﬁcant main effect for correctness, (F (1, 504)
= 151.87, p < .01, MS, = 640521.90) such that participants spent less time on problems
they got correct (M = 129.3, SD = 66.46) than on problems they got incorrect (M =

199.15, SD = 63.73 ). In order to make sure that this effect was not only caused by those

participants that did not answer a problem and were therefore assigned the maximum

67

amount of time (240 seconds) the same analysis was run excluding cases where
participants took all the time allotted. The exact same pattern of results was found.
Participants also spent signiﬁcantly more time solving incremental problems (M =
170.12, SD = 63.57) than insight problems (M = 162.36, SD = 82.62), F(1, 504) = 9.65, p
= .002, MS, = 40721.32. This difference however was only eight seconds which is
relatively small given the total amount of problem solving time available. Number of
tones did not inﬂuence problem solving duration differently, (F[1, 504] = .38, p = .54,
MS, = 1617.28). As for solution rate the interaction between task and problem type was
not signiﬁcant (F[1, 504] = .00, p = .97, MS, = 5.62), again indicating that task did not
inﬂuence incremental and insight problem solving differently. Any other interactions
were also not signiﬁcant.

Again two separate analyses were run to determine whether or not the different
target tones inﬂuenced problem solving duration differently. A 2x2x2x2 analysis of
variance was performed on problem solving duration for participants in the 2-tone
condition with factors of task (single or dual), target (low or high), problem type (insight
or incremental), and whether or not the problem was solved correctly (correct or
incorrect). Target tone did not affect problem solving duration (F[1, 200] = .85, p = .36,
MS, = 4007.91) and the interaction between task and target (H1, 200] = 2.87, p = .19,
MS, = 13532.94) was not signiﬁcant.

Looking at participants in the 3-tone condition, a 2x3x2x2 analysis of variance
was performed on problem solving duration with factors of task (single or dual), target
(low, medium, or high), problem type (insight or incremental), and whether or not the

problem was solved correctly (correct or incorrect). There also was no effect of target

68

tone (F[1, 280] = .82, p = .44, MS, = 3134.76) and no signiﬁcant interactions with target.
These ﬁndings indicate that problem solving duration did not differ across target tone for
participants in the 3-tone condition.

Secondary task performance - accuracy. Performance on the tone monitoring task
was analyzed for when participants were performing the task alone at the beginning of
the experiments and at the end of the experiment. In order to investigate the impact of the
problem solving task on the tone monitoring task participants performance while solving
incremental and insight problems was also analyzed.

In order to assess performance on the concurrent tone monitoring task at the
beginning of the experiment, participants’ hit rate (the propertion of target tones correctly
identiﬁed) and false alarm rate (the proportion of tones incorrectly judged to be the target
tone) was calculated. Participants were given the tone-monitoring task by itself before
attempting any problems. Overall, tone accuracy (the hit rate minus the false alarm rate,
M = .94, SD = .18) was signiﬁcantly different from zero (t[128] = 59.52, p < .01, MS, =
.02) indicating that participants were able to reliably detect the target tone when given the
tone task by itself. No difference in performance was found between participants in the 2-
tone condition (M = .96, SD = .17) and participants in the 3-tone condition (M = .93, SD
= .19), F (1,127) = .51, p = 48, MS, = .02. Looking at target effects, there was a trend
(F[1, 54] = 2.92, p = .09, MS, = .08) for participants in the 2-tone condition such that
participants given the high target tone (M = .92, SD = .24) were less reliable at detecting
than participants given the low target tone (M = .99, SD = .01). There was also a trend for
participants in the 3-tone condition (F[2, 740] = 2.3, p = .11, MS, = .08) such that

participants in the medium tone condition (M = .88, SD = .29) were less reliable than

69

participants in the high tone (M = .93, SD = .14) and low tone condition (M = .99, SD =
.02) at the detecting the target tone.

In order to determine the impact of the problem solving task on participants’
accuracy on the tone task, participants’ tone task performance while solving problems
was compared to their tone task performance only both at the beginning and at the end of
the experiment. Participants were given four minutes to solve each problem and were
asked to respond to the tone task for the whole four minutes. However, in order to get an
accurate reﬂection of participants’ performance on the secondary task while they were
actually solving problems (not just responding to the tone task while waiting for the
computer to move them on to the next problem) performance on the secondary task was
tied to participants’ submission of their answers. More speciﬁcally, participants hit rate
and false alarm rate was calculated up to the point when participants submitted their last
unique answer. (This point in time also corresponds to participants’ problem solving
duration.) An incremental and insight problem hit rate and false alarm rate were then
calculated by averaging across the hit rates and false alarm rates for the incremental and
insight problems. Again the false alarm rate was subtracted from the hit rate to calculate a
tone accuracy measure. A 2x4 analysis of variance was run on the accuracy measure with
a between subjects factor of number of tones (2 or 3) and a within subjects factor of dual

performance (tone only beginning, tone incremental, tone insight, and tone only end).

70

 

i-r

0.9

.iL.

0.8 i

0.7

 

 

l-——-l
I——I

0.6 -

0.5 a

Tone task
accuracy

0.4 >

0.3 -

0.2 ~

 

0.1 ~

ol— . . a“

Beginning Incremental Insight End

 

 

 

 

 

 

 

 

Figure 5. Mean tone task accuracy in Experiment 3 for the tone task at the beginning of
the experiment, the tone task while solving incremental problems, the tone task while
solving insight problems and the tone task at the end of the experiment. Error bars
represent standard errors.

There was a main effect of dual performance (F[3, 11] = 12.89, p <.01, MS, = .60). Post-
hoc tests showed that tone detection accuracy while participants were solving incremental
problems (t[47] = 8.46, p < .01, MS, = .04) was signiﬁcantly lower than accuracy for the
tone task alone at the beginning of the experiment. The same was true for tone task
accuracy during insight problem solving (t[46] = 7.11, p < .01, MS, = .04). There was no

difference in tone detection accuracy between incremental and insight problems (t[3 8] = -

1.83, p = .21, MS, = .02). Participants’ accuracy on the tone task during incremental

71

problem solving was also signiﬁcantly lower than on the tone task at the end of the
experiment, t(47) = -4.68, p < .01, MS, = .05. Tone detection accuracy was also lower
while solving insight problem compared to the tone task at the end of the experiment,
t(47) = -3.61, p = .001, MS, = .05. In order to test for practice effects in the dual-task
condition participants’ tone detection accuracy for the tone task at the beginning of the
experiment was compared to their accuracy on the tone task at the end of the experiment.
Results showed a trend, t[126] = 1.75, p = .08, MS, = .02, but in the opposite direction as
predicted by a practice effect. More speciﬁcally, participants in the single task condition
had greater tone detection accuracy (M = .94, SD = .21) than participants in the dual-task
condition (M = .87, SD = .30). This is most likely due to participants in the dual-task
condition getting tired of the tone task after listening and responding to the tones for the
whole experiment, see Figure 5.

In the overall analysis there was also a trend for number of tones (F[1, 37] = 3.13,
p = .09, MS, = .39) such that participants in the 2-tone condition were more accurate
overall (M = .86, SD = .12) than participants in the 3-tone condition (M = .72, SD = .25)
The interaction between number of tones and dual performance was found not to be
signiﬁcant (F[3, 111] = .27, p = .85, MS, = .01). An analysis looking at the effects of tone
accuracy based on target tone for both the 2-tone and 3-tone condition was not possible
due to extremely small cell sizes.

In order to test whether participants in the dual-task condition traded off their
performance on the tone task for their performance on the problem solving task a 2x2x2
analysis of variance on tone response time was performed with between-subjects factors

of problem type (insight or incremental), number of tones (2 or 3), and whether or not the

72

problem was solved correctly (correct or incorrect). In order to analyze the
correct/incorrect factor participants tone task accuracy for each individual problem was
again treated as a single case. Results showed that there were no effects of correctness
(F[1, 210] = .20, p = .15, MS, = .20) indicating that participants were not more likely to
ignore the tone task when they got a problem correct than when they got a problem
incorrect.

Overall the results indicate that problem solving inﬂuences tone monitoring
accuracy. When participants were solving problems their tone monitoring accuracy
decreased providing further evidence that problem solving and the tone monitoring task
have similar resource requirements.

Secondary task performance — response time. Participants’ response time to the
target tone was measured both while performing the tone task only and while solving the
problems. For this particular measure only the response time for hits was analyzed
because there were very few false alarms with reliable response times. Response times
were taken up until the participants submitted their ﬁnal solution; then an average
response time for hits was created. A 2x4 analysis of variance was run on response time
(in milliseconds) with a between subjects factor of number of tones (2 or 3) and a within
subjects factor of dual performance (tone only beginning, tone incremental, tone insight,
and tone only end). There was an overall main effect of dual performance (H3, 63] =
19.56, p < .01, MS, = 260953.58). Post-hoc tests revealed that participants responded
slower to the target tone while solving incremental problems than when only performing
the task at the beginning (t[22] = 5.81, p < .01, MS, = 35.812) and at the end of the

experiment (t[22] = 5.19, p < .01, MS, = 43.28). This was also the case comparing tone

73

response times for the tone task at the beginning (t[23] = 6.09, p < .01, MS, = 29.43) and
the end (t[23] = 6.17, p < .01, MS, = 32.61) to response times during insight problem
solving. There was no difference in tone response times between incremental and insight
problems (t[22] = 1.27, p = .22, MS, = 29.86) nor between the tone task at the beginning
of the experiment and the end of the experiment (t[562] = .19, p = .85, MS, = 16.37), see

Figure 6.

1200

1000 .

800 4

600 1

Tone task
response time (in ms)

400—

200-

 

 

 

 

 

 

 

Beginning Incremental Insight End

Figure 6. Mean tone task response time (in ms) in Experiment 3 for the tone task at the
beginning of the experiment, the tone task while solving incremental problems, the tone
task while solving insight problems and the tone task at the end of the experiment. Error
bars represent standard errors.

74

As for accuracy there was no main effect of number of tones in the overall analysis (F[1,
21] = .57, p = .60, MS, = 222052.42) and no interaction between number of tones and
dual performance (F[2,42] = .76, p = .69, MS, = 8969.78). These ﬁndings indicate that
response times to the target tone decreased as participants were asked to perform both the
tone task and the problem solving task.

To investigate any possible speed-accuracy trade off effects a 2x2x2 analysis of
variance on tone response time was performed with between-subjects factors of problem
type (insight or incremental), number of tones (2 or 3) and whether or not the problem
was solved correctly (correct or incorrect). In order to analyze the correct/incorrect factor
participants’ tone task response time for each individual problem was again treated as a
single case. There was no effect for correctness (F[1,85] = .04, p = .84, MS, = 2094.10)
and no signiﬁcant interactions with correctness. An analysis looking at the effects of
response time based on target tone for both the 2-tone and 3-tone condition was not
possible in this study due to extremely small cell sizes.

Overall the results show an increase in response times for the tone monitoring
task when participants are solving problems. This provides further evidence that problem
solving and the tone monitoring task have similar processing demands.

