University of Tennessee, Knoxville
Trace: Tennessee Research and Creative
Exchange
Doctoral Dissertations
Graduate School
6-1986
Math Anxiety: Relationship with Sex, College
Major, Mathematics Background, Mathematics
Achievement, Mathematics Performance,
Mathematics Avoidance, Self-Rating of
Mathematics Ability, and Self-Rating of
Mathematics Anxiety as Measured by the Revised
Mathematics Anxiety Rating Scale (RMARS)
Patricia Ann Preston
University of Tennessee - Knoxville
Recommended Citation
Preston, Patricia Ann, "Math Anxiety: Relationship with Sex, College Major, Mathematics Background, Mathematics Achievement,
Mathematics Performance, Mathematics Avoidance, Self-Rating of Mathematics Ability, and Self-Rating of Mathematics Anxiety as
Measured by the Revised Mathematics Anxiety Rating Scale (RMARS). " PhD diss., University of Tennessee, 1986.
http://trace.tennessee.edu/utk_graddiss/1252
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information, please contact [email protected].
To the Graduate Council:
I am submitting herewith a dissertation written by Patricia Ann Preston entitled "Math Anxiety:
Relationship with Sex, College Major, Mathematics Background, Mathematics Achievement,
Mathematics Performance, Mathematics Avoidance, Self-Rating of Mathematics Ability, and Self-Rating
of Mathematics Anxiety as Measured by the Revised Mathematics Anxiety Rating Scale (RMARS)." I
have examined the final electronic copy of this dissertation for form and content and recommend that it
be accepted in partial fulfillment of the requirements for the degree of Doctor of Philosophy, with a
major in Education.
Donald J. Dessart, Major Professor
We have read this dissertation and recommend its acceptance:
John Bradley, Ken McCullough, Paul Wishart
Accepted for the Council:
Dixie L. Thompson
Vice Provost and Dean of the Graduate School
(Original signatures are on file with official student records.)
To the Graduate Council:
I am submitting herewith a dissertation written by Patricia Ann Preston
entitled
"Math Anxiety:
Relationship with Sex,
College Major,
Mathematics Background, Mathematics Achievement, Mathematics Performance,
Mathematics Avoidance,
Self-rating of Mathematics Ability,
and
Self­
rating of Mathematics Anxiety as Measured by the Revised Mathematics
Anxiety Rating Scale
(RMARS)."
I have examined the f inal copy of this
dissertation for form and content and recommend that it be accepted in
partial fulfillment of the requirements for the degree of Doctor of
Philosophy,
with a major in Education.
We have read this dissertation
and recommend its acceptance:
Accepted for the Council:
Vice Provost
and Dean of The Graduate School
MATH ANXIETY:
BACKGROUND,
RELATIONSHIP WITH SEX,
MATHEMATICS ACHIEVEMENT ,
MATHEMATICS AVOIDANCE,
AND SELF-RATING
THE REVISED
SELF-RATING
COLLEGE MAJOR,
MATHEMATICS
MATHEMATICS PERFORMANCE,
OF MATHEMATICS ABILITY,
OF MATHEMATICS ANXIETY AS MEASURED BY
MATHEMATICS ANXIETY RATING SCALE
A Dissertation.
P resented for the
Doctor of Philosophy
Degree
The University of Tennessee, Knoxville
Pat ricia Ann Preston
June
1986
( RMARS )
Copyright
© Patricia Ann Preston, 1986
All rights reserved
DEDICATION
To my mom and dad
ACKNOWLEDGMENTS
Many people have contributed to making thi s d i s s ertation po ssible .
I
am es pec ially indebted to Donald De s s art , the chairman of my doctoral
committ ee.
Special thanks are due John Bradley , Ken McCullough , Paul
Wi shart , Carl Murphy. and Alan Lasater , members of my commit tee .
A particular not e of appreci at ion is due the ins truc tors and
admin i s trator s of the stud y , and the ent ire s t aff of the Mathematics
Department .
I
am gra t e ful to Li s a Hunt and es pecially Michael Keene for all
their sugge s t i o ns and edi t in g and t o Ann LaCava of the Graduat e School
for all her assistance.
But mos t of all
I
thank my husband , our ch ildren and their
grandparen t s for all their support and sacrif ice through the years .
iv
ABSTRACT
Mathematics educa t or s and psy chologi s t s blame "ma th anxiety" for
affecting mathema t i c s learning , performance , and enro llment , and , sub se­
quent l y , choice of college maj or and career .
Res earchers have yet to
agree on the prevalenc e , s t abili t y , and effects of math anxi e ty.
This s tudy (1) i nve s t i gated the prevalence and intensity of math
anxiety in c ollege st udent s ( as a whole , by major , and by sex) ,
( 2 ). de t ermined the s t a b i l i ty of mat h anxi ety over t i me , and ( 3) inve s t i­
gat ed those background and experiential factors re la ted to its oc currence
in college s t udents , us ing da ta gathered on 173 college s tudents in
mathema t i cs , educa t i on , and Engli sh clas srooms .
The da ta concerned c ol­
lege s tud ents ' math anxiety as measured by the Rev i sed Mat hema t i c s
Anxie ty Rat ing Scale ( RMARS) and sele cted cogn i t ive corre la tes of math
anxie ty. and were ana l yzed by analyses of variance , !-tests. and corre­
lat ional analyses.
Based upon the s ta t i s t i cal analyses , these re sults were achieved :
( 1 ) math anxiety is rela ted to cho i ce of college major , ( 2 ) males and
f emales do not differ i n math anxiety levels , ( 3) math anxiety leve ls
change li t t le over a short t i me int erval , ( 4) math anxiety shows rela­
t ively li t tle relati onship to mathema t i cs performance , ( 5 ) math anxiety
shows a moderate re la t i on ship t o mathematics ba ckground , achievement , and
avoidance , and ( 6 ) the hi gher one's level of math anxi et y ( as measured by
the RMARS). the lower one's self-ra ting of mathemat ic s abi l i ty and the
higher one's self-rating of mathematics anxiety.
v
Based upon the results, these conclusions we re dra wn : (1) improving
mat hemat i cs performance will require programs that do more than reduce
math anx i e ty, (2 ) re-entry students would appear to benefit most from
treatment of math anxiety , (3) ma th anxiety appea rs to be related to
inherent mathematical abili ties of students, (4 ) the RMARS seems to
adequat ely measure one's level of ma th
anxiety as perceived by oneself
for all groups except for the Technical Majors enrolled in Precalculus
Mathematics , (5) sex- rela ted diff erences in ma t h anxiety may exist, but
are probably much smaller than sugges ted previousl y , and (6) the reduc­
t ion of math anxie t y in the Technical Majors Groups could be attributed
primarily to the unique elements of these groups:
requisi t es , and posi t ion in the sequence .
vi
course content , pre­
TABLE OF CONTENTS
CHAPTER
1.
PAGE
INTRODU CTION
1
Statement of the Purpose
Research Questions
Definitions of Terms
Method
Assumptions of the Study
Limitations of the Study
Explanation of Notation
Statistical Treatment of the Data
Importance of the Study
Organization of the Study
•
II.
•
•
•
3
3
4
6
7
8
8
9
11
12
.
