MATH CONFIDENCE WORKSHOPS:
A MULTIMODAL GROUP INTERVENTION
STRATEGY IN MATHEMATICS ANXIETY/AVOIDANCE
BY
BARBARA STEVENSON PROBERT
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR. OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1983
Copyright 1983
by
Barbara S. Probert
A person who doubts himself is like a man who
would enlist in the ranks of his enemies and
bear arms against himself. He makes his fail
ure certain by himself being the first person
to be convinced of it.
Alexander Dumas
So long as a subject seems dull, you can be
sure that you are approaching it from the
wrong angle.
W. W. Sawyer
People are anxious because they accepted an
ideology that we must reject; that if we
haven't learned something so far it is prob
ably because we can't.
Sheila Tobias
I hope that any reader who has unhappy memories
of past attempts at learning mathematics will
be willing to accept, as a working hypothesis,
that the causes were other than his own lack of
intelligence.
Richard R. Skemp
ACKNOWLEDGMENTS
I would like to thank my chairman, Dr. Paul Schauble,
who has guided, supported, and inspired me throughout my
graduate school career. He embodies all the finest and
best qualities of a counseling psychologist and human being.
I would also like to thank my other committee members,
Dr. Rosie Bingham, Dr. Greg Neimeyer, Dr. Charles Nelson,
Dr. Max Parker, and Dr. Robert Ziller, who have given so
generously of their time, knowledge, and professional guid
ance. Their warm encouragement and high standards have
been invaluable.
Special thanks go to Dr. Jaquelyn Resnick, whose in
terest and professional expertise have meant so much to me,
and to Dr. James Archer, Director of the Counseling Center,
for his encouragement and recognition and for his support
of the Math Anxiety Clinic.
It would have been difficult to complete this project
without the support of the counselors and staff of the
Counseling Center. Helen Beckham and Jo Adams especially
offered encouragement and assistance in innumerable
thoughtful ways.
Appreciation is also expressed to John Dixon for his
valuable statistical consultation and to Barbara Smerage
for her professionalism and good spirit which went into the
typing of this manuscript.
I would especially like to acknowledge the members of
the Math Confidence Groups whose courage in facing their
anxieties was an inspiration to me, and especially to Mary
Smith and Martin McKellar who so generously gave of their
time to tell others of their success in overcoming math
anxiety.
Finally, I want to express my thanks and appreciation
to my family, to Walt, my husband, without whose loving
presence, constant encouragement, inspiration, and patient
understanding none of this would have been possible, to
Richard and Jim, our sons, and to my mother, Mrs. John L.
Stevenson, who has always believed in me.
TABLE OF CONTENTS
PAGE
ACKNOWLEDGMENTS. . . . . . . . . . iv
LIST OF TABLES . . . . . . . . . viii
ABSTRACT . . . . . . . . . . . x
CHAPTER
ONE INTRODUCTION . . . . . . . 1
Possible Causes for the Mathematics
and Science Crisis . . . . 7
Suggestions for Change . . . . 9
Purpose of the Study . . . . 13
Specific Objectives. . . . .. 15
TWO REVIEW OF THE LITERATURE . . . . 18
The Nature of Math Anxiety from the
Mathematics Educator's Perspective 19
Women and Mathematics. . . . ... 26
Math Anxiety and Test Anxiety. .. . 30
The Treatment of Math Anxiety. .. . 37
THREE METHOD . . . . . . . . . 47
Subjects . . . . . . .. .47
Instruments. . . . . . .. 50
Treatment. . . . . . . .. 54
FOUR RESULTS. . . . . . . . .. 59
FennemaSherman Mathematics Attitudes
Scales . . . . .. . . 59
Spielberger Trait and Test Anxiety
Inventories . . . . . .. 63
SelfReport Math Ability Ratings . 74
Analysis of Variance by Sex, Group
and Time . . . . . . . 76
Followup Questionnaire. . . ... 78
FIVE DISCUSSION . . . . . . . . 89
Summary and Interpretation of Results. 89
Implications of the Results. . ... 100
Future Directions for Research . . 101
APPENDICES
A FENNEMASHERMAN MATHEMATICS ATTITUDES
SCALES . . . . . . . . 105
B SPIELBERGER TEST AND TRAIT ANXIETY
INVENTORIES. . . . . . . .. 112
C MATHEMATICS BACKGROUND FORM. . . ... 116
D CONTROL GROUP GENERAL INFORMATION FORM . 122
E MATH CONFIDENCE WORKSHOP OUTLINES. .. . 124
F FOLLOWUP QUESTIONNAIRE. . . . ... 138
G INFORMED CONSENT FORMS . . . . . 142
H DUNCAN'S MULTIPLE RANGE TESTS FOR
TREATMENT AND CONTROL GROUPS . . . 146
I ANALYSES OF VARIANCE BY SEX, GROUP AND
TIME . . . . . . . . . 157
REFERENCE NOTES. . . . . . . . . .. 168
REFERENCES . . . . . . . . . . 169
BIOGRAPHICAL SKETCH. . . . . . . . .. 178
vii
LIST OF TABLES
TABLE PAGE
1 Math Confidence Treatment Group Subjects. 49
2 Control Group Subjects. . . . . .. 51
3 Comparison Between Pretreatment and Post
treatment Math Anxiety Scores, by Group . 60
4 Comparison Between Pretreatment and Post
treatment Confidence Scores, by Group . 61
5 Comparison Between Pretreatment and Post
treatment Math as a Male Domain Scores
by Group . . . . . . . . 62
6 Comparison Between Pretreatment and Post
treatment Usefulness Scores, by Group . 64
7 Comparison Between Pretreatment and Post
treatment Effectance Motivation Scores,
by Group . . . . . . . . 65
8 Comparison Between Pretreatment and Post
treatment Perception of Attitudes of
Teachers Scores, by Group . . . . 66
9 Comparison Between Pretreatment and Post
treatment ATrait Anxiety Scores, by
Group . . . . . . . . . 67
10 Comparison Between Pretreatment and Post
treatment Test Anxiety Scores, by Group . 69
11 Comparison Between Pretreatment and Post
treatment Test Anxiety Scores, Worry
Component, by Group . . . . . . 70
12 Comparison Between Pretreatment and Post
treatment Test Anxiety Scores, Emo
tionality Component, by Group . . . 71
13 Correlations Among Math Anxiety, Trait
Anxiety, and Test Anxiety in Treatment
Subjects . . . . . . . . 72
viii
Correlations Among Math Anxiety, Trait
Anxiety, and Test Anxiety in Control
Subjects . . . . . . . . .
Comparison Between Pretreatment and Post
treatment SelfReport Math Ability
Ratings, by Group . . . . . . .
Subjects' Perception of Extent to Which
Educational, Career, or Other Life
Decisions Were Positively Influenced by
the Math Group . . . . . . .
Subjects' Perception of Extent to Which
Life Decisions Had Been/Will Be Negatively
Influenced by Math Anxiety/Avoidance
After Math Group . . . . . ..
Subjects' Perception of Extent to Which
Math Anxiety Clinic and the Math Groups
Should Be Continued at the University . .
Subjects' Perception of Extent to Which
Math Group Was Important Compared to
Other Activities at the University
(Classes, Workshops, Other Academic
Activities) . . . . . . . .
Subjects' Perception of the Extent to
Which the Math Group Improved Their
Academic Performance. . . . . ..
Subjects' Perception of Their Level of
Math Anxiety. . . . . . . .
Subjects' Perception of Their Level of
Ability to Learn and Use Math . . .
Subjects' Perception of Their Level of
Test Anxiety. . . . . . . .
Subjects' Perception of Extent to Which
Positive Change Was Made in Specific
Behavioral Dimensions Addressed in Math
Group . . . . . . . . .
. 83
. 84
. 86
87
Abstract of Dissertation Presented to the Graduate
Council of the University of Florida in Partial
Fulfillment of the Requirements for the Degree of
Doctor of Philosophy
MATH CONFIDENCE WORKSHOPS:
A MULTIMODAL GROUP INTERVENTION
STRATEGY IN MATHEMATICS ANXIETY/AVOIDANCE
By
Barbara Stevenson Probert
April 1983
Chairman: Paul G. Schauble
Major Department: Psychology
Math anxiety has been shown to be a widespread phenome
non which seriously interferes with learning and severely
limits academic and career choices. This study investigated
the efficacy of a multimodal group intervention strategy
which was planned to address math anxiety as a complex,
multidimensional construct of interacting components. The
design included strategies to effect cognitive and behav
ioral change as well as to reduce the emotional aspects of
anxiety.
Six sevenweek Math Confidence Groups (N = 50) were
conducted. The experimental design was a repeatedmeasures
paradigm involving pre and posttreatment assessment on
selfreport Mathematics Attitudes Scales and Anxiety Inven
tories. All six groups showed statistically significant
posttest improvement on the Confidence in Learning
Mathematics Scale, the Worry Component of the Test Anxiety
Scale, and on their selfperception of mathematics ability.
Five groups showed significant improvement on the Math
Anxiety Scale, active enjoyment of mathematics, Test Anxiety,
and Emotionality Component of Test Anxiety.
An analysis of variance by sex, group and time found
males with significantly less math anxiety, greater confi
dence and more positive perceptions of teachers' attitudes
toward them as learners of mathematics. Treatment males
were significantly higher on the Usefulness Scale than treat
ment females at posttest. No other significant malefemale
differences were found. Control subjects at posttest were
found to be significantly different from treatment subjects
on all scales. At posttest no significant differences were
found between treatment and control subjects on any of the
designated scales.
The followup study which had an 84 percent return rate,
found that positive improvement was longlasting in such
areas as math performance, ability to learn and use mathe
matics, and in other behavioral dimensions, as well as in
the reduction of math anxiety and test anxiety. There was
also felt to be a greaterthanaverage extent to which per
formance in other courses and everyday life had been im
proved. Perhaps more importantly, there appeared to be a
longlasting positive selfconcept change in their perception
of themselves as learners of mathematics. These results
should be generalizable to a wide range of college students
with GPAs over 2.00.
CHAPTER ONE
INTRODUCTION
Mathematics has become increasingly important in almost
every aspect of our burgeoning technological society. Ex
pertise in mathematics, statistics, computer science, and
other mathematically related fields is today an essential
part not only of the space industry and the natural sciences,
but also the social sciences, business administration, edu
cation, the humanities, and everyday life. Fields that were
relatively free of mathematics ten years ago now require
skills in computers and systems analysis (Tobias & Knight,
1978). Experts predict that in the next twenty years as
many as 75 percent of the work force will need computer
skills (Turkington, 1982). Mathematical literacy is pres
ently required for understanding computer printouts, cost
benefit analyses, energy problems, inflation, unemployment,
the arms race, operating a business, reading the Wall Street
Journal, making investment decisions, comparison shopping
at the supermarket, and paying income taxes.
In 1267 English scientist Roger Bacon wrote, "Mathe
matics is the gate and key of the sciences." In 1972
University of California sociologist Lucy Sells in her much
cited study (1973), called mathematics a "critical filter"
not only for the sciences but for the majority of educational,
vocational, and professional goals. In addition, her study
illustrated the extent to which women are disproportion
ately affected by a lack of mathematical skills. Sells
surveyed the freshman class at Berkeley and found that
while 57 percent of the entering male students had four or
more years of high school mathematics, only 8 percent of
the females had a similar background. As a result of their
inadequate mathematics preparation or "math avoidance,"
92 percent of the women and 43 percent of the men were
ineligible for the calculus sequence and consequently for
threequarters of the available college majors.
As demands for high level mathematical backgrounds
increase, it would seem that more and more students would
be getting better and better prepared. The evidence, un
fortunately, does not indicate this to be the case. Accord
ing to Florida's Governor Graham (Cunningham, 1981) high
school students in the United States are being so poorly
trained in mathematics and the sciences that the country
faces a "national crisis" that some day may threaten the
very security of the American government. The demands of
Florida's new technology industries for highly trained,
skilled engineers, technicians, and machinists are not being
met. Graham believes that the main reason for the math
science crisis is the extreme shortage of qualified high
school mathematics, calculus, chemistry, and physics teach
ers. Even worse, less than half of Florida's 67 school
districts have teachers who are capable of teaching calculus.