4.1.3 Discussion

Experiment 3 was designed to ﬁnd a suitable concurrent task that would tax
similar resources as problem solving. Results showed that a concurrent tone monitoring
task led to decrements in problem solving performance. Participants’ problem solving

accuracy while performing the tone monitoring task decrease signiﬁcantly compared to

75

participants’ problem solving accuracy alone. Problem solving duration, however, did not
seem to be affected by the concurrent tone task. There was no increase in the amount of
time participants spend solving each problem in the dual-task condition compared to the
single task condition. Nevertheless, the decrease in problem solving accuracy alone
provides good evidence that the concurrent tone monitoring task has similar resource
requirements as problem solving. Navon and Gopher (1979) argued that if two tasks have
the same resource requirements then decrements should be seen in both tasks. This
experiment also showed that problem solving interfered with tone task performance.
Tone task accuracy, hit rate minus false alarm rate, while solving problems was
signiﬁcantly lower than tone task performance alone. Reaction time for the tone task also
increased signiﬁcantly while participants were solving problems compared to when they
were performing the tone task alone. These results provide evidence that the concurrent
tone monitoring task and problem solving share the same basic resources, which in turn
leads to decrements in task performance. Having shown that the tone monitoring task can
tax attentional resources it can be used in the next experiment to investigate incentive
effects on attention allocation.

Another purpose of this experiment was to establish the parameters of the
concurrent tone task for Experiment 3. Participants were either presented with a 2-tone
monitoring task or a 3-tone monitoring task. In the 2-tone monitoring task participants
were presented with their target tone and one other tone, in the 3-tone monitoring task
participants were presented with their target tone and two other tones. Problem solving
accuracy results showed a slight trend such that participants’ problem solving

performance was lower in the 2-tone condition than the 3-tone condition. Perhaps these

76

ﬁndings indicate that the 2—tone condition shares more resources with problem solving
than the 3-tone condition. In the 2-tone condition participants had to respond to their
target tone by pressing the foot pedal more often compared to the 3-tone condition. It is
possible then that planning and executing a response to a target tone interferes more with
problem solving than inhibiting a response to a non-target tone. Since participants in the
2-tone condition had to plan and execute a response more often than participants in the 3-
tone condition, it is possible that the trend for decreased problem solving accuracy in the
2-tone condition might indicate greater similarities between that version of the tone task
and problem solving.

Participants’ target tone was also manipulated such that participants in the 2-tone
condition were given either the low or the high tone as their target, while participants in
the 3-tone condition were given either the low, medium, or high tone as their target.
There were no effects of target tone on participants’ problem solving accuracy or
problem solving duration for the 2-tone condition. In the 3-tone condition results showed
that participants given the medium or high tone had lower problem solving accuracy than
participants given the low tone. This might be due to the similarity between the medium
and high tone. The tones were picked to be equally spaced in frequency but the medium
and the high tone sound much more similar compared to the low tone. It is possible that
participants had more trouble differentiating the medium and high tone leading to greater
decrements in problem solving performance. Looking at participants’ tone task
performance, this was found to be the case. Participants in the 3-tone condition were less
accurate when given the medium or the high target tone compared to the low target tone.

Additionally, it was noted that participants in the 3-tone condition were much more likely

77

 

to start consistently responding to another tone that was not their given target tone than
participants in the 2-tone condition. In order to avoid this type of conﬁrsion and since
there seem to be an indication of greater problem solving decrements the 2-tone condition
will be used in Experiment 4.

Throughout this experiment both incremental and insight problems were used to
investigate possible differences in how the concurrent tone monitoring task might affect
these two types of problems. Lavric, et al. (2000) found negative effects of a secondary
task on incremental problem solving but not insight problem solving. Experiment 3 did
not replicate these ﬁndings; instead the secondary task reduced both incremental and
insight problem solving. Why did Experiment 3 not replicate these previous ﬁndings?
Lavric, et al. used a secondary tone task that was similar to the tone task used in this
experiment, however, participants were asked to count the number of target tones instead
of responding by pressing a foot pedal. Keeping track of the number of tones involves
working memory to a greater degree than the responding to a target tone at the
appropriate moment in time. It is possible then that Experiment 3 did not replicate the
results found by Lavric, et a1. because of differences in the secondary task. Perhaps a
secondary task that taxes working memory to a greater degree would lead to different
effects on incremental and insight problem solving. Another possibility why Experiment
3 did not replicate Lavric, et al. is that they used only one incremental problem and one
insight problem in their study. It is possible that the differential secondary task effects are
actually a reﬂection of the properties of the problems that were chosen and not
incremental and insight problems overall. Further work will have to be done to

investigate these possibilities.

78

In summary, Experiment 3 showed that a concurrent tone monitoring task taps the
same resources as problem solving. Performance on both problem solving and the tone
monitoring task was reduced in the dual-task condition. This methodology can then be
used to test whether incentives lead to an increase in attention to the rewarded task.
Taxing participants’ attention by having them engaged in both the tone monitoring task
and the problem solving task should lead to a reduction in attention available for the
rewarded task (in this case problem solving) and may eliminate the incentive advantage
as participants do not have any additional attentional resources that can be shifted to the
rewarded task. Alternatively, if the problem solving task is protected by the incentive,
then performance on the concurrent tone monitoring task may drop without a change in
the incentive advantage seen for problem solving. These possibilities were tested in
Experiment 4.

4.2 Experiment 4

Experiment 4 was designed to test whether an incentive leads to a shift in
attention to the rewarded task. In order to test this, a dual-task approach was used.
Experiment 3 showed that a concurrent tone monitoring task taxes similar attentional
resources as problem solving. Performing both the tone monitoring task and problem
solving tasks simultaneously led to decrements in both tasks indicating a sharing of
resources by the two tasks. A concurrent tone task can therefore be used to test whether
incentives inﬂuence attentional mechanisms. In Experiment 4 it was predicted that if
incentives lead to a shift of all attentional resources to the rewarded task then problem
solving performance will increase even in the dual-task condition. On the other hand, if

incentives only lead to a shift of spare or additional resources then the incentive should

79

have no effect in the dual-task condition.

Additionally, Experiment 4 was designed to test whether an increase in attention
to the rewarded task due to an incentive can lead to deeper processing of the problems. In
Experiments 2a and 2b participants given an incentive showed greater recall for the
problems and their details than participants not given an incentive. It is possible then that
an increase in attentional resources leads to deeper processing of the problems and
therefore the increase in memory seen in Experiments 2a and 12b. Given this it was
predicted that performing a secondary task while solving problems will reduce
participants’ memory for the problems. Additional attention could also lead to a greater
level of understanding of the underlying structures of the problems. If this was the case
participants given an incentive would be more likely to recall problem details that are
directly related to solving the problem while participants not given an incentive might
also recall irrelevant details. A post—hoc examination of participants’ memory recall in
Experiments 2a and 2b showed that this seemed to be the case for one problem (Age
problem) which included an irrelevant piece of information. The problem was taken from
Ash and Wiley (2002) who asked participants to rate the importance of different problem
components for ﬁnding a solution. In their study the irrelevant piece of information was
rated as very unimportant for solving the problem. Scoring participants’ memory recall
from Experiments 2a and 2b for the irrelevant piece of information it was found that
participants given an incentive were less likely to recall the irrelevant information than
participants not given an incentive. This could be an indication that participant not given
an incentive are engaging in more surface processing of the problems while participants

given an incentive are engaging in more processing of the underlying structure of the

80

 

problem. Experiment 4 tested this possibility by adding irrelevant information to all the
problems and scoring participants memory recall for it. If incentives lead to an increase in
resources which causes deeper processing of the underlying structure of the problem then
it was predicted that participants in the incentive condition will recall less irrelevant
information than participants not given an incentive.

4.2.1 Method

Design. A 2x2x2 mixed design was used with between-subjects factors of
incentive (given or not) and task (single task or dual-task), and a within-subj ects factor of
problem type (incremental and insight). Again all participants completed the tone task
alone at the beginning of the experiment but unlike Experiment 3 the tone task at the end
of the experiment was dropped.

Participants. Three hundred and twenty Michigan State University students
participate in Experiment 4 for course credit (mean age 19.62). Again, the majority of the
sample was female (215 female, 105 male) reﬂecting the participant pool. No gender
effects were found.

Procedure. Participants were randomly assigned to either the incentive or non-
incentive and either the single task or dual task condition. The procedure was the same as
in Experiment 3 except for the following changes. Participants in the incentive condition
were informed of the incentive, the opportunity to leave the experiment early if they
solve four problems correctly, at the beginning of the experiment. All participants were
presented with the 2-tone monitoring task and participants were randomly assigned to
either the low or high target tone condition. Participants completed the practice tone

monitoring task and the actual tone monitoring task but in this experiment the ﬁnal tone

81

task at the end was not given. Participants, as in Experiments 2a and 2b, completed up to
six problems (three incremental and three insight). After four problems participants were
asked to complete the surprise memory question that asked them to write down as many
details of each problem as they could remember. The experiment took about 60 minutes
to complete.

Materials. The same set of problems as in Experiments 2a and 2b was used,
however an irrelevant piece of information was added to the text of each problem. The
irrelevant piece of information was not needed for solving the problem but this was not
necessarily apparent when ﬁrst looking at the problem. The text of the modiﬁed problems
can be found in the Appendix A. Problems were again presented in four different orders
ensuring that incremental and insight problems were presented in an alternating fashion.

The 2-tone monitoring condition from Experiment 3 was used as the secondary
task in this experiment. This version of the secondary task was chosen because it showed
greater problem solving performance decrements than the 3-tone condition. Additionally,
fewer participants in the 2-tone condition compared to the 3-tone condition confused their
target tone with another tone.

4.2.2 Results

The insight and incremental problems were again scored as either right or wrong.
As in the previous experiments participants’ insight and incremental scores were
calculated using the ﬁrst four problems presented in the experiment.

Incentive and dual—task eﬂects on solution. Table 9 presents the means and

standard deviations for incremental and insight scores.

82

Incremental Insight

 

Single task
Non-incentive (n = 80) .53 (.34) .36 (.33)
Incentive (n = 80) .66 (.36) .48 (.39)
Dual-task
Non-incentive (n = 80) .47 (.36) .29 (.32)
Incentive (n = 80) .48 (.36) .29 (.33)

 

Table 9. Mean incremental and insight scores (standard deviations in parentheses) for
participants in the single and dual-task conditions divided by incentive for Experiment 4.
As in Experiment 3 there were no order effects (F[3, 316] = 1.23, p = .30, MS, = .19).
Additionally there were no target effects (F[3, 318] = 1.99, p = .17 MS, = .31) indicating
that performance did not differ between participants that received the low or the high
target tone. Therefore all further analyses in this experiment will be presented collapsed
across order and target tone. A 2x2x2x2 analysis of variance was performed on the
incremental and insight scores with between-subjects factors of task (single or dual) and
incentive (given or not), and a within-subjects factor of problem type (insight and
incremental). There was a signiﬁcant effect of task (F[1, 316] = 17.36, p < .01, MS, =
2.500) indicating that performance in the dual-task condition decreased for both
incremental and insight problem solving (see Table 9). There was also a signiﬁcant effect
for incentive indicating that participants given an incentive outperformed participants not
given an incentive (F[1, 316] = 5.25, p = .02, MS, = .76). However, the signiﬁcant

interaction between incentive and task (F[1, 316] = 3.92, p = .049, MS, = .56) indicates

83

that the incentive effect is being driven by participants in the single task condition. Post-
hoc test showed that the incentive increase problem solving performance in the single
task condition (F[1, 159] = 8.63, p = .004, MS, = .66) but not in the dual-task condition
(F[1, 159] = .05, p = .82, MS, = .004), see Figure 7. There was a signiﬁcant main effect
of type of problem (H1, 316] = 51.92, p < .01, MS, = 5.26), indicating that participants
were more successful solving incremental problems than insight problems. However
there were no signiﬁcant interactions with problem type indicating that the dual-task and
the incentive did not inﬂuence incremental and insight problems differently. No other

interactions were signiﬁcant.