•
•
•
•
•
•
LITERATURE REVIEW
13
Descrip tions of Math Anxiety
Measurements of Math Anxiety
Studies Describing Math Anxiety in a College
Population
Summary
• • • •
•
III.
•
•
•
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•
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«
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METHOD
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33
37
38
40
41
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42
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RESULTS AND DIS CUSSION
Analysis of the Rev ised Mathematics Anxiety Rating
Scale
C hanges in �th Anxiety Levels
Correlation of the RMARS and the Six Background and
Experiential Factors
Sutntnary
•
•
•
•
•
•
•
V.
25
31
33
The Participants in the Study
The Measuring Instruments
The Curriculum of the Courses Involved in the Study
Procedures for the Groups
Summary
IV.
14
15
•
•
•
•
•
SUMMARY. CONCL�SIONS.
•
AND
.
II
•
•
•
SUGGESTIONS
Answers to Research Questions
Conclusions
Suggestions for Further Research
•
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vii
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42
53
58
71
72
72
77
79
PAGE
LIST OF REFERENCE S
81
APPENDICES
86
A.
B.
C.
D.
MATERIALS USED IN THE STUDY
STATISTICAL DATA
HUMAN SUBJECTS APPROVAL
CODING FOR MATHEMATICS BACKGROUND
•
•
•
•
•
VITA
•
•
•
•
•
87
92
103
105
107
viii
LIST OF TABLES
TABLE
PAGE
36
1.
Breakdown of Reject ed Consent ing Students by Cat egory
2.
Means and Standard Deviat i ons of Scores on the RMARS for
Five of the Groups (Male s and Females)
•
3.
45
Means and Standard Deviations of Scores on the RMARS for
Each of the S even Groups
50
Summary Table for One-Way Analys i s of Variance of Mean
Scores for the RMARS
51
•
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5.
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6.
•
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?he t T e s t s for Differences Be tween Pre t e s t and Pos tt e s t
Means of the RMAR S f o r Each o f t h e S even Groups
•
55
The t Tes t s for Differences B etween Pretest and Pos t t e s t
Means of the RMARS for Five o f t h e Groups (Males Only)
56
The t Tes t s for Differences Be tween Pre t e s t and Pos ttest
Means of the RMARS for Each of the Seven Groups
(Females Only)
57
•
7.
44
, "
Summary Table for two-Way AnalysiS of Variance of Mean
Scores for the ��S
•
4.
•
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8.
•
9.
•
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Correlat i onal Matrix for the Variables Shown in the Table
and RMAR S Scores for Males in Groups Shown
•
11 .
•
Correlational Matrix for the Variables S hown in the Table
and RMARS Scores for Groups S hown
•
10.
•
•
•
•
•
•
•
•
•
•
•
60
61
Corre la t i onal Matrix for the Variables Shown in the Table
and RMARS Scores for Females in Groups Shown
62
12 .
Means of the Variable s Shown in the Table for Groups Shown
63
13 .
Means of the Variables Shown in the Table for Males in
Groups S hown
64
Me ans of the Variables Shown in the Table for Females
in Groups Shown
65
•
•
14 .
•
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15.
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S t a t i s t ical Dat a -- Nont echnica l Majors (n
ix
•
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=
20 )
•
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•
93
PAGE
16.
11-
Statistical Data -- Technical Majors Enrolled in
. . . . . . . · . . .
Mathematics 1700 (n '" 17)
.
.
.
.
.
.
94
Statistical Data -- Technical Majors Enrolled in
Mathematics 1840 (n
==
53)
·
.
.
.
95
18.
Statistical Data
Elementary Education Majors (n
19.
Statistical Data
Mathematics Education Majors (n
20.
Statistical Data
Graduate Students (n
21-
Statistical Data
Control (n
x
==
24)
.
=
·
15)
=
=
31)
13)
97
99
100
101
CHAPTER I
INTRODUCT I ON
Mathemat ical sk i l l s are essential to any pe rson's success in techni­
cal f ields , as we ll as in the non technical fi elds of education, business ,
social and behavioral sciences , the humani t ie s , and the arts .
Addi tion­
al ly, mathematical s k i l ls are needed for personal life; we use mathemat­
ics for such routine activities as ch�£kb0o�ba lancing , compu ter billing ,
fi ling income tax returns , tipping , in terpr eting charts and graphs , and
budgeting .
Desp i t e the import ance of mathematical ski l ls in e ducational , occu­
pa t iona l , and routine act ivities, many students perform poor ly in mathe­
matics courses or avoid taking mathematics courses in high school and
colle ge , thus limi t ing their choice of careers to those which do not
requi re mathema tica l ski l ls ( Betz , 1978) .
The problems of p o or pe rformance in mathema tics courses and mathe­
matics-course
avoid ance have been ident ified as being particularly ap­
pa rent among women .
Fox, Fennema , and Sherman (1977 ) and Maccoby and
Jacklin (1974) found that women in secondary school mathematics courses
did not perform as we l l as men.
S tudying the hi g h scho o l backgrounds of freshmen entering
Univers ity of
Cali fornia-Berkeley
the
in 1972, S e l ls (197 8) found the
incid ence of ma thematics-course avoidance much highe r for females than
for males .
Only 43% of the males had not compl e t e d a second year of
algebra and a preca lculus course, com pared to 92% of the females .
1
Ernest
( 1 976 ) found a pa t t ern of high school mathema tics- cour s e avoidance among
females similar to that found by S e l l s.
His random sample of 50 males
and 50 females at the Unive r s i ty o f Cali forni a-S anta Ba rbara indi cated
that 64% of the males. compared t o 84% of the females , had not comple t ed
four years of high school mathema tics.
Fennema and Sherman ( 1 976 ) found
tha t an increas ing numb e r of inte llectua lly capable s tudent s , e sp ecially
femal e s , fai led to enroll in high school mathematics courses beyond those
requi red .
One impor tant affe c t i v e variable used to explain both ma themat icscour s e avoidance and poor ma t hema tics perf ormance is "math anxi ety"
(Be t z , 1978; Tobias, 1978; Aiken , 1976; Richard son and Suinn , 1972;
Gough , 1954 ) . Math anxiety is frequently refe rred to as "fee lings of,
ten s i on and anxi e ty that interfere wi th the manipula t ion of numbers and
the s olving of mathema t i cal problems in a wide variety of ordinary l i fe
and academic s i tuat i ons " (Richardson and Suinn, 1972, p . 55 1 ) .
Gough iden t i f i ed "mathemaphobia" as a major cause of fai lure in
mat hematics (Gough, 1954 ) .
She found s t udents afflicted wi th ma themapho-
b i a in element ary schoo l , junior high school, high school, and college.
She concluded tha t once mathema t ics courses become opt i onal , mathemaphob i a causes the enrollment in these cour ses to be rela tively low.
More recently, Suinn, Edie , Nicole t t i , and Spine l l i (1972 , p. 373 )
reported that roughly 28% of 397 undergraduates surveyed "exhibi ted
ext reme leve ls of tens i on as sociated wi t h mat hemat ics sit uat i ons or
number manipula ti ons."