Nationwide the picture is equally bleak. Cordes (1982)
presents the following statistics. In the 198182 school
year 50 percent of the U.S. high school math and science
teachers lacked proper training and taught with emergency
certificates. Math scores on the Scholastic Aptitude Tests
(SAT) since 1962, and three national assessments of science
achievement since 1969, reveal a steady decline. Elementary
students spend an average of one hour on science and less
than four hours on arithmetic out of the twentyfive instruc
tional hours in a school week. The muchheralded 1982 in
crease in average SAT scores which broke the 19year decline
proved to be a miniscule onepoint rise in mathematics.
The increase, furthermore, was due to better performance
by blacks and other minorities ("Blacks Do Better," 1982).
White scores remained unchanged.
The chairman of the National Science Board, Dr. Lewis M.
Branscomb, told the Senate Labor and Human Resources Com
mittee ("Panel Told High School Math Lacking," 1982) that only
onethird of the nation's students take mathematics beyond
the tenth grade, only 6 percent take four years of math,
and onethird of the high schools do not even offer suffi
cient math courses to qualify graduates to enter engineering
college. Shortages of mathematics teachers at the sec
ondary level are reported by over 90 percent of the states,
and approximately onethird of this country's science classes
are being taught by teachers who were not college science
majors. Math and science requirements are also low. Less
than 50 percent of our public high schools require more
than one year of math and science for graduation (Keisling,
1982). Today's students are not being equipped for the
computerized, technologically demanding society which
awaits them. John Ernest (1978), mathematics professor and
author of the Ford Foundation Study provocatively titled
"Mathematics and Sex," summed up the situation by stating
that "large numbers of students are graduating from high
school as mathematical illiterates" (p. 62).
While students in the United States appear to be fall
ing behind in mathematics and science achievement, students
in Japan, on the other hand, consistently receive some of
the top scores in international studies of both mathematics
and science (Comber & Keevers,1973; Glaser, 1976). One
crossnational study (Stigler, Lee, Lucker, & Stevenson,
1982) found children from Japan and Taiwan consistently
performing at a higher level than their American counter
parts as early as the first and fifth grades. The result
of the superior Japanese mathematical education is that more
than half their leadership in the private and public sectors
have had a science or engineering education (Tobias, 1981).
The majority of the elected officials in the United States,
in marked contrast, make, support, and carry out our
national policy with a relatively inadequate education in
mathematics and science.
All high school students in Japan, the Soviet Union,
and Germany take four years of mathematics. According to a
recent National Science Foundation study (Haines, 1982),
countries such as West Germany and Japan have a total work
force which, because of increased educational standards, has
at all levels a relatively high degree of skills in math and
science. The consequences have been a very rapid expansion
of technical industries which have not only matched but
surpassed our technology in some areas such as in computer
science.
Educators, scientists, the federal government, and
other policy makers are becoming increasingly alarmed by
the decline in both the quality and quantity of math and
science skills in the United States and the simultaneous
advances in such skills in Japan, West Germany, Russia,
and other countries. Many in the scientific community
believe the crisis may pose "as serious a threat to the
country's economic and military preeminence as did the
Soviet's launching of Sputnik 25 years ago" (Cordes, 1982,
p. 3).
It appears that there is agreement on the following
conclusions: There is a growing national problem of dimin
ishing math and science skills. Japan, Russia, and Germany
are surpassing this country in math and science education.
In time, if not corrected, this difference could make an
impact on our industrial productivity, perhaps even in our
national defense. Such a deficit of math and science skills
will certainly affect the quality of preparation given to
the nation's young people for living in a highly technologi
cal world.
Agreement is lacking, however, as to the causes, the
solutions, or even who should provide the leadership in
solving this complex problem. Funding poses an even larger
obstacle. The National Science Board, which sets policy for
the National Science Foundation, has named a commission to
diagnose and prescribe a cure for the growing national math
and science illiteracy (Cordes, 1982). There have been only
two other such special panels in the history of the board.
In order to upgrade math, science, and technology in the
schools, the Reagan Administration is considering the forma
tion of a "Cabinetlevel task force on the educational skills
needed for national economic growth and national security
purposes" (Cordes, 1982, p. 3). Administration officials
have been careful, however, to suggest that the federal gov
ernment should not be expected to supply the funding, en
force mandatory national policies or be the ultimate solu
tion to this problem. Nor is it realistic to expect business
interests to be of any significant aid.
As the controversy continues at the national level,
other work is being done and other measures being taken
nationwide to give insights into the causes for the problem
and suggestions for change. The mathscience crisis is
extremely complex. Assessments must be made and solutions
proposed at several levels.
Possible Causes for the Mathematics and
Science Crisis
One explanation for American children's comparatively
inferior mathematics performance may be that they receive
considerably less instruction in mathematics (Stigler
et al., 1982). In Taiwan and Japan children are in school
for five and onehalf days each week, attend school for
more weeks of the year, and spend a larger percentage of
the time in school studying mathematics, 2325 percent in
Japan as opposed to 1417 percent in the United States.
In addition to fewer numbers of hours taught, of im
portance also is the quality of those hours, how mathematics
is taught, and with what enthusiasm and expertise. Research
has shown that a negative attitude towards mathematics can
be the result of a negative experience with just one teacher
(Ernest, 1976; Poffenberger & Norton, 1956; Sells, 1973).
Many teachers, unfortunately, have been shown to have nega
tive attitudes toward mathematics (Aiken 1970; Ernest,
1976). Gray (1977) suggested that education majors,
especially in elementary education, were often those "who
have shut themselves off from many careers by their at
titude toward mathematics, the very attitude that should
not be passed on to their students (female or male)" (p.
375). These findings are particularly distressing in view
of the conclusions by Banks (1964) and Aiken (1970) that
of all the factors affecting student attitudes toward
mathematics, teacher attitudes were "by far the most signi
ficant contributing factor" (Banks, p. 17).
Posamentier and Stepelman's (1982) study of the increas
ing shortage of qualified mathematics teachers makes the
future look even more somber. They found that lucrative
fields such as computer programming were now attracting the
talented college students who formerly might have considered
teaching mathematics. The expanding career choices of women,
the declining attraction of teaching as a profession, and
private industry's increased competition appear to be the
major causes for the impending crisis in mathematics educa
tion (Paul, 1981).
Mathematician Peter Hilton (1980) suggested that the
principal causes of math incompetence and math avoidance
were "bad teaching, bad texts, and bad educational instru
ments" (p. 176). Others (Gough, 1954; Sawyer, 1943; Skemp,
1971) agreed that a fear of mathematics can be an under
standable result of bad teaching, poorly written textbooks,
mistaken beliefs and expectations, and a lack of understand
ing of the learning process.
Some mistaken beliefs are that mathematics and science
are elitist subjects understood by people, usually men, who
have a rare gift and who may be odd or different from other
people. A mystique then forms around math and science
courses. They are too difficult for most people to under
stand. Their perceived usefulness is low. A "minimalcy men
tality" (Sells, 1978b) arises. Just take the required courses
and try to get by with memorizing. Humanities and the
sciences become artificially split into two distinct groups.
In The Two Cultures and the Scientific Revolution C. P.
Snow (1959) analyzed the lack of communication between the
two camps. Their physical and administrative separation on
college campuses widen the gap further, and stereotyping
"mathematical/scientific minds" suggests that mathematical
and scientific reasoning are somehow separate and inborn
reasoning powers of the mind. According to physics pro
fessor J. V. Mallow (1981), author of Science Anxiety: Fear
of Science and How to Overcome It, this scientific elitism
has grown up only in the last 40 years.
Astronomer Carl Sagan, director of the Laboratory for
Planetary Studies at Cornell University, believes science
should once again be readily accessible to the public.
Children are natural scientists, he said, but are stifled
by parents and bored and misled in school until they be
lieve that they are too dumb to understand science. He saw
a danger in the growing split between a small scientific
elite and the scientific illiterate majority. Sagan con
sidered it "more than a crisis. It is a scandal. It is
suicide" (Cordes, 1982, p. 16).
Suggestions for Change
In the relatively few years since Sells' 1973 "critical
filter" research, the study of women and mathematics has
gained national attention. Sheila Tobias' popularization
of the term "math anxiety" (1976, 1978) together with the
writings of other respected educators and researchers
(Casserly, 1980; Ernest, 1976; Fennema, 1977; Fox, 1977;
Helson, 1980; Sherman, 1977) have contributed to this
prominence.
Although there are risks involved with the use of the
term "math anxiety" (Blum, 1978, Ernest, 1976; Luchins,
1979), several important efforts have developed concurrently
with the popularization of the term. Research attention has
been focused on the causes and consequences of sex differ
ences in mathematics achievement and on the societal, educa
tional, and career barriers experienced by women. Attempts
have been made to educate young women, their parents,
teachers, and counselors regarding the vital importance of
mathematics and the limitations imposed by math illiteracy.
The Mathematical Association of America funded two groups,
Blacks and Mathematics and Women and Mathematics, to provide
speakers and role models for high school girls. Lenore
Blum's Math/Science Network at Mills College actively en
courages young women to pursue careers in math and science.
At the post secondary level, intervention programs across
the country are demonstrating that math deficient but other
wise academically competent adults can learn mathematics
(Tobias & Weissbrod, 1980).
On another front, psychologists are collaborating with
mathematicians and physicists to gain understanding of the
processes involved in learning math and science. Cognitive
research findings are helping teachers to identify and remedy
problem areas, such as students' difficulties in replacing
their former naive theories with what they learn in math and
science classes and applying these new principles to real
life problems (Resnick, Note 1).
Educators are also revising mathematics standards in
the schools. Minimal competencies of college students have
been examined, and additional testing is now being required.
In the state of Florida, for example, the legislature re
cently mandated special competency tests for prospective
teachers as well as increased the level of math and English
courses required of lower division college students. Stu
dents will be required to take collegelevel academic skills
tests before they can advance to junior status. Basic
skills testing programs have been instituted at all levels
of education in an effort to overcome what Florida education
commissioner Ralph Turlington described as a "laxness" in
setting standards for schools (Haines, 1982).
The Florida college sophomore basicskills testing will
further reveal the already existing problem of math illiter
acy. As noted earlier, there are far too many students,
who, because of poor counseling and a myriad of interrelated
factors, discover too late that they should have learned
more math in high school. Many students, for example, try
to learn material for the first time in a fastpaced math
review course of several hundred students. Others believe
that they are in math "flunkout" courses and that everyone
else understands what to do. They may also believe that
they lack a "mathematical mind," that there is a ceiling on
ability and they have reached their ceiling. This can hap
pen anywhere from fractions all the way up to Calculus III.
And it can, and often does, happen to "A" students. Other
wise academically competent students can feel helpless,
unable to use their normal coping behaviors. As their
anxieties rise, their confidence falls. Comprehension,
memory, attention, and concentration all decline.
Often, but not always, the anxiety leads to the most
common and simplest means of reliefavoidance behaviors.
The students, consequently, may appear dumb, lazy, and
selfdefeating even to themselves. Many of these students
believe that they are beyond help, so firmly are they con
vinced that the problem is their own lack of mathematical
intelligence. And many professors, baffled by the students'
difficulties and not understanding the psychological blocks
they are experiencing, are also unable to help them. Some
students become angry and resentful of the large classes
and the math requirements when they "aren't ever going to
use math anyway." Some students, frustrated and bored by
years of rotelearning without understanding believe that
math and mathematicians must be dull and noncreative. These
students begin class with a strong, long established aversion
both to the subject and to the professor. This attitude
baffles the professors even further. Other students, de
termined to avoid math at all costs, proceed to plan their
entire academic and professional careers with that goal in
mind even if the costs include giving up their first, second,
and third career choices.