 

, ‘ 7
{I Non-incentive El Incentive

 

l——I

 

Solution rate
1—1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Single Dual-task

Figure 7. Mean solution rates for problems in Experiment 4 for the single and dual-task
conditions for participants either given an incentive or not. Error bars represent standard
errors.

Overall these results show that incentives lead to an increase in problem solving only in

84

the single task condition. Participants’ performance in the dual-task condition did not
increase when given an incentive. These ﬁndings provide evidence that incentives cause
an increase in attention to the rewarded task only when additional or spare resources are
available. When participants do not have any additional attentional resources that can be
shifted (as in the dual-task condition) incentives do not have an impact.

Problem solving duration. As in the previous experiments problem solving
duration was again determined for the last unique answer provided. A 2x2x2x2 analysis
of variance on problem solving duration (in seconds) was performed with between
subjects factors of task (single or dual), incentive (given or not), problem type (insight or
incremental), and whether the problem was solved correctly (correct or incorrect). In
order to analyze the correct/incorrect factor each problem for each participant was again
treated as a single case. There was a signiﬁcant main effect for task, (F11, 1264] = 4.79, p
= .03, MS, = 18469.19) such that participants spent less time on problems in the single
condition (M = 169.09, SD = 69.56) than in the dual-task condition (M = 171.45, SD =
71.95). However, as the means indicate this difference is only two seconds and given the
large amount of power behind this analysis it is unlikely that this is a meaningful
difference between the two conditions. There was also a main effect for correctness,
(F[1, 1264] = 370.10, p < .01, MS, = 14258201) indicating that participants spent less
time on problems they got correct (M = 135.26, SD = 69.83) than on problems they got
incorrect (M = 198.36, SD = 57.78). As in the previous experiments the same analysis
was rim excluding cases where participants took all the time allotted (240 seconds). The
exact same pattern of results was found. Participants spent signiﬁcantly more time

solving incremental problems (M = 175.71, SD = 63.23) than insight problems (M =

85

164.81, SD = 77.19), F(1, 1264) = 48.62 p < .01, MS, = 187318.82. This again is not
surprising given the nature of insight problems where participants can ﬁnd the
appropriate representation of the problem at any time. There was no effect for incentive,
(F[1, 1264] = .35, p = .56, MS, = 1344.69) but a signiﬁcant interaction between incentive
and task, (F[1, 1264] = 7.86, p =.005, MS, = 30261.68). Post-hoe tests showed that
participants in the dual-task condition who were not given an incentive spent more time
solving problems (M = 179.96, SD = 70.31) than participants in the dual-task condition
given an incentive (M: 164.87, SD = 73.10), F(1, 635) = 5.31 p = .02, MS, = 27291.5. In
the single task condition participants who were given an incentive (M = 168.27, SD =
71.33) spend the same amount of time solving problems than participants not given an
incentive (M = 169.91, SD = 67.82), F(1, 643) = .09 p = .76, MS, = 435.9. These ﬁndings
indicate that the dual-task leads to slower problem solving unless participants are given
an incentive. Whether this ﬁnding is actually meaningful and reliable however is
questionable and needs to be replicated. All other interactions were found not to be
signiﬁcant.

Secondary task performance - accuracy. In order to assess performance on the
concurrent tone monitoring task at the beginning of the experiment, participants’ hit rate
(the proportion of target tones correctly identiﬁed) and false alarm rate (the proportion of
tones incorrectly judged to be the target tone) were calculated. Participants were given
the tone-monitoring task alone before attempting any problems. Overall, tone accuracy
(the hit rate minus the false alarm rate, M = .97, SD = .10) was signiﬁcantly different
from zero (t[319] = 167.94, p < .01, MS, = .006) indicating that participants were able to

reliably detect the target tone when given the tone task by itself. Again, participants’ tone

86

detection hit rate and false alarm rate were calculated for when solving incremental and
insight problems. A 2x3 analysis of variance was run on the accuracy measure with a
between subject factor of incentive (given or not) and a within subjects factor of dual
performance (tone only, tone incremental, and tone insight). There was a main effect of
dual performance (F12, 316] = 129.49, p <.01, MS, = 2.44). Post-hoe tests revealed that
tone monitoring accuracy decreased when participants were solving incremental
problems (M = .74, SD = .21) compared to when they were performing the tone task
alone (M = .97, SD = .12), t(159) = 14.47, p < .01, MS, = .02. This was-also the case for
tone accuracy when participants were solving insight problems (M = .77, SD = .23),
t(159) = 11.35, p < .01, MS, = .02. Tone task accuracy did not differ across incremental
and insight problem solving (t[159] = .81, p = .21, MS, = .08). There was no incentive
effect (F11, 158] = .41, p = 52, MS, = .03) indicating that the incentive did not inﬂuence

tone monitoring accuracy differently, see Figure 8.

87

 

Non-incentive El Incentive j

 

 

H
l
H

0.9 .

0.8 1*

 

 

 

I“—'I
I‘—l

l-H

 

I-t

0.7 ~

0.6 -

0.5 -

Tone task
accuracy

0.4 ,,

0.3 ~

0.2 ~

0.1 -

 

 

 

 

 

 

 

 

 

 

 

Tone Only Incremental Insight

Figure 8. Mean tone task accuracy in Experiment 4 for participants in the incentive and
non-incentive conditions performing the tone task alone, the tone task while solving
incremental problems, and the tone task while solving insight problems. Error bars
represent standard errors.

In order to check for a possible tradeoff effect between problem solving
performance and tone monitoring accuracy a 2x2x2 analysis of variance on tone accuracy
was performed with between-subjects factors of incentive (given or not), problem type
(insight or incremental), and whether or not the problem was solved correctly (correct or
incorrect). In order to analyze the correct/incorrect factor participants tone task accuracy

for each individual problem was again treated as a single case. There was a signiﬁcant

effect for correctness, (F11, 632] = 9.05, p = .003, MS, = .53), however it was in the

88

opposite direction as would be expected. Participants were more accurate at responding
to the tone task when they got the answer correct (M = .79, SD = .23) than when they got
the answer incorrect (M = .73, SD = .25). Perhaps this is due to participants ignoring the
tone task when they realized they could not easily solve a problem. Most importantly
however there was no effect of incentive (F11, 632] = 1.71 p = .20, MS, = .10) and no
interaction between incentive and correctness (F11, 632] =.53, p = .47, MS, = .03). These
ﬁndings indicate that participants’ relative engagement with the tone task and the
problem solving task did not differ as a ﬁrnction of whether they solved the problem
correctly.

Secondary task performance — response time. As in Experiment 3 participants’
response time to the target tone was measured both while performing the tone task alone
and while solving the problems. Again since participants generally had very few false
alarms only the response times for hits were analyzed. A 2x3 analysis of variance was run
on response time (in milliseconds) with a between subject factor of incentive (given or
not) and a within subjects factor of dual performance (tone only, tone incremental, and
tone insight). There was a signiﬁcant effect for dual performance (F12, 316] = 194.70, p
< .01, MS, = 27419913). Post-hoe tests revealed that participants were slower at
responding to the tone task while solving incremental (M = 955.63, SD = 162.04)
problems compared to tone task only performance (M = 728.36, SD = 214.32), t(159) = -
15.67, p < .01, MS, = 14.71. Tone task response time while solving insight problems (M
= 947.77, SD = 178.76) was also slower compared to tone task only response time (M =

728.36, SD = 214.32), t(159) = -15.07, p < .01, MS, = 14.78. Tone task response times

89

while solving incremental problems and insight problems were not signiﬁcantly different

form each other, t(159) = .83,p = .41, MS, = 9.53 (see Figure 9).

 

Non-incentive El Incentive

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1200
1000
a — I ++
E :
x g 800,
en ar -— I
5 .E " ,
0 g 600 — "Iii-:51;
: d) 2;:
.2 2
8. 400 <
in
2
200 -
0 ,_,.,,,._.,..,.. 7 Ti ...... -: I
Tone Only Incremental Insight

Figure 9. Mean tone task response times (in ms) in Experiment 4 for participants in the
incentive and non-incentive condition while performing the tone task alone, the tone task
while solving incremental problems, and the tone task while solving insight problems.
Error bars represent standard errors.

There was no effect of incentive (F[1,158] = .63, p = .43, MS, = 50082.1) indicating that
tone response time did not differ between participants given an incentive (M = 865.94,
SD = 160.10) and participants not given an incentive (M = 886.37, SD = 165.48). There
were no signiﬁcant interactions. Overall these ﬁndings indicate that participants’ tone

task response times increased while solving problems compared to their tone task

performance alone. Incentive had no effect on response times.

90

Again it is possible that participants in the dual-task condition given an incentive
were slower to respond to the tone task in order to increase accuracy on the problems. To
test for a possible speed-accuracy tradeoff in the incentive condition a 2x2x2 analysis of
variance on tone response time was performed with between-subj ects factors of incentive
(given or not), problem type (insight or incremental), and whether or not the problem was
solved correctly (correct or incorrect). In order to analyze the correct/incorrect factor
participants’ tone task response for each individual problem was again treated as a single
case. There were no signiﬁcant effects for correctness (F11,632] = 1.36, p = .24, MS, =
38068.71) and incentive (F11,632] = 1.44, p = .23, MS, = 51862.09). Additionally, the
interaction between correctness and incentive was also not signiﬁcant, F (1,158) = .97, p
= .33, MS, = 36808.34). These ﬁndings indicate that there was no speed-accuracy
tradeoff for participants given the incentive.

Memory. As in Experiments 2a and 2b a coarse memory measure and a ﬁne
memory measure were created from participants responses to the memory question. A
2x2x2 analysis of variance was run on the coarse memory measure with between subjects
factors of task (single or dual) and incentive (given or not), and a within subjects factor of

problem type (incremental and insight). See Table 10.

91

 

Incremental Insight Total

Single task

Non-incentive (n = 80) .79 (.27) .86 (.26) .83 (.19)

Incentive (n = 80) .79 (.33) .88 (.25) .84 (.23)

Total (n = 160) .79 (.30) .87 (.26) .83 (.21)
Dual-task

Non-incentive (n = 80) .68 (.35) .77 (.34) .73 (.27)

Incentive (n = 80) .77 (.30) .84 (.30) .82 (.23)

Total (n = 160) .74 (.33) .80 (.32) .77 (.25)

 

Table 10. Mean coarse memory scores for incremental and insight problems (standard
deviations in parentheses) in the single and dual-task divided by incentive as well as the
totals across conditions for Experiment 4.

There was an effect for task (F [1, 316] = 5.50, p = .02, MS, = .59) indicating that
participants in the single task condition recalled more problems than participants in the
dual task condition. There was also an effect of incentive (F [1, 316] = 3.94, p = .048,
MS, = .43) indicating that participants’ given an incentive recalled more problems than
participants not given an incentive. However looking at the means in Table 10 one can
see that the incentive effect seems to be predominantly in the dual-task condition. The
interaction between task and incentive however was not signiﬁcant (F [1, 316] = 2.64, p
= .11, MS, = .28). Post-hoc tests revealed that, as expected from the means, there is no
effect of the incentive on participants’ coarse memory for the single task condition (F [1,

159] = .08, p = .78, MS, = .004). There is however a signiﬁcant effect for participants in

92

the dual-task condition, (F [1, 159] = 5.66, p = .02, MS, = .35). These ﬁndings are
surprising given the consistent ﬁndings in Experiments 2a and 2b that incentives increase
coarse memory recall. Perhaps this is an indication that the coarse memory measure is not
a good measure of participants’ problem memory. There was a signiﬁcant effect of
problem type (F [1, 316] = 10.65, p = .001, MS, = .79) such that participants remembered
more insight problems than incremental problems. This difference might have been due
to the fact that one insight problem is quite short and therefore might be easier to
remember than longer problems. There were no signiﬁcant interactions.