Richardson and Suinn ( 1 972 ) s t a ted that
mathemat ics anxiety may prevent a student from pas s ing funda­
mental mathemat ic s courses or prevent his pur suing advanced
cour ses in mathema t ics or the sci ences. We have found that a
number of volunteers for mathematics anxiety t reatment are
gradua t e students who have diff icul ty wi th the small but sig­
nificant number of ma themat ical form ula tions in their area of
specializati on, such as zoo logy or bus i nes s . (po 551 )
2
Math anxiety is believed to be more prevalent in women (Tobias,
1978; Fox, Fennema, and Sherman, 1977) causing among them a lower rate of
enrollment in mathematics courses.
As a result, women frequently cannot
enter into many fields because they lack mathematics prerequisites,
resulting in unequal educational and employment opportunities for them.
In summary, math anxiety has engendered much interest in both the
professional and popular literature.
Mathematics educators and psycholo­
gists have associated math anxiety with both mathematics-course avoidance
and poor mathematics performance.
Mathematics-course avoidance and poor
mathematics performance result in the failure to attain new mathematical
skills and the degeneration of previous skills.
Thus, math anxiety
affects mathematics performance and enrollment, and, subsequently, choice
of college major and career, particularly for women.
I
•
STATEMENT OF THE PURPOSE
The purpose of this study was to investigate the prevalence and
intensity of math anxiety in college students (as a whole, by major, and
by sex), to determine the stability of math anxiety over time, and to
determine those background and experiential factors related to the occur­
rence of math anxiety in college students. This purpose was accomplished
'
by using data gathered on college students in mathematics, education, and
English classrooms; analyzed by an analysis of variance, �-tests, and a
correlational analysis. The data concerned college students' math anxiety
and selected cognitive correlates of math anxiety.
II.
RESEARCH QUESTIONS
,To identify (1) the prevalence and intensity of math anxiety in
a
college population, (2) the stability of math anxiety over time, and (3)
3
the background and experiential factors influencing the occur rence and
stability of math anxiety, the study posited several specific questions:
1.
Is math anxiety related to choice of college major?
2.
Do females and males differ in their math anxiety levels?
3.
Do math anxiety levels change over a short time interval?
4.
Is math anxiety related to
(a)
mathematics background:
highest level of mathematics
course successfully completed?
(b)
mathematics achievement:
score on the ACT mathematics
subtest?
(c)
mathematics performance: grade received in current
mathematics-related course?
(d)
mathematics avoidance: lapse of time since last success­
fully completed mathematics course?
(e)
self- rating of mathematics ability?
(f)
self-rating of mathematics anxiety?
III.
DEFINITIONS OF TERMS
The following definitions of terms are used in this study :
1.
Math anxiety is "feelings of tension and anxiety that interfere
with the manipulation of numbers and the solving of mathematical problems
in a wide variety of ordinary life and academic situations" (Richardson
and Suinn, 1972, p. 554) as measured by Plake and Parker's (198 2 ) revised
version of the Mathematics Anxiety Rating Scale (RMAR S ) .
2.
Mathematics background is the highest level of mathematics
course successfully completed.
4
3.
Mathematics achiev ement i s the score on the ACT mathema t i c s
sub t e s t .
4 . Mathema tics perfo rmanc e i s the grade rece ived i n the mathema t i c s­
rela t ed cour s e currently enrolle d in .
5.
Mathemat ics avoidance i s the lapse of time since las t succ e s s­
full y compl e t ed ma themati c s cour s e.
6.
The Nontechnical Ma j or s Gr oup is compo sed of student s majo ring
i n accoun t i ng , advert i s ing , agr i culture , broadcas t i ng , home economics ,
human services , managemen t , marke t ing, nur s ing , phys ical therapy, pol i t i­
They were enro l led i n Mathema tics 1540-­
cal science , and psycho log y .
C o llege Algebra .
7.
The Technical Maj o r s G r oup is compo s ed of s tuden t s ma j o r ing in
archi t ecture , biology, chem i s t r y , computer sCi ence , engineering , geology,
mathemat ics , and phy s ic s .
Thes e s tuden t s were enrolled in Mathema t i c s
1 7 00--Precalculus o r Mathemat i c s l840-- S ingle Variable Calculus.
8.
The Elementary Educ a t i on Ma j ors Group is compo sed o f students
major ing in elementary educati o n .
They were enro lled in Mathemati cs
2 1 10 , 2 1 2 0 , or 21 30--S truc ture of the Numbe r Sys tem .
9.
The Mathematics Educ a t ion Ma j ors Group is compo sed of studen t s
ma j o ring in mathematics educ a t i on .
Ins t ruct ion 3 7 52--Teaching
of
They we re enrolled in Curriculum and
Mathemat i cs :
Geometry
and
Analysi s ,
Grade s 7 - 1 2 .
10.
The Graduate S tudent s Gr oup is composed of graduate s tudents
majo ring in educa t ional f i elds .
They were enrolled in Curriculum and
Ins truc t i on 56 10--Educat i onal S t a t i s t i c s .
11 .
The Control Group is compo s ed of studen t s enro lled in Eng l i s h
1 0 2D--Eng l i s h Compo s i t i on who we re n o t concurrent ly enro lled i n any
ma themati cs related cours es .
5
IV.
METHOD
During Winter Quarter, 1985, at The University of Tennessee,
Knoxville, data were collected from students enrolled in the following
lecture courses:
1.
Mathematics 1540, College Algebra;
2.
Mathematics 1700, Precalculus Mathematics;
3.
Mathematics 1840, Single Variable Calculus;
4.
Mathematics 2110-20-30, Structure of the Number System;
5.
Curriculum and Instruction 3752, Teaching of Mathematics:
Geometry and Analysis, Grades 7 - 12;
6.
Curriculum
and Instruction 56 1 0, Educational Statistics;
and
7.
English 1020, English Composition .
Four of the five sections of Mathematics 15 40, three of the four sections
of Mathematics 1700, and four of the nine sections of Mathematics 1840
participated in the study.
The one section of Mathematics 211 0, two of
the three sections of Mathematics 2120, and the one section of Mathemat­
ics 2130 also participated in the study, as did Curriculum and Instruc­
tion 3752 (one section) and Curriculum and Instruction 5610 (one sec­
tion) . Finally, 7 of the 11 0 English 1020 sections participated in the
study.
Students enrolled in these courses were from the colleges of
Agriculture, Architecture, Business Administration, Communications,
Education, Engineering, Home Economics, Liberal Arts, and Nursing. Their
majors included the areas of agriculture, architecture, business,
education, engineering, humanities, natural and physical science, and
social and behavioral science.
6
Measurement � Math Anxiety
Math anxiety wa s 3easured by the scores on Plake and Parker's ( 19 82)
revised ver s i on of the Mathematics Anxiety Rating Scale ( Richard son and
Suinn , 197 2), a 24- i tem scale developed to provid e an e f f i c i ent index of
math anxi e t y .
Thi s sca l e wi ll be discussed in more detail in Cha p t ers II
and III .
