Math anxiety and learn helpless

UNIVERSITY OF MIAMI
MATHEMATICS ANXIETY AND LEARNED HELPLESSNESS
By
Joseph Franke Kolacinski
A DOCTORAL TREATISE
Submitted to the Faculty
of the University of Miami
in partial fulfillment of the requirements for
the degree of Doctor of Arts
Coral Gables, Florida
August 2003
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

UMI Number: 3096372
Copyright 2003 by
Kolacinski, Joseph Franke
All rights reserved.
®
UMI
UMI Microform 3096372
Copyright 2003 by ProQuest Information and Learning Company.
All rights reserved. This microform edition is protected against
unauthorized copying under Title 17, United States Code.
ProQuest Information and Learning Company
300 North Zeeb Road
P.O. Box 1346
Ann Arbor, Ml 48106-1346

UNIVERSITY OF MIAMI
A treatise submitted in partial fulfillment of
the requirements for the degree of
Doctor of Arts
MATHEMATICS ANXIETY AND LEARNED HELPLESSNESS
Approved:
Gilbert Cuevas, Ph.D.
Professor of Teaching and Learning
Co-Chair of the Treatise Committee
Marvin V. Mielke, Ph.D.
Professor of Mathematics
Robert L Kelley, Ph.D.
Associate Professor of Mathematics
Associate Chair of Mathematics
Steven G. Ullmann, Ph.D
Dean of the Graduate School
Scott Ingold, Ed
Associate Dea
and Registrar
Enrollment
Shulim Kaliman, Ph.D
Professor of Mathematics

KOLACINSKI, JOSEPH FRANKS (D.A., Mathematics)
Mathematics Anxiety and Learned Helplessness (August 2003)
Abstract of a doctoral treatise at the University of Miami.
Treatise supervised by Professor Gilbert Cuevas, Professor Marvin Mielke and
Professor Robert L. Kelley.
No. of pages in text. 85
Two factors that have been shown to interfere with the learning of
mathematics are mathematics anxiety and learned helplessness. Mathematics
Anxiety is a negative emotional state associated with low mathematical
achievement. Learned helplessness is a response to uncontrollable adverse
stimulus that leads to motivational and cognitive deficits. This study explores the
relationship between these two phenomena.
In the first phase of this study, respondents were separated into four
attributional styles. Categories A1, A2, A3 and A4 consisted of the respondents
who tend to attribute failure in mathematics to lack of effort, environmental
factors, task difficulty and lack of ability respectively. Attribution Theory tells us
that the likelihood that a respondent would experience a helplessness response
increases as the index increases. It was therefore predicted that the mean
mathematics anxiety score of each of these categories would also increase as
the index increases. This study demonstrated this up to the limitations of the
data. Nothing could be inferred about category A2, because too few respondents
fell into that category, but otherwise the mean anxiety score of each category
showed a statistically significant increase coinciding with the known increased
likelihood of a helplessness response.

In the second phase of this study, students were exposed to an
intervention consisting of several methods known to alleviate or prevent
helplessness responses. Here it was predicted that the mathematics anxiety
score, a would decrease significantly between a pre-intervention survey and a
post-intervention survey. This did not happen. However, the mean value of a of
the comparison group increased significantly between the pre-intervention survey
and the post-intervention survey. This may indicate that the intervention
prevented a normal increase of mathematics anxiety for the experimental group.

In memory of my mother,
Mary Franke Kolacinski
iii

Acknowledgments
There were many people who played a roll in the completion of this
project. All of them have my thanks whether I mention them explicitly or not.
I’d first like to recognize my family and friends for their support and
encouragement over the years. Aside from the folks who will be mentioned
below, there are many people I’d like to thank here, but I will restrain myself and
mention only three; my brother, Richard Gadd, who always steers me in the right
direction when I ask him for advice, and two of my closest friends, Jason Foster
and Vicki Pearlman.
Probably the most difficult part of this process for me personally was
completing the paperwork for the Human Studies Committee. I’d like to thank
Ken Goodman, Julia Beutler and Linda Belgrave for their assistance with that
process.
Virtually everyone in the mathematics department was supportive over the
years. Professor Subramanian Ramakrishnan helped me to figure out which
statistical tests were appropriate to use and gave me some useful insight into
how to handle the data. Marta Alpar, Roneet Merkin, Patty Rua and Jay Stine
were gracious enough to allow me to collect data in their classes. Marta, Patty,
Jim Kell and Leticia Oropesa also helped collect data. All of them have my
gratitude. I would particularly like to thank Patty Rua for her assistance and
company.
Mike Rubino, a former student of mine, assisted by making a presentation
to the two classes in the experimental group. Mike is now himself in graduate
school and I wish him the best.
I count myself fortunate to have worked with each of the members of my
committee. Professors Marvin Mielke and Robert Kelley were co-chairs of the
iv

committee, while Professors Shulim Kaliman and Scott Ingold were committee
members. Their advice and suggestions uniformly made this a better project.
The two people who probably heard the most about this project over the
years are also two of my best friends, Elvira Loredo and John Beam. Both of
them were great sounding boards, made solid suggestions and were extremely
helpful.
My most profound thanks go to the third co-chair of my treatise committee,
Professor Gilbert Cuevas. Dr. Cuevas always made himself available and taught
me a great deal as this project progressed. He was supportive of the decisions I
made, wise in his council and very patient. It due to his assistance that this
treatise has turned out as well as it has.
v

Contents
1. Introduction 1
2. Review of Relevant Literature
Part 1 - Learned Helplessness 3
Treatment of Learned Helplessness 8
Part 2 - Mathematics Anxiety 12
Part 3 - Known Links and Some Speculations 19
3. The Study 32
4. Results, Conclusions and Recommendations 39
Instruments 39
Phase 1: The Correlational part of the Study 41
Developing an Attributional Model for Mathematics Anxiety 48
Phase 2: The Interventional part of the Study 52
Conclusions 56
References 63
Appendix A: The Phobos Inventory 66
Appendix B: The Mathematics Attribution Scale 68
Appendix C: Human Research Protocol Form 71
Appendix D: Informed Consent Memos 79
Tables and Figures
Figure 1 - Mean anxiety scores by attributional style 42
Figure 2 - Mean anxiety scores with confidence intervals 43
Figure 3 - The main effects plot 48
vi

Table 1 - Participants in correlational study by course
Table 2 - Typical attributions, locus of control and
Susceptibility to Learned Helplessness
Table 3 - Attributional styles of the respondents in phase 1
Table 4 - ANOVA results
Table 5 - Tukey-Kramer paired comparison test results
Table 6 - Kruskal-Wallis test results
Table 7 - Mann-Whitney Test Results
Table 8 - Results of two-sample t-test assuming unequal
variance, A1 vs. A3
Table 9 - Results of two-sample t-test assuming unequal
variance, A3 vs. A4
Table 10 - Correlation Coefficients
Table 11 - Linear regression, a as a function of F-A, F-T,
F-EN and F-EF
Table 12 - Linear regression, or as a function of F-A and F-T
Table 13 - Results of the paired, two-sample t-test for means
comparing pre and post intervention values for the
experimental group
Table 14 - Results of the paired, two-sample t-test for means
comparing pre and post intervention values for the
comparison group
33
34
41
42
43
45
45
47
47
49
50
51
54
55

■ Chapter I - Introduction
This study deals with some of the challenges and obstacles that students
face as they attempt to learn mathematics. More specifically, it addresses a
number of issues from the realm of “affective variables.” Laurie Hart Reyes says
that,
affective refers to students’ feelings about mathematics, aspects of the
classroom, or about themselves as learners of mathematics. The
definition is not intended to limit the affective domain to general feelings
such as liking/disliking of mathematics, nor is it meant to exclude
perceptions of the difficulty, usefulness and appropriateness of the
mathematics as a school subject. [Reyes, 1984, p. 558]
Over the last few decades, affective variables, particularly mathematics anxiety,
have been studied in the context of such things as gender and cultural
differences in mathematics achievement and shortages of qualified people in
technical fields. [Evans, 2000] The most compelling reason to study affective
variables is to find ways to help students learn mathematics more effectively.
[Reyes, 1984]
Affective Variables include things like mathematics anxiety, mathematical
self-concept, the perceived usefulness of mathematics, the perceived difficulty of
mathematics, learned helplessness and attributional styles. [Evans, 2000; Reyes,
1984] Of these, this study focuses on mathematics anxiety and learned
helplessness. Studies have shown that there is a negative correlation between
mathematics anxiety and achievement in mathematics. [Evans, 2000] Other
1

studies have established that learned helplessness produces a deficit in
mathematical performance. [Gentile & Monaco, 1986] A reasonable relationship
to explore is that between learned helplessness and mathematics anxiety.
The working hypothesis of this study is that there is indeed a relationship
between these two variables.

■ Chapter II - Review of Relevant Literature
Part 1 - Learned Helplessness
The term "learned helplessness" was first coined by M. E. P. Seligman
and J. B. Overmier (1967) to describe the effects of uncontrollable stimulus on
animals. In their earliest experiments a box was partitioned into two
compartments so that an electric shock could be administered through the floor
in either side of the box. This is referred to as a "shuttle box" because the shock
can be avoided by shuttling to the other side of the box. When a shock was
applied to one side of the box, a dog with no preconditioning that was placed in
the box would scramble across the barrier and escape the shock. Other dogs
were preconditioned with a series of shocks that they could not avoid. These
dogs thrashed about wildly when the shock was first applied, but would ultimately
lie down quietly and whine, failing to escape the shock. [Seligman & Maier,
1976]
In later studies it was determined that it was the uncontrollable nature of
the shocks, rather than the trauma of the shocks themselves that caused this
helplessness effect. To demonstrate this, M. E. P. Seligman and S. F. Maier
developed a triadic test design. Three groups of eight dogs were used. The
3

4
dogs in the "escape group" were placed in a harness and were able to terminate
any shocks that were administered by pressing a panel with their nose. A
second group, the "yoked group" was administered shocks that they were unable
to control. Each dog in the yoked group received shocks identical in number,
duration and pattern to the shocks given to a dog in the escape group. The
control group received no shock in the harness. Twenty-four hours later the dogs
were tested in the shuttle box. The escape group and the control group were
able to learn to avoid the shocks easily, while six of the eight dogs in the yoked
group failed completely to avoid shock. Thus it was the uncontrollable nature of
the shocks rather than the trauma of the shocks themselves that caused the
helplessness effect. [Seligman & Maier, 1976]
In fact, a helplessness response can be evoked even when the adverse
events are not totally unavoidable. As long as the reinforcement is non
contingent on the response, a helplessness effect is produced. An outcome is
non-contingent on a response if the probability that the response triggers the
desired outcome is equal to the probability that the outcome follows the absence
of the response. The subjects will therefore receive reinforcement whether they
respond or not. Thus a helplessness response is produced when the
reinforcement is or appears to be totally random and uncontrollable. [Mikulincer,
1994]
A study done by D. S. Hiroto in 1974 replicated the above results in
college students. Using a triadic design, the students were separated into three
groups. The students in the "escape group" were subjected to a painfully loud

noise, which they were able to turn off by pressing a button. The "inescapable
group" was subjected to the same noise, but had no means of shutting off the
noise. The control group, also called the “no-noise group”, was not subjected to
the noise at all. All three groups were then subjected to the same type of noise
in a setting where they had the ability to turn the noise off. Subjects in the control
group and the escape group were able to quickly learn how to shut off the noise,
while the members of the inescapable group did not learn to escape the noise.
Most merely sat passively and endured the noise. [Hiroto & Seligman, 1975]
In addition to these motivational deficits caused by exposure to
uncontrollable adverse events, cognitive deficits have been demonstrated as
well. For example, college students with the same triadic test conditions as
above were given a series of 25 five-letter anagrams, each with the same
pattern. Two types of cognitive deficits were observed. A student from the
escape group or the no-noise group was able to solve each anagram much more
readily than a student exposed to inescapable noise, who would try and fail to
solve the first problem in the allotted 100 seconds. [Seligman & Maier, 1976]
Furthermore, a student from the escape group or the no-noise group
discovered the pattern after about three consecutive successes, while a subject
from the inescapable noise group needed approximately seven consecutive
successes before noticing a pattern. Thus exposure to uncontrollable events
made each individual anagram more difficult and inhibited the subject's ability to
notice or learn a pattern. Subsequent experiments showed that exposure to
unsolvable problems produced exactly the same effect as did inescapable noise.

