Title Page
 Table of Contents
 List of Tables
 Review of the literature
 Appendix A: Fennema-Sherman mathematics...
 Appendix B: Spielberger test and...
 Appendix C: Mathematics background...
 Appendix D: Control group general...
 Appendix E: Math confidence workshop...
 Appendix F: Follow-up question...
 Appendix G: Informed consent...
 Appendix H: Duncan's multiple range...
 Appendix I: Analyses of variance...
 Reference notes
 Biographical sketch

Title: Math confidence workshops
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00097424/00001
 Material Information
Title: Math confidence workshops a multimodal group intervention strategy in mathematics anxietyavoidance
Physical Description: xi, 179 leaves : ; 28 cm.
Language: English
Creator: Probert, Barbara Stevenson, 1929-
Publication Date: 1983
Copyright Date: 1983
Subject: Mathematics -- Study and teaching -- Psychological aspects   ( lcsh )
Mathematics -- Study and teaching   ( lcsh )
Psychology thesis Ph. D   ( lcsh )
Dissertations, Academic -- Psychology -- UF   ( lcsh )
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Thesis: Thesis (Ph. D.)--University of Florida, 1983.
Bibliography: Bibliography: leaves 169-177.
Additional Physical Form: Also available on World Wide Web
Statement of Responsibility: by Barbara Stevenson Probert.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00097424
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000352460
oclc - 09723260
notis - ABZ0427


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Table of Contents
    Title Page
        Page i
        Page ii
        Page iii
        Page iv
        Page v
    Table of Contents
        Page vi
        Page vii
    List of Tables
        Page viii
        Page ix
        Page x
        Page xi
        Page 1
        Page 2
        Page 3
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        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
    Review of the literature
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
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        Page 96
        Page 97
        Page 98
        Page 99
        Page 100
        Page 101
        Page 102
        Page 103
    Appendix A: Fennema-Sherman mathematics attitudes scales
        Page 104
        Page 105
        Page 106
        Page 107
        Page 108
        Page 109
        Page 110
    Appendix B: Spielberger test and trait anxiety inventories
        Page 111
        Page 112
        Page 113
        Page 114
    Appendix C: Mathematics background form
        Page 115
        Page 116
        Page 117
        Page 118
        Page 119
        Page 120
    Appendix D: Control group general information form
        Page 121
        Page 122
    Appendix E: Math confidence workshop outlines
        Page 123
        Page 124
        Page 125
        Page 126
        Page 127
        Page 128
        Page 129
        Page 130
        Page 131
        Page 132
        Page 133
        Page 134
        Page 135
        Page 136
    Appendix F: Follow-up questionnaire
        Page 137
        Page 138
        Page 139
        Page 140
    Appendix G: Informed consent forms
        Page 141
        Page 142
        Page 143
        Page 144
    Appendix H: Duncan's multiple range tests for treatment and control groups
        Page 145
        Page 146
        Page 147
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        Page 149
        Page 150
        Page 151
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        Page 153
        Page 154
        Page 155
    Appendix I: Analyses of variance by sex, group and time
        Page 156
        Page 157
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        Page 159
        Page 160
        Page 161
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        Page 167
    Reference notes
        Page 168
        Page 169
        Page 170
        Page 171
        Page 172
        Page 173
        Page 174
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    Biographical sketch
        Page 178
        Page 179
        Page 180
        Page 181
Full Text







Copyright 1983


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
Richard R. Skemp


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


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.



ACKNOWLEDGMENTS. . . . . . . . . . iv

LIST OF TABLES . . . . . . . . . viii

ABSTRACT . . . . . . . . . . . x


ONE INTRODUCTION . . . . . . . 1

Possible Causes for the Mathematics
and Science Crisis . . . . 7
Suggestions for Change . . . . 9
Purpose of the Study . . . . 13
Specific Objectives. . . . .. 15


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

Fennema-Sherman Mathematics Attitudes
Scales . . . . .. . . 59
Spielberger Trait and Test Anxiety
Inventories . . . . . .. 63
Self-Report Math Ability Ratings . 74
Analysis of Variance by Sex, Group
and Time . . . . . . . 76
Follow-up Questionnaire. . . ... 78

FIVE DISCUSSION . . . . . . . . 89

Summary and Interpretation of Results. 89
Implications of the Results. . ... 100
Future Directions for Research . . 101


SCALES . . . . . . . . 105

INVENTORIES. . . . . . . .. 112







TIME . . . . . . . . . 157

REFERENCE NOTES. . . . . . . . . .. 168

REFERENCES . . . . . . . . . . 169

BIOGRAPHICAL SKETCH. . . . . . . . .. 178




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 A-Trait 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


Correlations Among Math Anxiety, Trait
Anxiety, and Test Anxiety in Control
Subjects . . . . . . . . .