Meas urement � Background and Experient ial Factors
The responses on the S tudent Inf orma tion Ques tionnaire ( S IQ ) devel­
oped by the inve s t i g a tor d e termined the two factors of c o llege ma jor and
sex ( fo r the two-way analys is of variance) and the six factors of mathe­
mat i c s background , ma th ema t ics achievemen t , mathema t i c s performance,
mathema t i c s avoidance, s e lf-rat ing of mathematics abili ty. and s e l f­
rating of mathema t i c s anxiety ( for the correla t i on s tudy) .
Procedures
During the second week of class the students received wr it ten ex­
planations o f the s t udy , and each part icipant s igned a cons en t form .
( Copies of the cons ent f o rm s are included in Appendix A . )
The RMARS and
the SIQ we re admini s t e r e d t o each student dur in g the second week of
clas s;
seven weeks la ter , the RMARS was admini stered again .
V.
ASSUMPTIONS OF THE STUDY
The following assumpt i on s are impli cit in this s tudy:
1.
B e cause the SIQ and the RMARS required s tudents to answer ques­
t i ons about themselves , the usefulnes s of the s e instruments depende d on
the s tude n t s' a bi l i ty to remember inf ormat i on and feelings ac cura t ely and
on their wi llingnes s t o report thes e items candidly.
7
2.
The inve s t igator tr eated the RMARS scores as int erval data as
did previous authors (Brush , 1 9 78 ; Rounds
&
Hende l , 19 80a; and Resnick,
Viehe , and S egal , 1 9 8 2 ) .
3.
I t wa s as sumed tha t the cla s s e s were formed rand om l y through
computer as signment .
VI.
1.
LIMITATIONS OF THE STUDY
The s tudy wa s limi ted to student s enro lled in tho s e cour s e s
l i s t ed in S e c t i on
IV .
Therefore, t h e conclusi ons a r e appl icable only to
tho s e popula t i ons or s imilar popula t i ons .
2.
O f the 600 s tudent s who ini tially cons ented to part icipate in
the s tudy , da ta on only 1 7 3 were actually analyzed because of selecting
cri teria di scussed in Chapter III .
VI I .
EXPLANATION OF NOTATION
The following symbols will be used in this study :
T8 :
the Technical Maj or s Group enrolled in Mathema t i c s 18 40
T7 :
the Technical Maj ors Group enrolled in Mathemat i cs 1700
N:
the Nontechnica l Ma j or s Group
M:
the Mathematics Educ a t i on Ma j or s Group
E:
the Elementary Education Majors Group
G:
the Graduat e S tudents Group
c:
the Control Group
Ma :
male
Fe:
female
Pr :
pre test, admini s t ered during the second week of schoo l
Po :
po s ttest, admini s t e red seven weeks la ter
SIQ :
S tudent Information Que s t i onnaire
8
Rs:
Plake and Parker's revised version of the Mathematics Anxiety
Rating Scale (also RMARS)
These symbols are used together to indicate various combinations.
PrRsT8, for example, represents the pretest scores of the RMARS (adminis­
tered during the second week of school) to the Technical Majors Group
enrolled in Mathematics 1840.
VI II.
STATISTICAL TREATMENT OF THE DATA
Levels of math anxiety (as measured by the RMARS) by sex and major
were compared by a two-way analysis of variance design; � < .05 was
considered significant.
Post hoc comparisons of significant effects were
made through Scheffe ' s method.
Changes in levels of math anxiety (as measured by the RMARS) from
the beginning of the quarter to seven weeks later were ascertained
through a � -test for correlated samples; � < .05 was again considered
significant.
Student's t-values were calculated both within each major
and separately for males and females within each major.
Pearson product-moment correlation coefficients were calculated to
describe the degree of relationship between math anxiety (as measured by
the RMARS) and (1) mathematics background, (2) mathematics achievement,
( 3 ) mathematics performance, (4) mathematics avoidance, (5) self-rating
of mathematics ability, and (6) self-rating of mathematics anxiety.
Correlations were calculated both within each major and separately for
males and females within each major.
Analysis of the RMARS
The RMARS was given to seven groups:
the Nontechnical Majors Group,
the Technical Majors Group enrolled in Mathematics 1700, the Technical
9
Maj o r s Group enro lled in Mathemati c s 18 40 , the E lementary Educati on
Maj o r s G r oup , the Mat hemati cs E duca tion Maj o r s Gr oup , the Graduate S tu­
dents Group. and the Cont rol Group .
resul t e d:
Thus , a 2 x 7 fact orial design
2 ( male vs . female) x 7 (Nontechni ca l Ma jors vs . Technical
Maj o r s enrolled in Mat hemati c s 17 00 vs . Techni c a l Maj o r s enrolled in
Mat hema ti c s 1840 vs . E l ementary Educati on Ma jors vs. Mathemati c s E duca­
ti on Ma jors vs. Gradu a t e S tu dents vs. Cont rol ) .
The analysis of variance
was computed wi th the &MARS as the dependent vari able .
The followi ng
nul l hypo thes es were t es t ed:
HoI:
The re are no signifi cant di fferences be tween male and
female means on the RMARS acros s m a jo r s .
H02 :
The re a r e no significant di fferences among the
RMARS
m e ans for the Nont echnical Major s , Techni cal Maj o r s enrol led in
Mathemati c s 17 00 , the Techni cal Maj o r s enrol l e d in Mathemati cs 18 40 ,
the E l ementary E d uc a ti on Maj ors , the Mathema t i c s E ducation Ma jors ,
the Graduate S tudent s , and the Control groups .
H03:
The interacti ons ar e each zer o .
Changes in Levels of Math Anxi ety
The RMARS was given during the second we ek of class ( prete s t ) and
s even
week s
later ( po s t tes t ) to
the seven group s .
The following null
hypotheses were tested :
H04:
There are no signi ficant di ffer ences betw een pretest and
p o s t t es t means on the RMARS wi thin each ma jor.
HoS :
There are no signi f i cant di fferences betw een RMARS pre­
t es t and pos t te s t means for males and females wi thin each major.
10
Degree of Relationship Between --theRMARS Scores and the Six Background
and Experiential Factors
-----
Comparisons were aade between pretest RMARS scores and the six
background and experiential factors (described in the preceding sections)
by calculating the Pearson product-moment correlation coefficients for
each of the seven groups and separately for males and females within each
group.
The following null hypothesis was tested:
Ho6:
The correlation coefficients are equal to zero.
IX.
IMPORTANCE OF THE STUDY
The further study of math anxiety is worthwhile for several reasons.
Most colleges and universities have developed criteria to help students
determine which level of mathematics course is appropriate for them.
These criteria include
ACT (mathematics) cutoff points, recommended high
school background courses, and mathematics placement tests.
Although
Tobias (1978), among others. has postulated that math anxiety may explain
poor mathematics performance, information about a student's math anxiety
is seldom used to provide placement guidance in mathematics courses.
Using established levels of math anxiety to guide students in selecting
their mathematics coursework might help place'students in appropriate
mathematics courses.
Mathematics instructors could also use knowledge of
a group's math anxiety to plan more effective class lectures.
Further study of the problem would also yield further insight into
the multidimensionality of math anxiety. The RMARS, which mainl y measures
the dimensions of mat�ematics evaluation and problem-solving anxiety, may
prove adequate in determining the math anxiety of students majoring in
nonmathematics-related fields.