6
[Seligman & Maier, 1976]
Studies on learned helplessness in humans indicate that the helplessness
response is related to a number of consequences of a person's personality, in
particular, the subject’s involvement in the unsolvable problem and their
expectations of control over their environment. [Dor-Shav & Mikulincer, 1992]
The causal attributions made by a subject in interpreting his or her failure
determine both the subject’s involvement in the problem and his or her
expectation of control. There are three dimensions to causal attribution: locus,
stability and globality. The locus dimension determines if the person will attribute
failure to internal or external causes. Stability is concerned with whether the
causes will remain steady over time and globality with whether the causes will
remain the same over many situations. In particular, one would expect that
attributing failure to internal, stable and global causes would lead to
helplessness, while attributing failure to external, unstable and specific causes
would lead to reactance, an improvement in performance on subsequent tasks.
[Abramson, Seligman & Teasdale, 1978]
A subject’s attributional style determines that subject’s characteristic
response to frustration, which can be categorized in four ways. Intrapersistent
subjects will respond to frustration by trying to reach their goals through their own
devices. Extrapersistent subjects will try to attain their goals through outside
assistance. Intrapersistance and Extrapersistance are collectively referred to as
"need persistence." Intrapunative subjects will respond to frustration by blaming
themselves, while extrapunative subjects will defend their egos by blaming an

outside force. Together, these responses are known as "ego defensiveness."
[Dor-Shav & Mikulincer, 1992]
One of the salient differences between need persistence and ego
defensiveness subjects is their expectation of success after failure. Need
persistence subjects will expect to succeed in future tasks, while the ego
defensiveness subjects will expect failures to recur. In addition, an internal locus
is assumed to increase ego involvement, while an external locus is assumed to
decrease ego involvement since either the responsibility or the solution is shifted
to external forces. [Dor-Shav & Mikulincer, 1992]
Thus intrapersistant subjects will attribute failure to lack of effort, an
internal and unstable cause. This should lead to an optimistic attitude and ego
involvement and in turn reactance. Extrapersistant subjects will typically attribute
failure to bad luck, which is external and unstable. These subjects should then
show an optimistic attitude and a decrease in ego involvement, leading to
reactance, but to a lesser degree than the intrapersistant group.
The intrapunative group will blame failure on a lack of ability, leading to a
pessimistic attitude and ego-involvement and hence to helplessness. Finally the
extrapunative subjects should attribute failure to task difficulty, causing a
pessimistic attitude and low ego involvement. These subjects, then, should
display helplessness at a lower level than the intrapunative group. [Dor-Shav &
Mikulincer, 1992]

Treatment of Learned Helplessness
It has been established that Learned Helplessness is a predictor of low
academic achievement. Consider a college student who fails his or her first
examination in a college course. If the student attributes the failure to an
unstable cause such as a headache, helplessness deficits will be short lived
because the headache will go away. If the student attributes the failure to a
stable cause such as lack of ability the deficits will tend to persist because the
perceived cause will persist. [Peterson, Maier & Seligman, 1993]
Several studies have also shown that interventions based upon
helplessness theory can be used to improve the grades of college students.
[Peterson, Maier & Seligman, 1993] Wilson and Linville used the reasoning
above to develop just such an intervention, which improved the grades of college
students. A group of college students were told that their grades would tend to
improve over the course of their college career. This encouraged them to
attribute initial failures and disappointments to unstable causes. In comparison
to the control group, which was not given this intervention, the grades of the
experimental group did, in fact, improve. [Wilson & Linville, 1985]
There are many techniques that are recommended to either treat an
existing helplessness response or to lessen the likelihood of a helplessness
response in a normal subject. The relevant question here, then, is whether these
techniques will also alleviate mathematics anxiety.
Gentile and Monaco created a list of strategies to prevent helplessness
responses in mathematics students. Many of their preventative methods deal

9
with attributional style and frustration tolerance. Even early in a student’s
“mathematics career” it is useful to provide him or her with attributions involving
effort, persistence and strategy. Students should be made to understand that
certain mathematical concepts are difficult but can be mastered with adequate
effort and the correct strategy. Attributions that emphasize inherent ability and
aptitude should be avoided. [Gentile & Monaco, 1986]
Previous work should be reviewed and students should be shown how it
leads to the concepts that are currently being studied. Students should then be
given some early success experiences to help then fit the new concepts into their
cognitive schemata. [Gentile & Monaco, 1986]
It is also important to de-emphasize the dichotomy between success and
failure. First of all, the students’ work should be evaluated, with good thinking
and partially correct work noted. Problems should not merely be graded as right
or wrong. In addition, students should be required to correct their errors allowing
them to learn to do the problems correctly and giving them an eventual
successful outcome for their effort. Explanation of errors should give the
students a sense that they have some control over the outcomes of their exams,
instead of success and failure seeming to be random. [Gentile & Monaco, 1986]
Another way to circumvent a helplessness response is to provide the
subject with experiences in which he or she can control the outcome. This
process is sometimes known as “immunization.” This is equivalent to exposing
the dogs in the shuttle box experiments to escapable shocks before treating them
with inescapable shocks. In cases where animals were initially exposed to

10
escapable shocks, the helplessness effect was virtually eliminated. [Peterson,
Maier & Seligman, 1993] Methods for treating a helplessness response are
similar to the methods for preventing such a response.
Depression and helplessness are most likely to occur and will be most
severe whenever:
(a) The perceived probability of a positive outcome is very low or the
perceived probability of an adverse outcome is very high.
(b) The outcome in question is either highly adverse or highly desirable.
(c) The subject suspects that the outcome is uncontrollable, or...
(d) The subject attributes the uncontrollability to global, stable and internal
factors. [Abramson, Seligman & Teasdale, 1978, pp. 68-70]
These four areas suggest methods for treating a helplessness response.
If the perceived probability of an adverse outcome is very high or the
perceived probability of a positive outcome is very low, one can attempt to
change the subject’s perception of the probabilities of these events. This can be
accomplished by manipulating the environment to remove adverse outcomes or
provide for desirable outcomes. If it is possible, the actual probabilities of the
outcomes can be altered. If the outcome in question is either highly adverse or
highly desirable, the subject’s perceptions can again be modified. In this case
the adverse outcome can be made to seem less adverse, while the very
desirable outcome can be made to seem less desirable.

11
These things can be accomplished through helping the subject reevaluate
unattainable goals and encouraging him or her to replace them with realistic
and/or attainable alternatives. [Abramson, Seligman & Teasdale, 1978]
In the event that the subject perceives an outcome to be beyond his or her
control, this perception can be changed. If a successful response is not yet
within the person’s ability, the necessary skills can be learned. Otherwise, the
subject’s erroneous belief that his or her responses will fail must be modified.
One means to this end is to provide for the performance of relevant and
successful responses from the subject. This is equivalent to repeatedly dragging
the dog in the shuttle box across the barrier until it learns that the shock is in fact
avoidable. After this therapy is repeated 30 or 40 times, the dog begins to
respond on its own. [Peterson, Maier & Seligman, 1993]
Changing the subject’s attribution of past failures from a lack of ability to a
lack of effort can also increase a subject’s expectation of controllability. This has
been shown to lead to more successful responses. This is generally referred to
as “attributional retraining.” Attributional retraining also forms the basis for
treatment in the situation in which a subject has attributed uncontrollability to a
global, stable and internal factor. If this attribution can be replaced with an
attribution to a specific, unstable and external factor, the subject should become
less likely to exhibit a helplessness response and more likely to show reactance.
[Abramson, Seligman & Teasdale, 1978] Most of the available studies involving
academic applications have used some form of attributional retraining. As
mentioned above, Wilson and Linville showed that changing attributions from

12
stable to unstable led to increased academic performance among college
students. Other studies have worked with changing the “lack of ability” attribution
to an attribution of “lack of effort”, also a shift from stable to unstable. Evidence
also exists that a change in attribution from an internal factor to an external one
has led to an alleviation of a helplessness response. [Wilson & Linville, 1982]
Part 2 - Mathematics Anxiety
Unlike "learned helplessness" which is clearly defined and carefully
researched, Mathematics Anxiety lacks even a universally accepted definition
[Reyes, 1984, p. 563]. In order to better understand what is involved with
mathematics anxiety, we will begin our discussion with a look at the general
concept of anxiety as viewed by psychologists.
The notion of “anxiety” as a psychological construct dates back at least as
far as Freud, who characterized it by motor innervations or discharges, a
consciousness of these and feelings of “unpleasure.” An essential part of
Freud’s understanding of anxiety was that, because it is unpleasant, anxiety is
likely to be repressed or internalized and reside mainly in the unconscious. Once
there, the effects of the anxiety become masked or distorted, making the source
difficult to discern. Because, in Freud’s view, anxiety can be unconscious,
subjects cannot report their anxiety in a meaningful way, nor can it be readily
observed. [Evans, 2000]

13
After the Second World War, the philosophy of the psychology community
shifted in part to make psychological work more scientific. So that data could be
more readily collected, anxiety was assumed to be an observable phenomenon
and as something that subjects could reliably report. Thus, “anxiety” came to be
understood merely as manifest or expressed anxiety. If a subject did not report
anxiety, it was assumed there was none. Freud’s ideas fell into disuse. [Evans,
2000]
As this reinterpretation of anxiety continued, psychologists began to
question whether to view anxiety as a constant personality trait or as a response
to stimulus. Spielberger (1970, 1972) attempted to answer this question when
he defined anxiety as “a palpable, but transitory, emotional state or condition
characterized by feelings of tension and apprehension and heightened
autonomic nervous system activity.” Although this has some similarity to Freud’s
definition it is important to note that Spielberger’s ideas, like other late 20th
century work, view anxiety purely as a manifest phenomenon. [Evans, 2000] In
Spielberger’s work, two types of anxiety are discussed. The first, the “A-state” or
state anxiety is defined as the “unpleasant emotional state or condition which is
characterized by activation or arousal of the autonomic nervous system.” State
anxiety occurs specifically when an individual is confronted with an experience
that he or she finds threatening or stressful. The second type, trait anxiety, or the
A-trait, can be described as a propensity toward experiencing state anxiety.
Thus, an individual with a high level of trait anxiety will tend to experience the A-

14
state more severely and more frequently that an individual who is less trait
anxious. [Reyes, 1984].
The term “anxiety” has numerous definitions in the psychological literature.
In many expositions, “anxiety” is distinguished from “fear” even though these
terms are used interchangeably in other contexts. In some expositions, fear is
the intellectual process of assessing something and recognizing or believing that
it is a threat. Anxiety is the emotional and physiological response to
encountering that, which is feared. Aaron Beck writes: “A person with a fear of
small animals perceives these animals to be dangerous. However, he does not
experience anxiety until he finds himself exposed to a small animal or imagines
himself in such a situation.” [Beck, Emery & Greenberg, 1985, p. 9] Notice that
in both these definitions the primary definition of anxiety refers to an immediate
response to stimulus. Other expositions invert these notions of fear and anxiety.
In Learned Helplessness. A Theory for the Age of Personal Control, by Peterson,
Maier and Seligman, fear is described as a set of reactions, emotional,
physiological and behavioral, triggered by explicit signals that danger is present.
Anxiety, on the other hand, involves similar emotional, physiological and
behavioral reactions, but without an overt or clearly definable stimulus. Under
these definitions, the intensity of the reactions evoked by anxiety are not justified
by the perceived cause of the anxiety. [Peterson, Maier & Seligman, 1993, p. 70]
Anxiety or state anxiety provokes a number of reactions, both behavioral
and physiological. The immediate physiological reactions can include sweating,
trembling, muscle tension, increased heart rate and other symptoms and will

15
cause an individual to cope with the perceived threat through various possible
methods. These methods include, but are not limited to, inaction,
combativeness, repression and rationalization. Some of these responses will
improve an individual’s performance but, more often, a response to the A-state
will cause a person’s performance to decrease and may even have a negative
impact on the individual. Anxiety that leads to a positive outcome such as
increased performance is called “facilitative” while, if the consequences are
negative the anxiety is said to be “debilitative.” [Reyes, 1984].
The most commonly accepted definition of mathematics anxiety,
introduced by Richardson and Suinn in 1972 draws on these notions.
“Mathematics Anxiety,” they say, “involves feelings of tension and anxiety that
interfere with the manipulation of numbers and the solving of mathematical
problems in a wide variety of ordinary life and academic situations." Another
widely accepted definition, by Byrd (1982), includes both facilitative and
debilitative anxiety occurring in any situation in which mathematics is
encountered. Both of these definitions view mathematics anxiety as a form of
state anxiety experienced in mathematical situations. Other researchers view
mathematics anxiety merely as a lack of confidence in one’s ability to learn
mathematics. [Reyes, 1984, p. 565]. Some even take a broader view. In her
book Defeating Math Anxiety. Anita Kitchens writes, “Any feeling that prevents
you from learning mathematics in a natural way as you did as a young child, or
from performing in a way that demonstrates what you have learned, is math

16
anxiety.” [Kitchens, 1995, P. 7] This interpretation, one could argue, could
include the entire range of affective variables.
People suffering from mathematics anxiety typically recall their initial
realization that they were having difficulty with mathematics as feeling like
"sudden death." This reaction has been documented at all levels of mathematics
education from elementary to graduate school. It is generally coupled with a
feeling that some new concept or operation is completely incomprehensible.
Many have described it as a curtain being drawn or running into an impassible
wall. The feeling is described as "instant and frightening."
This sudden onset is thought to stem from students' tendency to resort to
learning by rote when faced with difficult concepts. They will try to memorize all
the information that they need to get by without trying to understand the
underlying concepts. This causes a latency period in mathematics anxiety during
which, because grades are not at first affected, neither the student nor the
teacher realizes that there is a problem with the student's understanding of the
material. When the pattern of reiterated failure inevitably occurs, it is sudden and
dramatic. No one is aware that the difficulty may have been building for years.
[Tobias, 1992]
It is possible that, prior to the "sudden and dramatic” realization above, a
student’s initial response to these repeated failures will be to become over
anxious and try harder to comprehend or memorize the formulas the student
feels will help him or her to regain control. The student’s anxiety becomes
debilitative, actually exacerbating the problem and diminishing the student’s

17
ability to get back on track. The more anxious the student becomes, the harder
he or she tries. The harder he or she tries, the worse the student is able to do.
The worse the student is able to do, the more anxious he or she becomes. Thus
a "vicious cycle" is set into motion. This is an example of the Yerkes-Dodson
law, which states that increased motivation is actually detrimental to performance
in more complex tasks. The greater the complexity of the task, the lower the
degree of motivation that leads to optimal performance. [Skemp, 1987]
These repeated failures then cause further exposures to tasks related to
these concepts to become highly charged with emotion. We then have a
situation in which it is previous experience, rather than the task at hand, that is
the strongest determining factor in the student's success or failure. People
exposed to repeated failure "find that there is a great deal of inertia in even
attempting a problem." [Buxton, 1991, p. 115]
There have been several attempts to build a cohesive theory of
mathematics anxiety. Laurie Buxton built a model around what he calls “math
panic.” Buxton considered the interaction of reason and emotion. In a situation
in which a subject feels a threat of impending failure, such a strong negative
emotional response is evoked that the person is incapable of reasoning
effectively, shutting off all reasonable thought about the problem. [Buxton, 1991]
Another model, developed by Byrd (1982), took more of a case study approach.
It was built from interviews with six college students who showed signs of
mathematics anxiety. These students experienced anxiety in a variety of settings
and in virtually every setting it was debilitating. This anxiety caused these