Comparison Between Pretreatment and Post-
treatment Self-Report 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


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



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


Six seven-week Math Confidence Groups (N = 50) were

conducted. The experimental design was a repeated-measures

paradigm involving pre- and posttreatment assessment on

self-report 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 self-perception 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 male-female

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 follow-up study which had an 84 percent return rate,

found that positive improvement was long-lasting 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 greater-than-average extent to which per-

formance in other courses and everyday life had been im-

proved. Perhaps more importantly, there appeared to be a

long-lasting positive self-concept 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.


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

three-quarters 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 techno-logy 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 1981-82 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 twenty-five instruc-

tional hours in a school week. The much-heralded 1982 in-

crease in average SAT scores which broke the 19-year decline

proved to be a miniscule one-point 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

one-third of the nation's students take mathematics beyond

the tenth grade, only 6 percent take four years of math,

and one-third 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 one-third 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

cross-national 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


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 "Cabinet-level 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 math-science 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 one-half days each week, attend school for

more weeks of the year, and spend a larger percentage of

the time in school studying mathematics, 23-25 percent in

Japan as opposed to 14-17 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


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 college-level 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 basic-skills 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 fast-paced math

review course of several hundred students. Others believe

that they are in math "flunk-out" 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 relief--avoidance behaviors.

The students, consequently, may appear dumb, lazy, and

self-defeating 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 rote-learning 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 math-science

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 1-4 as a part of a low-cost 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


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


Specific Objectives

The specific objectives of this research were to


1. the pre- to posttreatment change on the following


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-


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' self-reported 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


the literature, and Chapter Three will describe how the

study was conducted. Chapters Four and Five will describe

the results and discuss their implications.


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


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 paired-word

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 one-third experienced extreme levels of

anxiety associated with number manipulations or situations

involving mathematics. In Betz's study from one-fourth to

one-half 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 one-fourth 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 rote-learning appeared as a recurring theme.

Reviewing the writing of a number of these math educators

provided insights pertinent to math anxiety intervention


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 rote-learning. 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 twenty-five 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 self-confidence 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 hard-working

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 theirs--indeed, . 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 schematic-learning; it is rote-learning.

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. Rote-learning 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 anxiety-provoking situation. Trying

to memorize more and more rules and methods without under-

standing provides no basis for long-term retention. Progress

is impeded, self-esteem 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 Yerkes-Dodson

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 "tongue-tied

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 memorize-what-to-do 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


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


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 sex-role

socialization and other societal influences were responsible

for the sex differences at the higher levels of math and


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 sex-role 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 sex-role ideology which results in

differential expectations and socialization practices. One

such commonly accepted belief is that mathematics is a male


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 visual-spatial and mathematical

abilities were "well-established" 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 sex-related 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 sex-related dif-

ferences in elementary school children's mathematical learn-

ing (Fennema, 1977) and few sex-related 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 sex-related 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

one-third 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 Fennema-Sherman 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 test-anxious

students in evaluative situations to the detrimental ef-

fects of learned, task-irrelevant anxiety drives. Learned

task drives and task-relevant 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


Wine's (1971) direction of attention interpretation

suggested that test-anxious students divided their attention

between "self-relevant" and "task-relevant" responses in

contrast to low test-anxious students who focused their

attention completely on the task. Woolfolk and Richardson

(1978) summarized four dimensions of anxious functioning

found in test-taking situations as follows: 1) Negative

self-talk which may include self-escalating, self-perpetu-

ating worry, self-criticism, self-condemnation, and

preoccupation with bodily reactions, 2) Self-evaluative,

self-oriented thinking instead of task-oriented thinking,

3) Ineffective response to bodily signs of tension, and

4) Irrational, maladaptive beliefs about self and the


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 affective-physiological 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


Deffenbacher (1980) after reviewing the literature on

worry and emotionality components made the following sugges-

tions for anxiety-reduction treatment programs: 1) Cogni-

tive restructuring of worry combined with training in task-

oriented self-instruction 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) Self-managed

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 self-control

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

self-control 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

self-control 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 task-oriented 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 self-report 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 self-perpetuating cycle.

The individual is caught in a type of vicious
cycle, a self-perpetuating 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 task-irrelevant 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


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 short-term desensitization

approaches. The marathon desensitization group (MDG) re-

ceived a standard systematic desensitization procedure

using the entire nine-item 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 self-control 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 mathematics-related activities.
(p. 283)

Treatments involving cognitive strategies have also

been applied to math anxiety. Albert Ellis's (1962)

rational-emotive 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 self-statements 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, cognitive-oriented 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. Sixty-nine female

students participated in a three-hour 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 one-half 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

Fennema-Sherman 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.