What then are the implications? Too many students,
especially women and minorities, are not fluent in a key
language, mathematics, which opens up academic and vocational
opportunities. It is this lack of fluency which undermines
feelings of competency. "Math illiteracy" keeps people from
being able to understand discussions in all fields which
rest on mathematical metaphors. Being able to do math and
science is to have power, to have a sense that you have the
tools needed to speak the language of technical arguments
and to make intelligent decisions on political or financial
issues which have a mathematical or scientific base. Lack
ing mathematical competence is to be cut off from full
participation in our increasingly technological society.
Purpose of the Study
One component, therefore, of solving the mathscience
crisis is to help these math deficient but otherwise aca
demically competent students to "learn how to learn" mathe
matics in what can be called Math Confidence Workshops.
The purpose of this study was to establish such a program.
The goals were to help the students 1) replace their self
defeating attitudes, beliefs, and behaviors with more bene
ficial ones, 2) manage their anxiety more effectively,
3) gain confidence in their mathematical intuition,
reasoning powers, and overall ability to learn mathematics,
and 4) gain control, to stop feeling helpless, and to use
already established academic coping behaviors.
The problems involved included 1) educating students,
counselors, and faculty that such an intervention was avail
able and possible; 2) getting students to come for help
(Tobias (1978) suggested that it can take as long as three
years of "patient development" before even learning the
number of potential users); 3) assessing which students
would benefit from such a program and screening out and/or
providing alternative interventions for other students;
4) designing a multifaceted intervention which would meet
the needs of students at varying levels of avoidance be
havior, anxiety, and mathematical and academic expertise;
5) accomplishing Numbers 14 as a part of a lowcost inter
vention at a University Counseling Center with the endorse
ment of the Department of Mathematics (although without
their financial or professional contribution to the program
development).
There are a wide variety of math anxiety reduction
programs at colleges and universities across the country.
Tobias and Weissbrod in the Harvard Educational Review
(1980) see the development of effective, controlled, inter
vention techniques as 'essential in reversing mathematics
underachievement at the postsecondary level. There have
been, however, only a "handful" of controlled investigations
of these treatments (Richardson & Woolfolk, 1980) and
"systematic evaluation of programs to remediate math anxiety,
both counseling and educational programs, are sorely needed"
(p. 285).
In summary, it has been established that mathematics
has become increasingly important in our society, that the
lack of mathematical competence among students and the
public at large has reached crisis proportions, and that
there is a need for nationwide interventions at multiple
levels to meet this crisis. For many students psychological
interventions are needed to address the math anxiety which
they are experiencing. The theoretical basis for under
standing the concept of math anxiety is poorly defined
(Anton & Klisch, in press). Empirical research is limited
on the nature of math anxiety, its effects, prevalence, and
strategies for treatment. Interventions have leaned heavily
on test anxiety research which, after a history of unidimen
sional approaches, has currently suggested a complex con
ceptual model of test anxiety (Meichenbaum & Butler, 1980)
and multidimensional treatments which address this com
plexity. It was the purpose of this study to determine the
efficacy of a multidimensional group intervention approach
in the treatment of math anxiety as reported by college
students.
Specific Objectives
The specific objectives of this research were to
investigate
1. the pre to posttreatment change on the following
scales:
a. Math Anxiety
b. Confidence in Learning Mathematics
c. Math as a Male Domain
d. Usefulness of Mathematics
e. Effectance Motivation in Mathematics
f. Test Anxiety
g. Worry component of test anxiety
h. Emotionality component of test anxiety
2. treatment subjects' perception of their ability
in mathematics
3. maintenance effects of anticipated treatment im
provement.
It was anticipated that
1. there wouldbe significant pre to posttreatment im
provement on all scales or, in cases of nonsignificant post
test improvement, that the posttreatment scores would be
comparable to those of the nonanxious comparison group, the
Psychology I control group, or the math classes control group.
2. there would be a significant improvement in sub
jects' selfreported math ability ratings.
3. subjects would report continued improvement in
treatment areas including ability to learn and use mathe
matics, performance in mathematics courses, decrease in math
and test anxiety, and in other specific behavioral dimen
sions addressed in the math groups up to 1 1/2 years after
the intervention program.
Having set forth the purpose, specific objectives, and
need for the present study, the next chapter will review
17
the literature, and Chapter Three will describe how the
study was conducted. Chapters Four and Five will describe
the results and discuss their implications.
CHAPTER TWO
REVIEW OF THE LITERATURE
In this section the relevant literature has been
divided into several main categories: background informa
tion and possible causes of negative attitudes toward mathe
matics from the perspective of mathematics educators, women
and mathematics, the relationship of math anxiety to test
anxiety, and empirical studies of the treatment of math
anxiety.
The concept of math anxiety is not a new one. As
early as 1954 Gough wrote on "mathemaphobia"; in 1957
Dreger and Aiken identified "number anxiety" in a college
population; in 1966 Natkin devised a simple pairedword
association treatment of "mathematical anxiety"; and in
1972 Richardson and Suinn developed a Mathematics Anxiety
Rating Scale (MARS).
Although systematically collected information on the
prevalence of math anxiety is somewhat limited, math anxiety
has been found to be a frequent problem of college students
(Betz, 1978; Probert, Note 2; Richardson, Note 3). Richard
son surveyed 400 undergraduate students and found that
approximately onethird experienced extreme levels of
anxiety associated with number manipulations or situations
involving mathematics. In Betz's study from onefourth to
onehalf of 652 undergraduate subjects reported that math
made them feel "uncomfortable and nervous" and "uneasy and
confused" (p. 443). Approximately half of the 80
students in mathematics classes for elementary school
teachers surveyed by Probert reported some extent of
anxiety when faced with various situations involving mathe
matics. Only onefourth of the students indicated that
they were not "uptight" or "ill at ease" during math tests
(p. 56).
Controlled research on the nature of math anxiety is
even more limited than on its prevalence. Anton and Klisch
(in press) have noted that as a result of the poorly de
fined theoretical basis underlying the concept of math
anxiety there is a "virtual absence" of controlled research
on the variables which lead to negative cognitive and emo
tional responses to mathematics. Lacking these data, it is
necessary to look elsewhere for the needed background in
formation on the complex nature of math anxiety, its mul
tiple causes, origins, and perpetuators.
The Nature of Math Anxiety from the Mathematics
Educator's Perspective
From as early as 1943, educators in mathematics have
identified fear of mathematics, mathemaphobia or mathophobia
as a widespread phenomenon, speculated as to its causation
and cure, written books and articles on the subject, and
helped students overcome it in their classrooms. These
teachers did not hesitate to identify members of their own
profession as major contributors to the problem. The
condemnation of rotelearning appeared as a recurring theme.
Reviewing the writing of a number of these math educators
provided insights pertinent to math anxiety intervention
strategies.
An English mathematician and educator, W. W. Sawyer,
wrote Mathematician's Delight (1943) primarily to "dispel
the fear of mathematics" (p. 7). Sawyer identified bad
teaching as the cause for the dislike or dread of mathe
matics. Bad teaching, according to Sawyer, stresses parrot
learning instead of understanding, does not encourage mathe
matical reasoning, intuition or imagination, and encourages
the belief that mathematicians are a race apart with almost
supernatural powers. Mathematics has been presented too
often as "imitation mathematics," as dull drudgery, some
thing far removed from everyday life. Sawyer believed that
the first step toward overcoming the problem was to get rid
of the fear, to go back to the earliest stage where confi
dence was lost. He envisioned mathematical reasoning and
imagination developing gradually through direct experience
with real objects. Mathematical reasoning is not separate
from other reasoning powers of the mind. The same methods
of reasoning are used by people in their everyday lives,
but they are not aware of it. "The important thing is to
learn how to strike out for yourself. Any mistakes you
make can be corrected later. If you start by trying to be
perfect, you will get nowhere. The road to perfection is
by way of making mistakes" (p. 24).
In Vision in Elementary Mathematics (1964) Sawyer re
emphasized the problems arising from the too frequent expec
tation of failure generated by the loss of confidence which
bad teaching causes and by the common belief that only
geniuses can learn mathematics. He additionally pointed
out the widespread incorrect assumption that memorizing is
easy and understanding is difficult. Teachers, unfortunately,
as well as students often believe that only the truly gifted
can understand what mathematics really means. The others
will just have to get by with rotelearning. The truth is
exactly the opposite; memorizing what is not understood is
extremely difficult.
In 1954 Sister Mary Fides Gough, a teacher of mathe
matics for more than twentyfive years, suggested that
"mathemaphobia" was a major cause of the many failures she
saw in mathematics classes. This disease, she said, needed
no defining, was "almost as common as the common cold"
(p. 290), and could undermine selfconfidence years before
being detected. Early embarrassment by a teacher, missed con
cepts such as fractions because of absences from school, fear
of failure, teachers who require memorizing instead of
understanding or who suggest that mathematicians are born
with a magic gift, and "hereditary mathemaphobia" ("My
father never could learn mathematics and I can't learn it
either")all contribute to the development of the phobia.
Gough suggested that students' failure to master mathe
matical reasoning comes from their fears and from their
belief that such ability is beyond them.
Another mathematician, Richard Skemp, became so con
cerned with the problem of intelligent and hardworking
students who "couldn't do mathematics" that he returned to
college for a degree in psychology in order to help them.
Skemp wrote in The Psychology of Learning Mathematics (1971)
that many people acquire a "lifelong dislike, even fear, of
mathematics" because of a lack of good teaching especially
in the early stages. He stated that the first two principles
of the teaching of mathematics were
1) Concepts of a higher order than
those which a person already has cannot
be communicated to him by a definition,
but only by arranging for him to encounter
a suitable collection of examples.
2) Since in mathematics these examples
are almost invariably other concepts, it
must first be ensured that these are already
formed in the mind of the learner. (p. 32)
According to Skemp the vast majority of textbooks
violate the first of these principles. Regarding the second
principle, if a particular level of mathematics was not
understood perfectly, almost all remaining levels suffered.
Because many students learn to do manipulations by rote
learning with a most inadequate understanding of the under
lying principles, it was no wonder that mathematics became
a mystery to them. "For those with feelings of dislike,
bafflement, or despair toward mathematics," Skemp suggested
"the fault was not theirsindeed, . these responses
may well have been the appropriate ones to the non
mathematics which they encountered" (p. 114).
Skemp stated further that bad teaching in the form of
a series of meaningless rules can be described as a series
of "insults to the intelligence." And it is probably the
more intelligent students who are the most upset by these
rules without reasons but who do not realize that the fault
is not theirs. Teachers, perhaps meaning well but acting
in ignorance, either present definitions or rules which are
not meaningful or else do not give the preliminary ideas
basic to the understanding of the new ones. The students,
without the schemas or concepts necessary for comprehension
readily available in their minds, only accept the teacher's
authority if any learning is to take place at all. Such
learning is not schematiclearning; it is rotelearning.
Sooner or later, however, the entire defective system
breaks down. As mathematics becomes more advanced, the
increasing amount of information to be memorized poses an
impossible task for any learner. Rotelearning cannot be
adapted to seemingly different problems which are based on
the same mathematical principles. Schematic learning is
more adaptable and does not impose such impossible burdens
on the memory.
The students, not knowing what the problem is or per
haps thinking themselves incapable of real understanding,
find themselves in an anxietyprovoking situation. Trying
to memorize more and more rules and methods without under
standing provides no basis for longterm retention. Progress
is impeded, selfesteem sags, and anxiety mounts. As the
anxiety mounts, a vicious circle is established. Anxiety
makes it even more difficult for students to learn. So the
harder they try, the less able they are to understand, and
the more anxious they become. According to the YerkesDodson
Law, with increases in arousal or anxiety, task performance
increases up to a certain point, beyond which additional
anxiety or motivation leads to a decrease in performance.
The optimal level of arousal decreases with the complexity
of the task. For complex tasks, such as doing algebra, the
optimal level is lower than for simple tasks. When even a
mathematics book or a calculus class has become a condi
tioned stimulus for anxiety, the problem is exacerbated.