However, many students taking calculus
(which is required in mathematics-related fields) claim that they
11
experi ence math anxi e ty even though they s c ore rela ti ve ly low on ins t ru­
ments that measure mat h anxi e t y . Math anxiety may thus encompass mo re
dimensions than thos e inc l uded in the current measuring i ns t ruments .
Final ly, further s tudy of the prevalence of math anxi e ty at The
Unive rsi ty of Tenness e e, Knoxvi l le, a large , S outhern , s t ate universi ty,
would help com plete the overall pi c ture of the prevalence of math anxi e ty
i n the Uni t e d S tates .
X.
ORGANIZAT ION OF
THE
STUDY
Chapter I inc ludes a s ta t ement of the purpos e, a lis t of the re­
s ea rch questi ons , d e f i ni tions of terms pertaining to the s tudy, a brief
des c ripti on of the method , limi tati ons and assum ptions of the s tudy, an
explanation of the no t ati on , a- brief dis c ussion of the s t atisti cal treat­
ment of the data, and a dis c ussio n of the s tudy 's im por tanc e .
Chapter II is a l i t e ra ture review of the des c ri p ti ons and me as ure­
m ents of math anxi e t y .
Als o inc luded a r e res earch s tudi es pe r t ai ning t o
the problem.
Chapter III des c ri bes the procedures, the s ubjec ts, and the mea­
suri ng i ns t ruments us e d in the current study.
Chapter
IV
repor ts the results of the statis ti ca l analysis of the
data .
Chap ter V summ ariz es the s tudy and states the conclusi ons .
12
CHAPTER I I
LITERATURE REVIEW
For at lea s t thirty years, psycholog i s t s and mathematics educators
have been interested in anx i e ty over mathem a t i c s .
This anxiety t akes
several nam es, including ma themaphobia, number anx i e ty. mathematics anx­
i ety, mathophobia, and math anx i e ty . Few s tudi es in the 19 5 0' s and 1 9 60 ' s
explored the ex tent to which math anxiety correla tes wi th success in
mathem a t i cs.
The feminis t movem ent in the 1970 ' s and ar ti cles in such
popular magaz ines as Saturday Revi ew,
MS,
Tim e, and Newsweek, finally
brought math anxiety to the public' s at tention .
s ent, interest in the problem has int ens i f i ed,
From 1975 to the pre­
and a ser ious movem ent to
under s t and math anxi e ty has beg un.
In 1975 Laz a rus ( S atur day Review), for exam ple, claimed that "mo s t
people d i s l ike--or fear--ma thematl cs" ( p . 46) . He blam ed the curr icula i n
u s e a t mos t s ch oo l s for this ave r s i on .
In 1976 � magazine carri ed an
art icle by Shei la Tobias enti tled "Why is a smart girl like you count ing
on your f inge rs?"
Tobias referred to math anxi ety as a " condi ti on that
d i s propo r t i onately af fects females" ( p. 56).
(Tobias has also wri t ten a
book on the sub ject, Overcom ing Math Anx iety, 1 978 .)
In 1977 Tim e re­
por ted that females in part ic ular ar e ex c luded from technical majors in
col lege because of their avoidance of m a thema tics .
W i lliam s and K ing
( New swe ek, 1980) reported on the d i sput e about sex diff erences in mathe­
m a t ics abi l i ty .
Som e cla im ed tha t the d i ff erences are environm ental
( To bi as, Ivans), wh i le o thers claimed that they are genetic (B enbow and
13
S tanl ey).
However , tw o years later , Tim e (1982 ) repor ted that sex
di f ferences in m athemati c s abi li ty do no t exi s t ( U si ski n and Senk) , that
previous s tudi e s had ac tually measured mathem ati c s perform anc e , not in­
nat e abi li ty.
Thi s survey ci t e s pu bli shed material on the descri p tions of math
anxi e ty , on the meas ur ement s of math anxi e ty , and on the research s tudi es
pertaining t o m at h anx i et y in a co l lege populati o n .
I
•
D E S CRIPTIONS OF MATH ANXIETY
Al though in 1954 Si s te r Mary Fi des Gough s t a t ed that "mathephobi a
ne eds no defi ning" si n c e " the term i s self- de fi ni tive" ( p . 290 ) , psychol­
ogi s t s and mathemati c s e d ucators have si nce attem pted to define mathemat­
i c s anxi ety and i t s coun t er part s.
Of parti cular i n t e r e s t ar� the fol lowing four defi ni tions whi ch are
each as s oci ated w i th th ei r ow n instrum ent for measuri ng math anxi ety .
Fi rs t , D reger and Aiken ( 1957 ) i nves ti gated the presence of "a syndrom e
of em otional reacti ons t o ari thmeti c and m athem ati c s , tentati vely desig­
nated ' num ber anxi e t y'" ( p . 344 ) , in college s tudent s .
Probably the mos t w e ll-known des cri p ti on o f math anxi e ty com es f rom
Ri chard s on and Suinn ( 1 972 ) , who s t ated that math anxi e ty involves " feel­
ing s of tension and anxi ety that interfere wi th the manipulati on of
numbers and the solving o f mathem ati cal probl em s in a wide vari ety of
ordi nary li fe and acad emic situations· ( p . 551 ).
Also , F ennema and S herman ( 1976 ) described math anxi e ty as " feeling s
o f anxi ety , dread , nervousness and associ ated bodily sym ptom s related to
doing mathemati c s " ( p . 32 6 ) .
And Sandman ( 1 9 80 ) defined math anxiety as
" the uneasiness a s tudent feels in si tuations involving mathem ati cs"
( p . 149 ) .
14
Other researchers report simi1ar definit ions of math anxie ty .
In
1 974 , Lazarus re ferred to "mathophobi a" as " an irra t i onal and impedi t ive
d read of mathema t i c s
A s tudent can develop this emo tional and
•
inte llectua l bloc k , making fur ther progre s s in mathema t i c s and closely
related fields very d i f f i cul t " ( p . 16 ) .
"I can' t" syndrome ( p . 57) .
Tobias ( 19 76 ) descri bed i t as an
Donad y and Tob ia s ( 19 77 ) found math anxiety
a "nonra t ional di s t a s t e for and avoidance of ma th and math-related sub­
j ec t s" ( p . 7 1 ) .
Kogelmen and Warren ( 19 7 8 ) found i t an " intens e emo­
ti onal reac tion t o math based on pa s t exper iences " ( p . 9 ) .
Auslander
( 19 7 9 ) defined math anxiety as the "experience of mental disorganizat ion ,
pani c , and fear tha t prevents a person from learning mathematic s "
( p. 1 7 ) .
Finally, Wagner ( 19 80 ) s tated that math anxiety i s " t en s i o n ,
throbbing templ es , t h o u g h t s like ' I don' t know w h a t i t means ,'
know how , '
'I don ' t understand , '
II.
'I can ' t , '
'I don' t
'I hat e it ' " ( p . 58 ) .
MEASUREMENTS OF MATH ANXIETY
Measuremen t s of math anxiety are needed for diagno s i s and evaluati on
purposes .