Sex-role 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

cognitive-attentional 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 long-term
follow-up 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, "one-shot"
treatment studies that pit artificially
truncated treatment procedures against
each other and rarely investigate the
longer-term durability of effects. (p. 285,



Participants in this study were 50 students, 35 females

and 15 males, who self-reported to the University Counseling

Center in response to flyers announcing seven-session 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

mathematics-based 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 two-credit 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-


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.


The Fennema-Sherman 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

five-point Likert scale of (1) Strongly Disagree to (5)

Strongly Agree. Scoring of all negatively worded items was


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 split-half 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 SAT-M (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


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 Fennema-Sherman

Mathematics Attitude Scales. Possible scores range from

10 to 50. Higher scores indicate perception of more positive

teachers' attitudes.

The six Fennema-Sherman Mathematics Attitudes Scales

are contained in Appendices A 1-6.

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 four-point 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 A-Trait Scale of the State-Trait 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 four-point 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 1-2.


The experimental design was a repeated-measures paradigm

involving pretreatment and posttreatment assessment of vari-

ables on self-report 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 A-Trait Scale,

a measure of relatively stable anxiety. The purpose of the

follow-up 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 Fennema-Sherman 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 post-testing general information

(see Appendix D). Follow-up questionnaires (see Appendix

F) were mailed to all treatment subjects in October, 1982,

approximately six months, one year, and one and one-half

years, respectively, after the Spring, 1982, Fall, 1981,

and Spring, 1981, treatment interventions.


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


General Procedure

All groups met for seven weekly, two-hour 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 self-defeating 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

self-scientists, 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

self-evaluation; 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 self-image 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.


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


Fennema-Sherman 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



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*


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



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***


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


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***


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.


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 Fennema-Sherman 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 A-Trait Anxiety Inventory

(see Appendix H-7). Additionally, none of the differences

between pretreatment and posttreatment means reached sig-

nificance, as shown in Table 9. Inasmuch as the A-Trait

scale by definition measures "relatively stable individual

differences in anxiety proneness" (Spielberger, Gorsuch,

and Lushene, 1970, p. 3), no changes in trait anxiety were


Table 6

Comparison Between Pretreatment and Posttreatment
Usefulness Scores, by Group

Pretreatment Posttreatment

Group n M SD M SD F


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


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


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*


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


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


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'

Table 9

Comparison Between Pretreatment
A-Trait Anxiety Scores,

and Posttreatment
by Group

Pretreatment Posttreatment

Group n M SD M SD F


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


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 product-moment 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

A-Trait scale of the State-Trait 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


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*


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


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**


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


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**


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.
aA-Trait Scale of State-Trait 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.
aA-Trait Scale of State-Trait 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


Self-Report 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


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
Self-Report Math Ability Ratings, by Group

Pretreatment Posttreatment

Group n M SD M SD F


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**


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 self-report
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 male-female 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 male-female 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 I-11.

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.

Follow-up Questionnaire

Out of 50 treatment subjects, 42 (84 percent) responded

to the follow-up 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 follow-up questionnaires are pre-

sented in Tables 16 through 24. These findings provide

strong evidence of the subjects' self-reported 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


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


4.89 1.96 5.63 1.01 4.79 1.12 5.19 1.33

Note. Subjects responded using a seven-point scale from
(1) very small extent to (7) very large extent.
an = 9 in 1 1/2 year follow-up.

bn = 19 in 1 year follow-up.

cn = 14 in 6 month follow-up.

dn = 42.


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


2.22 1.48 1.95 1.35 2.43 1.09 2.17 1.29

Note. Subjects responded using a seven-point scale from
(1) very small extent to (7) very large extent.
an = 9 in 1 1/2 year follow-up.

bn = 19 in 1 year follow-up.

Cn = 14 in 6 month follow-up.

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


6.11 1.45 6.68 .95 6.36 .84 6.45 1.04

Note. Subjects responded using a seven-point scale from
(1) not at all important to (7) extremely important.
an = 9 in 1 1/2 year follow-up.

bn = 19 in 1 year follow-up.

cn = 14 in 6 month follow-up.

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

Spring, 1981a Fall, 1981b Spring, 1982c Totald


3.44 1.33 4.53 .96 4.36 .75 4.24 1.05

Note. Subjects responded using a five-point scale from
(1) bottom 20 percent to (5) top 20 percent.
an = 9 in 1 1/2 year follow-up.

bn = 19 in 1 year follow-up.

cn = 14 in 6 month follow-up.

dn = 42.


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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

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