18
students to avoid courses, majors, jobs, careers and colleges with stringent
mathematics requirements. In both of these models we again see mathematics
anxiety viewed as a form of state anxiety. [Reyes, 1984] Joseph and Nancy
Martinez, in their book Math Without Fear cast a wider net. Mathematics anxiety
“is not a discrete condition.” they write, it is a complex construct. It seldom has a
single cause or a single effect. They continue, “It has multiple causes and
multiple effects, interacting in a tangle that defies simple diagnosis and simplistic
remedies. [Martinez & Martinez, 1996, p. 2]
One factor that is consistent is the belief that there is a relationship
between mathematics anxiety and mathematical achievement. Studies have
found a consistent negative correlation between these two factors with low
anxiety linked to high achievement, although a cause and effect relationship has
not been demonstrated. [Reyes, 1984]
Further confounding the issue, a number of weaknesses have been
pointed out regarding these studies. Jeff Evans points out one of the most
significant in his book Adults' Mathematical Thinking and Emotions. Evans
looked at the two most commonly used measures of mathematics anxiety, the
Mathematics Anxiety Scale (MAS) (Fennema and Sherman, 1976) and the
Mathematics Anxiety Rating Scale (MARS) (Richardson and Suinn, 1972). In a
review of the items on each inventory, he found that in both cases mathematics
anxiety was viewed as debilitating and that the mathematics anxiety measured
was assumed to be a form of chronic or trait-anxiety. [Evans, 2000]

19
Thus, even putting aside competing definitions, there are a number of
reasonable concerns with the notion of anxiety in general and mathematics
anxiety in particular. One is that modern conception of anxiety disregards the
effects of anxiety in the subconscious, although these may be relevant. Another
is that, when a model of mathematics anxiety is specific enough to be potentially
useful, that model views mathematics anxiety as a form of state anxiety, while
the instruments we use to study mathematics anxiety view it as a form of trait
anxiety limiting the scope and the usefulness of the studies. [Evans, 2000]
Clearly, better models are called for.
Part 3 - Known Links and Some Speculations
Even in the early animal experiments that formed the basis of learned
helplessness theory there was evidence of a relationship between the notions of
fear and anxiety on the one hand and the notion of learned helplessness on the
other. In studying animals that were exposed to uncontrollable stressors, such
as the inescapable shocks that were part of the shuttle box experiments, it was
observed that these stressors cause fear in the animals. These generated more
fear, in general, than controllable stressors and following the exposure to the
uncontrollable stressors, the animals showed signs of anxiety for an additional 48
to 72 hours. [Peterson, Maier & Seligman, 1993]

20
There are experiments that indicate that increased levels of fear and
anxiety at the time of the exposure to the inescapable shock are necessary to
cause a helplessness effect. Tranquilizers such as diazepam, which reduce
feelings of fear and anxiety, have been administered to rats prior to their
exposure to inescapable shock. In these rats, the subsequent deficits in shuttle
box learning were eliminated and no helplessness effect was observed.
[Peterson, Maier & Seligman, 1993]
Observations done at the time of the shuttle box testing readily
demonstrated that both fear and helplessness responses could be measured in
the same animals and that the two seemed to coincide. In order to determine if
the learning deficits attributed to helplessness theory were actually the effects of
fear and anxiety, a number of rats were exposed to either inescapable shock or
no shock at all. Twenty-four hours later these same rats were tested in a
standard shuttle box environment. Before the shuttle box tests, the rats were
injected with diazepam, naltrexone or a control substance. The researchers
observed the rats for the presence and intensity of behavior associated with fear
and anxiety. Diazepam eliminated the fear experienced by the rats when the
shock occurred, but the subsequent helplessness effect was unaffected.
Naltrexone was already known to alleviate the helplessness response. In this
study the rats injected with naltrexone experienced a greater level of fear and
anxiety yet the helplessness effect was still eliminated and these rats learned at
the same rate as those that did not receive the inescapable shock. Thus,
although uncontrollable stressors produce high levels of fear and anxiety, it

21
appears that the level of fear and anxiety at the time of the shuttle box testing
does not cause the helplessness effect. [Peterson, Maier & Seligman, 1993]
Let us now turn our attention to mathematics anxiety. Consider the
prevalent views of mathematics in the population. Many parents and teachers
often treat mathematics as something difficult and mysterious. These people
present mathematics as something painful and worthy of fear while showing that
they fear it themselves. Mathematics is also presented as being very important
for success in later life, but something only within the grasp of the very bright.
[Tobias, 1992, pp. 52-53] In addition, an inability to do mathematics is treated as
a normal state of affairs and nothing to be ashamed of. People will readily
discuss their inability to do mathematics problems, while no one will freely admit
to being unable to read. [Zaslavsky 1994, p. 5] Although these attitudes are cited
as causes of mathematics anxiety, they also coincide with the conditions that
make a helplessness response more likely or more severe. We can speculate
that the emphasis on the importance of mathematics to success in later life
would, to the student struggling with mathematics, make an adverse outcome
seem to be very likely. Abramson lists this among the things that increase the
likelihood and severity of a helplessness response. [Abramson, Seligman &
Teasdale, 1978, pp. 68-70] The beliefs that only the very bright can do
mathematics and that it is normal for people to have difficulties in mathematics
perpetuate the notion that some people can learn mathematics and others
cannot. This encourages those who have trouble in mathematics to attribute

22
their failure to a lack of ability, the internal and stable cause that makes a
helplessness response most severe.
Within this context, then, consider the impact of constant failures on a
student trying to learn mathematics. Suppose that student worked a problem
incorrectly, and the reason that the work was incorrect was not explained, or
explained in a way he or she did not understand. To the student, the adverse
event, getting a bad grade or losing points because of an incorrect answer would
be non-contingent on whatever effort the student put into the problem or into
studying. Consider the impact of seemingly getting problems wrong or right at
random. It is reasonable to expect that this apparent lack of control on the part of
the student could manifest itself as a helplessness response. Like the dog or the
rat that is exposed to inescapable shocks, the student may stop trying because
whatever he tries seems to have no effect on the eventual outcome.
Experiments in learned helplessness have shown that exposure to
unsolvable problems leads to a decreased performance on subsequent tasks.
Extrapolating this situation to math students, exposing a student to a question
beyond his or her ability could well trigger a helplessness response and thus the
ordering of questions on an exam should have a meaningful impact on student
test performance. Towle and Merrill (1972) found this was the case on a test
consisting of mathematical items. In their study, students who were given a test
on which the items were ordered from difficult to easy scored significantly worse
than those who took exams on which the ordering of the questions was either
random or from easy to difficult. [Spies-Wood, 1980] Richard Skemp, in his

23
book, The Psychology of Learning Mathematics, attributes the same effect to
anxiety:
...a good teacher can, by initially asking questions that the learner can
answer, reduce anxiety and build up confidence, and thereby improve
performance: a bad teacher can reduce an averagely intelligent pupil to tongue-
tied incompetence. [Skemp, 1987, p. 94]
The genesis of much of the ongoing research into mathematics anxiety
was actually a study of “math avoidance” especially by females. In 1974, Lucy
Sells circulated a report on the mathematical preparation of entering freshmen at
the University of California, Berkeley. The study showed that 57 percent of the
male students in the freshman class had completed four years of high school
mathematics. Only eight percent of the female students had a comparable math
background. Two years later, Sheila Tobias began to popularize the concept of
mathematics anxiety to partially explain this math avoidance and other gender
differences in mathematics. Her work on math anxiety formed the basis for a
number of “math clinics” and other interventions aimed at attracting more women
into mathematical fields. [Tobias & Weissbrod, 1980, p. 64] Tobias’ work had an
immediate impact. For the first time, educators began looking at mathematics
anxiety as a psychological state that could explain these differences rather than
focusing on skills deficits. It was quickly shown that native ability was not the
underlying cause of the gender differences in math avoidance and performance.
Unfortunately, mathematics anxiety also fails to explain these gender
differences. Although women have been shown to display, or at least report,
significantly higher levels of mathematics anxiety, these do not explain gender
differences in mathematical performance or math avoidance. In fact, at least

24
among high school students, these “anxiety effects” have been shown to
manifest themselves more strongly in male students. Possible explanations for
this apparent contradiction include a greater willingness on the part of girls and
women to admit to feelings of anxiety and the possibility that women are more
capable of coping with feelings of anxiety than are men. [Hembree, 1990]
Early in the study of these gender differences it was established that it
was persistence rather than ability that accounted for the gender differences in
mathematics performance. Numerous studies in the late seventies showed that
there is no biological explanation for these differences in mathematical
performance. At the same time, other factors were shown to be linked to gender.
Prominent among these were expectations of success and attributional style. In
general, women and girls were shown to be more likely to attribute failure in
mathematics to a lack of intelligence, while men and boys tend to attribute such
failures to a lack of effort. [Tobias & Weissbrod, 1980]
Notice that this would be consistent if it were a helplessness effect rather
than mathematics anxiety that was at the root of these gender differences. Thus,
even if levels of mathematics anxiety were equal, men and women would have
very different ways of responding to them. Since women tend to attribute failure
to ability, they are, as we have seen, much more likely to exhibit a helplessness
response. [Dweck & Licht, 1980] They would tend to give up and avoid working
at and studying mathematics because they believe that whatever effort they
invest in the process will have little effect on the eventual outcome. Men on the
other hand, tend to attribute failures in mathematics to a lack of effort. This tends

25
to make them less likely to exhibit a helplessness response and more likely to
experience reactance, leading to the increased effort and the greater persistence
identified by researchers as being responsible for the greater mathematical
performance of men.
The mathematics anxiety explanation for math avoidance follows a similar
vein. Although it has never been put forth as a single and unique explanation for
math avoidance, many researchers believe that, for some people, previous
experiences with mathematics could be severe enough and unpleasant enough
to effect their decisions regarding academic programs and career goals. The
general relationship is that, to avoid the unpleasant feelings of mathematics
anxiety, some students will stop studying mathematics. [Tobias & Weissbrod,
1980] Again this could be consistent with a helplessness response as those
earlier unpleasant experiences could be such that they convince a person that
their successes and failures in mathematics are not contingent on their actions.
In this case the person in question would avoid mathematics due to a
helplessness response.
Much has been made in recent years about the differences in the
mathematical achievements of Asian children and American children. When we
look at the attributional styles of these two groups, we see the same thing that we
saw in the comparison of American men and women. When asked why some
students don’t do as well in mathematics as others, American children point to a
lack of ability, while Asian children appeal to a lack of effort. [Tobias, 1992] As is
the case when comparing the mathematical achievement of men and women, it

26
is reasonable to suspect that helplessness theory can help to explain these
differences. Although the information is not readily available, it would be
interesting to discover if there is a corresponding difference between the
mathematics anxiety scores of these two groups.
Ann B. Oaks, at the 1989 National Conference on Women in Mathematics
and the Sciences proposed that there is a cognitive dimension to mathematics
anxiety and, in a number of ways, makes statements that support the view that
much of what is attributed to mathematics anxiety is explainable as a
In her view, the root cause of mathematics anxiety lies in the resistance
that some students have toward gaining a conceptual understanding of
mathematics. These students do not look at mathematics as a cohesive
discipline unto itself, they view it as a meaningless set of procedures for
transforming one set of symbols into another. Their main goal in the
mathematics classroom is to learn how to perform these manipulations easily.
They do not see the usefulness of reasoning and creativity in mathematics and
so, they are unable to generalize what they have learned to even slightly different
circumstances and their verification skills are lacking. In this view, working hard
to learn mathematics consists merely of trying to memorize algorithms. Since
very few people are capable of retaining such a large amount of information
without putting it into some meaningful framework, these students fail repeatedly.
Since their failure follows hard work, they conclude that the failures are a result of
a lack of ability or mathematics anxiety itself. Indeed, many of the students

27
interviewed by Oaks claimed that math anxiety was the primary factor preventing
them from being successful at mathematics. This caused them to avoid
mathematics, rather than to work at it. [Oaks, 1989] As she puts it:
Lefcourt (1982) explained that anxiety is produced by a
combination of two factors: negative results coupled with a lack of control
over the situation. The students in our study have learned that in the
mathematics classroom they are likely to fail, and they know from
experience that there is nothing they can do to keep this from happening.
Therefore, they experience the anxiety normal for an individual in this
situation.
In addition, because they have worked hard and have not
experienced success, these students are forced to shift their
understanding of what causes success for them away from controllable
factors (such as effort and getting outside help) to uncontrollable factors
such as ability and (as they view it) math anxiety. [Oaks, 1989, p. 198]
As before, consider Oaks’ views on mathematics anxiety through the lens
of helplessness theory. At the core of her view of mathematics anxiety is a
fundamental lack of understanding on the part of the students. Since the
students are focused on naive symbol manipulations, they will have little
understanding why, for example, 2(x + y) = 2x + 2y, but (x + yf * x2+ y2since
these appear very similar when viewed purely as operations on symbols without
the context that understanding the meanings of the symbols brings. Without this
understanding and even an aversion on the part of the students to gain a
conceptual understanding of the underlying mathematics, the students will be
incapable of understanding any explanation that their teacher might give them as
to why certain answers are correct and others are incorrect. The students’
successes and failures would then seem to be arbitrary and uncontrollable to the
students, which is the sort of experience that leads to a helplessness response.