In Skemp's statistics class for psychology majors, he
found that his first task was to convince many students
that they were capable of comprehending mathematics. Skemp
pointed out that good teachers can reduce anxiety, build up
confidence, and improve performance by starting with ques
tions which they know students can answer. Other teachers
can reduce a pupil of average intelligence to "tonguetied
incompetence" (p. 128). It was Skemp's hope that all those
who have had unsuccessful attempts at learning mathematics
would "be willing to accept, as a working hypothesis, that
the causes were other than (their) own lack of intelligence"
(p. 129).
More recently Lazarus (1974) and Zacharias (1976) both
wrote about mathophobia as a widespread phenomenon which
can seriously impair performance. Lazarus defined matho
phobia as "an irrational and impeditive dread of mathe
matics . (an) emotional and intellectual block making
further progress in mathematics and closely related fields
very difficult" (p. 16). The attitude and the anxiety make
learning difficult, pessimistic predictions are justified,
frustration feeds the anxiety, and the attitude worsens
further. Lazarus gave credit to Zacharias for coining the
term "mathophobia" and speculated that mathophobes consti
tute a clear majority of people in this country. A complex
interaction of factors seems to be responsible. The educa
tional system was cited as promoting mathophobia by not
providing early diagnoses of the problem or even by teaching
the memorizewhattodo approach rather than a real under
standing of the material. Parents were cited for trans
mitting negative attitudes or adopting pessimistic expecta
tions. The nature of mathematics and the mathematics
curriculum were also cited. The sequence in which mathe
matical topics are presented to students tends to be
historical or based on the perspective of adult logic
rather than on studies of children's developing capabili
ties. Mathematics, in contrast with almost all other
subjects, tends to build on itself cumulatively. Missing
a concept, for whatever cause, can have lasting and
cumulative results.
Perhaps the most serious problem of all, according to
Lazarus, is the probability that a significant proportion
of mathematics teachers may themselves be suffering from
mathophobia. As to why people who dislike mathematics
would put themselves in the position of teaching it, Lazarus
suggested that a partial answer lies in the incorrect belief
in the "mathematical ceiling"the level at which people
first experience difficulty in learning mathematics. Some
teachers, believing that they have reached their "ceiling,"
have lost all pleasure and fascination in the subject,
never want to learn anything more about mathematics, and
discourage probing questions and exploration of new tech
niques. They still may feel capable of teaching any level
of mathematics as long as it is below their individual
"mathematical ceilings." Lazarus felt strongly that an
"indiscriminate (though not uncritical) love of the subject"
(p. 22) was an essential element to excellent teaching.
Indifference and negative attitudes will be passed on to
students. Mathematics may then become dull, pointless
drudgery.
Women and Mathematics
Sawyer (1943, 1964), Gough (1954), Skemp (1971),
Lazarus (1974), and Zacharias (1976) all wrote of the dif
ficulties in learning mathematics encountered by a large
proportion of students, both male and female. Recent
research has illustrated that many females in our culture
experience pressures and negative messages which may addi
tionally affect their learning of mathematics and/or their
decisions whether to enroll in or to avoid higher level
mathematics.
The study of women and mathematics is a relatively
recent phenomenon prompted by the increasing realization
that women with apparently equal aptitudes are dispropor
tionately represented in the sciences and other fields
requiring mathematical competence. In response to Lucy
Sells' (1973) study on "math avoidance" at the University
of California, Sheila Tobias (1976, 1978) and others popu
larized the term "math anxiety" and suggested that sexrole
socialization and other societal influences were responsible
for the sex differences at the higher levels of math and
science.
Mathematics has been defined in our culture as mascu
line (Fox, 1977). Textbooks, tests, literature, television
programs, and the media all contribute to this stereotype.
Role models are lacking for females in mathematics and
science. Parents, counselors, teachers, and peers are
likely to perpetuate sexrole stereotypes by believing and
reinforcing sex differential expectancies for math achieve
ment (Probert, Note 2). And women themselves are more apt
to underestimate their ability to solve mathematical prob
lems and to perceive themselves as mathematically incompe
tent (Fox, 1977).
Bem and Bem (1970) speak of a nonconsciouss ideology"
which they define as those implicitly accepted beliefs and
attitudes of which one is unaware because the same message
is disseminated by all reference groups and alternative
conceptions of the world are not even examined. They sug
gest that an American woman is trained to "know her place"
because of the pervasive sexrole ideology which results in
differential expectations and socialization practices. One
such commonly accepted belief is that mathematics is a male
domain.
John Ernest's (1976) study, "Mathematics and Sex,"
concluded that mathematics is a sexist discipline, that the
immorality of the sex differences in mathematics performance
is that they are caused by stereotypes, attitudes, restric
tions, and constraints. Elizabeth Fennema (1974) agreed
with Ernest that these sex differences are "a major failure
of our pedagogical system" (p. 609).
It was not until 1974 that there began to be serious
questioning (Fennema, 1974, 1977) of the common assumption
that, at least as early as adolescence, males were innately
superior in mathematical achievement and that this superi
ority increased with age and with the difficulty of the
material. This belief in male superiority was reflected in
Maccoby and Jacklin's (1974) highly quoted review of the
literature on psychological gender differences which con
cluded that boys' greater visualspatial and mathematical
abilities were "wellestablished" differences. Less well
known was the fact that these differences although well
established were literally very small (Hyde, 1981; Sherman,
1977, 1979). Tobias (1982) argued further that "until and
unless girls can experience the world as boys do, we cannot
assume that sex differences in math are genetic" (p. 14).
While the question of sexrelated differences in mathe
matical aptitude is still being researched and debated
(Benbow & Stanley, 1980; Schafer & Gray, 1981; Tobias, 1982),
it is now widely accepted that there are no sexrelated dif
ferences in elementary school children's mathematical learn
ing (Fennema, 1977) and few sexrelated differences before
high school (Aiken, 1976; Fennema, 1974, 1977; Maccoby &
Jacklin, 1974). In addition, when Fennema and Sherman
(1977) controlled for mathematics background and general
ability, few differences in achievement were found during
high school, and score distributions overlapped considerably.
There are, however, large sexrelated differences in
students electing to study mathematics at the upper levels
of high school and in college (Ernest, 1976; Fennema &
Sherman, 1977; Sells, 1978a). Although Ernest (1976) found
no statistically significant sex differences in the grades
achieved in university level mathematics courses, the female
dropout rate in many math classes was almost double that
of males, and attrition rates were higher for women than
for men among mathematics majors. These differences in
course selection and dropout rates contribute to large sex
related differences in academic and career opportunities.
Math Anxiety and Test Anxiety
Math anxiety and test anxiety appear to have many
common features, and researchers (Hendel & Davis, 1978) have
suggested that the two concepts may be functionally similar.
It appears, however, that not all people who have high
scores on math anxiety scales also have high ratings on
test anxiety scales. The issue is complicated by an overlap
in item content inasmuch as math anxiety scales have items
relating to mathematics tests.
Suinn (1970) reported that of the students requesting
treatment in a behavior therapy test anxiety program, over
onethird had problems centering around mathematics anxiety.
Suinn and Richardson (1971) found that students in a mathe
matics anxiety treatment group had significantly higher
scores on the Suinn Test Anxiety Behavior Scale (STABS) than
did the controls. More recently other researchers (Betz,
1978; Probert, Note 2) have reported on the relationship
between math anxiety and trait and test anxiety. Higher
levels of math anxiety, as measured by a modified version
of the FennemaSherman Mathematics Anxiety Scale, were found
to be significantly but moderately correlated with higher
levels of trait anxiety, overall test anxiety, and emo
tionality and worry components of test anxiety.
In their review of the literature Richardson and
Woolfolk (1980) conclude that "clearly, math anxiety is
related to test anxiety, but the two are by no means equiva
lent phenomena" (p. 278).
Anton and Klisch (in press) observed many parallels
between math anxiety and test anxiety and suggested that
examination of the test anxiety literature would be helpful
for understanding math anxiety. Although the literature on
test anxiety dates back over 40 years (Spielberger,
Gonzalez, Taylor, Algaze, & Anton, 1978), George Mandler
and Seymour B. Sarason (1952) are generally credited
with the first important theorizing in the area. Mandler
and Sarason, influenced by Hullian drive theory, attributed
the relatively poorer performance of high testanxious
students in evaluative situations to the detrimental ef
fects of learned, taskirrelevant anxiety drives. Learned
task drives and taskrelevant anxiety drives, they theorized,
facilitated test performance. Alpert and Haber (1960) con
tributed the constructs of facilitating and debilitating
anxiety. Much of the early research focused upon the
debilitating effects of test anxiety on cognitive task
performance.
Wine's (1971) direction of attention interpretation
suggested that testanxious students divided their attention
between "selfrelevant" and "taskrelevant" responses in
contrast to low testanxious students who focused their
attention completely on the task. Woolfolk and Richardson
(1978) summarized four dimensions of anxious functioning
found in testtaking situations as follows: 1) Negative
selftalk which may include selfescalating, selfperpetu
ating worry, selfcriticism, selfcondemnation, and
preoccupation with bodily reactions, 2) Selfevaluative,
selforiented thinking instead of taskoriented thinking,
3) Ineffective response to bodily signs of tension, and
4) Irrational, maladaptive beliefs about self and the
world.
There is now general acceptance of Liebert and Morris's
(1967) suggestion that test anxiety consisted of two major
components, worry and emotionality. The worry component
was described as "primarily cognitive concern about the
consequences of failure" (p. 975). Emotionality was seen as
the affectivephysiological reactions which were evoked by
increased autonomic arousal. Particularly pertinent to those
interested in treatment interventions has been the consis
tent reporting (Deffenbacher, 1980; Tryon, 1980) that the
worry component has been significantly negatively related
to intellectual and cognitive performance; emotionality, on
the other hand, appears to be unrelated to performance
measures.
Deffenbacher (1980) after reviewing the literature on
worry and emotionality components made the following sugges
tions for anxietyreduction treatment programs: 1) Cogni
tive restructuring of worry combined with training in task
oriented selfinstruction should have promising results.
2) Cognitive restructuring, by providing coping skills for
the preexamination period as well as for the actual test
taking time, could reduce avoidance behaviors and improve
the quality of preexamination learning. 3) Selfmanaged
relaxation for the reduction of emotionality could be
added to cognitive restructuring coping skills inasmuch as
some studies show an interaction between emotionality with
worry levels. 4) Because emotionality is highest at the
beginning of an examination and decreases during the
course of the test, relaxation training might most oppor
tunely be cued to the period just prior to the examination
(Deffenbacher, 1977).
There are well over 50 controlled outcome studies of
test anxiety appearing in the literature (Denney,1980).
Systematic desensitization, growing out of Wolpe's (1958)
seminal work based on counter conditioning and extinction,
is still the most common treatment intervention. Since
Wolpe's original formulation, however, there has been a
questioning of his mechanistic interpretation of change.
As an alternate hypothesis, it has been suggested that the
principal mechanism for anxiety reduction in systematic
desensitization involves changing subjects' beliefs in
their ability to cope with certain situations (Murray &
Jacobson, 1978) and/or their sense of efficacy or mastery
(Bandura, 1977). Cautela (1969) and Goldfried (1971) made
important contributions toward reconceptualizing systematic
desensitization as a "procedure for developing selfcontrol
instead of a passive desensitization" (Murray & Jacobson,
1978, p. 677).
A recent review of 49 test anxiety outcome studies
(Allen, Elias, & Zlotlow, 1980) reported the following:
there were differences on performance measures of test
anxiety between treated and untreated groups for just 50
percent of all behavior therapy studies since 1970 and
for only 33 percent of those which involved systematic de
sensitization. Denney (1980) reviewed 18 studies using
selfcontrol procedures and found the following rates of
improvement on performance measures: 33 percent (1'of 3)
of applied relaxation techniques, 50 percent (4 of 8) of
selfcontrol training techniques, and 71 percent (5 of 7)
of cognitive coping techniques. It can be noted that when
cognitive restructuring was incorporated (i.e., cognitive
coping techniques), the rate of success was markedly higher.