As in the previous experiments a ﬁne memory measure was created by scoring the
participants’ responses to the memory questions for the amount of detail or
descriptiveness, of each problem (see Appendix B). Two raters, blind to condition,
independently scored each of the problem responses and inter-rater reliability was found
to be satisfactory (K = .89). A 2x2x2 analysis of variance was performed on the ﬁne
memory measure with between subjects factors of task (single or dual), and incentive

(given or note), and 3 within subjects factor of problem type (incremental and insight).

See Table 11.

93

Incremental Insight Total

 

Single task
Non-incentive (n = 80) 2.35 (1.19) 2.50 (1.19) 2.43 (1.01)
Incentive (n = 80) 2.58 (1.33) 2.73 (1.12) 2.65 (1.07)
Total (n = 160) 2.46 (1.26) 2.62 (1.16) 2.54 (1.04)
Dual-task
Non-incentive (n = 80) 1.97 (1.31) 2.08 (1.28) 2.03 (1.10)
Incentive (n = 80) 2.47 (1.28) 2.48 (1.23) 2.48 (1.25)
Total (n = 160) 2.21 (1.32) 2.28 (1.27) 2.25 (1.12)

 

Table 11. Mean ﬁne memory scores for incremental and insight problems (standard
deviations in parentheses) in the single and dual-task incentive and non-incentive
conditions 8 well as the totals across conditions for Experiment 4.

As in the coarse memory measure there was an effect for task, F(1, 316) = 5.87, p = .02,
MS, = 13.51, indicating that participants in the dual task condition remembered fewer
problem details than participants in the single task condition. There was also an effect of
incentive (F11, 316] = 7.92, p = .005, MS, = 18.22), such that participants in the incentive
condition remembered more problem details than participants in the non—incentive
condition. Post-hoe tests showed that unlike the coarse memory measure participants in
both the single task (F11, 159] = 1.92, p = .049, MS, = 2.21) and the dual task (F11, 159]
= 6.64, p = .01, MS, = 8.1) remembered more problem details when given an incentive
than when not given an incentive. There was no effect for problem type (F11, 316] =

1.47, p = .23, MS, = .90) and no signiﬁcant interactions.

94

Overall the results for the coarse and ﬁne memory measure show that incentives
increase problem recall even in the dual-task condition. This is somewhat surprising since
it was hypothesized that the increase in problem recall seen in Experiments 2a and 2b is
due to an increase in attention to the rewarded task. In the dual-task the results show that
participants are not able to shift additional attentional resources to the problem solving
task, how then is there still an increase in problem memory? Perhaps the increase in
problem recall in the single and dual-task is due to different mechanisms that both lead to
an increase in memory. This was further investigated by looking at participants’ recall of
irrelevant information.

Irrelevant information. Participants’ memory recall was scored for the irrelevant
information that had been added to the problems (see Appendix A). If a participants’
problem recall contained the irrelevant information it was scored as a 1, if it did not it
was scored as a 0. An irrelevant incremental score and irrelevant insight score was then
calculated by averaging across the appropriate scores. A 2x2x2 analysis of variance was
run on the irrelevant scores with between subjects factors of task (single or dual) and
incentive (given or not) and a within subjects factor of problem type (incremental and

insight). For means and standard deviations see Table 12.

95

Incremental Insight

 

Single task
Non-incentive (n = 80) .20 (.33) .28 (.32)
Incentive (n = 80) .16 (.29) .21 (.28)
Dual-task
Non-incentive (n = 80) .13 (.26) .24 (.32)
Incentive (n = 80) .21 (.34) .33 (.35)

 

Table 12. Mean irrelevant information scores for incremental and insight problems
(standard deviations in parentheses) in the single and dual-task divided by incentive for
Experiment 4.

There was no effect of task, (F11, 316] = .24, p = .63, MS, = .03) nor an effect of
incentive, (F11, 316] = .36, p = .55, MS, = .05). There was an effect for problem type
(F11, 316] = 20.34, p < .01 MS, = 1.27) such that participants remembered more
irrelevant information for insight problems than incremental problems. Again this might
be due to one insight problem being shorter which might lead people to remember it
more. Interestingly, there was a signiﬁcant interaction between task and incentive (F11,
316] = 6.52, p = .01, MS, = .86). Post-hoc tests revealed that in the dual-task condition
participants given an incentive recalled more pieces of irrelevant information than
participants not given an incentive (F11, 159] = 4.66, p = .03, MS, = .33). There was a
slight trend in the single task condition (F11, 159] = 2.05, p = .16, MS, = .13) and the
means suggest the opposite pattern of ﬁndings from the dual-task condition. Participants

given an incentive recalled fewer pieces of irrelevant information than participants not

96

given an incentive, see Figure 10.

Overall these ﬁndings may suggest qualitative differences in processing between
participants given an incentive in the single task and dual—task conditions. Participants in
the single task condition given an incentive may be processing the underlying structure of
each problem and may therefore be less likely to recall the irrelevant information.
Alternatively, participants given an incentive in the dual-task condition may still want to
reach the incentive but are not be able to shift any additional attentional resources to the
problem solving task. This may then lead participants to engage in more superﬁcial
processing of the problem which requires fewer resources. Superﬁcial processing may
then lead to a greater verbatim recall and therefore greater recall of the irrelevant

information.

97

El Non-FIEentive [:1 Incenfiyej

0.5
0.4 ,

0.3

 

I—i—d

0.2 ~

Irrelevant
information score

0.1«

 

 

 

 

 

 

 

 

 

Single Dual

Figure 10. Mean irrelevant information score for problems in Experiment 4 for the single
and dual-task conditions for participants either given an incentive or not. Error bars
represent standard errors.
4.2.3 Discussion

Experiment 4 was designed to investigate whether incentives lead to an increase
in problem solving performance by causing either a shift of all attentional resources or
only spare or additional resources to the rewarded task. Results showed that incentives
led to an increase in problem solving accuracy only in the single task condition. In the
dual-task condition participants’ problem solving accuracy was equal to participants not
given an incentive. These results indicate that incentives lead to a shift in resources to the
rewarded task only if additional attentional resources are available. This suggests that the
incentive used in this work is at least in part different from a goal. Research on goal

setting has shown that participants will allocate their resources to goal-relevant tasks

98

while ignoring goal-irrelevant tasks (e.g., Locke & Bryan, 1969). If incentives functioned
exactly like goals then participants given an incentive in the dual-task condition of this
experiment should have shown an increase in their problem solving performance and a
dip in their concurrent tone task performance. Instead the incentive did not increase
problem solving performance in the dual-task condition, indicating a shift of attention
only when spare resources are available. It is somewhat surprising that participants
performed both the problem solving and the tone task so diligently given that the
incentive was based only on their problem solving performance. It is possible that
participants felt compelled to perform both tasks because the experimenter was in the
room at all times and could have noticed when a participant stopped responding to the
target tone. Another possibility however is that the participants underestimated the
disruptive effects of the tones on their problem solving abilities. This underestimation
may have led participants to believe their problem solving performance was greater than
it actually was, eliminating any need to ignore the unrewarded tone task. Further studies
including a think out loud methodology or detailed questioning after each problem would
help elucidate these possibilities.

Problem solving duration was again found to be a less reliable factor than
problem solving accuracy. As in the previous experiments, problem solving duration was
not inﬂuenced by incentives. There was however an interaction between incentive and
task such that participants in the dual-task condition that had not been given an incentive
spent more time solving problems than participants in any other condition. The meaning
and reliability of this ﬁnding however is unclear and should be replicated before being

interpreted.

99

The incentive also did not seem to have an impact on secondary task performance.
Tone monitoring accuracy and response time did not differ between participants given an
incentive and participants not given an incentive. Additionally, there were no tradeoffs
between problem solving performance and tone monitoring accuracy and response time.
It was possible that the incentive would have caused participants to simply ignore the
secondary task since participants had a lot to gain from performing well on the problem
solving task but not from the secondary task. However, overall secondary task
performance indicates that participants in the incentive condition were trying to complete
both tasks at the same time.

In Experiments 2a and 2b it was found that participants given an incentive
recalled more problems and more details about the problems than participants not given
an incentive. Results looking at participants memory recall in this experiment showed
that the incentive again increased problem memory. The incentive increased problem
recall for both the single and the dual-task condition despite problem recall being lower
in the dual-task condition than in the single task condition. These ﬁndings are surprising
in light of the problem solving accuracy data indicating a shift of attentional resources
only for the single task condition. If there are no additional attentional resources for
participants to shift to the problem solving task in the dual-task condition, how then are
participants in the dual-task condition able to remember more problems when given an
incentive? It is possible that participants in the dual-task condition are using a different
mechanism for remembering problems than participants in the single task condition.
Perhaps the single task condition participants can use the additional attention that has

been shifted to the problem solving task to engage in more processing of the underlying

100

structure of the problem. Deeper processing then would lead not only to an increase in
problem solving performance but also better memory for the problems. On the other
hand, participants in the dual-task condition do not have additional resources but they do
want to reach the incentive. This might lead participants to engage in more superﬁcial
processing by using a guessing strategy because it requires fewer resources. A guessing
strategy simply requires surface processing of the problems as the solver needs to operate
only within the reahn of the problem. (Processing the underlying structure of a problem,
however, requires the solver to step outside of the realm of the problem to link this
problem with their previous knowledge, such as how to set up an algebraic equation.) It is
possible then that participants in the dual-task condition given an incentive were still
trying to solve the problem but were unable to devote as many resources, leading to a
more surface processing of the problem. Surface processing then would lead to lower
problem solving but could still increase problem recall. This recall however should be
qualitatively different from the recall produced by participants given an incentive in the
single task condition. Results looking at the amount of irrelevant information in
participants’ memory recall provide evidence for this possibility. It was found that
participants given an incentive in the dual-task condition recalled more irrelevant pieces
of information than participants not given an incentive. The opposite pattern was true for
participants in the single task condition; participants not given an incentive recalled more
irrelevant information than participants given an incentive. These results suggest that
participants given an incentive in the single task condition seem to be more likely to
process the problems’ underlying structures while participants in the dual-task condition

seem to be more likely to process the problems on a surface level. These ﬁndings provide

101

further evidence that incentives lead to systematic changes in cognitive processes
involved in problems solving.

Overall, the results of Experiment 4 show that incentives seem to lead to a shift of
attentional resources when spare or additional resources are available. These additional
resources then lead to deeper processing of information and greater problem solving

performance.

102

5 GENERAL DISCUSSION
5.1 Summary of Experimental Results

This work set out to answer two major questions. One, do incentives, and
therefore motivation, inﬂuence problem solving performance? Two, what cognitive
mechanisms involved in problem solving are inﬂuenced by incentives? Across ﬁve
experiments (Experiments 1a and 1b, Experiments 2a and 2b, and Experiment 4)
including four different problem sets, the incentive reliably increased overall problem
solving performance. The incentive, the opportunity to leave the experiment early, was
consistently effective such that it increased problem solving performance for all sixteen
problems presented. The probability of all 16 problems showing an effect in the expected
direction by a sign test is .000015. On average, the increase in solution rates in the
incentive conditions, as a percentage of solution rates in the non-incentive conditions was
above 20%. These ﬁndings provide good evidence that incentives do inﬂuence problem
solving.