28
Furthermore, as Oaks points out, the continued failures of these students,
especially subsequent to what they consider to be hard work, causes them to
change their attributions of failure from lack of effort and other controllable factors
to uncontrollable factors such as a lack of intelligence or ability. Those who
attribute failure to such stable and internal factors are the most likely to
experience a helplessness effect. That these students subsequently stop
working at mathematics could be evidence of a helplessness effect taking place.
Finally, many of Oaks’ students blamed their lack of success in
mathematics on mathematics anxiety itself. This rational may be more
comfortable to the students’ self-image than attributing their failures to a lack of
intelligence, but it is still an internal and stable attribution which would have the
same effect as these other attributions toward bringing about a helplessness
response. [Oaks, 1989]
We can also see evidence of the possible usefulness of helplessness
theory when we examine some of the interventions that have been used to
alleviate mathematics anxiety.
Oaks states that, in her view, interventions that try only to alleviate anxiety
are unlikely to have an effect on a student’s long-term problems with
mathematics. In her course, she attempts to increase her students
understanding by having them work both alone and in groups in a non
threatening atmosphere. The students share their discoveries with each other
and write papers describing their reasoning and thoughts as they tried to solve
certain problems. It is possible for her students to earn an “A” on these papers

29
without ever generating the correct answers. The results are said to be
encouraging, with the students gaining a new sense of control over the
mathematics they do. [Oaks, 1989] Oaks appears to be attempting to shift
attributions from a lack of ability to a lack of effort and lessening the dichotomy
between success and failure for the students. Both of these techniques have
been shown to alleviate helplessness responses.
At American University, Weissbrod and Adams attempted an intervention
that provided students with positive mathematical experiences. Groups made up
their own syllabi and engaged in group work in which each member of the group
selected two problems, one that the student could do and one that he or she
could not. These problems then formed the basis of the group work. [Tobias
and Weissbrod, 1980] In allowing the students to work on problems they were
capable of solving, Weissbrod and Adams provided each group with the sort of
success experience that is known to “immunize” against a helplessness effect.
Aurelia Skiba, a high school mathematics teacher wrote about her
approach to working with math anxious students in the March 1990 issue of the
Mathematics Teacher. Again, large portions of her technique could actually be
aimed at alleviating a helplessness effect. When she states, “If I start with easy
problems and praise each step that is correct, I find that the students can
accomplish significantly more than [their] memories would suggest”, she is giving
the students early success experiences and “immunizing” them against a

30
Furthermore, when these students practice techniques, they do so with a
teacher’s guidance throughout. Corrections are made throughout the process
and so end with a high rate of success. Not only would this continue the
“immunization” process but also, it seems that this would lessen the dichotomy
between success and failure, further alleviating a helplessness response.
Finally, appealing to the example regarding the Asian and American
children, Skiba places heavy emphasis on the importance of effort in learning
mathematics. “I try to instill this concept of the ‘virtue of effort’ in my students."
She writes, “Once they believe they are working hard and trying their best, they
succeed.” [Skiba, 1990] Again we see a technique, attributional retraining,
recognized in alleviating helplessness responses applied to treat mathematics
anxiety.
Gentile and Monaco (1986) may have been the first to actually propose
that there is a link between mathematics anxiety and learned helplessness. They
write:
Given the large number of people who show signs of math anxiety,
it seems to us to be worth exploring their causal explanations of their own
difficulties. However, if learned helplessness is to be a reasonable
account of how they might have acquired their math anxiety, there needed
to be, in our view, at least one objective demonstration that the learned
helplessness manipulation produces a mathematics performance deficit
as well as producing certain varieties of attributions. [Gentile & Monaco,
1986, p. 166]
They were able to show exactly this. In their experiment, sixty-four high school
students were given a set of multiplication problems to solve and were given
failure feedback. These students subsequently showed a helplessness deficit in
a parallel set of multiplication problems as well as on a set of pattern recognition

31
problems of the form “25 is to 5 as is to 8.” Thus, helplessness effects
were shown to occur in a mathematical context. Furthermore, the attributions
made by these students were similar to those in other research. In this case,
girls were more likely to attribute their failures to internal factors such as lack of
ability or effort while boys were likely to blame their failures on external factors
like problem difficulty or clarity. Interestingly, there was not a corresponding
difference in the magnitude of the helplessness effect, the performance of the
boys and the girls were depressed an equal amount. [Gentile and Monaco, 1986]
Gentile and Monaco did not try to measure or quantify the mathematics anxiety
of these students.
There is ample evidence, anecdotal and otherwise, to suggest interaction
between the concepts of mathematics anxiety and learned helplessness.
Notions from helplessness theory appear relevant and continue to further
illuminate the study of mathematics anxiety both in theory and in practice. The
study that is the basis of this paper further investigates this relationship.

■ Chapter III - The Study
The purpose of this study was to investigate the relationship between
Mathematics Anxiety and Learned Helplessness. This was done in two parts.
The first phase of this project was a correlational study in which a large sample of
students was partitioned by attributional style to indicate the students’ propensity
toward learned helplessness. The mean mathematics anxiety scores of these
attributional styles were then examined to determine if the known differences in
helplessness responses corresponded to differences in mathematics anxiety
scores. The second phase was an interventional study. A smaller group of
students was exposed to an intervention consisting of several methods known to
lessen helplessness responses. After the students were exposed to the
intervention, they were again given questionnaires to discover if there was a
corresponding decrease in their mathematics anxiety scores.
Nine mathematics classes taught at the University of Miami were chosen
to participate in the correlational part of the study. These classes were selected
to give a cross section of the freshmen and developmental level mathematics
courses offered at the university. The students in these classes who were
eighteen years of age or older were asked to participate in the study by
32

33
completing both the Phobos Inventory, which measures levels of Mathematics
Anxiety, and the Mathematics Attribution Scale, which measures students’
attributions regarding success and failure in mathematics. In all, 193 students
agreed to complete the questionnaires and returned usable information. Table 1
shows the courses the respondents were recruited from and indicates the
number of respondents participating from each course.
Table 1 - Participants in correlational study by course
Course Number of Respondents
MTH 099 - Intermediate Algebra 30
MTH 101 - Algebra for College Students 19
MTH 103 - Finite Mathematics 43
MTH 107 - Precalculus I 45
MTH 108 - Precalculus II 26
MTH 1 1 1 - Calculus I 30
TOTAL 193
Several responses were deemed unusable because the information returned was
incomplete or illegible or because the respondent was under the age of eighteen.
Recall that it has been shown that there is a relationship between the
attributions a person makes regarding failure and his or her susceptibility to
learned helplessness. [Dor-Shav & Mikulincer, 1992] The researcher used this
knowledge to investigate the link between learned helplessness and
mathematics anxiety. There are three dimensions to causal attribution: locus,
stability and globality. The locus dimension determines if the person will attribute
failure to internal or external causes. Stability is concerned with whether the
causes will remain steady over time, and globality with whether the causes will
remain the same over many situations. Specifically, if someone attributes failure

to an internal and stable cause, such as a lack of ability, that person expects
failure to recur and helplessness results. If the perceived cause is internal and
unstable, such as a lack of effort, the subject tends to have an optimistic attitude
leading to reactance, an increase in performance on subsequent tasks. The
notion of globality is less useful here, since the study only relates to a single
topic, mathematics. The different attributional styles and their propensity toward
learned helplessness are summarized in table 2. [Dor-Shav & Mikulincer, 1992]
Table 2 - Typical attributions, Locus of Control and susceptibility to Learned
Helplessness:
Category A1 (F-EF) Category A4 (F-A)
Internal Interpersistent Subjects Intrapunative Subjects
“Lack of Effort” “Lack of Ability”
Locus High Reactance High Helplessness
Category A2 (F-EN) Category A3, (F-T)
External Extrapersistent Subjects Extrapunative Subjects
“Bad Luck” “Task Difficulty”
Low Reactance Low Helplessness
Unstable Stable
Stability
The attributional style of each of the 193 respondents was established
using the Mathematics Attribution Scale. The MAS generates eight scores
indicating how likely a subject is to attribute success and failure to four

35
attributions based on locus and stability. Thus there are scores indicating how
likely it is that a subject will attribute failure to effort (F-EF), environmental factors
(F-EN), task difficulty (F-T) and innate ability (F-A). Similar scores are generated
for success attributions. The largest of the four failure scores was used to
determine in which of 4 categories a respondent was placed. In the event of a
tie, that respondent was not categorized.
Thus, the outcome of this phase of the study was to stratify the sample
into the four categories of attributional styles that indicate a person's propensity
for learned helplessness from low (A1) to high (A4). pAi is defined to be the
mean mathematics anxiety score for attributional style Ai. A hypothesis test with
null hypothesis, “H0: pai = |M(i+i)” and alternative hypothesis
“Ha: pAi = m-a (i+i) is not so” was conducted using an Analysis of Variance
(ANOVA). The Tukey-Kramer paired comparison test was then used to
determine if there was a significant pairwise difference in these means.
It was expected that the mean anxiety score would increase significantly
as the index increases, that is, the working hypothesis of this part of the study
was that pAi < PA2 < PA3 < PA4-
The second or interventional phase of this study attempted to show that
methods known to alleviate learned helplessness will also alleviate mathematics
anxiety.
To this end, four classes taught by the researcher were asked to
participate. These classes consisted of two sections of MTH 103 (Finite
Mathematics) and two sections of MTH 107 (Precalculus I). One section of each

36
course was included in an experimental group while the other was kept as a
comparison group. The students in these sections were tested at the beginning
of the semester using the Phobos Inventory of Mathematics Anxiety and the
Mathematics Attribution Scale. These scores were also used as part of the
correlational part of this study. The sections making up the experimental group
were exposed to information and activities aimed at preventing or lessening
helplessness responses throughout the semester.
The intervention was based upon two facts: exposure to adverse events
that are perceived as uncontrollable often leads to a helplessness response; and
a helplessness response is most severe when a person attributes failure to
internal and stable causes. The researcher attempted to both prevent and
alleviate helplessness responses.
Attributional retraining is the primary method for alleviating a helplessness
response. Thus, the students in the experimental group were encouraged
throughout the semester to adopt attributions involving effort and strategy, and to
attribute failure to unstable causes rather than stable ones. Several methods
were used to encourage students in the experimental group to adopt attributions
involving effort and strategy. A former student of the researcher made a
presentation to each class in the experimental group emphasizing the importance
of effort and strategy to success in mathematics. He spoke of his own
experiences in taking MTH 107, emphasizing that, although his early grades in
the class were not as high as he would have liked them to be, he was eventually
able to succeed in the class through a combination of hard work and good study

habits. He then described these habits and reminded the students of the on-
campus resources available to assist them with their mathematics classes. The
classes in the comparison group heard no such presentation. The experimental
group watched the Nova episode “The Proof which chronicles Dr. Andrew Wiles
quest to prove Fermat’s Last Theorem. The discussion following the video
emphasized attributions involving effort, particularly noting how Dr. Wiles solved
what is possibly the most difficult problem in all of mathematics through 7 years
of intense work. The experimental group was also given an extra credit
assignment in which the students were asked to watch and review the film Stand
and Deliver. In the film a high school math teacher inspires underachieving
students to work hard and tap potential they never knew they had. The
comparison group participated in similar activities that did not encourage
attributions toward effort but instead involved attributions of inherent ability.
These activities were built around the short film “N is a Number”, a biography of
Paul Erdos and the feature film A Beautiful Mind. To further emphasize the
importance of effort to learning mathematics, the students in the section of MTH
107 that was a part of the experimental group were provided with several “extra
practice” worksheets to supplement their regular homework assignments. These
worksheets were made available to the students in the comparison section of
MTH 107 but they were not handed out.
Methods for preventing a helplessness response were also employed. To
prevent a helplessness response, one can attempt to lessen the impact of
adverse events and give the student some expectancy of control. Recall that

38
one factor that makes a helplessness response more likely or more severe is the
dichotomy between success and failure. [Gentile & Monaco, 1986] Thus, this
part of the intervention included giving students in the experimental group extra
credit assignments in which they corrected and explained any errors they had
made on their exams. This activity should make a helplessness response less
likely by lessening the dichotomy of success versus failure with respect to the
exams. The corresponding activity for the comparison group was sets of
additional challenging problems relating to the material on each test. The
experimental group was also told, following their first test that grades usually
improve on the second test. This encouraged them to attribute any failures to
unstable causes. The comparison group was not given this information.
At the end of the semester the students were again tested with the
Phobos Inventory and the Mathematics Attribution Scale. Methods for verifying
changes in paired data were then applied to determine if there was a significant
difference between the pre-experiment and post-experiment Mathematics
Anxiety scores. The working hypothesis of this portion of the study is that the
mathematics anxiety scores of the experimental group should decrease
significantly from the pre-intervention survey to the post intervention survey. The
results of the study are presented in chapter 4.