Component analytic studies have looked at the efficacy
of cognitive restructuring and relaxation which are both
used in cognitive modification (Meichenbaum, 1972). Two
such studies (Wine, 1971; Holroyd, 1976) found that the ef
fective coping strategy involved was cognitive restructuring
while a third study (Hahnloser, 1974) found that both
components had to be incorporated in order for cognitive
modification to be effective.
Tryon (1980) reported four procedures which were found
to change students' grades: cognitive counseling (Holroyd,
1976), study counseling (Allen, 1973), study counseling with
systematic desensitization (Allen, 1971), study counseling
with relaxation (Allen, 1973). All four included cognitive
interventions which helped subjects replace negative self
reference thoughts with taskoriented thinking. In general,
Tryon concluded that study skills alone were found to be
less effective than study skills in conjunction with another
treatment procedure.
Allen (1972) was the first reviewer to point out that
the various behavior therapy treatment approaches, system
atic desensitization, anxiety management, implosion, cue
controlled relaxation, autogenic training, active coping
relaxation, and biofeedback, all focus on emotionality re
duction. Allen found that in order to obtain reliable
cognitive performance improvement, it was necessary to com
bine such approaches with some form of cognitive treatment
approach. Wine (1980) was emphatic in her criticism of test
anxiety treatment approaches which evolved out of other
anxiety treatment techniques rather than from the research
findings on the nature and effects of test anxiety. Wine
(1971) wrote that ". . by training test anxious subjects
to relax in the presence of progressively more stressful
stimuli, a systematic desensitization treatment approach
assumes that the emotional arousal component of test anxiety
is its defining characteristic" (p. 101).
Wine stated there was mounting evidence to show that
it was the cognitive worry component (i.e., negative self
preoccupation and attention to evaluative cues rather than
to task cues) which was shown to be the most important
characteristic of test anxiety.
Wine (1980) summarized her review by stating that the
test anxiety treatment literature "reveals that researchers
in this area, by and large, continue to adhere to an emo
tional reactivity interpretation of test anxiety. The
evidence points to the inescapable conclusion, however, that
cognitively based treatment strategies are more powerful in
effecting cognitive performance change and as effective in
reducing selfreport test anxiety level as are emotionality
based approaches" (p. 375). Tryon (1980) in her review of
the test anxiety literature concluded that "systematic de
sensitization and similar treatments designed to reduce the
emotional aspects of test and mathematics anxiety should
probably fall into disuse" (p. 366).
Meichenbaum and Butler (1980) propose a complex con
ceptual model of test anxiety as interacting components
which result in a kind of selfperpetuating cycle.
The individual is caught in a type of vicious
cycle, a selfperpetuating trap in which the
meaning system, internal dialogue, behavioral
acts, and interpretation of consequences feed
upon each other. In this framework, test
anxiety should not merely be equated with
poor study skills, or taskirrelevant internal
dialogue, or irrational beliefs, or unrealis
tic expectations. Instead, test anxiety is
a construct that summarizes this entire chain
of events. (p. 204)
Consequently, complex cognitive treatment packages
(Wine, 1980; Meichenbaum & Butler, 1980) may be the most
effective treatments of all. Tryon (1980) suggested the
efficacy of "complex, multimodal package treatments which
influence the individual's meaning system, internal dialogue,
behavioral acts, and interpretation of behavioral outcomes"
(p. 366). Multimodal interventions such as stress
inoculation training (Meichenbaum, 1975), anxiety manage
ment training (Richardson, 1976), and multimodal behavior
therapy (A. Lazarus, 1976) are among those treatment
strategies which address test anxiety as a multidimensional
construct.
The Treatment of Math Anxiety
Many of the behavioral therapy treatment procedures
which have been used to treat test anxiety have been applied
to math anxiety. Treatment studies of math anxiety in the
empirical literature date back only to 1970 when Suinn,
Edie, and Spinelli treated mathematics anxiety in 13 col
lege students by means of two shortterm desensitization
approaches. The marathon desensitization group (MDG) re
ceived a standard systematic desensitization procedure
using the entire nineitem hierarchy in five treatment blocks
massed within four consecutive hours on one evening. The
accelerated massed desensitization group (AMDG) received
only the highest three items of the hierarchy in two treat
ment blocks for two consecutive hours. The AMDG showed as
much improvement in MARS scores and in mathematics per
formance on the Differential Aptitude Test (DAT), with a 10
minute time limit, as did the MDG. The fact that there was
no control group makes improvement on both measures difficult
to evaluate.
Suinn and Richardson (1971) found that Anxiety Manage
ment Training (AMT) was as effective as standard systematic
desensitization in reducing math anxiety as measured by the
MARS in a study of 24 college students. A significant im
provement in DAT scores was achieved only by the desensi
tization group. The control group consisted of 119 untreated,
nonmathanxious psychology students. Anxiety management
training (AMT) is a nonspecific anxiety selfcontrol program
which does not use anxiety hierarchies. Subjects, instead,
were instructed to generate anxiety responses and then
trained to develop competing responses, such as relaxation
or feelings of success.
A third study (Richardson & Suinn, 1973) compared
traditional systematic desensitization, accelerated massed
desensitization (AMD), and anxiety management training (AMT)
in the treatment of mathematics anxiety. All three treat
ments were found to have significant, equivalent improvement
on the math anxiety scale (MARS), but no significant dif
ferences were found on the mathematics performance measure
(DAT). Two control groups were formed by selecting students
with high scores on the MARS from a group participating in
research to earn credit for education courses. The second
group was selected for comparison on the MARS after it was
discovered that the MARS scores of the first group were much
higher than those of the treatment subjects. It was felt
that there might be a reduction in scores due to regression
toward the mean. The first group was retained for comparison
on the DAT. None of the control group subjects had ex
pressed interest in the math anxiety reduction program.
Tryon (1980) reviewed the above three studies and sug
gested that "the threats to internal validity in these
studies make it difficult to draw conclusions about the
effectiveness of the treatment procedures" (p. 364). Tryon
seemed particularly concerned about the absence of a con
trol group in the first study and the nonequivalent control
groups in the other studies.
There was also a highly selective method of obtaining
subjects for treatment in the three studies. Students were
eliminated not only for severe psychological disturbances
but also for inadequate mathematics backgrounds, lack of
ability, apathy about school, vocational or other personal
difficulties, and anxiety "primarily connected with test
taking in general" (p. 213). Generalizability is in ques
tion especially because math anxiety and math avoidance
often are caused by and/or result in inadequate backgrounds
in mathematics (Tobias, 1978).
In regard to the performance measure, Richardson and
Suinn suggested that the improvement found in DAT scores
in the first two studies may have been "due, at least in
part, to the practice effects involved in retesting" (1973,
p. 216) on the same form. They suggested further that
the use of available equivalent forms of the DAT might
remedy the problem.
The problem of performance improvement appears, how
ever, to be much more complex than changingDAT forms. Ex
tensive test anxiety research, reviewed earlier, concluded
that it was cognitively based treatments which were more
effective in achieving improvement in performance and as
effective in reducing emotional arousal as emotionality
reduction treatments such as those used in the previous
three studies. Richardson and Woolfolk commented later
(1980) in their review that
these three studies encouraged the belief
that behavior therapy programs of this type
have an impact on math anxiety, but they do
not clearly demonstrate effectiveness in
improving math performance, in maintaining
this improvement, or in modifying other at
titudes that may mediate participation and
pleasure in mathematicsrelated activities.
(p. 283)
Treatments involving cognitive strategies have also
been applied to math anxiety. Albert Ellis's (1962)
rationalemotive therapy has influenced a majority of the
current cognitive restructuring approaches. Ellis pointed
out that anxiety and other maladaptive emotional reactions
are often the result of maladaptive, irrational thoughts,
beliefs, and expectations. There is empirical support for
this basic assumption that selfstatements are capable of
eliciting emotional responses (Goldfried, 1977), and it is
this assumption that has influenced cognitive relabeling
procedures used in anxiety reduction.
Typical "irrational" beliefs which have been shown to
create problems for the math anxious are "other people have
mathematical minds, but I don't so I can't do math"; "people
are either mathematical or verbal, but not both"; "if I
got the answer that fast, it must be wrong"; "only men can
do 'real' math"; "mathematicians are geniuses who have
never had any difficulty doing math"; "there is only one
correct way to do a math problem."
Stanley Kogelman and Joseph Warren developed five
session therapy workshops described in their book, Mind
Over Math (1978), in which they focus on changing attitudes
and irrational beliefs in order to help people overcome
their fear of mathematics. They argue that it is the emo
tional blocks, the intense emotional reactions to mathe
matics, which make teaching and learning virtually impossi
ble. Although both Kogelman and Warren are mathematicians,
their main focus is on the psychological intervention which
they believe is necessary before learning math can be
possible. Although no empirical research has been pub
lished, Kogelman and Warren stated that they had been able
to help everyone who came to their workshops.
A multimodal, cognitiveoriented intervention strategy
for reducing mathematics anxiety was reported by Hendel
and Davis (1978). They compared the effectiveness of a
diagnostic clinic, participation in a support group, and
enrollment in a mathematics course. Sixtynine female
students participated in a threehour diagnostic clinic as
part of a Math Anxiety Program in Continuing Education for
Women at the University of Minnesota. After receiving a
report of their mathematics performance and a recommendation
for registering in one of three special mathematics classes,
subjects then chose to enroll in one of the mathematics
classes, enroll in a class and concurrently participate in
a support group, or discontinue the program. Pretesting
was in September; posttesting was in February, two weeks
after the classes ended. Representativeness of the complete
data sets is in question because posttesting data were com
pleted by only 47 of the original 69 subjects (8 of the 22
women in the mathematics course, 11 of the 15 women who
participated in both the course and the group, and 28 of
the 32 women in the diagnostic clinic only group).
The multifaceted counseling support group met for
seven weeks for one and onehalf hours each week and in
cluded the following: cognitive restructuring, mathematics
autobiography, diary, games and weekly goal setting, as
sertiveness for asking questions in class, and a brief
introduction to desensitization relaxation exercises.
Results indicated that all three groups decreased sig
nificantly in MARS scores, with maximum improvement for
subjects enrolled in the mathematics course and the coun
seling support group and minimum improvement for subjects
in the diagnostic clinic only group. Again, the lack of
a control group makes the results difficult to evaluate.
In 1975 Sheila Tobias (1978) and Robert Rosenbaum
established the country's first Math (Anxiety) Clinic at
Wesleyan University. After an interview with a clinic
counselor, students with inadequate backgrounds in mathe
matics can take one of two special courses, algebra review
or precalculus. A psychology laboratory is available as an
option to the students enrolled in the courses. Auslander
(1979), math teacher at the clinic, reported on attitude
changes of participating students as measured by four
FennemaSherman Scales (1976): mathematics anxiety, con
fidence in learning mathematics, usefulness of mathematics,
and attitude toward success in mathematics. Auslander
found the following after the 1977 courses: 1) total
students showed a significant decrease in math anxiety,
with a "distinct decrease" for women while the men showed
little change. 2) There was a marked decrease in degree
of usefulness ascribed to mathematics for men with a
smaller decrease for women. 3) Pretesting showed signifi
cantly greater anxiety and less confidence among algebra
students as compared to precalculus students. Posttesting
showed no significant differences between the two. Pre
calculus students' anxiety had increased and confidence
had decreased while algebra students' anxiety had decreased
and their confidence increased.
Auslander suggested as possible reasons for the in
crease in anxiety among the precalculus students and the
decrease among algebra students the following: the algebra
course was supportive and sensitive to students' needs, and
students were reviewing material previously learned. The
precalculus course was less supportive, and students were
learning new material.
In 1978 the precalculus course was modified to include
more class participation and to cover somewhat less material.