O f the in s truments designed to measure math anxiety , four
paper-and-penci l , s e l f- report ins truments will be reviewed : ( 1 )
the
"Numb er Anxiety " i t em s of the Taylor Scale of Manif e s t Anxiety , (2 ) the
Mathemati cs Anxiety S c a le of the F ennema-Sherman Mathema t i c s A t t i tudes
Scales, ( 3 ) the Anxie t y Toward Ma thematic s Scale of the Mathemat i cs
At t itudes Inventory, and ( 4 ) the Mat hema t i c s Anxi ety Rat ing Scale .
The "Number Anxie ty" � of the Taylor Scale � Manifes t Anxiety
Dreger and Aiken ( 1 95 7 ) included three more i t ems on the Taylor
Manifes t Anxiety Scale that were " specifically des i gned to measure
feeling s of anxie ty conce rning working with numbers" (p. 345 ) .
15
The three
i t ems were:
(1 ) "1
of ten nervous when I have to do ari thme ti c ," (2 )
am
"Many times when I see a math problem I jus t 'freeze up,'" and (3 ) "I was
never as good in math as in o ther subjects ."
Reliabi li ty and vali di ty
data about thi s instrument are lacking .
The Mathemati cs Anxi e ty Scale of the Fennema-Sherman Mathemati cs �
tudes Scales
The Mathemati cs Anxiety S ca l e (MAS; Fennema and Sherman , 197 6 ) is
one of nine scales dev e l o pe d by Fennema and Sherman to measure atti tude s
related to mathemati c s learni ng .
a five- point Likert format .
MAS i s a 12-i tem, self-ra ting s ca l e in
Items are general, e . g ., "Mathemati c s make s
me feel uneasy and confus ed" (i tem 7 ) ,
S tudents are asked to i ndi cate
the degree to whi ch they agree wi th each s ta t ement, from " s t rongly agr e e"
t o " s t rongly di sagre e ."
mately 5 minutes .
Admini s t ra ti on time of the scale i s approxi-
A ma th anxi e ty score i s calculated addi tively by
s co ri ng six of the i tems negatively and the other six posi ti vely, a hi gh
MAS score indi cating a low level of ma th anxi e ty .
MAS was developed for
use wi t h high school s tudents, grade s 9-1 2 .
Fennema and Sherman repo r t ed s cant reliabili ty and vali di t y data,
but more information ha s recently becom e avai lable .
a spli t-half re li abi l i ty coeffi c i ent of . 92 .
f ound that MAS correl a t ed hi ghi y ( r
�
Betz (1978) repo r t ed
Round s and Hendel (1 980a)
- . 65) wi th the Mathemati c s T e s t
Anxi e ty S ca le o f the MARS , concluding that MAS seemed mai nl y t o measure
mat hema ti cs tes t anxi e t y .
Dew (1982 ) ( reported again in Dew, Galassi,
and Galassi; 1983) found the MAS t o have an internal con s i s t ency reli a bi li ty coeffi cient o f . 72 and a 2-week tes t-retest reliabi li ty of .87 .
She also supported the c ons truct vali di ty of MAS .
1983) ( reported again
in
Finally. Li ng (1982 ,
Frary and Li ng, 1983) factor analysed five of
the nine Fennema and Sh erman math atti tude scales (including MAS) and a
16
t e s t anxi ety scale.
Math anxiety, test anxi e ty , and three of the atti-
tude scal e s all loaded on one factor.
The Anxiety Towa rd Mathemat ics Scale of the Mat hematics At t i tudes
Inventory
The Anxiety Toward Mathematics Scale (ATMS; Sandman , 1 973 , 1 97 4 ) is
one of six scales of the Mat hematics At titude Inventory (MAl).
A s ix-
i t em s e l f-ra ting scale in a four-point Likert format , it measur es the
"uneasiness a s tudent feels in s ituations involving mathemat ics"
( S andman , 1 980, p. 1 4 9).
I t ems are general , e . g. , "working wi t h numbers
u p se t s me," and s tudent s indicate whether they s trong ly agree , agree ,
di sag re e , or st rong l y di sagree wi th each i t em.
the sca le i s approximately four minutes.
Administra tion time of
A math anxi ety score is calcu-
lated by scoring ad di tively, a high AIMS score indicating a high level of
math anxi ety.
AIMS was designed to measure the a t t i tudes of seventh-
through twelf th-graders toward mathematics.
S and man (1 980) claimed support for the construct val i d i ty of the
MAl.
Hi s factor analysi s of the scores obtained from 5 , 03 4 repre senta-
t ively selected secondary mathematics s tudent s yi elds a factor st ructure
that i s "ea s i ly" int e rpre table with reference to each of the six scales.
He calcul a t ed a Cronback al pha reli abi li ty coef fici ent of . 76.
Dew
(1 982, and reaf firmed in Dew, Galas si and Ga las s i 1 983 )
port e d a two-week t e s t-re tes t reliabi li ty of .75 .
re-
However , Dew found an
int ernal consistency reli abi l i ty coef ficien t of . 21 . The cons truct val i d i t y of the ATMS was not suppor ted by Dew.
The Mathematics Anxiety Rat ing Scale
The Mathema tics Anxiety Rat ing Scale (MARS; Richar dson and Suinn ,
1 972) is a s ing le inst rument developed by Richard son and Suinn to measure
17
"f eelings of tension and anxiety that int e r f e re wi t h the mani pulation of
numbe rs and the solving of mathemat i cal problems in a wid e vari ety of
ordinary life and acad em i c si tuat ions" ( p. 55 1 ) .
MARS is a 98- item self­
rat ing sca le in a f ive-point Likert format ( some resear chers used a 94i t em version because a printing error omi t t e d the last 4 i t ems) .
Items
are spec i fi c , e . g. , "Being given a homework assi gnment of many difficult
p robl ems whi ch is due the next class mee t ing" ( Ri chardson and Suinn ,
1 9 7 2, i t em 72).
S tudents are asked to respond t o e a ch i t em according to
how much they are "frightened by i t nowadays."
Administe ring the sca le
takes approxima tely 4 5 minu tes , and the student ' s mat h anxi ety score is
calcul a t e d by summing the response wei ghts . ( We i ghts range from 1 to 5
corresponding to the leve l of anxiety checked , from 1 meaning "not at
a l l" to 5 meaning "very much") .
o f ma th anxiety .
R e li abi l i ty .
MARS .
MARS
A high MARS score ind i cates a high level
was developed for use wi th college students .
Many researchers have c o l le c t e d normative data on the
Using a sample of 39 7 underclassmen ( 8 0% fema le ) enro lled in
educa t i on classes at a large state university in Missouri , Richardson and
S u i nn ( 1 9 7 2) r e po r t ed an internal consist ency re liabili ty coeff i cient of
. 97 .
two
A seven-week test-re t es t reliabi li ty coef f i ci ent obtained
of
the
classes ( n
=
from
35 ) was . 85 .
S uinn , Edi e , Nicole t t i , and Spinelli ( 1 972) collec ted data o n a
sample of 1 1 9 students at a large Colorado stat e univers i ty who volun­
teered to part i cipat e in the study .
A two-we ek tes t- r e t est reliabi li ty
coefficient was .78 .