■ Chapter IV - Results, Conclusions and
Recommendations
Instruments
Two instruments were used in this study. The Phobos Inventory
(Appendix A) is designed to measure levels of mathematics anxiety. It is a thirty
question Likert style questionnaire that Ronald Ferguson (1986) adapted from
the Mathematics Anxiety Rating Scale (MARS) developed by Richardson and
Suinn (1972). The first ten items on the inventory are designed to measure
numerical or computational anxiety. Items 11 through 20, measure mathematics
test anxiety, while questions 21 through 30 measure abstraction anxiety. Each
item on the inventory describes a situation involving mathematics and the
respondent is asked to indicate how much that item frightens him or her on a
scale ranging from 1 (not at all) to 5 (very much). [Ferguson, 1986] Traditionally,
the responses are totaled to generate a math anxiety score ranging from 30 to
150. Under this scheme, unanswered questions would skew the results toward a
low anxiety result. To allow for an occasional blank or indeterminate response,
the researcher generated three sub-scores by finding the mean of the actual
responses from questions 1 through 10,11 through 20 and 21 through 30
respectively. These sub-scores were then summed, generating math anxiety
39

40
scores that range from 3 to 15 with each sub-score contributing between 1 and 5
points to the total. This anxiety score will be denoted by a.
The attributional styles of the respondents were determined using the
Mathematics Attribution Scale (Appendix B), developed by Elizabeth Fennema,
Patricia Wolleat and Joan Daniels Pedro (1979). Recall that there are four
attributional styles that are relevant here. Characterized by their standard
attributions, these can be classified as “effort” (A1), “environmental factors” (A2),
“task difficulty” (A3), and “ability” (A4). The MAS is a thirty-six-item Likert style
questionnaire. Nine events involving mathematics are described. After each
event is a list of four possible causes or attribution statements for that event, one
for each of the four relevant attributional styles. The respondents are asked to
determine whether each cause could be an explanation for the associated event.
The possible responses range from “1” meaning “strongly disagree” to “5”
meaning “strongly agree.” Thus, the higher the value, the more strongly the
respondent believes that the attribution statement could describe the cause of
the event in question. Eight of the events are used in the evaluation of the
instrument; the ninth is not scored. Four of these describe successful outcomes
and the other four describe unsuccessful outcomes. The MAS therefore
generates eight scores, four indicate how likely the respondent is to attribute
failure to effort, environmental factors, task difficulty and innate ability, (F-EF, F-
EN, F-T and F-A respectively) while the remaining scores measure the same
attributions for success. [Fennema, Wolleat & Pedro, 1979] As was done in the

41
case of the Phobos Inventory, the mean of the responses actually received for
the relevant items was used in place of the sum of those responses.
Phase 1: The Correlational part of the study
In the corelational part of the study, the 193 respondents were classified
by their attributional styles with regard to failure. Recall from chapter 2, part 1,
that it was a person’s attributions of and responses to failure that determined his
of her susceptibility to learned helplessness. Each student was categorized
according to his or her maximum failure score. Forty students could not be
categorized because of ties in their largest scores. The results are summarized
in table 3. It is striking that so few students fell into category A2. Further
research should be conducted to determine if this is a statistical abnormality or if
this is a normal characteristic of college students.
Table 3 - Attributional Styles of the respondents in phase 1
Category Largest Failure
Score
from the MAS
Standard
Attribution
#of
Respondents
Mean value
of or
A1 F-EF Effort 58 6.47
A2 F-EN Environment 5 6.86
A3 F-T Task 48 7.04
A4 F-A Ability 42 8.61
The corresponding mean total anxiety score from the Phobos Inventory for each
of these categories is shown in table 3. As predicted in chapter 3, the mean
anxiety score increased with the index. And so we have:
M-A1 < PA2 < PA3 < PA4.
This is shown graphically in figure 1.

42
Figure 1 - Mean anxiety scores by attributional style
Category
A single factor ANOVA was performed to determine if these increases are
significant. The results of the ANOVA, shown in table 4, show a p value of
.0000075, indicating that there is a statistically significant difference between the
means of at least two of the four categories at a confidence level greater than
99%. As we can see in figure 2, if the means of each category are compared
using a 95% confidence interval, it appears that pAi and pA3 are significantly
smaller than pA4.
Table 4 - ANOVA results
Source of Variation SS df MS F P-vaiue F crit
Between Groups 115.69 3 38.56 9.65 0.0000075 2.67
Within Groups 595.51 149 3.00
Total 711.19 152

43
Figure 2 - Anxiety score means of A1 through A4 with confidence intervals
Individual 95% CIs For Mean
Based on Pooled StDev
Category
A1
N
58
Mean
6.474
StDev -----
1.866
A2 5 6 . 860 1.784 {---- _- _*____ _.---------- )
A3 48 7 . 042 1.842 (------* - - - )
A4 42 8.612 2 .342 (------* -------)
Pooled StDev = 1.999 6.0 7.2 8.4
This was further investigated using a Tukey-Kramer paired comparison test. As
the results in table 5 indicate, it is indeed the case that pAi and jj,A3are
significantly smaller than pA4. The confidence intervals containing the differences
of the means between A1 and A4 and between A3 and A4 do not contain zero
and therefore the means of the anxiety scores of these categories are
significantly different at a confidence level of at least 95%.
Table 5 - Tukey-Kramer paired comparison test results.
Tukey's pairwise comparisons
Family error rate = 0.0500
Individual error rate = 0.0104
Critical value = 3.67
Intervals for (column level mean) - (row level
mean)
A2
A3
A4
A1 A2 A3
-2.805
2 .032
-1.580 -2.620
0.444 2.256
-3.189 -4.206 -2.666
-1.087 0 .703 -0.474

44
And so, even though this does not support the entire of the hypothesis that
Pai < pa2 < PA3 < pa4 at a 5% level of significance, it does support the overall
notion that there is a relationship between the phenomena of mathematics
anxiety and learned helplessness. In particular, the attributional style most prone
to a helplessness response displayed levels of anxiety significantly higher than
the group least prone to such a response. The ability attribution may be the most
salient here, as the mean anxiety score for that attribution was significantly
higher than the mean anxiety scores of the effort and task attributions, which
were not significantly different from each other according to these tests. It is
possible that the anxiety score for the ability attribution would be significantly
higher than the environment attribution as well, but it is difficult to infer anything
meaningful about the environmental attribution, because so few respondents fell
into category A2.
Both the ANOVA and the Tukey-Kramer Paired Comparison Test assume
that the data being analyzed is normally distributed with equal variance. [Rice,
1995] Since this is not necessarily the case here, it is prudent to bolster these
findings using some non-parametric methods. A Kruskal-Wallis Test was
performed on the data to determine if there existed a significant difference in the
median anxiety scores of categories A1, A2, A3 and A4. Let j]Ak be the median
anxiety score of attributional style Ak. The difference is indeed significant as we
can see in table 6. With p < 0.05, the median anxiety scores are different at a
confidence level greater than 95%.

45
Table 6 - Kruskal-Wallis Test Results
Category N Median Ave Rank Z
A1 58 6.500 61 .0 -3 .50
A2 5 7 .000 70 .2 -0 .35
A3 48 7 .050 74 .4 -0.49
A4 42 8.400 102 .9 4 .45
Overall 153 77 .0
H = 22.26 DF = 3 P = 0 .000
H = 22.27 DF = 3 P = 0.000 (adjusted for ties)
As is the case with the ANOVA, this tells us that there is a significant
difference between at least two of the categories, but it does not give us
information as to which of the categories are different. Thus Mann-Whitney
Tests were conducted on pairs of attributional styles. Again, no meaningful
information could be inferred about category A2, since so few respondents fell
into that category. The results regarding the other attributional styles however,
were more definitive than those from the ANOVA and Tukey-Kramer tests. The
relevant results are given in table 7.
Table 7 - Mann-Whitney Test results
Mann-Whitney Test and Cl: A3, A1
A3 N = 48 Median = 7.050
A1 N = 58 Median = 6.500
Point estimate for rjA3 - rjA1 is 0.600
90.0 Percent Cl for rjA3 - r/A1 is (-0.000,1.299)
W = 2837.5
Test of r]A3 = rjA1 vs rjA3 > rjA1 is significant at 0.043 9
The test is significant at 0.0438 (adjusted for ties)

46
Table 7 (continued) - Mann-Whitney Test results
Mann-Whitney Test and Cl: A4, A3
A4 N = 42 Median = 8.400
A3 N = 48 Median = 7.050
Point estimate for r]Ai - rjA3 is 1.528
90.0 Percent Cl for T]A4: - i]A3 is (0.722,2.300)
W = 2313.0
Test of /7a4 = ?7a3 v s rjAi > rjA3 is significant at 0.0006
The test is significant at 0.0006 (adjusted for ties)
Thus ?7ai < 77A3 is shown with a 5% level of significance. The results for the other
relationship are stronger, and show that tja3 < 77A4 is true at a better than 1% level
of significance. Recall that the hypothesis of this phase of the study was that
Pai < pa2 < pa3 < P-A4- This relationship is true for the medians of the anxiety
scores for every attributional style that was large enough to yield useful results.
It is reasonable to conclude that the Mann-Whitney and Kruskal-Wallis tests give
better information in this situation because they do not assume any underlying
distributions on the data and, the Mann-Whitney allows one-sided tests as well
as two-sided tests. In addition, testing for results with respect to the median
rather than the mean makes the results less sensitive to outliers.
Two-sample t-tests were conducted to determine if this relationship could
be demonstrated with regard to the means of the anxiety scores for each of the
attributional styles using one-tailed tests. The results were similar to the results
from the Mann-Whitney and Kruskal-Wallis tests. Once more, nothing
meaningful could be determined regarding the environmental attribution,

47
category A2, but the hypothesis was otherwise supported by these tests with
respect to the other attributional styles as is shown in tables 8 and 9.
Table 8 - Results of two-sample t-test assuming unequal variance, A1 vs. A3
A1 A3
Mean 6.47 7.04
Variance 3.48 3.39
Observations 58 48
Hypothesized Mean Difference 0
df 101
tStat -1.57
P(T<=t) one-tail 0.06
t Critical one-tail 1.66
P(T<=t) two-tail 0.12
t Critical two-tail 1.98
Here, using a one-tailed test, since p « 0.06 < 0.10 we can reject the null
hypothesis that pAi = pa3 and accept the alternate hypothesis that ^Ai < pA3 at a
level of significance less than 10%. The result that p,A3 < |aA4 is much stronger
and can be accepted at a better than 1% level of significance.
Table 9 - Results of two-sample t-test assuming unequal variance, A3 vs. A4
A3 A4
Mean 7.04 8.61
Variance 3.39 5.48
Observations 48 42
Hypothesized Mean Difference 0
df 78
tStat -3.5
P(T<=t) one-tail 0.0004
t Critical one-tail 1.66
P(T<=t) two-tail 0.0008
t Critical two-tail 1.99

48
The hypothesis of phase one of the study is therefore verified up to the limitations
of the data. That is, jmi < pa3 < pa4 at a 10% or better level of significance.
Developing an attributional model for mathematics anxiety
To further explore this relationship; the failure scores from the MAS were
compared to a, the anxiety score from the Phobos Inventory, for all 193
respondents. The main effects plot is shown in figure 3, below. It shows the
mean value of a for each value of the four scores, F-EF, F-EN, F-T and F-A from
the MAS, plotted against that value. Examining this figure, there appears to be
little relationship between the scores F-EF and F-EN and the anxiety scores.
The scores F-T and F-A however, appear to have linear relationship with a, with
the correlation appearing stronger with respect to F-A.
Figure 3 - The Main Effects Plot
F-EF F-EN F-T F-A a v e
2? 10.0
8
'T) 8.5
to
o
■5 7.0
o
-
©
< 4.0
<5.0 1.01.0 4.5 2.0 5.0 1.0
MAS SCORES

49
The correlation coefficients further support this observation. As is evident
in table 10, the correlation coefficient increases as we progress from the scores
related to the attributional styles associated with reactance to those related to
helplessness. Thus, the more likely an attributional style is to have a
helplessness response, the more closely the related MAS score correlates with
the mathematics anxiety score. The correlation coefficient p .53 between a and
F-A indicates a fairly strong relationship considering the self-reporting nature of
the data at hand.
Table 10 - Correlation Coefficients
MAS Score Correlation coefficient
with anxiety score, a
F-EF 0.028678
F-EN 0.181144
F-T 0.397659
F-A 0.530908
An attempt was made, using linear regressions to find a function that
would model a in terms of F-A, F-T, F-EN and F-EF. The initial attempt, involving
all four of these factors is shown in table 11.
This model is significant at a confidence level of at least 99%, given that
the value of “Significance P « 3.90 x 10 ~9 < 0.01. The value of “Adjusted R2” ^
0.29 is again acceptable given the nature of the data. A better model is possible
however. The large P-values for F-EN and F-EF as well as the small values of
the coefficients of these variables indicate that these factors contribute little to the
model.

50
Table 11 - Linear regression, or as a function of F-A, F-T, F-EN and F-EF
Regression Statistics
Multiple R 0.550
R Square 0.302
Adj. R Square 0.287
Standard Error 1.815
Observations 193
ANOVA
df SS MS F Significance F
Regression 4 268.13 67.03 20.34 6.15 x 10 ~14
Residual 188 619.62 3.30
Total 192 887.75
Coefficients
Standard
Error tStat P-value
Intercept 2.110 0.895 2.357 0.019
F-A 1.045 0.169 6.179 3.90 x 10 ~9
F-T 0.539 0.271 1.990 0.048
F-EN 0.096 0.218 0.442 0.659
F-EF -0.117 0.151 -0.772 0.441
Other models were tried. The significance of interactions, (factors such as
F-A x F-T) was tested as was the significance of quadratic factors such as (F-A)2.
None of these made a significant contribution to the model. The model based on
just F-A and F-T was the best fit and is shown in table 12.