Another purpose of this work was to investigate the nature of the mechanism by
which incentives might inﬂuence problem solving. One possibility investigated was that
incentives lead to persistence with one problem solving approach. Persistence with one
problem solving approach would lead to differences in problem solving performance
between incremental and insight problems. Experiments 1a and 1b speciﬁcally
investigated the effect of an incentive on incremental and insight problems however both
types of problems were used throughout all the experiments in this work, in essence
further testing the predictions. In Experiments 1a and 1b participants were either in the

incentive condition or in the non-incentive condition and completed several incremental

103

and insight problems. Across all the problems in Experiments 1a and 1b (as well as
Experiments 2a and 2b and Experiment 4) the incentive increased both incremental and
insight problem solving. The interaction between problem type and incentive that would
be predicted by a mechanism that leads to an increase in persistence with one approach
was never found in any experiments in this work. More speciﬁcally, the hypothesized
interaction was rejected with an average p value of .59 across different samples, different
problems, and different levels of problem difﬁculty. These ﬁndings indicate that the
increase in problem solving due to the incentive is not caused by an increase in
persistence with one approach; instead the incentive is inﬂuencing a mechanism that is
beneﬁcial to both incremental and insight problem solving.

Another mechanism investigated in this work was problem solving duration.
There has been some research showing that individuals given an incentive will spend
more time on their task than individuals not given an incentive (e. g., Miller & Home,
1990). Experiments 2a and 2b measured participants’ problem solving duration. Results
showed that participants in the incentive condition spent about the same amount of time
solving problems as participants in the non-incentive condition. These ﬁndings indicate
that an increase in problem solving duration does not seem to be the factor leading to the
incentives effects seen throughout the experiments in this dissertation.

Experiments 2a and 2b also investigated participants’ depth of processing.
Previous research has shown that motivation can lead to deeper processing of information
(e. g., Eysenck & Eysenck, 1982). Experiments 2a and 2b investigated whether incentives
lead to deeper processing of information by assessing participants’ memory for the

problems they completed. It was predicted that if incentives lead to an increase in

104

problem solving by causing deeper processing then participants in the incentive condition
should remember more problems and their details than participants in the non-incentive
condition. Results of Experiments 2a and 2b showed exactly this. Participants in the
incentive condition remembered more problems and gave more details about the
problems than participants in the non-incentive condition. These ﬁndings indicate that
incentives seem to lead to deeper processing which leads to an increase in memory for
the problems. Looking across both problem solving duration and the memory measure,
the results of Experiments 2a and 2b suggest that incentives lead to deeper processing of
the problems without causing a major increase in the time spent on each task.

In order to further investigate the increase in memory due to the incentive,
Experiments 3 and 4 were designed to investigate incentive effects on attention allocation
using a dual-task approach. Little research has investigated the effects of a secondary task
on problem solving; therefore Experiment 3 was run to establish a secondary task that
would lead to performance decrements in problem solving. More speciﬁcally a
concurrent tone monitoring task was tested to determine how it would inﬂuence problem
solving performance. Additionally, different parameters for the task were investigated.
Results showed decrements in both problem solving performance and tone monitoring
performance when participants were asked to perform the two tasks simultaneously.
These decrements indicate that the tone monitoring task and the problem solving tasks
tax the same resources and were therefore suitable to use in a dual-task context.

Experiment 4 was designed to investigate whether incentives lead to an increase
in problem solving by causing a shift of attentional resources to the rewarded task.

Taxing participants’ attentional resources by using a dual-task approach allows an

105

investigation of how participants allocate their attention to the tasks they are performing.
In Experiment 4 participants in the incentive and non-incentive condition solved
incremental and insight problems while either in a single task or dual-task context.
Results showed that problem solving performance only improved for participants given
an incentive in the single task condition. Participants’ performance in the dual-task
condition did not differ across incentive. These ﬁndings indicate that incentives seem to
cause a shift in attention to the rewarded task but only when additional attention is
available. When participants do not have any or very few additional resources that can be
shifted to the rewarded task then incentives are ineffective and do not lead to an increase
in performance.

Additionally, Experiment 4 tested whether incentives lead participants to engage
in more processing of the underlying problem structure. This was examined by adding
irrelevant information to each of the problems presented and then scoring participants
memory recall for the amount of irrelevant information mentioned. Results showed a
trend such that participants given an incentive in the single task condition recalled fewer
pieces of irrelevant information than participants not given an incentive. However, in the
dual-task condition the ﬁndings were reversed. Participants given an incentive recalled
signiﬁcantly more pieces of irrelevant information than participants not given an
incentive. These ﬁndings indicate that when participants can shift additional attentional
resources to the rewarded task (as in the single task condition) greater processing of the
underlying problem structure occurs. In the dual-task condition however participants do
not have additional resources to devote to the problem solving task leading to more

surface processing and therefore greater recall of irrelevant information.

106

5.2 Incentives and Attentional Resources

Attention allocation. Experiments in this dissertation have shown that incentives
lead to an increase in problem solving accuracy and deeper processing of information
when additional attentional resources are available. Attention allocation then is an
important component of processing that inﬂuences the effectiveness of incentives.
Participants must have additional resources available for an incentive to increase problem
solving performance. If there are no additional resources incentives are ineffective, as
seen in the dual-task condition in Experiment 4. What then determines how much
attention is allocated to the rewarded task? In Experiment 4 of this dissertation
participants were asked to both solve problems and respond to the concurrent task
simultaneously however the incentive was based only on their problem solving
performance. Despite this participants allocated their attention across both problem
solving tasks and the concurrent tone monitoring task. Yet in the goal setting literature it
has been found that participants will ignore any goal-irrelevant information and only
allocate their resources to goal-relevant information. What might be causing this
difference in how participants allocate their attention in response to either a goal or an
incentive? Kahneman (1973) proposed that an individual’s momentary intentions will
inﬂuence the allocation of attentional resources. Participants in Experiment 4 in this
dissertation were asked to practice the tone task and reach a certain level of proﬁciency
before they were allowed to proceed with the experiment. Perhaps this inﬂuenced the
relative amount of importance that participants attributed to their tone task performance.
On the other hand, participants in the goal setting experiments reviewed in this

dissertation (e. g., Locke & Bryan, 1969; Rothkopf & Billington, 1979) did not engage in

107

any practice or previewing of the goal-relevant and goal-irrelevant information. As
mentioned earlier, it is also possible that participants in Experiment 4 perceived the
situation to be easier than it actually was. Participants might have thought they were able
to perform the tone task and solve problems correctly simultaneously without decreases
in performance. In the goal setting experiments participants might have been more aware
of their limitations. Participants’ interpretation of the situation and allocation of their
attention might be the ﬁrst step in determining how incentives will inﬂuence
performance. Once participants have interpreted the situation and allocated their
attentional resources accordingly the incentive steps in. If there are spare resources and
the incentive is interpreted as important, additional resources will be shifted to the
rewarded task and performance will increase. If however there are no additional
resources to spare, no ﬁrrther attention can be shifted to the rewarded task, rendering the
incentive ineffective at improving performance.

Perhaps attention allocation also explains the mixed incentive effects found in the
literature. As mentioned in the introduction Camerer and Hogarth (1999) have found
positive, negative, and null effects of incentives on performance. Positive effects might
be seen when participants have plenty of additional resources available (as in the single
task condition in Experiment 4) while null effects are seen when participants’ have no
additional resources (the dual-task condition of Experiment 4). The question then
becomes how do negative incentive effects occur? Since an important aspect of incentive
effects might be how participants’ interpret the experimental situation, it is possible that
negative effects are seen because of misinterpretations of the situation. Participants might

interpret a situation and allocate their attention that is inconsistent with the question of

108

interest. For example, as mentioned in the discussion of Experiments 1a and 1b, McGraw
and McCullers (1979) gave participants an incentive for solving water jar problems based
on accuracy but used problem solving duration as an indicator of incentive effects
(despite telling participants that time on task is not crucial). Results showed an increase
in problem solving duration for participants in the incentive condition which McGraw
and McCullers believed to be evidence for detrimental incentive effects. However, given
the instructions that time does not matter, this ﬁnding seems to be more a reﬂection of
participants’ interpretation of the situation than of incentive effects. Participants
interpreted the situation correctly by allocated their attentional resources to maximize
problem solving accuracy to reach the incentive. The incentive did not mention time on
task, therefore participants ignoring that variable. It is possible then that the negative
incentive effects seen in the literature are caused by participants’ allocating their
attentional resources in a manner that is inconsistent with the question of interest in the
research.

A similar argument that has been made by Kemmelrneier, et al. (2004) that have
shown misinterpretation effects on the Wason card selection task due to an incentive.
More speciﬁcally, results showed that participants in the incentive condition gave more
complex answers than participants in the non-incentive condition (e. g., participants were
less likely to include the most obvious card in their answers) when they got the problem
wrong. Kemmelrneier, et al. believe that this is an indication that participants given an
incentive are interpreting the problem solving situation differently than participants not
given an incentive.

Surface versus deep processing. Experiment 4 in this dissertation showed that

109

incentives do not have any effect on problem solving performance when no additional
resources are available to be shifted to the rewarded task. Do incentives then have
absolutely no effect unless there are additional resources? Are participants simply
discounting the incentive? The ﬁndings from the memory question in Experiment 4
indicate that the incentive still seems to cause an increase in processing of sorts even
when participants do not have the additional resources to increase problem solving. In the
dual-task condition of Experiment 4 participants given an incentive still showed an
increase in memory for the problems and their details. Their recall however contained a
greater amount of information irrelevant for solving the problems than participants given
an incentive in the single task condition. These ﬁndings suggest that participants given an
incentive in the dual-task condition engaged in more surface processing of the problems
while participants in the single task condition engaged in more structural level processing
of the problems. This provides evidence that participants in the dual-task condition are
not just discounting the incentive; instead giving an incentive seemed to encourage
participants to do more of whatever their resources available allowed them to do. For
example, in Experiment 4 participants given an incentive in the dual-task condition had
very few additional or spare resources but still seemed to want to reach the incentive; this
led participants to engage in more surface processing perhaps by trying to guess the
answer to the problems. A guessing strategy does not require a lot of resources and is
therefore ideal in situations where resources are limited. Since a guessing strategy
requires very little processing of the problems’ underlying structure, participants were
less likely to distinguish between pieces of information that are relevant and irrelevant for

solving the problem. This suggests that incentives will lead to an increase in performance

110

when additional resources that are required for successful task completion are available.
When no additional resources are available participants might try to ﬁnd different
compensation strategies to still meet the incentive. These strategies however are much
less effective at increasing performance.

These ﬁndings obviously have several implications for the effectiveness of
incentives in certain situations. For example, in a classroom setting if students are given
problems that are difﬁcult and do not leave many spare attentional resources, an incentive
might actually encourage more superﬁcial or surface processing of the problems. On the
other hand, if an incentive is given for problems that do not tax all attentional resources
they may be effective in encouraging students to understand the underlying structure of
the problems. This surely would not be the desired effect in a classroom setting. Further
studies need to be done to investigate when incentives lead to deeper processing and
when they lead to surface processing. Once this is better understood incentives can be
used appropriately.