Results showed 1) a significant decrease in students'
anxiety with a "distinct decrease" for women and little
change for men, 2) a significant increase in confidence for
total students with greater increase for women than for men,
3) a marginally significant increase in the value placed on
success in mathematics with somewhat more for women than
for men, 4) the significantly higher levels of math anxiety
found at protesting among women decreased to nonsignificance
at posttesting, 5) the precalculus students were signifi
cantly less anxious and more confident than the algebra
students in both pre and posttesting, and 6) there was no
decrease in degree of usefulness ascribed to mathematics
found at posttesting. Auslander concluded that the sup
portive atmosphere of the precalculus class which resulted
in less anxiety, more confidence, and no decline in the
degree of usefulness was "both healthier and more produc
tive" (p. 20) and more than made up for the fact that
somewhat less material was covered.
Serious methodological problems arise, however, in this
study. There was no control group; performance measures
would have been readily available but were not supplied;
and no data were reported on numbers of students or on any
of the statistical analyses. The study does point out,
nevertheless, that the atmosphere in a mathematics class
appears to have a definite effect on anxiety and confidence
levels. These levels have, in turn, been shown to have a
measurable effect on cognitive performance. Revision of
mathematical curricula according to the suggestions of
Sawyer (1943, 1964), Gough (1954), Skemp (1971), Lazarus
(1974), and Zacharias (1976) appears to be a fruitful area
for future study.
In summary, the history of the literature of math
anxiety is a relatively short one. Math anxiety has been
shown to be a prevalent phenomenon on college campuses,
but not enough is known from the existing empirical research
about the nature of math anxiety, its causes, or its cures.
Educators in mathematics have suggested that the fear of
mathematics is the expected result of bad teaching, poorly
written textbooks, and faulty beliefs and expectations.
Sexrole socialization has made learning mathematics even
more difficult for many women.
Math anxiety treatment strategies may be placed on a
continuum from psychological intervention alone, to psycho
logical intervention in combination with a math class, to
a math class alone. Psychological interventions began,
as did the early test anxiety studies, with behavior therapy
strategies such as systematic desensitization. As a
cognitiveattentional perspective of test anxiety has
found increasing empirical support, more emphasis has been
placed on restructuring cognitive and attentional processes.
Realization that both test and math anxiety are complex,
multidimensional constructs must, in turn, lead to multi
faceted approaches which have more prospect of making
lasting, significant changes.
Additional systematic investigations of more complex
math anxiety treatments, both psychological and educational,
are sorely needed (Richardson & Woolfolk, 1980; Tryon,
1980). Richardson and Woolfolk concluded their review by
suggesting the pressing need for further investigations.
Such efforts should include longterm
followup concerning changes in anxiety,
attitudes toward mathematics, educational
and occupational choices, and possible
generalized benefits to student's posi
tive mental health or coping skills in
other areas of living. Perhaps such re
search could most profitably emphasize the
evaluation of ongoing counseling or edu
cational programs in their natural environ
ment, like the Wellesley and Wesleyan
projects, rather than familiar, "oneshot"
treatment studies that pit artificially
truncated treatment procedures against
each other and rarely investigate the
longerterm durability of effects. (p. 285,
286)
CHAPTER THREE
METHOD
Subjects
Participants in this study were 50 students, 35 females
and 15 males, who selfreported to the University Counseling
Center in response to flyers announcing sevensession Math
Confidence groups cosponsored by the Counseling Center and
the Department of Mathematics. All students responding
were scheduled for an initial individual screening inter
view. Students with severe psychological problems were
referred for individual counseling. A few students applied
who were confident of their mathematical ability and who
were not anxious about mathematics. They were referred to
math tutors and/or to study skills counseling. All treatment
subjects were required to be learning math. For those stu
dents not enrolled in a mathematics, statistics, or other
mathematicsbased class, special arrangements were made
with the students for regular, structured mathematics study.
After Spring term, 1981, criteria for acceptance also in
cluded a minimum 2.00 grade point average as a means of
limiting treatment to math deficient but otherwise academi
cally competent students, the designated population for this
study. Students in the two Spring, 1981, groups took the
Math Confidence Workshops as a special twocredit course
through the College of Education.
Participants' grade point averages ranged from 1.79 to
3.96; mean GPA was 2.94 (S.D. = .65). Average age of sub
jects was 26 with a minimum age of 18 and a maximum of 55
(S.D. = 7.97). There were 43 Caucasians, 1 Black, 3 Spanish,
and 3 "other." Table 1 presents the treatment subjects
by group and sex. Due to students' class and work conflicts,
it was not possible to assign the students to groups ran
domly.
Control group subjects were in three categories.
Twenty subjects were undergraduate education majors enrolled
in MAE 3810 (10 subjects) and MAE 3811 (10 subjects), Math
for Elementary Schoolteachers I and II. The study was ex
plained to students in these two courses, and the 20 sub
jects volunteered to participate in the study. Students
in these classes were selected to control for the effects
of being enrolled in a mathematics class during the desig
nated treatment period.
The second and third groups were students participating
in research to earn credit for an introductory psychology
course. The second group of 34 students responded to a
request for subjects to participate in a study investigating
attitudes toward mathematics. These students were selected
to serve as a nonanxious comparison group. The third group
of 20 subjects responded to a request for subjects who had
negative attitudes toward mathematics. Of the latter group,
Table 1
Math Confidence Treatment Group Subjects
Group Male Female Total
1. Spring, 1982 5 3 8
2. Spring, 1982 2 6 8
3. Fall, 1981 4 7 11
4. Fall, 1981 3 6 9
5. Spring, 1981 0 5 5
6. Spring, 1981 1 8 9
TOTAL 15 35 50
12 indicated interest in participating in a Math Confidence
Group. These 12 subjects were chosen to serve as a com
parable mathanxious control group.
Control subjects' grade point averages ranged from
1.3 to 4.00; mean GPA was 2.82 (S.D. = .61). Average age
of subjects was 20 with a minimum age of 18 and a maximum
of 42 (S.D. = 4.04). There were 62 Caucasians, 1 Black, 2
Spanish, and 1 "other." Table 2 presents the control
subjects by group and sex. All 'subjects, treatment and
control, were volunteers.
Instruments
The FennemaSherman Mathematics Attitudes Scales
(Fennema & Sherman, 1976) were used to assess six variables.
These scales were designed for use with high school students
and were adapted by Betz (1978) for use with college stu
dents. All items were responded to by students using a
fivepoint Likert scale of (1) Strongly Disagree to (5)
Strongly Agree. Scoring of all negatively worded items was
reversed.
The Math Anxiety Scale (MAS) is designed to measure
"feelings of anxiety, dread, nervousness, and associated
bodily symptoms related to doing mathematics" (Fennema &
Sherman, 1976, p. 4). Half of the ten items were posi
tively worded, while the other half were negatively worded.
Lower scores indicate higher levels of math anxiety; higher
scores indicate more positive attitudes toward math, that
Table 2
Control Group Subjects
Group Male Female Total
Psychology 1 14 20 34
Psychology 2 4 8 12
Math Classes 2 18 20
TOTAL 20 46 66
is, less math anxiety. Possible scores range from 10 to
50. A splithalf reliability coefficient of .89 was found
for the original Mathematics Anxiety Scale (Fennema &
Sherman, 1976), while a reliability coefficient of .92 was
obtained for the revised version used in this study. Cor
relations of MAS scores with math background (r = .30),
performance on the SATM (r = .40), and a measure of con
fidence in learning mathematics (r = .84) provide evidence
for its validity (Probert, Note 2).
The Confidence in Learning Mathematics Scale was
designed to measure "confidence in one's ability to learn
and to perform well on mathematical tasks" (Fennema &
Sherman, 1976, p. 4). Possible scores range from 10 to 50.
Higher scores on this scale are indicative of greater con
fidence in learning mathematics.
The Math as a Male Domain Scale measures "the degree
to which students see mathematics as a male, neutral, or
female domain." Attitudes are assessed on "(a) the relative
ability of the sexes to perform in mathematics; (b) the
masculinity/femininity of those who achieve well in mathe
matics; and (c) the appropriateness of this line of study
for the two sexes" (Fennema & Sherman, 1976, p. 3). Pos
sible scores range from 9 to 45. Higher scores indicate
less tendency to view math as a male domain, less tendency
to view males as innately better in math or math as a more
appropriate field of study for males than for females.
"Students' beliefs about the usefulness of mathematics
currently and in relationship to their future education,
vocation, or other activities" (Fennema & Sherman, 1976,
p. 5) were measured on the Mathematics Usefulness Scale.
Possible scores range from 10 to 50. Higher scores indi
cate more positive attitudes toward the usefulness of
mathematics.
The Effectance Motivation in Mathematics Scale was
used to measure "effectance as applied to mathematics.
The dimension ranges from lack of involvement in mathematics
to active enjoyment and seeking of challenge" (Fennema &
Sherman, 1976, p. 5). Possible scores range from 10 to 50.
Higher scores indicate more active enjoyment of mathematics.
The subjects' perceptions of the attitudes of teachers
were assessed using the Teacher Scale of the FennemaSherman
Mathematics Attitude Scales. Possible scores range from
10 to 50. Higher scores indicate perception of more positive
teachers' attitudes.
The six FennemaSherman Mathematics Attitudes Scales
are contained in Appendices A 16.
The Test Anxiety Inventory (TAI: Spielberger, Gonzales,
Taylor, Anton, Algaze, Ross, & Westberry, 1980) consists of
20 statements describing feelings and reactions that can
occur when taking tests. Subjects responded to each item
using a fourpoint scale of (1) Almost Never, (2) Sometimes,
(3) Often, and (4) Almost Always. Scores may range from
20 to 80, and higher scores indicate higher levels of
anxiety. Correlations between the TAI and Sarason's (1958)
Test Anxiety Scale range from .85 to .95, and the TAI pro
vides subscales for Worry and Emotionality components of
test anxiety.
The ATrait Scale of the StateTrait Anxiety Inventory
(STAI: Spielberger, Gorsuch, & Lushene, 1970) was used to
measure "relatively stable individual differences in
anxiety proneness" (p. 3). The students were asked to re
spond to each item using a fourpoint scale with response
categories identical to those used on the TAI. Total
scores range from a minimum of 20 to a maximum of 80. The
scoring weights were reversed so that higher scores indi
cate higher levels of trait anxiety. The above two scales
are contained in Appendices B 12.
Treatment
The experimental design was a repeatedmeasures paradigm
involving pretreatment and posttreatment assessment of vari
ables on selfreport measures. The purpose of the study was
to determine the efficacy of the multidimensional group
treatment strategy. Pre to posttreatment change was in
vestigated on the following scales:
1) Math Anxiety
2) Confidence in Learning Mathematics
3) Math as a Male Domain
4) Usefulness of Mathematics
5) Effectance Motivation in Mathematics
6) Test Anxiety
7) Worry component of test anxiety
8) Emotionality component of test anxiety.
It was anticipated that there would be significant pre to
posttreatment improvement on all scales or, in cases of non
significant posttest improvement, that the posttreatment
scores would be comparable to those of the nonanxious com
parison group, the Psychology I control group, or the math
classes control group. It was also anticipated that there
would be significant improvement in treatment subjects'
perception of their ability in mathematics. No component
of the intervention was aimed at changing attitudes toward
teachers. No change on the Teacher Scale, therefore, was
predicted nor was a change predicted for the ATrait Scale,
a measure of relatively stable anxiety. The purpose of the
followup study was to assess the predicted maintenance
effects of the anticipated treatment improvement.
Data were collected from treatment subjects (a) just
prior to an initial screening interview during approxi
mately the first three to four weeks of the term and
(b) during the last session of the treatment. The Fennema
Sherman Mathematics Attitudes Scales and the Spielberger
Anxiety Inventories were administered both pre and post
treatment. Mathematics background information (see Appendix
C) was collected pretreatment. The initial screening in
terview, which included a discussion of the background
information, was conducted by the principal investigator.
The FennemaSherman Mathematics Attitudes Scales and
the Spielberger Anxiety Inventories were administered to
control subjects during approximately the same time periods
as pre and posttreatment data were collected from treat
ment subjects. Data were collected from the Math for Ele
mentary Schoolteachers classes in the Spring of 1981. Data
from the psychology students, collected during Spring term,
1982, included pre and posttesting general information
(see Appendix D). Followup questionnaires (see Appendix
F) were mailed to all treatment subjects in October, 1982,
approximately six months, one year, and one and onehalf
years, respectively, after the Spring, 1982, Fall, 1981,
and Spring, 1981, treatment interventions.