51
Table 12 - Linear regression, a as a function of F-A and F-T
Regression Statistics
Multiple R 0.547
R Square 0.299
Adj. R Square 0.292
Standard Error 1.809
Observations 193
ANOVA
df SS MS F Significance F
Regression 2 265.796 132.898 40.599 2.09 x 1 0 ~ 1b
Residual 190 621.951 3.273
Total 192 887.747
Coefficients
Standard
Error tStat P-value
Intercept 1.917 0.776 2.471 0.014
F-A 1.043 0.168 6.190 3.63 x 10 ~9
F-T 0.556 0.255 2.181 0.030
Thus, in addition to the relationships noted above, there is a model
describing a that is based upon the scores for the two attributions, ability and
task difficulty, that lead to a helplessness response. Recall that the other two
attributional styles, effort and environment, lead to reactance rather than
helplessness.
or = 1.917 + 1.043(F-A) + 0.556(F-T) + e
It may be possible to use this model to predict mathematics anxiety.
It is interesting that F-EF, the score for the effort attribution, does not
correlate with the anxiety score and that it contributes little to the model of a in
table 11. One might expect to find a strong negative correlation between F-EF
and a since the effort attribution leads to high reactance rather than
helplessness. That this is not the case is an interesting question warranting

52
further research. Recall that intrapersistent subjects, who attribute failure to lack
of effort, expect success rather than failure on future tasks. [Dor-Shav &
Mikulincer, 1992] It is therefore possible that their attributions regarding failure
have little effect on their overall attitudes about mathematics and on their level of
mathematics anxiety in particular. Oaks mentions a phenomenon that is another
possible explanation. When students become convinced that they cannot
succeed at mathematics, they avoid working at it. This allows a student to blame
failure on lack of effort, allowing him or her save face. [Oaks, 1989] Oaks
proceeds to quote a student who explains her feelings on the matter.
When I feel myself starting to slip, I put up the books because I
don’t want to slip and I’m scared. It’s easier to put up the books because
then you say, “Well, I didn’t study, and I got this bad grade. But it’s O. K.
because l didn’t study and I didn’t deserve it anyway.”
But that little fear of “I studied; I tried and look at my grade” is scary.
I’m scared that if I do open the book and I do try to study, that I’m not
going to get it and that I’m going to be a failure anyway. You don’t want to
find out that that you’re stupid and you couldn’t handle it.
[Oaks, 1989, pg. 199]
Students in this situation may have inflated F-EF scores, masking a relationship
between a and F-EF that would otherwise be discernable.
Phase 2: The Interventional Part of the Study
In phase 2 of the study students in an experimental group were exposed
to an intervention designed to lessen helplessness responses. There were thirty-
six students in the experimental group and twenty-seven in the comparison group
who responded to both the pre-intervention questionnaire and the post
intervention questionnaire. Recall that the hypothesis of this phase of the study

53
was that although the intervention was designed to lessen a helplessness
response, there would be a corresponding decrease in the mathematics anxiety
score, a of the students in the experimental group. There was also a tacit
assumption that the scores of the students in the comparison group would not
change. Neither of these things happened. For the experimental group, there
was no discernable change in a at all, much less a statistically significant one.
There was also no significant change in any of the failure scores from the MAS.
These facts were established using a paired two-sample t-test for means. The
results for the experimental group are summarized in table 13.

54
Table 13 - Results of the paired, two-sample t-test for means comparing pre and
post intervention values for the experimental group.
Pre anx Postanx Pre F-EF Post F-EF Pre F-EN Post F-EN
Mean 7.53 7.55 3.57 3.60 2.68 2.78
Variance 3.84 4.31 0.74 0.80 0.35 0.38
Observations 36 36 36 36 36 36
Pearson Correlation 0.74 0.55 0.59
Hypothesized Mean Diff. 0 0 0
df 35 35 35
tStat -0.08 -0.17 -1.07
P(T<=t) one-tail 0.47 0.43 0.15
t Critical one-tail 1.69 1.69 1.69
P(T<=t) two-tail 0.94 0.87 0.29
t Critical two-tail 2.03 2.03 2.03
Pre F-T Post F-T Pre F-A Post F-A
Mean 3.63 3.55 3.41 3.42
Variance 0.34 0.40 0.75 0.80
Observations 36 36 36 36
Pearson Correlation 0.62 0.83
Hypothesized Mean Diff. 0 0
df 35 35
tStat 0.81 -0.08
P(T<=t) one-tail 0.21 0.47
t Critical one-tail 1.69 1.69
P(T<=t) two-tail 0.42 0.94
t Critical two-tail 2.03 2.03
Hembree (1990) did an overview of research done on mathematics anxiety and
noted that whole-class interventions were not effective in the treatment of
mathematics anxiety. Phase two of this study may be another example in
support of Hembree’s findings. However, examining the data for the comparison
group, as shown in table 14, gives us another possible explanation.

55
Table 14 - Results of the paired, two-sample t-test for means comparing pre and
post intervention values for the comparison group
Pre anx Postanx Pre F-EF Post F-EF Pre F-EN Post F-EN
Mean 6.96 7.61 3.17 3.56 2.64 2.68
Variance 3.02 5.93 0.69 0.65 0.42 0.39
Observations 27 27 27 27 27 27
Pearson Correlation 0.73 0.77 0.35
Hypothesized Mean Difference 0 0 0
df 26 26 26
tStat -2.00 -3.63 -0.26
P(T<=t) one-tail 0.03 0.00006 0.40
t Critical one-tail 1.71 1.71 1.71
P(T<=t) two-tail 0.06 0.0012 0.79
t Critical two-tail 2.06 2.06 2.06
Pre F-T Post F-T Pre F-A Post F-A
Mean 3.46 3.69 2.88 3.20
Variance 0.23 0.34 0.57 0.78
Observations 27 27 27 27
Pearson Correlation 0.50 0.68
Hypothesized Mean Difference 0 0
df 26 26
t Stat -2.14 -2.54
P(T<=t) one-tail 0.02 0.01
t Critical one-tail 1.71 1.71
P(T<=t) two-tail 0.04 0.02
t Critical two-tail 2,06 2.06
Notice that there is a statistically significant increase between the pre and post
intervention values of a, F-A, F-T and F-EF. For the one-tailed tests, all these
results are significant at a level of 5% or better. For the two-tailed tests, the
increases in F-A, F-T and F-EF are significant at the 5% level, while the increase
in a is significant at the 10% level. One possible explanation for this is that an
increase in anxiety is normal at the end of a semester. The corresponding
increases in F-A and F-T are consistent with this according to the linear

regression model given in table 12, and although an increase in F-EF might be
suspected of relating to a decrease in a, the regression models did not support
that fact. Verifying that an increase in mathematics anxiety is normal over the
course of a semester is an obvious subject for further research. If this is indeed
the case, these results would seem to indicate that the intervention was
successful in preventing a normally occurring increase in mathematics anxiety.
Further research should be done to verify this assumption. If such an increase in
mathematics anxiety is normal, it might be fruitful to revisit some of the studies
reviewed by Hembree. Treatments that appeared to be ineffective in treating
mathematics anxiety may have, in actuality had a significant preventative effect.
Conclusions
This study has shown a relationship between mathematics anxiety and
learned helplessness. Separating students into attributional styles showed that,
with the exception of the one style for which there was insufficient data, as the
likelihood of a helplessness response increased, the mean and median
mathematics anxiety score of that group would increase as well. A regression
model was developed that predicted the mathematics anxiety score as a function
of the two attribution scores most closely related to helplessness. It also appears
that an intervention aimed at lessening helplessness responses prevented a
normal increase in mathematics anxiety.
To summarize the findings, in the correlational phase of the study, the
respondents were separated into four attributional styles. Category A1 consisted

57
of those who tend to attribute failure to lack of effort. Categories A2, A3 and A4
contained the respondents who tend to attribute failure in mathematics to
environmental factors, task difficulty and lack of ability respectively. Attribution
Theory tells us that the likelihood that a respondent would experience a
helplessness response should increase as the index increases. It was therefore
predicted that the mean mathematics anxiety score of each of these categories
would also increase as the index increases. That is,
|M 1 < HA2 < PA3 < M-A4-
This was established up to the limitations of the data. Nothing could be inferred
about category A2, because too few respondents fell into that category. With
that exception there was significant evidence that this relationship exists, and so,
PA1 < PA3 < HA4
was shown with a better than 10% level of significance. This was further
supported by non-parametric methods. This relationship holds true for the
medians of these categories as well as the means. Thus the relationship,
T]A1 < T1A3 < T1A4
was established with a better than 5% level of significance.
It was also shown that the scores generated by the Mathematics
Attribution Scale could be used to model a, the mathematics anxiety score
generated by the Phobos Inventory. The scores most closely related to
helplessness, F-A and F-T, measuring the likelihood that a respondent would
attribute failure in mathematics to lack of ability and task difficulty were the only
scores that had a significant effect on the model and so,

58
a = 1.917 + 1.043(F-A) + 0.556(F-T) + e
is a model which might be used to predict mathematics anxiety. The adjusted R-
square value of 0.292 is large enough to be considered meaningful given the
nature of the data at hand.
Finally, in the interventional phase of the study, students in an
experimental group were exposed to an intervention consisting of several
methods known to alleviate or prevent helplessness responses. Here it was
predicted that the mathematics anxiety score, a would decrease significantly
between a pre-intervention survey and a post-intervention survey. This did not
happen. However, the mean value of a of the comparison group increased
significantly between the pre-intervention survey and the post-intervention
survey. This may indicate that the intervention prevented a normal increase of
mathematics anxiety for the experimental group.
The results of this study support a re-examination of the concept of
mathematics anxiety. Recall that a number of weaknesses in the theory of
mathematics anxiety were explored in part 2 of chapter 2. These included the
fact that there are competing definitions of mathematics anxiety and that the
instruments available do not measure precisely what the various models define
mathematics anxiety to be. This study has shown that it is possible to reinterpret
mathematics anxiety using the theories of other affective variables that do not
share these weaknesses. A more cohesive, well-formed and useful model can
be built.

59
How can educators use this information to help students displaying what is
now interpreted as mathematics anxiety? It has been shown in various studies
that learned helplessness effects can be treated and immunized against.
[Abramson, Seligman & Teasdale, 1978; Gentile & Monaco, 1986] This study
has provided evidence that these methods, particularly those proposed by
Gentile and Monaco may provide a mitigating effect on mathematics anxiety.
Further research should be conducted to determine the value of incorporating
these methods on a large scale and to study other methods of treating learned
helplessness and adapting their use in the mathematics classroom.
The most important thing to remember is that helplessness occurs when
negative outcomes such as bad grades become non-contingent on a student’s
efforts. If a student does not understand why he or she is receiving poor marks
helplessness can result.
This has direct consequences in the area of testing. The quality and
nature of the feedback a student receives can affect the development of a
helplessness response. When a student misses a problem, mathematics
instructors must take care to express as clearly as possible the reason the
problem is incorrect and what the student must do in the future to work similar
problems correctly. Errors must be explained so that students maintain some
expectancy of control. It therefore seems reasonable that multiple-choice exams,
on which problems are simply marked right or wrong, should be avoided
altogether. At least the manner in which they are graded should be altered to
provide meaningful feedback to the students.

60
No feedback will be meaningful unless the students have a sufficient
conceptual understanding of the material. Thus mathematics instructors need to
be certain that they teach, not only processes and algorithms, but the reasoning
and rationale behind those procedures as well. To quote Laurie Buxton:
I have often watched a teacher, with sound control, a lively manner,
excellent relationships with the class, and a clear unhesitating
presentation - and wondered what was wrong. I then saw that
there was no discussion of concepts, and yet, something was being
described. It was the behavior of the symbols. The sort of thing
that I have heard is as follows:
Here's our equation:
3x - 6 = 14 - 2x
Take the -6 to the other side and it becomes +6
3x = 20 - 2x
Now bring the -2x over... [Buxton, 1995, p. 205]
Buxton finishes this description and summarizes, "The teacher is talking about
what the symbols are doing, not what the operation is about and the concepts on
which it is based." [Buxton, 1995, p. 206] Without this explanation students will
be unable to discern when it is appropriate to use certain techniques and when it
is not and any resulting feedback will seem arbitrary and random.
Part of this is a curriculum issue that needs to be addressed in elementary
and mathematics education programs. Educators in general need to make
certain that the teachers placed in the classroom are knowledgeable enough and
skilled enough to properly explain the material at hand. They should also be able
to judge when it is appropriate to quote rules and theorems and when it is not
and to discern when a student has given a reasonable response and when he or
she has not.

61
Unfortunately, many teachers in the United States lack these
qualifications. Liping Ma conducted a study that compared the mathematical
understanding of elementary school teachers in the United States and China. In
her study she interviewed twenty-three U. S. teachers who were considered
“better than average” and found some disturbing results. Many had only a
procedural knowledge of the topics they were teaching and made statements that
were mathematically incorrect. For example, twenty-one of these teachers
attempted the computation 1% - >2 but only nine of them completed their
computations and reached the correct answer of 314 Worse, only one of the
twenty-three teachers was capable of creating a conceptually correct
representation of the problem and this representation was pedagogically
unsound because it involved a fractional number of children. A number of the
teachers displayed a strong commitment to “teaching for understanding” but this
was undermined by the their limited knowledge of mathematics. [Ma, 1999]
This is an untenable situation. If teachers lack a sufficient understanding
of mathematics to explain the rationale behind different algorithms to their
students, their feedback will seem random and unconnected to the matter at
hand. If students try hard to do well, yet they are unable to understand their
mistakes and learn how to correct them, their effort will seem non-contingent on
their successes and failures. In this event, helplessness and anxiety can result
and interfere with the students’ efforts to learn mathematics. If, on the other
hand, there were knowledgeable teachers in the classroom leading their students
to a genuine, conceptual understanding of mathematics, these difficulties could

62
be eliminated. Students with a deep understanding of mathematics would be
able to learn from their errors rather than repeating them and would avoid the
frustrations that lead to helplessness in mathematics. Thus it is important that
the teachers placed in the classroom are as knowledgeable as possible.
Mathematics teachers must also understand how students learn if they are
to be effective. Not simply how students process information and conceptualize
ideas, teachers must understand the challenges and obstacles that students face
as they attempt to learn mathematics. This study has begun to do that. With
sufficient effort and study, interpreting mathematics anxiety through learned
helplessness and other models might lead to more useful insights. It could well
allow educators to better understand the point of view of the so-called “math
anxious” student and open other avenues leading to means of alleviating the
problem.