5.3 Insight versus Incremental Problems

Throughout the experiments in this work both incremental and insight problems
were used due to their proposed underlying differences (see Metcalfe & Wiebe, 1987;
Schooler & Melcher, 1995; Schooler, et al., 1993). Incremental problems are argued to be
solved in a step by step fashion with a clear path to solution while insight problems are
argued to be solved with an “Aha” experience and have no clear path to solution. It is
surprising then that no differences between incremental and insight problem solving were
found. Experiments 1a and 1b, Experiments 2a and 2b, as well as Experiment 4 showed

no differences in how the incentive affected incremental and insight problem solving.

lll

The incentive consistently increased performance for both types of problems.
Additionally, Experiment 3 and Experiment 4 showed no difference in how the secondary
task affected incremental and insight problems. Instead results consistently showed a
negative effect due to the secondary task for both insight and incremental problems.
Why, despite the proposed underlying problem solving differences did the incentive and
the secondary task inﬂuence incremental and insight problem solving equally? One
possibility is that the problems used in this dissertation were poorly deﬁned as
incremental and insight problems. Problems used were taken from previous studies that
deﬁned each as either incremental or insight. There was no independent assessment done
speciﬁcally for this dissertation. Perhaps this was an oversight that would have resulted in
a different classiﬁcation of problems and therefore different results. However, given the
large variety of problems used in this dissertation and the general acceptance of the
problems uses as incremental and insight problems within the literature I doubt this
would have changed the ﬁndings much.

Another possibility is that incremental and insight problems are not as different as
proposed in the literature. Chronicle, MacGregor, and Ormerod (2004) recently
demonstrated that some hill-climbing processes used in transformation (or incremental)
problems are also present in insight problems. More speciﬁcally, results showed that
participants experienced the same difﬁculties conceptualizing the next step to take in a
traditional 6-coin problem (where participants need to rearrange 6-coins to form a certain
pattern) and a modiﬁed 6-coin problem requiring insight to ﬁnd the solution. Chronicle,
et al. argue that these ﬁndings suggest that there should be a common ﬁ'amework for

understanding both incremental and insight problems. Similarly, Weisberg (1992) has

112

argued that all problem solving, including insight problem solving, should be seen as a
step-by-step cyclical process that involves retrieval of information from memory and
attempts to apply the information. If the retrieved information does not lead to a solution
a new search is initiated. The results ﬁom this dissertation, that the incentive and the
secondary task inﬂuence incremental and insight problem solving equally, are certainly
consistent with the notation that incremental and insight problems may share more
problem solving processes than previously conceptualized. Future research needs to be
done to investigate the commonalities and differences between incremental and insight
problem solving. A dual-task approach (as well as incentives) may be particularly useful
in exploring problem solving processes as different secondary tasks can be used to tax
different aspects of problem solving.
5.4 Cognitive Psychology and Motivation

Historically cognitive psychology has seen motivation and incentives as a factor
irrelevant to the study of cognition. As mentioned in the introduction Simon (1994) even
went so far as to suggest that motivation would not greatly alter participants’
performance. If Simon’s proposal was correct then the leave early incentive in this
dissertation should have had a very small to no effect on problem solving. Instead the
incentive increase problem solving across all the experiments presented in this work.
Additionally, Experiment 4 presents good evidence that the incentive seems to lead to an
increase in performance by causing a shift of additional resources to the rewarded task.
The availability of attentional resources is seen as having systematic effects on cognition;
therefore if motivation affects cognition via changes in attentional resources then

motivation differences will have systematic effects on cognition. This work then provides

113

evidence that motivation does alter performance by inﬂuencing cognitive mechanisms
and suggests that the current position, that motivation can always be ignored when
studying cognitive processes, needs to be re-evaluated.
5.5 Future Directions

The experiments in this work represent the first steps to understanding how
motivation inﬂuences cognitive mechanisms. However there are still many questions left
unanswered. Experiment 4 showed that incentives lead to a shift in attentional resources
when participants have additional resources available to them. This can be further
investigated by pairing problem solving with a variety of secondary tasks. If incentives
lead to a shift in additional resources then depending on the secondary tasks’ resource
requirements a range of problem solving performance may be seen. Secondary tasks
whose resource requirements are more similar to the resource requirements of problem
solving may leave fewer additional resources that can be shifted to the rewarded task; this
then may lead to smaller incentive effects. On the other hand secondary tasks whose
resource requirements are different from the resource requirements of problem solving
may leave plenty of additional resources that can be shifted to the rewarded task; this
then might lead to better performance for participants given an incentive. For example, in
a pilot study I conducted participants were presented with two nonsense words before
attempting each problem and were asked to try to remember each nonsense word. After
four minutes, at the end of each problem, participants were asked to recall the nonsense
words. Results showed that participants in the incentive condition outperformed
participants in the non-incentive condition and the secondary task had no effect. This

relatively easy pre-Ioad task and problem solving do not share as many resource

114

requirements as the concurrent tone monitoring task and problem solving, leaving
additional resources available to shift to the rewarded problem solving task. Perhaps this
is why no secondary task effects were seen in this pilot study and the incentive increased
problem solving even in the dual-task condition.

Another way of investigating a continuum of incentive effects is by manipulating
how participants interpret the experimental situation. In the dual-task condition of
Experiment 4 participants seemed to devote enough attention to both problem solving and
the tone task to perform both tasks reasonably successfully. However, the amount of
attention participants devote to each aspect of the two tasks could be manipulated by
differentially emphasizing the two tasks. The more emphasis there is on the problem
solving task the more likely the incentive should be to increasing problem solving
performance. Alternatively, the more emphasis there is on the secondary task the less
likely it is that the incentive will improve problem solving performance. This type of
design could show differential effects of incentives depending on the attention available
for the rewarded task.

Deeper processing of information. Experiment 4 provided some evidence that
incentives can lead to more processing of the underlying structure of the problem than
surface processing. There was a trend such that participants given an incentive in the
single task condition recalled fewer pieces of irrelevant information than participants not
given an incentive. Additionally, participants given an incentive in the dual-task
condition recalled signiﬁcantly more pieces of irrelevant information than participants
not given an incentive. These ﬁndings are quite intriguing and suggest incentives lead to

more structural processing but only when additional resources are available. The

115

 

irrelevant information used in Experiment 4 was added without any controls and assumed
to be irrelevant for solving the problems. A better controlled experiment needs to be run
where the importance of each problem component for solving the problem is known. In
order to determine the importance of each problem component a pilot study can be run
where participants rate the importance of each component for solving the problem (a
similar study was done by Ash & Wiley, 2002). If the results of Experiment 4 are due to
more structural processing then it would be predicted that participants in the incentive
condition would recall more problem solving components rated as important to the
problem solving process than participants not given an incentive. In a dual-task condition
the opposite effect would be expected. Another possible way of exploring this effect
would be to look at unrelated irrelevant information such as background color of the
screen or paper that the problem was presented on. If incentives focus participants on the
underlying structure of the problem then this type of unrelated irrelevant information
would be unlikely to be remembered by participants in the incentive condition compared
to participants in the non-incentive condition.

Similarly, a transfer experiment could also be used to test whether incentive lead
to more structural processing. Participants could be given a series of problems that have
different surface features but whose underlying structure is the same. If incentives lead to
more structural processing then participants in the incentive condition may be able to
transfer their knowledge from problem to problem and greater problem solving
performance may be seen compared to participants in the non-incentive condition.
Participants not given an incentive may engage in more surface processing and see each

problem as different. This might lead to less transfer between problems and lower

116

problem solving performance compared to participants in the incentive condition.
Individual diﬂerences and incentives. If incentives do lead to a shift in resources it
may also be interesting to explore the role of individual difference variables in the
relationship between incentives and problem solving performance. One individual
difference that has recently received a lot of attention is working memory capacity.
Hambrick and Engle (2003) deﬁne working memory capacity as the limited-supply
cognitive resource that can be allocated ﬂexibly depending on the demands of the task.
Working memory’s function is to bring memory representations into the focus of
attention, and to keep these representations in a highly activated and accessible state as
long as they are needed. It is possible then that the degree to which an incentive increases
problem solving performance depends on individual differences in working memory
capacity. For example participants with high working memory capacity might be able to
take advantage of the incentive to a greater degree leading to greater problem solving
performance than participants with low working memory capacity. Since participants
with high working memory have more resources available to them overall, they may have
more spare or additional resources available to shift to the rewarded task. Participants
with low working memory capacity are already operating with a smaller amount of
resources which leaves them with fewer additional resources to move to the rewarded
task. These possible differences could be investigated by assessing participants’ working
memory span and correlating it with participants’ problem solving performance in the
incentive and non-incentive condition. Participants working memory capacity would be

predicted to lead to differences in how an incentive affects problem solving performance.

117

5.6 Conclusions

Whereas this dissertation does not answer all the questions regarding motivation
and cognitive mechanisms involved in problem solving it does however answer two
major questions. One, despite the mixed results found by Camerer and Hogarth (1999)
results consistently show that incentives and therefore motivation can inﬂuence problem
solving (and by extension, other cognitive tasks). Two, incentives do inﬂuence cognitive
mechanisms. More speciﬁcally, incentives were found to lead to deeper processing due to
a shift of additional attentional resources to the rewarded task. These ﬁndings suggest
that a complete understanding of cognitive processes also requires understanding how

motivation affects them.

118

APPENDIX A

Text and solution rates of the problems used in Experiments 1a and 1b, Experiments 2a

and 2b, Experiment 3, and Experiment 4.

119

Experiment I a and Experiment 1b
Incremental Problems
Dinner Party Problem (solution rate: 89%)
Mary won’t eat ﬁsh or spinach, Sally won’t eat ﬁsh or green beans, Steve won’t eat
shrimp or potatoes, Alice won’t eat beef or tomatoes. If you are willing to give such a
bunch of fussy eaters a dinner party, which items from the following list can you serve:
green beans, creamed codﬁsh, roast beef, roast chicken, celery, and lettuce.
Store Problem (solution rate: 71%)
Smith is a butcher and president of the street storekeepers’ committee, which also
includes the grocer, the baker, and the pharmacist. They all sit around a table.
0 Smith sits on Jones’ left.
0 Davis sits at the grocer’s right.
0 Bailey, who faces Jones, is not the baker.
Assign each storekeeper to the correct store.
Stakes Problem (solution rate: 4%, not included in any analyses)
Three people play a game in which one person loses and two people win each round. The
one who loses must double the amount of money each of the other two players has at that
time. The three players agree to play three games. At the end of three games, each player
has lost one game and each person has $8. What was the original stake of each player?
(Hint: at all times the total amount of money between the three players must add up to
$24)

Card Problem (solution rate: 55%)

120

Three cards from an ordinary deck are lying on a table, face down. The following
information is known about those three cards (all the information refers to the same three
cards):
0 To the left of a Queen, there is a Jack.
0 To the left of a Spade, there is a Diamond.
0 To the right of a Heart, there is a King.
0 To the right of a King, there is a Spade.
Can you assign the proper suit to each picture card?
Bachelor Problem (solution rate: 53%)
Five bachelors, Andy, Bill, Carl, Dave, and Eric, go out together to eat ﬁve evening
meals (Fish, Pizza, Steak, Tacos, and Thai) on Monday through Friday. It was understood
that Eric would miss Friday’s meal due to an out of town wedding. Each bachelor served
as the host at a restaurant of his choice on a different night. The following information is
known:
0 Carl hosted the group on Wednesday.
0 The fellows ate at a Thai restaurant on Friday.
0 Bill, who detests ﬁsh, volunteered to be the ﬁrst host.
0 Dave selected a steak house for the night before one of the fellows hosted
everyone at a raucous pizza parlor.
Which bachelor hosted the group each night and what food did he select?
Flower Problem (solution rate: 61%)
Four women, Anna, Emily, Isabel, and Yvonne, receive a bunch of ﬂowers from their

partners, Tom, Ron, Ken, and Charlie. The following information is known:

121

o Anna’s partner, Charlie, gave her a huge bouquet of her favorite blooms; which
aren’t roses.
0 Tom gave daffodils to his partner (not Emily).
0 Yvonne received a dozen lilies, but not from Ron.
What type of ﬂowers (carnations, daffodils, lilies, or roses) were given to each woman
and who is her partner?
Job Problem (solution rate: 81%, not included in any analyses)
Lebrun, Lenoir, and Leblanc are, not necessarily in that order, the accountant,
warehouseman, and traveling salesman of a ﬁrm. The salesman, a bachelor, is the
youngest of the three. Lebrun, who is Lenoir’s son in law, is taller than the
warehouseman. Who has what job?
Insight Problems
Water Lilies Problem (solution rate: 44%)
Water lilies double in area every 24 hours. At the beginning of the summer, there is one
water lily on a lake. It takes 60 days for the lake to become completely covered with
water lilies. On what day is the lake half covered?
Checker Games Problem (solution rate: 61%)
Two men play ﬁve checker games and each wins an even number of games, with no ties.
How is that possible?
Horse Problem (solution rate: 58%)
A man bought a horse for $60 and sold it for $70. Then bought it back for $80 and sold it
for $90. How much money did he make in the horse business?