Therapists
A male Counseling Center staff psychologist and the
principal investigator served as therapists for two of the
treatments. A female, advanced graduate student in
Counselor Education, was cotherapist for another treatment
group. The remaining three groups were led by the principal
investigator.
General Procedure
All groups met for seven weekly, twohour sessions and
followed essentially the same treatment procedures.
Rationale and Goals. Subjects were given a rationale
that emphasized that 1) they had the intelligence to learn
mathematics; 2) their selfdefeating beliefs, self
statements, expectations, and behaviors directly influenced
their anxiety and other negative emotions and resulted in
their poor performance in mathematics; 3) they would be
selfscientists, learning to understand their own problems
(assessment), devising their individual treatment plans,
carrying out the plans, and reassessing as they progressed;
and 4) their treatment plans would incorporate coping
skills which they could learn and use effectively. Overall
goals would be to 1) replace their maladaptive attitudes,
beliefs, and behaviors with more beneficial ones; 2) manage
their anxiety more effectively; 3) gain confidence in their
mathematical intuition, reasoning powers, and ability to
learn mathematics; 4) focus more on doing math and less on
selfevaluation; 5) learn to have a higher frustration
tolerance for making mistakes and for not solving a problem
immediately; and 6) gain control, to stop feeling helpless,
and to use already established academic coping behaviors.
The entire process would involve a selfimage change.
Format. In general, each session began with group
"rounds." Discussions included homework assignments, im
provements made in coping behaviors, and identification of
problem areas. Discussions were informal, and participants
were encouraged to acquire facilitative interaction skills.
Observational Learning (Modeling). A group setting
made it possible for students to meet other intelligent
adults who have had anxiety and negative feelings about
math and about themselves as learners of math. All three
therapists recounted personal experiences of math anxiety
and how they had been successful in managing their anxiety
and in learning mathematics. The film, Math Anxiety: We
Beat It, So Can You!, provided many additional examples of
people of all ages overcoming math anxiety. Inasmuch as
modeling is more effective if the subjects observe someone
they perceived as a peer (Bandura, 1969), male and female
students from previous Math Confidence groups were invited
to the first session of each group to recount their ex
periences and to answer questions. Finally, group members
provided additional sources of positive reinforcement and
concern for the improved performance of fellow members.
To enhance this effect, members were encouraged to tele
phone each other between sessions and to think of each
other during scheduled math exams.
Homework. Homework assignments were an integral part
of the treatment. Each week subjects received an assignment
based on the concepts and techniques discussed during the
treatment session.
Session Outlines. Outlines of the seven sessions may
be found in Appendix E.
CHAPTER FOUR
RESULTS
These data were analyzed by repeated measures analyses
of variance. An interaction was found in the analysis be
tween groups on all scales with the exception of the trait
anxiety measure. These inconsistent levels of change pre
cluded combining the six intervention groups, and as a
consequence they were examined separately. Duncan's Mul
tiple Range Tests (see Appendix H) illustrate the different
patterns of significance pretest and posttest.
The efficacy of the multidimensional group intervention
was determined by pre and posttreatment measures on several
scales.
FennemaSherman Mathematics Attitudes Scales
Table 3 presents the comparison of means of Math
Anxiety scores. These results indicated that all treatment
groups except Treatment 5 (n = 5) showed significant pre
to posttreatment differences. On a closely related measure,
the Confidence Scale (see Table 4), the improvement of all
six treatment groups reached significance.
Pre to posttherapy mean score improvement reached
significance on the Math as a Male Domain Scale for four
of the six treatment groups as shown in Table 5, while
Table 3
Comparison Between Pretreatment and Posttreatment
Math Anxiety Scores, by Group
Pretreatment Posttreatment
n M SD M SD F
Treatment
1 8 16.88 4.36 33.75 6.52 68.48*
2 8 18.38 4.24 32.63 6.05 66.31*
3 11 18.73 8.49 29.45 8.94 30.56*
4 9 18.89 5.95 34.45 8.87 28.27*
5 5 16.40 6.35 22.40 7.54 6.21
6 9 14.11 5.62 27.89 5.19 50.70*
Control
Psychology 1 34 36.18 8.26 36.24 7.52 0.01
Psychology 2 12 25.17 11.26 23.42 11.37 3.60
Math Classes 20 30.25 10.07 30.90 10.15 0.71
Note. Possible socres range from 10 to
indicate higher levels of math anxiety.
*P < .001.
50. Lower scores
Table 4
Comparison Between Pretreatment and Posttreatment
Confidence Scores, by Group
Pretreatment Posttreatment
n M SD M SD F
Treatment
1 8 22.88 4.42 34.50 5.43 51.88***
2 8 24.13 2.70 34.75 4.90 27.74***
3 11 23.73 10.10 34.10 9.73 22.19***
4 9 23.67 6.56 37.33 8.26 14.31**
5 5 21.40 10.90 29.20 6.69 8.77*
6 9 18.67 5.68 29.78 5.21 84.75***
Control
Psychology 1 34 38.74 8.42 38.94 7.88 .12
Psychology 2 12 25.92 8.94 24.83 8.85 3.04
Math Classes 20 32.75 9.62 32.25 10.17 .56
Note. Possible
are indicative of
*p < .05.
**p < .01.
***p < .001.
scores range from 10 to 50.
Higher scores
greater confidence in learning mathematics.
Table 5
Comparison Between Pretreatment and Posttreatment
Math as a Male Domain Scores, by Group
Pretreatment Posttreatment
Group n M SD M SD F
Treatment
1 8 35.75 7.42 39.25 4.95 5.81*
2 8 30.00 4.57 36.63 5.21 10.60**
3 11 35.27 7.36 40.00 4.73 13.95***
4 9 33.89 7.54 39.33 5.12 4.58
5 5 31.40 8.88 33.60 6.43 1.12
6 9 29.22 5.59 35.33 4.58 33.24***
Control
Psychology 1 34 37.27 6.37 36.50 7.19 1.15
Psychology 2 12 38.50 5.87 37.00 5.83 1.76
Math Classes 20 36.85 5.99 36.60 5.70 0.06
Note. Possible scores range from 9 to
indicate less tendency to view math as a
< 05.
** < .01.
***p< 001.
45.
Higher scores
male domain.
three groups showed significant differences on the Useful
ness Scale (see Table 6). The levels of posttest improve
ment for Group 4 on the Math as a Male Domain Scale and for
Groups 4 and 6 on the Usefulness Scale, while not statis
tically significant, were actually higher than any of the
control group scores.
The levels of improvement of five groups on the Effec
tance Motivation Scale were statistically significant.
These results are presented in Table 7. No component of
the intervention strategy was aimed at changing attitudes
toward teachers, and, as anticipated there were no signifi
cant differences in the pre to posttreatment scores on
the Perception of Attitudes of Teachers Scale (see Table 8).
Control subjects did not show any significant changes from
pre to posttesting on any of the FennemaSherman Scales.
Spielberger Trait and Test Anxiety Inventories
There were no significant differences among the pre
test or the posttest means of the six treatment groups and
the three control groups on the ATrait Anxiety Inventory
(see Appendix H7). Additionally, none of the differences
between pretreatment and posttreatment means reached sig
nificance, as shown in Table 9. Inasmuch as the ATrait
scale by definition measures "relatively stable individual
differences in anxiety proneness" (Spielberger, Gorsuch,
and Lushene, 1970, p. 3), no changes in trait anxiety were
predicted.
Table 6
Comparison Between Pretreatment and Posttreatment
Usefulness Scores, by Group
Pretreatment Posttreatment
Group n M SD M SD F
Treatment
1 8 34.88 3.04 43.00 5.35 17.20**
2 8 33.88 4.49 39.63 3.78 8.36*
3 11 32.45 12.19 39.36 7.50 12.42*
4 9 39.00 4.69 41.78 4.29 2.24
5 5 32.80 8.04 36.60 4.45 2.24
6 9 38.11 3.14 40.44 5.22 2.58
Control
Psychology 1 34 40.15 6.87 39.68 6.62 0.38
Psychology 2 12 39.17 5.51 38.42 5.79 .46
Math Classes 20 39.70 4.93 39.70 5.47 .00
Note. Possible scores
scores indicate more pos
ness of mathematics.
range from 10 to 50. Higher
itive attitudes toward the useful
*P < .01.
**p < 001.
Table 7
Comparison Between Pretreatment and Posttreatment
Effectance Motivation Scores, by Group
Pretreatment Posttreatment
Group n M SD M SD F
Treatment
1 8 19.50 3.51 30.50 5.70 33.79*
2 8 23.38 5.29 31.88 3.72 20.43*
3 11 25.00 9.09 31.00 9.91 20.20*
4 9 27.67 5.90 35.33 7.62 23.25*
5 5 21.20 8.23 25.00 7.11 4.75
6 9 21.78 9.48 29.11 7.91 26.52*
Control
Psychology 1 34 31.38 9.10 31.24 9.20 .06
Psychology 2 12 25.91 7.62 26.00 6.33 .01
Math Classes 20 27.00 7.17 27.55 7.83 .24
Note. Possible scores range from 10 to 50. Higher
scores indicate more active enjoyment of mathematics.
*P < .001.
Table 8
Comparison Between Pretreatment and Posttreatment
Perception of Attitudes of Teachers Scores, by Group
Pretreatment Posttreatment
Group n M SD M SD F
Treatment
1 8 25.13 7.80 25.13 6.83 .00
2 8 30.25 5.97 28.88 5.54 .29
3 11 24.36 10.16 25.64 10.83 .52
4 9 28.22 5.33 29.00 5.45 .24
5 5 23.40 8.47 25.20 10.78 .78
6 9 22.56 9.51 23.22 5.95 .10
Control
Psychology 1 34 36.41 6.43 36.38 6.54 .00
Psychology 2 12 28.00 9.34 28.83 8.47 .98
Math Classes 20 31.95 5.59 31.15 6.92 .34
Note. Possible scores range from 10 to 50. Higher
scores indicate perception of more positive teachers'
attitudes.
Table 9
Comparison Between Pretreatment
ATrait Anxiety Scores,
and Posttreatment
by Group
Pretreatment Posttreatment
Group n M SD M SD F
Treatment
1 8 42.13 11.91 37.50 10.41 1.64
2 8 40.88 7.62 37.25 7.67 2.54
3 11 43.73 14.79 37.35 11.31 9.69
4 9 44.00 9.80 37.67 8.65 3.22
5 5 41.00 5.66 40.80 4.82 .05
6 9 42.56 10.50 39.22 8.54 2.52
Control
Psychology 1 34 36.15 7.26 36.15 7.30 .00
Psychology 2 12 40.92 9.17 44.25 12.11 4.33
Math Classes 20 37.70 6.70 37.55 7.22 .02
Note. Possible scores range from 20 to 80. Higher
scores indicate higher levels of trait anxiety.
There were significant differences, however, between
pretreatment and posttreatment test anxiety scores (see
Table 10). All treatment groups except Treatment 5 showed
significantly lower posttest levels of test anxiety. No
significant changes were shown by control groups.
On the comparison of the Worry component of test
anxiety between pre and posttherapy means, there was a
statistically significant positive change for all inter
vention groups. No significant changes were found for con
trol groups. Groups 1, 2, 3, 4, and 6 showed significant
improvement on the emotionality measure. Although Group 5
showed an average improvement in scores of 1.6, it was not
statistically significant, while a mean score improvement
of .94 for Psychology 1 control group was significant.
This was, in part, due to the relatively greater n of the
control group. Nonsignificant F ratios were found for the
other two control groups.