References
Abramson, L, Seligman, M. E. P. & Teasdale, J. (1978) Learned Helplessness in
Humans: Critique and Reformulation. Journal of Abnormal Psychology, 87
(1)49-74.
Beck, A. T., Emery, G. & Greenberg, R. L. (1985). Anxiety Disorders and
Phobias, A Cognitive Perspective. Basic Books
Buxton, L. (1991). Math Panic. Portsmouth, NH: Heinemann
Dor-Shav, N. & Mikulincer, M. (1992). Learned Helplessness, Causal Attribution
and Response to Frustration. Journal of General Psychology, 117 (1),
47-58.
Dweck, C. & Licht, B. (1980). Learned Helplessness and Intellectual
Achievement. In Garber, J, & Seligman, M. E. P. (Ed.), Human
Helplessness Theory and Application (pp. 197-222). New York, NY:
Academic Press
Evans, J. (2000). Adults’ Mathematical Thinking and Emotions, A Study of
Numerate Practices. New York, NY: Routledge-Farmer
Fennema, E., Wolleat, P. & Pedro, P.O. (1979). Mathematics Attribution Scale:
An Instrument Designed to Measure Students ’Attributions of the Causes
of Their Successes and Failures in Mathematics. Corte Madera, CA:
Select Press
Ferguson, R. D. (1986). Abstraction Anxiety: A Factor of Mathematics Anxiety,
Journal for Research in Mathematics Education, 17(2), 145-150
Gentile, J. R. & Monaco, N. M. (1986). Learned Helplessness in Mathematics,
What Educators Should Know, Journal of Mathematical Behavior, 5,
159-178
Hembree, R. (1990). The Nature, Effects, and Relief of Mathematics Anxiety.
Journal for Research in Mathematics Education, 21 (1), 33-46
Hiroto, D. S. & Seligman, M. E. P. (1975). Generality of Learned Helplessness in
Man, Journal of Personality and Social Psychology, 31 (2), 311-327
Kitchens, A. N. (1995). Defeating Math Anxiety. Chicago, IL: Irwin Career
Education Division
63

64
Ma, L. (1999) Knowing and Teaching Elementary Mathematics, Teachers’
Understanding of Fundamental Mathematics in China and the United
States. Mahwah, NJ: Lawrence Erlbaum Associates
Martinez, J. G. R, & Martinez, N. C. (1996). Math Without Fear: A Guide for
Preventing Math Anxiety in Children. Boston, MA: Allyn and Bacon
Mikulincer, M. (1994). Human Learned Helplessness.
New York, NY: Plenum Press
Oaks, A. B. (1989). A Cognitive Root to Math Anxiety. In Keith, S. Z. & Keith, P.
(Ed.), Proceedings of the National Conference on Women in Mathematics
and the Sciences (pp. 197-200). St. Cloud, MN.
Peterson, C., Maier, S. F., & Seligman, M. E. P., (1993). Learned Helplessness -
A Theory for the Age of Personal Control. New York, NY: Oxford
University Press
Reyes, L. H. (1984). Affective Variables and Mathematics Education. The
Elementary School Journal, 84 (5), 558-581.
Rice, J. A. (1995). Mathematical Statistics and Data Analysis. Belmont, CA:
Duxbury Press
Seligman, M.E.P. & Maier, S.F. (1976). Learned Helplessness: Theory and
Evidence. Journal of Experimental Psychology: General, 105 (1), 3-46.
Skemp, R. (1987). The Psychology of Learning Mathematics.
Hillsdale, NJ: Lawrence Erlbaum Associates
Skiba, A. E. (1990). Reviewing an Old Subject: Math Anxiety. Mathematics
Teacher, 87, 188-189.
Spies-Wood, E. (1980). Learned Helplessness and Item Difficulty Ordering.
Psychologia Africana, 19, 29-40.
Tobias, S. (1993). Overcoming Math Anxiety. New York, NY:
WW Norton and Co.
Tobias, S. & Weissbrod, C. (1980). Anxiety and Mathematics, an Update.
Harvard Educational Review, 50 (1), 63-70.
Wilson, T. D. & Linville, P. W. (1982). Improving the Academic Performance of
College Freshmen: Attribution Theory Revisited. Journal of Personality
and Social Psychology, 42 (2), 367-376.

65
Wilson, T. D. & Linviile, P. W. (1985). Improving the Performance of College
Freshmen With Attributional Techniques. Journal of Personality and Social
Psychology, 49 (1), 287-293.
Zaslavsky, C. (1994). Fear of Math, Howto Get Over it and Get On With Your
Life. New Brunswick, NJ: Rutgers University Press.

Appendix A
PHOBOS INVENTORY
[Adapted from Ferguson (1986)]
DIRECTIONS: For each of the following items, indicate how much that item frightens you or causes
you stress nowadays. Use a five point scale ranging from:
1______ 2______ 3 4______ 5
not at all very much
Circle the selected responses on the answer sheet provided.
1. Determining the amount of change you should get back from a purchase involving several
items.
2. Listening to a salesman show you how you would save money buying his higher priced
item because it reduces long term expenses.
3. Listening to a person explain how he or she figured out your share of the expenses on a
trip, including meals, transportation, etc.
4. Reading your W-2 form showing your annual earnings and taxes.
5. Figuring the sales tax on an item that costs more than $1.
6. Hearing some friends make bets on a game as they quote the odds.
7. Juggling class times around to determine the best course schedule.
8. Deciding which courses to take in order to come out with the proper number of credit hours
for graduation.
9. Working on a concrete, everyday application of mathematics that has meaning to you, such
as figuring how much money you can spend on recreation after paying the bills.
10. Figuring the monthly budget.
11. Signing up for a math course.
12. Walking into a math class.
66

67
13. Raising your hand in a math class to ask a question.
14. Thinking about a final examination in a math class.
15. Thinking about an upcoming math examination one day before.
16. Thinking about an upcoming math examination one hour before.
17. Waiting to have a math test returned.
18. Realizing that you have a certain number of math classes to take in order to fulfill the
requirements for graduation.
19. Receiving your final math grade in the mail.
20. Being given a "pop" test in a math class.
21. Having to work a math problem that has x's and y's instead of 2's and 3's.
22. Being told that everyone is familiar with the Pythagorean Theorem.
23. Realizing that an instructor has just written some algebraic formulas on the chalkboard.
24. Being asked to solve the equation x - 5x + 6 = 0.
25. Being asked to discuss a proof of a theorem about triangles.
26. Trying to read a sentence full of symbols such as:
A = {x|x2- 2x = 3, x in R}.
27. Listening to a friend explain something they have just learned in calculus.
28. Opening up a math book and not seeing any numbers, only letters, on the entire page.
29. Reading a description in the Undergraduate Bulletin of the topics to becovered ina math
course.
30. Having someone lend me a calculator to work a problem and not being able to tell which
buttons to push to get the answer.

Appendix B
Mathematics Attribution Scale
Elizabeth Fennema, Patricia Wolleat and Joan Daniels Pedro
University of Wisconsin - Madison
You are going to read about an event which could have happened to you. In addition,
you are going to see four possible causes of that event. You are going to respond to how
you feel about whether the causes listed could really explain the event if it had happened
to you. Each event and its possible causes are listed in a group. In each group an event is
followed by four possible causes. You are to read the event carefully and then respond to
how you feel about each of the causes of the event.
EVENT A: A part of your math homework was wrong.
CAUSES:
1. You just can't seem to remember to do the steps.
2. You were careless about completing it.
3. The part marked wrong included a step which was more difficult.
4. You were unlucky.
Event A says "A part of your math homework was wrong." Numbers 1, 2, 3 and 4 are
possible causes for that event. Look at Number 1. Think about whether this could be a
cause for Event A, "A part of your math homework was wrong." It says, "You just can't
seem to remember to do the steps." Do you STRONGLY AGREE, AGREE, DISAGREE
or STRONGLY DISAGREE that this could be a cause for Event A, or are you
UNDECIDED? Indicate how you feel about Number 1 as a possible cause for the event.
Circle the correct letter; A = STRONGLY AGREE, B = AGREE, C = UNDECIDED,
D - DISAGREE and E = STRONGLY DISAGREE.
Now look at Number 2, "You were careless about completing it." Do you STRONGLY
AGREE, AGREE, DISAGREE or STRONGLY DISAGREE that this could be a cause
for Event A, or are you UNDECIDED? Indicate how you feel about Number 2 as a
possible cause for the event. Circle the correct letter on your answer sheet. Now mark
how you feel about Numbers 3 and 4 as possible causes of Event A. Then go to each of
the remaining events and mark on your answer sheet how you feel about each possible
cause for that event.
68

69
EVENT B: You got the grade you wanted for the semester in Algebra.
5. The content of the class was easy.
6. You spent a lot of time each day studying Algebra.
7. The teacher is good at explaining Algebra.
8. You have a special talent for math.
EVENT C: You had trouble with some of the problems in the daily assignment.
9. There was no time to get math help because of a schedule change for the day.
10. You don't thinkin the logical way that math requires.
11. You didn't take the time to look at the book.
12. They were difficult word problems.
EVENT D: You have not been able to keep up with most of the class in Algebra.
13. Students sitting around you did not pay attention.
14. You haven't spent much time working on it.
15. The material is difficult.
16. You have always had a difficult time in math classes.
EVENT E: You have been able to complete your last few assignments easily.
17. The Problems were more interesting.
18. The effort you put into homework at the beginning helped.
19. You're a very able math student.
20. You lucked into working with a helpful group.
EVENT F: You were able to understand a difficult unit of Algebra.
21. The way your teacher presented the unit helped.
22. Your ability is more obvious when you are challenged.
23. You put hours of extra study time into it.
24. The problems were easy because they had been covered before.
EVENT G: You received a low grade on a chapter test.
25. You're not the best student in math.
26. You studied, but not hard enough.
27. There were questions you'd never seen before.
28. The teacher had spent too little class time on the chapter.

70
EVENT H: You have passed most tests with no trouble.
29. The teacher made learning math interesting.
30. Like everyone says, you’re good at math.
31. But, you spent hours of extra time on this class.
32. The units were the beginning group, the easy ones.
EVENT I: There were times when you were not able to solve equations.
33. It was a task that did not interest you.
34. Despite studying, you didn’t understand it well enough.
35. Your friends’ lack of attention in class was part of the problem.
36. But then you didn’t spend time doing homework.

Appendix C
.UNIVERSITYQFMIAMI
HUMANRESEARCH PROTOCOL FORM
BEHAVlQRALSCiEMCESSUBCOMMITTEE
1. Title of Project
Mathematics Anxiety and Learned Helplessness
2. Principal Investigator and Collaborators:
Principal Investigators:
Dr. G. Cuevas, Professor
Dept, of Teaching and Learning
305.284.5192
Dr. M. Mielke, Professor
Dept, of Mathematics
305.284.2575
Dr. R. Kelley, Professor
305.284.2575
Collaborators:
Joseph Franke Kolacinski, Lecturer
Department of Mathematics
305.284.2308
3. Performance Site:
University of Miami, Main Campus
4. Proposed Start Date:
August 2002
5. Funding Agency:
not applicable
71

72
6. Project Objectives
The purpose of this study is to establish if a significant relationship exists
between Mathematics Anxiety and Learned Helplessness. This will be done in
two parts. One group of students will be recruited for a simple correlational
study. A smaller group will be exposed to interventions known to lessen
helplessness responses. These students will then be surveyed to discover if
there is a corresponding drop in mathematics anxiety.
7. Recruitment Procedure:
(x) Other (specify):
A variety of classes will be selected at the University of Miami, ranging in
difficulty from MTH 099 (Intermediate Algebra) to MTH 111 (Calculus I).
Students in these classes will be surveyed. In addition, two sections of
two courses, MTH 103 and MTH 107 taught by J. Kolacinski will
participate in the longitudinal portion of the study. One section of each
course will serve as an experimental group while the other will be a control
group.
8. Methods and Procedures:
The purpose of this study is to investigate the relationship between mathematics
anxiety and learned helplessness.
Learned helplessness is a response to uncontrollable adverse events. Simply
put, if a subject believes that he or she is unable to affect the environment, he or
she will passively endure adverse events, making no attempt to change or
improve the outcome. Helplessness responses lead to a number of cognitive
and motivational deficits.
It has been shown that there is a relationship between a person's attributional
style and his or her susceptibility to learned helplessness. There are three
dimensions to causal attribution: locus, stability and globality. The locus
dimension determines if the person will attribute failure to internal or external
causes. Stability is concerned with whether the causes will remain steady over
time, and globality with whether the causes will remain the same over many
situations. Specifically, if someone attributes failure to an internal and stable
cause, such as a lack of ability, that person expects failure to recur and
helplessness results. If the perceived cause is internal and unstable, such as a
lack of effort, the subject tends to have an optimistic attitude leading to
reactance, an increase in performance on subsequent tasks.