Marriage Problem (solution rate: 49%)

122

 

A man in a town married 20 women in the town. He and the women are still alive, and he
has had no divorces. He is not a bigarnist and not a Mormon and yet he broke no law.
How is that possible?

Sock Problem (solution rate: 50%)
If you have black socks and brown socks in your drawer, mixed in the ratio of 4:5, how
many socks will you have to take out to be sure of having a pair the same color?

Policeman Problem (solution rate: 61%)
A woman did not have her driver’s license with her. She failed to stop at a railroad
crossing, then ignored a one-way trafﬁc sign and traveled three blocks in the wrong
direction down the one-way street. All this was observed by a policeman, yet he made no
effort to arrest the woman even though there was nothing stopping him. Why?

Experiments 2a and 2b and Experiment 3
Incremental problems
Age Problem (solution rate: 59%)
Ann is twice as old as her son. They were both born in June. Ten years ago Ann was
three times as old as her son. What are their present ages?
Water Problem (solution rate: 36%)

Given containers of 163, 14, 25, and 11 ounces, and a source of unlimited water, obtain
exactly 77 ounces of water.

Job Problem (solution rate: 5 7%, not included in any analyses, not given in
Experiment 3)
Lebrun, Lenoir, and Leblanc are, not necessarily in that order, the accountant,

warehouseman, and traveling salesman of a ﬁrm. The salesman, a bachelor, is the

123

youngest of the three. Lebrun, who is Lenoir’s son in law, is taller than the
warehouseman. Who has what job?
Insight problems

Month Problem (solution rate: 67%)
What occurs once in June and twice in August, but never occurs in October?

Matchstick Problem (solution rate: 44 %)
Correct the arithmetic statement expressed in Roman numerals by moving a single
matchstick from one position in the statement to another.

XI = 111 + 111

Prisoner Problem (solution rate: 56%, not included in analyses, not given in
Experiment 3)
A prisoner was attempting to escape from a tower. He found in his cell a rope that was
half long enough to permit him to reach the ground safely. He divided the rope in half,
tied the two parts together, and escaped. How could he have done this?

Experiment 4
Irrelevant information in bold.
Incremental problems
Age Problem (solution rate: 65%)
Ann is twice as old as her son. They were both born in June. Ten years ago Ann was
three times as old as her son. What are their present ages?
Water Problem (solution rate: 36%)

Given containers of 163, 14, 25, and 11 ounces, and a source of unlimited water, obtain

exactly 77 ounces of water (1 milliliter = .034 ounces).

124

Job Problem (solution rate: 51%, not included in any analyses)
Lebrun, Lenoir, and Leblanc are, not necessarily in that order, the accountant,
warehouseman, and traveling salesman of a ﬁrm. The salesman, a bachelor, is the
youngest of the three. Lebrun, who is Lenoir’s son in law, is taller than the
warehouseman. Who has what job?
Insight problems

Month Problem (solution rate: 46%)
What occurs once in June and twice in August, but never occurs in October regardless if
you are looking at a Gregorian or Julian calendar?

Matchstick Problem (solution rate:26%)
Correct the arithmetic statement expressed in Roman numerals by moving a single
matchstick from one position in the statement to another. Remember putting a smaller
number in front of a larger number means subtraction.

XI = IH + 111

Prisoner Problem (solution rate: 61%, not included in any analyses)
A prisoner was attempting to escape from a tower. He found in his cell a rope that was
half long enough to permit him to reach the ground safely. He divided the rope in half,

tied the two parts together, and escaped. How could he have done this?

125

APPENDIX B

Scoring guide (and examples of participants' responses) for the ﬁne memory measure

used in Experiments 2a & 2b, and Experiment 4.

126

Score of I
An answer should receive a score of 1 when there are very few or no details given about
the problem. Questionnaires that only list problem names or very sparse details about
each problem should receive a 1. For example:
Age problem: Age problem between Ann and her son
Month problem: Problem with months
Water problem: Water problem
Matchstick problem: The matchstick problem
Job problem: Job problem
Prisoner problem: Prison problem
Score of 2
An answer should receive a score of 2 when there are some details about the problem
given but most of the details of the problems are still unclear or not given. For example:
Age problem: The ﬁrst problem was about Ann and her son. It was about their
ages.
Month problem: The month problem where you say what happens in two months
and not another on.
Water problem: getting an exact amount of water in a container
Matchstick problem: Arithmetic matchstick problem having to move one
matchstick
Job problem: There was a problem about three men that had different jobs and

you had to match each man with their job.

127

Prisoner problem: There was a problem about a rope and how he could have
escaped.
Score of 3
An answer should receive a score of 3 when most of the major details about the problem
are given but the problem might be lacking an important detail or there might be some
major mistakes within the problem. For example:
Age problem: Ann and her son 2x now 3x 10 years ago.
Month problem: 1 in June, 2 in August, none in October.
Water problem: A question that wanted you to get exactly 77 ounces of water
using 4 different amount containers.
Matchstick problem: Another asked about match sticks and roman numerals. You
were supposed to move one match to make the problem correct.
Job problem: Leblanc, Lebrun, Louis have different occupations traveling
salesman for a ﬁrm, warehouse worker, and something else, Leblanc was the
youngest, bachelor.
Prisoner problem: The rope problem with a man trying to escape out of a tower
with only one rope. He split the rope in half and escaped.
Score of 4
An answer should receive a score of 4 when all the essential details needed to solve the
problem are given. For example:
Age problem: Ann is twice the age of her son, ten years ago, she was three times

the age of her son, how old is Ann and her son?

128

 

Month problem: What happens once in June, twice in August, and never in
October?
Water problem: You are given a container with 163, 25, 14, and 11 ounces and an

unlimited source of water, put exactly 77 ounces of water into one container.

 

Matchstick problem: Given, “XI=III+HI in Roman Numerals, move one of the
matchsticks to make the statement correct.

Job problem: Leblanc, Lenoir and Lebrun are brothers. One of them is a

 

salesman, one’s an accountant and one’s warehouseman. Lenoir is Lebrun’s
father-in-law. The salesman is the youngest and a bachelor. Lenoir is taller than
the warehouseman.

Prisoner problem: A prisoner is trying to escape from prison. In his jail cell ﬁnd a
rope. The rope is only half long enough for him to make it safely down from his
cell. The prisoner divides the rope in half and is able to safely make it down. How

is this possible?

129

REFERENCES

Amabile, T. M. (1987). The motivation to be creative. In S. Isaksen (Ed.), Frontiers in
Creativity Research: Beyond the basics (pp. 223 — 254). Buffalo, NY: Bearly.

Amabile, T. M., Hennessey, B. A., & Grossman, B. S. (1986). Social inﬂuences on
creativity: The effects of contracted-for reward. Journal of Personality and Social
Psychology, 50, 14-23.

Anderson, J. R. (1987). Skill acquisition: Compilation of weak-method problem solutions.
Psychological Review, 94, 192-210.

Ash, 1. K., & Wiley J. (2002). Ah-ha, I knew it all along: Differences in hindsight bias
between insight and algebra problems. In W. Gray & C. Schunn (Ed.), Proceedings of the
24th Annual Conference of the Cognitive Science Society (pp. 63-69). Hillsdale, NJ:
Erlbaum.

Baddeley, A. D. (2002). Is working memory still working? European Psychologist, 7, 85-97.

Baddeley, A. D., & Hitch, G. (1974). Working memory. In G. H. Bower (Ed), The
Psychology of Learning and Motivation, vol. 8 (pp.47-89). New York, New York:
Academia Press.

Bechara, A., Tranel, D., & Demasio, H. (2000). Characterization of the decision-making
deﬁcit of patients with ventromedial prefrontal cortex lesions. Brain, 123, 2189-2202.

Beilock, S. L., & Carr, T. H. (2002). On the fragility of skilled performance: What governs
choking under pressure? Journal of Experimental Psychology: General, 130, 701-725.

Beilock, S. L., Bertenthal, B. I., McCoy, A. M., & Carr, T. H. (2004). Haste does not always
make waste: Expertise, direction of attention, and speed versus accuracy performing
sensorimotor skills. Psychonomic Bulletin & Review, 11, 373-379.

Beilock, S. L., Carr, T. H., MacMahon, C., Starkes, J. L. (2002). When paying attention
becomes counterproductive: Impact of divided versus skill-focused attention on novice

and experienced performance of sensorimotor skills. Journal of Experimental
Psychology: Applied, 8, 6-16.

Broadbent, D. E. (1958). Perception and Communication. New York: Pergamon Press.
Burns, B. D., & McFarlane, D. (2003). Webpages without a server as general experimental

software. Presented at the Thirty-third Annual Meeting of the Society for Computers in
Psychology, Vancouver, CA.

130

.41

Camerer, C. F., & Hogarth, R. M. (1999). The effects of ﬁnancial incentives in experiments:
A review and capital-labor production framework. Journal of Risk and Uncertainty, 19,
7-42.

Cherry, E. C. (1953). Some experiments on the recognition of speech, with one and two cars.
Journal of the Acoustical Society of America, 25, 975-979.

Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of
physics problems by experts and novices. Cognitive Science, 5, 121-125.

Chronicle, E. P., MacGregor, J. N., & Orrnerod, T. C. (2004). What makes an insight
problem? The roles of heuristics, goal conception, and solution in knowledge-lean

problems. Journal of Experimental Psychology: Learning, Memory, and Cognition, 30,
14-27.

Craig, F. I. M., & Tulving, E. (1975). Depth of processing and retention of words in episodic
memory. Journal of Experimental Psychology: General, 104, 268-294.

Craik, F. I. M., Govoni, R., Naveh-Benjamin, M., & Anderson, N. D. (1996). The effects of
divided attention on encoding and retrieval processes in human memory. Journal of
Experimental Psychology: General, 125, 159-180.

Crano, W. D. (1991). Pitfalls associated with the use of ﬁnancial incentives (and other
complex manipulations) in human social research. Basic and Applied Social Psychology,
12, 369-390.

Damasio, A. R. (1994). Descartes ’ error: Emotion, reason, and the human brain. New York:
Grosset/Putnarn.

Deci, E. L. (1971). Effects of externally mediated rewards on intrinsic motivation. Journal of
Personality and Social Psychology, 18, 105-115.