From their study of 59 elementary educa t i on ma jors enrolled in
mathema t i cs methods courses at the University of Akr on , Sovchik, Meconi,
18
and Steiner (198 1) reported MARS (98-item
cients of .918 and
.
98 2
version)
reliability
coeffi­
.
More recently, Dew (1982) collected data on a sample of 196 students
enrolled in introductory classes at the University of North Carolina at
Greensboro.
She reported (reported again in Dew, Galassi, and Galassi;
1983) a reliability coefficient of .96 for the MARS and obtained a
two­
week test-retest reliability coefficient of .87.
Validity
•
.
Several types of information allowed researchers to de­
termine construct validity.
Two groups of researchers found negative
correlations between MARS scores and the numerical ability test in the
Differential Aptitude Tests.
Richardson and Suinn (1972) collected data
on a sample of 30 upperclassmen (about equally divided between males and
females) enrolled in an advanced psychology class at a large state uni­
versity in Missouri.
The Pearson product-moment correlation coefficient
between subjects' scores was -. 64.
Suinn, Edie, Nicoletti, and Spinelli (1972) gathered
data on a
sample of 44 of the 119 students in their original Colorado sample,
calculating
correlations of -.35 for the Original testing and -.32 for
the retesting (conducted 2 weeks later) .
Further support for the construct validity of the MARS was obtained
from three studies which showed decreases in MARS scores after treatment
interventions.
Richardson and Suinn (1912) collected data from 10
Missouri students; Suinn, Edie, and Spinelli (1910) collected data from
13 Colorado students; and Suinn and Richardson (1911) collected data from
24 Colorado students.
For all three studies, the decrease in MARS scores
was statistically significant.
19
Support for the validity of the MARS was further provided by Brush
(19 78),
who collected data on a sample of 109 upperclassmen majoring in
Humanities, Social Science, or Physical Science at a private coeduca­
She reported negative correlations between MARS
tional university.
scores and the number of years of mathematics taken in high school
(�
•
-.44), MARS scores and enrollment in calculus in college (�= -.21),
and MARS scores and grades in previous mathematics courses (� = -.29).
Studying a sample of 106 mathematics and psychology students,
Morris, Ke11away, and Smith (1977) reported negative correlations between
MARS scores for mathematics students and first exam grade (�
final exam grade (�
=
•
-.21),
-.21) and course grade (�= -.22); and between MARS
scores for psychology students and first exam grade (� = -.37) and course
grade (�
=
-.30).
More recently, Dew (1982) and Dew, Galassi, and Galassi (1983) have
prOVided data in support of the validity of MARS.
Dew gathered
data on
a sample of 63 students randomly selected by gender from a larger sample
of 769 students in introductory classes at the University of North
C arolina at Greensboro.
She found that MARS scores have significant
inverse relationships to mathematics performance (as measured by computa­
tional problems, �= -.39, and word problems, r = -.41).
Dimensionality.
Researchers disagreed whether MARS is unidimen­
sional or multidimensional.
Richardson and Suinn (19 72) stated that MARS
items are "heavily dominated by a single homogeneous factor, presumably
mathematics anxiety" (p. 553).
Richardson and Woolfolk (1980) also found
just one factor involving evaluative academic and problem-solving situa­
tions, accounting for 76% of the variance. They performed a principal
components factor analysis with a varimax rotation of the factors on MARS
20
scores (9a-item version) from the Richardson and Suinn (1972) study (397
underclassmen, 80% female, enrolled in education classes at a large state
Almost all MARS items correlated above .40 with
university in Missouri).
total scores.
Other researchers found the MARS to be two- or three-dimensional.
Brush (1978) also performed a principal components factor analysis with a
varimax rotation of the factors on MARS scores (94-item version), the
details of which were not contained in the report.
Having gathered data
on a sample of 189 upperclassmen majoring in Humanities, Social Science,
or Physical Science at a private coeducational university,
she reported
that the factor analysis indicated the presence of two factors:
Solving Anxiety (45 items) and Evaluation Anxiety (31 items).
of items loading on the former are "adding up 976
+
Prob1em­
Examples
777 on paper" (item
14) and "figuring the sales tax on a purchase that costs more than $1.00"
(item 48).
Examples of items that loaded on the latter are "thinking
about an upcoming math test one day before" (item 74) and "being given a
homework assignment of many difficult problems which is due the next
class meeting" (item 72).
Morris, Kellaway and Smith (1978) conducted a study of 106 mathe­
matics and psychology students and identified three subscales of the MARS
(94-item version): (1)
Math Class Anxiety (8 items), (2) Math Studying
Anxiety (9 items), and (3) Math Test Anxiety (10 items).
The first
subscale includes the MARS item "walking into a math class" (item 28);
the second
includes the MARS item "studying for a math test" (item 34);
and the third includes the MARS item "taking an examination (quiz) in a
math course" (item 53).
No information was provided about how the
21
subsca1es were ident i fi e d or how the items on each subsca le we re chosen.
A complete li st of the i t ems on each subscale was unavailable.
Rounds and Hende l ( 1980a) co llected data from 35 0 female partici­
pants in a ma them a t i c s -anxiety treatment program at a large midwe s tern
universi ty.
They performed a principal componen t s factor ana lysis wi th a
direct oblimin and a varimax rotat ion of the factors on MARS scores ( 94i tem vers ion).
to . 30.
Factor-pattern loadings were
all greater than or equal
Factor 1, wi th an e i genvalue of 29. 12, was labeled Mat hematics
T e s t Anxiety and inc l ud e d 42 items such as "taking an examina tion ( quiz)
in a math course" ( i t em 53) and "buying a ma th t ex t book" ( item 23).
Factor 2, wit h an eigenvalue of 7. 68, was labeled Numerica l Anxiety and
included 44 items such as "having someone wat ch you as you tota l up a
column of figures" ( i t em 2), "totaling up a dinner bi ll that you think
overcharged you" ( it em. 10) , and "determining the grade point average for
your las t term" ( item 18).
Resnick, Viehe , and Segal� ( l982) studied freshmen (n
private , nons ectarian , coeducat iona l institution .
=
1106) at a
They factor analyzed
the MARS ( 98-it em ve r s ion) scores us ing a principal component analys i s
and a varimax rota tion.
They ident ified three factors:
( 1) Evaluat ion
Anx iety ( 19 item s) , ( 2) Social Responsibility Anxi e ty ( 4 items) , and ( 3)
Ari thmetic Computation Anxiety ( 7 items). Evaluat ion anxiety had an
eigenvalue of 30. 15 ,
factors .
compared with 5. 08 and 4. 35 for the other two
MARS i tem 75 , "thinking about an upcom ing math test 1 hour
before , " loaded on the Evaluation Anxiety fac tor;
MARS item 12, "being
t reasurer for a club , " loaded on the Soc ial Res pons ibility Anxi ety fac­
tor;
and MARS item 69, "being given a s e t of multiplicat ion problems to
so lve," loaded on the Ari thmetic Computation Anxiety factor.
22
Thus, Brush (1978); Morris, Kellaway, and Smith (1978); Rounds and
Hendel (1980a); and Resnick, Viehe, and Segal (1982) each identified at
least two factors within the MARS,
while Richardson and Suinn (1972) and
Richardson and Woolfolk (1980) concluded that MARS was unidimensional.