73
Typical attributions, Locus of Control and susceptibility to Learned Helplessness:
Internal
Locus
External
There will be two phases to this study, a correlational phase and a longitudinal
phase.
In the first phase of this study, we attempt to determine if there is a correlation
between mathematics anxiety and learned helplessness. As stated previously, it
has been shown that there exists a relationship between a person's attributional
style and their susceptibility to learned helplessness. We will therefore test
approximately 200 students enrolled in freshman and developmental level
mathematics classes with both the Phobos Inventory, which measures levels of
mathematics anxiety, and the Mathematics Attribution Scale, which measures
students’ attributions regarding success and failure in mathematics. The
outcome of this phase of the study will be a stratification of the sample into the
four attributional styles that indicate a person's propensity for learned
helplessness from low (A1) to high (A4). It is expected that the mean anxiety
score will increase significantly as the index increases.
Students will be given these surveys in class, but the instructor of any given
class will not survey the students and the instructor will not be present in the
classroom when the students are surveyed.
The second phase of this study will attempt to show that the methods known to
alleviate learned helplessness will also alleviate mathematics anxiety.
To this end, two or more sections of a college mathematics course such as MTH
101, MTH 103 or MTH 107 will be chosen. The students in these sections will be
tested at the beginning of the semester using the Phobos Inventory of
“Lack of Effort” “Lack of Ability”
(A1) (A4)
High Reactance High Helplessness
“Bad Luck” “Task Difficulty”
(A2) (A3)
Low Reactance Low Helplessness
Unstable Stable
Stability

Mathematics Anxiety and the Mathematics Attribution Scale. As was the case
with the students in the correlational phase of the study, students will be given
these surveys in class, but the instructor of any given class will not survey the
students and the instructor will not be present in the classroom when the
students are surveyed. The section or sections that make up the experimental
group will be exposed to information and activities aimed at preventing or
lessening helplessness responses throughout the semester.
The intervention is based upon two facts: exposure to adverse events that are
perceived as uncontrollable often leads to a helplessness response; and a
helplessness response is most severe when a person attributes failure to internal
and stable causes. We will attempt to both prevent and alleviate helplessness
responses.
Attributional retraining is the primary method for alleviating a helplessness
response; thus, the experimental group will be encouraged throughout the
semester to adopt attributions involving effort and strategy, and to attribute
failure to unstable causes rather than stable ones. Methods of accomplishing
this will include:
1) a presentation from a former student emphasizing the importance of
effort to success in mathematics.
2) a showing of the Nova episode “The Proof which chronicles Dr.
Andrew Wiles 7-year effort to prove Fermat’s Last Theorem.
3) an extra credit assignment in which the students review the film Stand
and Deliver. In the film a high school math teacher inspires
underachieving students to work hard and tap potential they never knew
they had.
4) After the first test, the students will be informed that grades usually
improve on the second test, encouraging them to attribute any failures to
unstable causes.
Methods for preventing a helplessness response will also be employed. To
prevent a helplessness response, we attempt to lessen the impact of adverse
events and give the student some expectancy of control. This part of the
intervention will include:
1) Extra credit assignments in which the students in the experimental
group correct and explain any errors they made on their exams. This
activity should make a helplessness response less likely by lessening the
dichotomy of success verses failure with respect to the exams.
2) An attempt will be made to provide the students in the experimental

75
group with success experiences, giving them a greater expectancy of
control. When a new topic is covered in class the initial examples will be
simple and straightforward, and will only later move to more challenging
problems.
3) On exams the test items will be ordered from easiest to most difficult.
This should either prevent a helplessness response during the course of
the exam, or at least postpone it until late in the test.
Much of the intervention with the experimental group will take the form of extra
credit assignments, but these assignments are all variations of standard
assignments that have been used in University of Miami Mathematics classes.
Students have traditionally been eager to participate in these assignments. It will
be made clear to the students that the data is being collected anonymously and
that any choice they make about filling out the survey will have no effect on their
ability to participate in the extra credit assignments. Students in the control
group will have the opportunity to earn the same number of extra credit points as
those in the experimental group through similar assignments that do not
encourage particular attributions.
At the end of the semester the students will again be tested with the Phobos
Inventory and the Mathematics Attribution Scale. Methods for verifying changes
in paired data will be applied to determine if there is a significant difference
between the pre-experiment and post-experiment Mathematics Anxiety scores.
To accomplish this, each participant’s pre and post intervention scores must be
linked so that they can be compared. To maintain anonymity each student will
be identified by a randomly generated five-digit number. Two copies of this
number will be sealed in separate envelopes and, prior to the initial survey, both
envelopes in each pair will be marked with a particular student’s name. One
envelope will be given to the student during each survey and the student will be
asked to place the number on the survey’s cover sheet. No records will be kept
identifying which 5-digit number is sealed in which pair of envelopes and no
attempt will be made to match a particular student to a particular 5-digit number
or to a particular set of responses.
9. Participants - check all that apply
(x) University of Miami Students
10. Federal Regulations have established guidelines for the inclusion of
women,
minorities, and children in research involving human subjects, whether or
not it is supported by NIH.

76
Please check those you are including: (x) Women (x) Minorities
(x) Participants under the age of
21
11. Number of Participants to be recruited: 150 - 250
Age of participants: 18 and over (depends on classes selected)
Sex of participants: both (proportions depend on classes selected)
12. Records:
Participants’ records regarding this protocol will be maintained
(x) other (specify):
In the files of Joseph Kolacinski
13. Confidentiality:
Describe the provisions which have been made for preservation of
anonymity or confidentiality in the transmittal of data:
(x) Other (specify):
For the correlational part of this study, data will be anonymous; no
identifying information will be collected. In the longitudinal part of the
study, there is a need to link pre-experiment scores and post-experiment
scores, but data will still be collected anonymously. Each participant will
be given a randomly generated five-digit number in a sealed envelope.
Each participant will copy this number onto his or her survey. No record
of these numbers will exist and there will be no attempt to link a particular
set of answers to a particular participant. In addition, no instructor will
survey his or her own students and a class’s instructor will not be present
when surveys are conducted.
14. Deceptive Techniques:
(x) Not applicable.
In order to avoid any possible deception, slightly different versions of the
informed consent memo will be given to the control group and the
experimental group. This will avoid potential disruptions to the learning
process, such as students from the different groups comparing extra
credit assignments and attempting to determine how the different
assignments relate to the study.

77
After the second questionnaire is given, the students will be debriefed and
told explicitly how the activities of the two groups differed, and how the
activities of the experimental group might have an effect on mathematics
anxiety.
15. Investigator’s Evaluation of Potential Physical, Psychological, or Social
Risk to
Subjects:
None.
16. Informed Consent: (attach to this form)
(x) to be sent out as a non-returned cover memo.
Please also refer to item 14.
17. Study Results:
Describe the procedure that will be used to inform the subjects of the
results of the study.
Subjects will be able to get information about the results of the study by
contacting Joseph Kolacinski after the study’s completion.
18. Medical facet (check one):
(x) This research does not have any medical facet.
19. Assurances
I affirm that no change will be made in the methods of procedure or the
informed consent statement of this study without prior approval of the
reviewing committee.
I affirm that the Principal Investigator will prepare a summary of the project
annually, including all information specified by the Guidelines for
Behavioral Research Involving Subjects at the University of Miami.
I affirm that I have received a copy of the University of Miami’s guidelines
for Behavioral Research involving Human Subjects, and agree to follow
and abide by them.

78
I received a copy of the Multiple Project Assurance of Compliance with
DHHS Regulations for Protection of Human Research Subjects.
The Undersigned are fulltime faculty members who assume responsibility
for this study.
Principal Investigator ______________________ _____
Dr. Gilbert Cuevas (Signature) (Date)
Dept, of Teaching and Learning
Dr. Marvin Mielke (Signature) (Date)
Dr. Robert Kelley (Signature) (Date)
Department Chair ______________________ _____
Dr. Alan Zame (Signature) (Date)

Appendix D
Informed Consent Memos
The following materials were handed out to the students participating in
this study.
The first version of the informed consent memo was given to the students
who were involved only in the correlational part of the study. No identifying
information was needed on these questionnaires.
The remaining two versions were provided to the students who are
participating in the interventional part of the study. Each of these students was
identified using a random number as described in the second and third versions
of the informed consent memo. The second version of the memo was given to
the comparison group; the third was given to the experimental group.
79

80
Informed Consent
[Version 1 - used only in the correlational part of the study]
Purpose
You are being asked to participate in a study concerning college students’
attitudes about mathematics. This study is part of a doctoral thesis and is being
conducted to investigate one possible cause of Mathematics Anxiety.
Procedures
As a participant in this study, you will be requested to answer the questions on
the enclosed questionnaire honestly and carefully. It should take approximately
20 minutes to complete the questionnaire.
Risks
There are no anticipated risks to you if you participate in this study.
Benefits
No benefit can be promised to you from your participation in this study.
Compensation
You will not be compensated for your participation in this study.
Alternatives
You may refuse to participate in this study. Nothing bad will happen to you if
you refuse to participate in this study.
Eligibility
Students under the age of 18 may not participate in this study.
Confidentiality
To protect your right to privacy as a volunteer participant in this study, all
information is being collected anonymously. There will be no attempt to link a
particular set of answers to a particular student.
Right to Withdraw
Your participation is voluntary; you have the right to withdraw or to skip any
questions if you want to.

81
Further Information
If you wish to find out the results of this study, you may contact Joseph
Kolacinski at (305) 284-2308 or <jfk@math.miami.edu> in the Department of
Mathematics. The study should be completed by January, 2003.
Questions regarding this study or your participation should be directed to Joseph
Kolacinski or Dr. G. Cuevas at (305) 284-3141. If you have questions about your
rights as a research participant, you may call Maria Arnold, Institutional Review
Board Director at (305) 243-2079. You may keep this copy of this cover letter
for your records.
Thank you for your assistance.

82
Informed Consent
[Version 2 - given to the comparison group]
Purpose
Procedures
As a participant in this study, you will be asked to fill out a questionnaire, both
now and toward the end of the semester. Please fill out the questionnaire
honestly and carefully. It should take approximately 20 minutes to complete the
questionnaire.
Risks
Benefits
Compensation
Alternatives
You may refuse to participate in this study and you may end your participation at
any time. Nothing bad will happen to you if you refuse to participate or if you
stop participating in this study.
Eligibility
Students under the age of 18 may not participate in this study.
Confidentiality
The information gathered in this study is being collected anonymously. To
protect your right to privacy as a volunteer participant in this study, the following
precautions have been taken:
• Since the results of your survey need to be compared to the results from
the end of the semester, you will be identified by a randomly generated
five-digit number.
• Two slips of paper containing this number will be sealed in envelopes.
You will be given one of these envelopes each time you complete the
questionnaire. You will write this number on the cover sheet of your
questionnaire and then discard the envelope and the slip of paper
containing the number when you are done.

83
• No record of these numbers will exist.
• There will be no attempt to link a particular set of answers to a particular
student.
• Your instructor will not be present when the surveys are conducted and
will not know which students participated in the survey nor which students
completed which questionnaire.
Right to Withdraw
Your participation is voluntary; you have the right to withdraw or to skip any
Further Information
for your records.

84
Informed Consent
[Version 3 - given to the experimental group]
Purpose
Procedures
As a participant in this study you will be asked to:
• Fill out a questionnaire, both now and toward the end of the semester both
honestly and carefully. It should take approximately 20 minutes to
complete the questionnaire.
• Participate in certain extra credit assignments.
• Listen to information presented throughout the semester.
Risks
Benefits
Compensation
Alternatives
You may refuse to participate in this study and you may end your participation at
any time. Nothing bad will happen to you if you refuse to participate or if you
stop participating in this study. In particular, you will be able to participate in any
extra credit assignment whether or not you decide to participate in the survey.
Eligibility
Students under the age of 18 may not participate in this study. Students under
the age of 18 will have the same opportunities for extra credit as every other
student.

85
Confidentiality
The information gathered in this study is being collected anonymously. To
protect your right to privacy as a volunteer participant in this study, the following
precautions have been taken:
• Since the results of your survey need to be compared to the results from
the end of the semester, you will be identified by a randomly generated
five-digit number.
• Two slips of paper containing this number will be sealed in envelopes.
You will be given one of these envelopes each time you complete the
questionnaire. You will write this number on the cover sheet of your
questionnaire and then discard the envelope and the slip of paper
containing the number when you are done.
• No record of these numbers will exist.
• There will be no attempt to link a particular set of answers to a particular
student.
• Your instructor will not be present when the surveys are conducted and
will not know which students participated in the survey nor which students
completed which questionnaire.
Right to Withdraw
Your participation is voluntary: you have the right to withdraw or to skip any
Further Information
for your records.

Vita
Joseph Franke Kolacinski, the son of William Victor Kolacinski, a police
officer and Mary Franke Kolacinski, an artist, was bom in Brooklyn, New York on
24 January 1964. He is named for his maternal grandfather who was one of the
great pen and ink illustrators of the 1920’s and 30’s.
Joseph grew up, mostly, in Lake Worth, Florida where he had many
strange and fascinating adventures. He graduated from Lake Worth High School
and did his undergraduate work at Palm Beach Junior College and Florida
Atlantic University. He began studying at F. A. U. with the goal of teaching high
school mathematics, but his first education class at that institution inspired him to
continue on to do graduate work. In mathematics. He eventually earned a
Doctor of Arts degree in Mathematics from the University of Miami in August,
2003.
Joseph currently resides, along with his two cats, in Miami, Florida where
he teaches Mathematics to college students and hopes to have many more
strange and fascinating adventures.
Permanent Address: Post Office Box 24-8805
Coral Gables, FL 33124
jfk@math.miami.edu

Math anxiety and learn helpless

More Related Content

Viewers also liked (6)

Similar to Math anxiety and learn helpless (19)

Recently uploaded (20)

Math anxiety and learn helpless