Deci, E. L. (1972a). Intrinsic motivation, extrinsic reinforcement, and inequity. Journal of
Personality and Social Psychology, 22, 113-120.

Deci, E. L. (1972b). The effects of contingent and noncontingent rewards and controls on
intrinsic motivation. Organizational Behavior and Human Performance, 8, 217-229.

Deci, E. L., Koestner, R., & Ryan, R. M. (1999). A meta-analytic review of experiments
examining the effects of extrinsic rewards on intrinsic motivation. Psychological Bulletin,
125, 627-668.

Dominowski, R. L. (1995). Productive problem solving. In S. M. Smith, T. B. Ward, & R. A.
Finke (Eds), The Creative Cognitive Approach (pp. 73-95). Cambridge, MA: MIT Press.

Eisenberger, R. (1992). Learned industriousness. Psychological Review, 99, 248-267.

131

 

 

Eysenck, M. W., & Eysenck, M. C. (1982). Effects of incentive on cued recall. Quarterly
Journal of Experimental Psychology: Human Experimental Psychology, 34A, 489-498.

Farmer, E. W., Berrnan, J. V., & Fletcher, Y. L. (1986). Evidence for a visuospatial scratch
pad in working memory. Quarterly Journal of Experimental Psychology, 38A, 675-688.

Fitts, P. M., & Posner, M. I. (1967). Human Performance. Monterey, CA: Brooks/Cole.

Gehring, W. J ., & Willoughby, A. R. (2002). The medial frontal cortex and the rapid
processing of monetary gains and losses. Science, 295, 2279-2282.

Gilhooly, K. J ., Logie, R. H., Wetherick, N. E., & Wynn, V. (1993). Working memory and
strategies in syllogistic-reasoning tasks. Memory & Cognition, 21, 115-124.

Glucksberg, S. (1962). The inﬂuence of strength of drive on functional ﬁxedness and
perceptual recognition. Journal of Experimental Psychology, 63, 36-41.

Hambrick, D. Z., & Engle, R. W. (2003). The role of working memory in problem solving. In
J. B. Davidson, & R. J. Stemberg (Eds), The Psychology of Problem Solving (pp. 176-
206). New York, New York: Cambridge University Press.

Hitch, G. J., & Baddeley, A. D. (1976). Verbal reasoning and working memory. Quarterly
Journal of Experimental Psychology, 28, 603-621.

Jenkins, G. D., Mitra, A., Gupta, N., & Shaw, J. D. (1998). Are ﬁnancial incentives related to
performance? A meta-analytic review of empirical research. Journal of Applied
Psychology, 83, 777-787.

Kahneman, D. (1973). Attention and Eﬂ'ort. Englewood Cliffs, NJ: Prentice Hall.

Kemmelrneier, K., Bless, H., Schwartz, N., & Bohner, G. (2004). What research participants
learn from rewards: A conversational logic analysis of rewarding reasoning performance.
Cahiers de Psychologie Cognitive/Current Psychology of Cognition, 22, 267-287.

Klauer, K. C., Stegrnaier, R., Meiser, T. (1997). Working memory involvement in
propositional and spatial reasoning. Thinking and Reasoning, 3, 9-47.

Knoblich, G., Ohlsson, S., & Raney, G. E. (2001). An eye movement study of insight
problem solving. Memory & Cognition, 29, 1000-1009.

Kruglanski, A. W., Friedman, I., & Zeevi, G. (1971). The effects of extrinsic incentive on
some qualitative aspects of task performance. Journal of Personality, 39, 606-617.

132

 

 

 

 

Kuhl, R., & Kazén, M. (1999). Volitional facilitation of difﬁcult intentions: Joint activation
of intention memory and positive affect removes Stroop interference. Journal of
Experimental Psychology: General, 128, 328-399.

LaMere, J. M., Dickinson, A. M., Henry, M., Henry, G., & Poling, A. (1996). Effects of
multicomponent monetary incentive program on the performance of truck drivers.
Behavior Modiﬁcation, 20, 385-405.

Lavric, A., Forstrneier, S., & Rippon, G. (2000). Differences in working memory
involvement in analytical and creative tasks: An ERP study. Neuroreport: For Rapid
Communication of Neuroscience Research, 11, 1613-1618.

Lepper, M. R., Greene, D., & Nisbett, R. E. (1973). Undermining children's intrinsic interest
with extrinsic reward: A test of the "overjustiﬁcation" hypothesis. Journal of Personality
and Social Psychology, 28, 129-137.

Lezak, M. D. (1994). Domains of behavior from a neuropsychological perspective: The
whole story. In W. D. Spaulding (Ed.), Integrative views of motivation, cognition, and
emotion (pp. 23-55). Lincoln, NE: University of Nebraska Press.

Locke, E. A., & Bryan, J. F. (1969). The directing function of goals in task performance.
Organizational Behavior and Human Performance, 4, 35-42.

Locke, E. A., & Latham, G. P. (1990). A theory of goal setting and task performance.
Englewood Cliffs, NJ: Prentice-Hall.

Locke, E. A., & Latham, G. P. (2002). Building a practically useful theory of goal setting and
task motivation. American Psychologist, 5 7, 705-717.

Logan, G. D., & Etherton, J. L. (1994). What is learned during automatization? The role of
attention in constructing an instance. Journal of Experimental Psychology: Learning,
Memory, and Cognition, 20, 1022-1050.

Logan, G. D., Taylor, S. E., & Etherton, J. L. (1996). Attention in the acquisition and
expression of automaticity. Journal of Experimental Psychology: Learning, Memory, and
Cognition, 22, 620-638.

Luchins, A. (1942). Mechanization in problem solving: The eﬂect of Einstellung.
Psychological Monographs, 54, (Whole No. 248).

Lunney, G. H. (1970). Using analysis of variance with a dichotomous dependent variable: An
empirical study. Journal of Educational Measurement, 7, 263-269.

Maier, N. R. F., & Casselman, G. G. (1970). Locating the difﬁculty in insight problems:
Individual and sex differences. Psychological Reports, 26, 103-117.

133

Metcalfe, J ., & Wiebe, D. (1987). Intuition in insight and non-insight problem solving.
Memory & Cognition, 15, 238-246.

McGraw, K., & McCullers, J. (1979). Evidence of a detrimental effect of extrinsic incentives
on breaking a mental set. Journal of Experimental Social Psychology, 15, 285-294.

Miller, A., & Horn, H. L. (1990). Inﬂuence of extrinsic and ego incentive value on

persistence after failure and continuing motivation. Journal of Educational Psychology,
82, 539-545.

Naveh-Benjamin, M., Craik, F. I. M., Guez, J., & Dori, H. (1998). Effects of divided
attention on encoding and retrieval processes in human memory: Further support for

asymmetry. Journal of Experimental Psychology: Learning, Memory, and Cognition, 24,
1091 -1 104.

Navon, D., & Gopher, G. (1979). On the economy of the human-processing system.
Psychological Review, 86, 214-255.

Ohlsson, S. (1992). Information processing explanation of insight and related phenomena. In
M. Keane, & K. Gilhooly (Eds), Advances in the Psychology of Thinking (vol. 1, pp. 1-
44). London, OK: Harvester Wheatsheaf.

Pokay, P., & Blumenfeld, P. C. (1990). Predicting achievement early and late in the
semester: The role of motivation and use of learning strategies. Journal of Educational
Psychology, 82, 41-50.

Rheinberg, F., Vollmeyer, R. & Burns, B. D. (2000). Motivation and self-regulated learning.
In J. Heckhausen (Ed.), Motivational psychology of human development (pp. 81-108).
North-Holland: Elsevier.

Riedel, J. A., Nebecker, D. M., & Cooper, B. L. (1988). The inﬂuence of monetary
incentives on goal choice, goal commitment, and task performance. Organizational
Behavior and Human Decision Processes, 42, 155-180.

Rothkopth, E., & Billington, M. (1979). Goal-guided learning from text: Inferring a
descriptive processing model from inspecting times and eye movements. Journal of
Educational Psychology, 71, 310-327.

Saari, L. M., & Latham, G. P. (1982). Employee reactions to continuous and variable ratio

reinforcement schedules involving monetary incentives. Journal of Applied Psychology,
67. 506-508.

Schooler, J. W., & Melcher, J. (1995). The ineffability of insight. In S. M. Smith, T. B.
Ward, & R. A. Finke (Eds), The Creative Cognitive Approach (pp. 97-133). Cambridge,
MA: MIT Press.

134

Schooler, J. W., Ohlsson, S., & Brooks, K. (1993). Thoughts beyond words: When language
overshadows insight. Journal of Experimental Psychology: General, 122, 166-183.

Simon, H. A. (1994). The bottleneck of attention: Connecting thought with motivation. In W.
D. Spaulding (Ed.), Integrative views of motivation, cognition, and emotion (pp. 1-21).
Lincoln, NE: University of Nebraska Press.

Smith, E. E., & Jonides, J. (1999). Storage and executive processes in the frontal lobes.
Science, 283, 1657-1661.

Smith, S. M. (1995). Getting into and out of mental ruts: A theory of ﬁxation, incubation, and
insight. In R. J. Stemberg, & J. E. Davidson (Eds), The Nature of Insight (pp. 125-155).
Cambridge, MA: MIT Press.

Spaulding, W. A. (1994). Introduction. In W. D. Spaulding (Ed.), Integrative views of
motivation, cognition, and emotion (pp. ix-xii). Lincoln, NE: University of Nebraska
Press.

Stemberg, R. J., & Davidson, J. E. (1995). The Nature of Insight. Cambridge, MA: MIT
Press.

Toms, M., Morris, N., & Ward, D. (1993). Working memory and conditional reasoning.
Quarterly Journal of Experimental Psychology, 46A, 679-699.

Treisman, A. M. (1964). Verbal cues, language, and meaning in selective attention. American
Journal of Psychology, 77, 206-219.

Vansteenkiste, M., Simons, J ., Lens, W., Sheldon, K. M., & Deci, E. L. (2004). Motivating
learning, performance, and persistence: The synergistic effects of intrinsic goal contents

and autonomy-supportive contexts. Journal of Personality and Social Psychology, 87,
246-260.

Vollmeyer, R. & Rheinberg, F. (1998). Motivationale Einﬂiisse auf Erwerb und Anwendung
von Wissen in einem computersimulierten System. [Motivational inﬂuences on the
acquisition and application of knowledge in a simulated system]. ‘ Zeitschrift ﬁir
Pc'idagogische Psychologie, 12, 1 1-23.

Wason, P. C. (1966). The psychology of reasoning. In B. M. Foss (Ed.), New horizons in
psychology. Oxford, England: Penguin Books.

Weisberg, R. W. (1992). Metacognition and insight during problem solving: Comment on
Metcalfe. Journal of Experimental Psychology: Learning, Memory, and Cognition, 18,
426-432.

Wickens, C. D. (1980). The structure of attentional resources. In R. S. Nickerson (Ed.),
Attention and performance VIII (pp. 239-257). Hillsdale, NJ: Erlbaum.

135

Wickens, C. D. (1984). Processing resources in attention. In R. Parasuraman & R. Davies
(Eds), Varieties of attention (pp. 63-101). Orlando, F 1: Academic Press.

Wieth, M., 8L Burns, B. D. (2000). Motivation in insight verse incremental problem solving.

In L. Gleitrnan & A. K. Joshi (Ed.), Proceedings of the T wenty-second Annual Meeting of
the Cognitive Science Society (pp. 550-564). Hillsdale, NJ: Lawrence Erlbaum.

136

 

   

rgljjljijijjiljjl