Pearson productmoment correlation coefficients were
calculated to describe the degree of relationship among
pretreatment scores of the 50 treatment subjects and of the
66 control subjects on the Mathematics Anxiety Scale, the
ATrait scale of the StateTrait Anxiety Inventory, and the
total score, Emotionality score, and Worry score of the
Test Anxiety Inventory. These relationships are shown in
Table 13 for treatment subjects and in Table 14 for control
subjects. For treatment subjects no statistically signifi
cant relationship was found between math and trait anxiety.
Table 10
Comparison Between Pretreatment and Posttreatment
Test Anxiety Scores,
by Group
Pretreatment Posttreatment
Group n M SD M SD F
Treatment
1 8 48.88 11.68 31.63 6.71 13.53*
2 8 46.00 12.02 35.75 11.41 12.27*
3 11 51.91 19.31 42.45 15.24 11.14*
4 9 54.33 15.50 36.11 13.57 9.92*
5 5 56.60 11.65 48.60 7.83 4.48
6 9 53.67 13.47 41.00 7.56 10.22*
Control
Psychology 1 34 35.88 9.77 33.82 8.89 5.01
Psychology 2 12 52.50 13.81 50.67 13.74 .91
Math Classes 20 42.65 12.93 42.65 13.54 .00
Note. Scores may range from 20 to 80.
indicate higher levels of test anxiety.
*p < .01.
Higher scores
Table 11
Comparison Between Pretreatment and Posttreatment
Test Anxiety Scores, Worry Component, by Group
Pretreatment Posttreatment
Group n M SD M SD F
Treatment
1 8 17.37 5.53 12.25 2.92 6.11*
2 8 16.87 3.76 13.88 3.83 22.91***
3 11 19.36 8.39 16.64 6.64 4.64*
4 9 20.67 7.16 14.22 5.04 6.85*
5 5 22.40 4.28 18.00 4.18 7.87*
6 9 20.00 5.41 15.11 3.14 7.52**
Control
Psychology 1 34 13.47 3.55 12.74 3.38 2.99
Psychology 2 12 19.67 5.61 18.66 5.52 1.18
Math Classes 20 15.85 5.48 15.65 5.39 .11
Note. Possible scores range from 8 to
indicate higher levels of worry.
*p < 05.
**p < .01.
***p < .001
Higher scores
Table 12
Comparison Between Pretreatment
Test Anxiety Scores, Emotionality
and Posttreatment
Component, by Group
Pretreatment Posttreatment
Group n M SD M SD F
Treatment
1 8 20.75 5.39 13.25 2.76 9.66**
2 8 18.75 5.50 14.88 4.76 6.14*
3 11 21.73 7.30 17.09 5.68 25.01***
4 9 21.78 5.87 14.33 5.89 10.90**
5 5 22.20 5.36 20.60 2.61 .90
6 9 21.89 5.84 16.89 3.41 7.69**
Control
Psychology 1 34 15.26 4.33 14.32 3.80 4.18*
Psychology 2 12 21.33 5.26 20.92 5.40 .15
Math Classes 20 18.15 5.23 18.20 5.70 .01
Note. Possible scores range from 8 to 32. Higher scores
indicate higher levels of emotionality.
*p < .05.
**p < .01.
***p < .001.
Table 13
Correlations Among Math Anxiety, Trait Anxiety, and
Test Anxiety in Treatment Subjects
Scale 2 3 4 5
1. Math anxiety .15 .51** .45** .53**
2. Trait anxiety .36* .37* .36*
Test anxiety
3. Total score .96** .95**
4. Emotionality .84**
5. Worry
Note. All correlations are based on n = 50.
aATrait Scale of StateTrait Anxiety Inventory.
bTest Anxiety Inventory.
*p < .01.
**p < .001.
Table 14
Correlations Among Math Anxiety, Trait Anxiety, and
Test Anxiety in Control Subjects
Scale 2 3 4 5
1. Math Anxiety .52* .73* .72* .69*
2. Trait Anxiety .70* .67* .67*
3. Total .96* .96*
4. Emotionality .85*
Note. All correlations are based on n = 66.
aATrait Scale of StateTrait Anxiety Inventory.
bTest Anxiety Inventory.
*p < .001.
Higher levels of math anxiety (as indicated by lower scores
on the Math Anxiety Scale) were related to higher levels of
test anxiety and both Emotionality and Worry components of
test anxiety (as indicated by higher scores on the TAI
scale). A moderately significant relationship was found
between trait and test anxiety, and trait and the Emotion
ality and Worry components of test anxiety. Strong rela
tionships, as expected, were found among test anxiety and
Emotionality and Worry.
For control subjects a statistically significant rela
tionship (.52) was found between math and trait anxiety,
and strong relationships were found for the remaining
correlations.
SelfReport Math Ability Ratings
Subjects in treatment groups and the two psychology
control groups were asked pre and posttreatment to rate
their own math ability (see Table 15). The subjects' per
ception of improvement in their ability in mathematics was
statistically significant for all six intervention groups.
There was no change in means for either of the control
groups.
Thus it can be seen that, with the exception of Treat
ment Group 5, all groups met the anticipated criteria for
improvement, i.e., significant pre to posttreatment im
provement on designated scales, or, in cases of nonsig
nificant posttest improvement, that the posttreatment scores
Table 15
Comparison Between Pretreatment and Posttreatment
SelfReport Math Ability Ratings, by Group
Pretreatment Posttreatment
Group n M SD M SD F
Treatment
1 8 2.63 0.74 4.50 1.41 22.18**
2 8 3.13 0.64 4.75 1.16 25.17**
3 11 2.45 1.37 4.73 1.74 46.64**
4 9 2.56 1.24 5.00 1.41 30.25**
5 5 2.75 0.50 4.25 0.96 10.29*
6 9 2.00.. 1.12 4.11 0.93 19.00**
Control
Psychology 1 34 5.03 1.09 5.00 1.04 .20
Psychology 2 12 3.83 1.03 3.67 1.15 2.20
Note. The following scale was used in the selfreport
math ability ratings: (1) Terrible, (2) Very Poor, (3) Poor,
(4) Average, (5) Good, (6) Very Good, (7) Excellent.
*p < .05.
**p < .001.
were comparable to those of the nonaxious comparison group,
the Psychology I control group, or the math classes control
group. All six groups showed significant pre to post
treatment improvement on the Confidence in Learning Mathe
matics Scale, the Worry component of test anxiety, and in
subjects' perception of their ability in mathematics. Sig
nificant pre to posttreatment improvement was found for all
but Group 5 on the Math Anxiety, Effectance Motivation, Test
Anxiety, and Emotionality component of test anxiety scales.
For the Math as a Male Domain and Usefulness of Mathematics
scales all but Group 5 met the criteria of either significant
pre to posttest improvement or had higher posttest scores
than any of the control groups.
Analysis of Variance by Sex, Group and Time
Although it was not a part of the original purpose of
the study, an analysis of variance by sex, group (control
and treatment), and time was performed after the original
analyses. These results may be found in Appendix I. Sig
nificant main effects were found for malefemale differ
ences on the Math Anxiety, Confidence, and Teacher Scales,
with males being found with less math anxiety, greater con
fidence in their ability to learn mathematics, and more
positive perceptions of teachers' attitudes toward them as
learners of mathematics. Significant malefemale differ
ences were not found for Math as a Male Domain, Usefulness,
Effectance Motivation, Trait Anxiety, Test Anxiety, Worry,
or Emotionality.
Significant differences were found for time (pre to
posttreatment) and for group x time interaction for all
scales except Teacher. On the Usefulness of Mathematics
Scale there was also a significant interaction between group
and sex as well as between group and sex and time.
Further analysis of the group x time interaction found
that at pretest control subjects (males and females) were
significantly different (p < .001) from treatment subjects
(males and females) on all 10 scales. At posttest sig
nificant differences were found between treatment and con
trol subjects only on the Teacher scale. Pre and posttest
F values may be found in Appendix I11.
When the interactions on the Usefulness of Mathe
matics scale were examined, it was found that the control
males had significantly higher scores (p < .01) than the
treatment males did at pretest. Treatment males, however,
were higher at posttest, but the difference was not sig
nificant. Similar results were found for females, with
control females having significantly higher (p < .01) scores
at pretest,and treatment females having nonsignificantly
higher scores at posttest. Treatment females were nonsig
nificantly higher than treatment males at pretest. Treat
ment males were significantly higher than treatment females
at posttest (p < .05). The higher scores of control males
when compared to control females both pre and posttest were
not significantly different.
Followup Questionnaire
Out of 50 treatment subjects, 42 (84 percent) responded
to the followup questionnaire which was mailed during Fall
term, 1982. It was not possible to locate three of the sub
jects whose questionnaires were returned by the post office
from their last known address. Hence, only five of the sub
jects who received questionnaires failed to return them.
Results from the followup questionnaires are pre
sented in Tables 16 through 24. These findings provide
strong evidence of the subjects' selfreported continued
improvement in several areas, including performance in math
courses, ability to learn and use math, decrease in math and
test anxiety, and in other specific behavioral dimensions
addressed in the math group up to 1 1/2 years after the
intervention program. Additionally, it appeared there was
also supporting evidence that math anxiety was to a large
extent no longer a negative influence in their life
decisions.
Table 16
Subjects'Perception of Extent to Which Educational,
Career, or Other Life Decisions Were Positively
Influenced by the Math Group
Spring, 1981a Fall, 1981b Spring, 1982c Totald
M SD M SD M SD M SD
4.89 1.96 5.63 1.01 4.79 1.12 5.19 1.33
Note. Subjects responded using a sevenpoint scale from
(1) very small extent to (7) very large extent.
an = 9 in 1 1/2 year followup.
bn = 19 in 1 year followup.
cn = 14 in 6 month followup.
dn = 42.
80
Table 17
Subjects' Perception of Extent to Which Life
Decisions Had Been/Will Be Negatively
Influenced by Math Anxiety/Avoidance
After Math Group
Spring, 1981a Fall, 1981b Spring, 1982c Totald
M SD M SD M SD M SD
2.22 1.48 1.95 1.35 2.43 1.09 2.17 1.29
Note. Subjects responded using a sevenpoint scale from
(1) very small extent to (7) very large extent.
an = 9 in 1 1/2 year followup.
bn = 19 in 1 year followup.
Cn = 14 in 6 month followup.
dn = 42.
Table 18
Subjects' Perception of Extent to Which Math Anxiety
Clinic and the Math Groups Should Be Continued
at the University
Spring, 1981a Fall, 1981b Spring, 1982c Totald
M SD M SD M SD M SD
6.11 1.45 6.68 .95 6.36 .84 6.45 1.04
Note. Subjects responded using a sevenpoint scale from
(1) not at all important to (7) extremely important.
an = 9 in 1 1/2 year followup.
bn = 19 in 1 year followup.
cn = 14 in 6 month followup.
dn = 42.
Table 19
Subjects' Perception of Extent to Which Math Group
Was Important Compared to Other Activities at the
University (Classes, Workshops, Other Academic
Activities)
Spring, 1981a Fall, 1981b Spring, 1982c Totald
M SD M SD M SD M SD
3.44 1.33 4.53 .96 4.36 .75 4.24 1.05
Note. Subjects responded using a fivepoint scale from
(1) bottom 20 percent to (5) top 20 percent.
an = 9 in 1 1/2 year followup.
bn = 19 in 1 year followup.
cn = 14 in 6 month followup.
dn = 42.
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CHAPTER FIVE
DISCUSSION
This chapter is divided into the following sections:
1) summary and interpretation of the results of the study,
2) implications of the results, and 3) future directions
for research.
Summary and Interpretation of Results
The results of this study clearly support the efficacy
of Math Confidence Workshops as a multidimensional group
intervention strategy to help students gain confidence in
their ability to learn and use mathematics and to reduce
their math anxiety.
Perhaps the strongest support for this conclusion comes
from the significant results on the Confidence in Learning
Mathematics measure which includes such statements as "I
am sure I could do advanced work in mathematics," "I have
the ability to get good grades in math courses," and "I
think I could handle more difficult mathematics." All six
treatment groups showed statistically significant pre to
posttreatment improvement differences when compared to
control groups.
Higher levels on the Confidence Scale have been shown
to be significantly related to higher levels of performance