This discrepancy seems to be largely a matter of interpretation of the
factor analysis, not a matter of the actual results of the procedure.
In
fact, Resnick, Viehe, and Segal (1982) concluded:
very important to note that although the MARS
It is .
does have a multidimensional structure,
there is a single
primary dimension, Factor 1
[Evaluation Anxiety], accounting
for the largest part of the variance, with the two other fac­
tors accounting for significantly less.
•
•
In fact, Richardson and Suinn were �orrect in stating that the
MARS as a test is highly reliable and "indicates that the test
items are heavily dominated by a single homogeneous factor,"
(p. 45)
Relationships Between the Math <Anxiety Measures
Dew (1982) found that
other (E
=
MARS
and MAS correlate strongly with each
-.68), indicating that they share common variance (46. 24%)
"that can be assumed to represent the construct of mathematics anxiety"
(p. 117).
Rounds and Hendel (1980b) found a correlation of -. 55 between
MARS and MAS.
In particular, MAS correlated
-. 65
with the Mathematics
Test Anxiety Scale and -.27 with the Numerical Anxiety Scale.
Revised Versions of MARS
Three groups of researchers have developed revised versions of the
MARS.
Richardson and Woolfolk (1980) chose the 40
MARS
items that most
highly correlated (from .74 to . 56) with total MARS scores.
These items
described evaluative academic and problem-solving situations.
Richardson
and Woolfolk (1980) stated that
this 40-item scale is presumably at least as reliable, stable,
and valid as the original AMRS [sic] and is almost certainly
23
dominated by a single homogeneous factor of anxiety concerning
evaluative test-taking and problem-solving mathematics situa­
tions.
We recommend its use in clinical and mathematics anx­
iety research. (p. 274)
Rounds and Hendel (1980a) developed scales representing the two
MARS factors they identified from their factor analysis.
"sequential strategy of item selection
•
•
•
They used a
with the total sample to
create the 15- to 20-item MARS factor derived scales" (p. 141).
These
scales were subsequently tested for certain expected discriminant or
convergent relationships between the factor-derived measures of math
anxiety and other specific anxiety scales and the measure of mathematics
performance.
Rounds and Hendel report that the internal consistency
reliability coefficient alpha was .93 for the Mathematics Test Anxiety
Scale and .87 for the Numerical Anxiety Scale.
These coefficients "com-
pared favorably" (p. 144) with the one reported by Richardson and Suinn
(1972) for the total MARS (.97).
Rounds and Hendel also reported a
Pearson product-moment correlation coefficient of .34 between the two
scales.
They claimed that this coefficient supports that the two scales
are independent math anxiety scales.
Plake and Parker (1982) developed a 24-item version of the MARS by
choosing the items they believed measure "class-related anxiety in statistics courses" (p. 552).
A principal components factor analysis with a
normalized varimax rotation of this shortened version of MARS revealed
two factors:
(l) Learning Mathematics Anxiety and (2) Mathematics Eval-
uatio n Anxiety.
An example of an item that loaded on the former is
"watching a teacher work an algebraic equation on the blackboard " (item
25). and an example of an itern that loaded on the latter is "being given
a homework assignment of many difficult problems which is due the next
class meeting"
(p. 72). Plake and Parker investigated the 24-item MARS'
24
internal consistency and relationship to scores on the total MARS scale'.
They reported an internal consistency reliability of . 98
and a correla-
tion coefficient of .97 between their 24-item version and the original
MARS.
III.
STUDIES DESCRIBING MATH ANXIETY
IN A COLLEGE POPULATION
Research focusing on math anxiety in a college population has dealt
with the prevalence and intensity of math anxiety and the relationships
between math anxiety and mathematics course and exam grades, sex of the
student, age of the student, number of years of high school mathematics
taken. college major. number of years elapsed since last mathematics
course completed. and score on the ACT mathematics subtest.
The results
of these studies are seemingly inconsistent and inconclusive; the various
researchers did not use the same instruments to measure math anxiety. nor
did they use the same types of students. e. g., all females, only freshmen, only participants in a math anxiety reduction project.
Dreger and Aiken (1957) administered a three-item Number Anxiety
Scale to measure the math anxiety of 704 basic mathematics students at a
large Florida university.
They reported that 3Sr. of the students in that
sample had "high" levels of math anxiety.
They concluded that "number
anxiety" and general anxiety appeared to be separate constructs. that
"number anxiety" and general intelligence did not seem to be related, but
that high "number anxiety" was
matics
grades (E
-.44. n
significantly
704; �
•
�
related
.51 . n
-
=
to
lower
mathe-
40).
Aiken (1970) reported only one study dealing with math anxiety
conducted during the 1960's.
In this study, Natkin (1966, 1967) devised
25
a treatment to reduce mat h anxiety which invo lved u s ing Galvani c Skin
Reac t ions to measure math anxiety .
Richard son and Suinn ( 1 9 7 2 ) admini s t ered the MARS to 397 freshmen
and s ophomo res ( 80% fema l e ) in beginning educ a t ion classes at a large
M i s s o ur i s t a t e unive r s i ty . They found tha t ma th anxi ety wa s a "fairly
commo n" problem in thei r sample .
However , no s i gn i f i cant dif ferences
exi s t e d be tween mean MARS scores for males and f emales .
The Pearson
pro duct-moment co rrelat ion coefficient between MARS scores and Differen­
t i al Ap t i tude T e s t s c ores ( a commonly use d t e s t made up of mathematical
problems that range from s imple t o increasingly compl ex ) was - . 64
(£ < . 01 ) , " indicat ing that high
MARS
performance on the ma thema t i c s tes t "
s c or e s are a ss o c i ated wi th poor
( p o 553 ) .
Based on the res u l t s of admini s t ering a rev i s e d ve rsion of the
Mathema t i c s Anxiety S c a le (MAS ; Fennema and Sherman , 1 9 7 6 ) to 65 2 under­
classmen enrolled in ba s i c mathema t i c s , precalculus or psychology, Betz
1978 concluded that mat h anxiety occurred "f requently" among college s t u­
dent s , especially among women and student s wi th " inadequate" high s chool
backg rounds .
She con j e ctured that math anxiety "may be problematic even
for those studen t s who plan maj ors and/or careers requiring extensive
math background " ( p . 44 6 ) .
Betz also found that lower reported levels of
math anxi ety were rela ted to higher achievement in mathema tics as mea­
sured by test score s on the
ACT
Ma thema t i c s subt e s t , and lower test
anxie ty a s measured by Spielberger ' s Tes t Anxiety Inventory.
Brush ( 1 9 7 8 ) conduc t ed a study involving two samples of upper­
classmen at a priva t e c o educational univer s i t y .
Both samples contained
Humanit i e s , Social S c ience , and Phy si cal S c i ence ma jors , apprOXimately
evenly divided between males and female s .
s i gnificant d i f ference s (!
7 . 12
26
and F
She repo rted that there were
=
5 . 63 , £ < . 01 ) between MARS
(94 -item version) scores of Humanities, Social Science, and Physical
Science majors, from highest to lowest, respectively .
With regard to sex
differences on MARS scores, Brush observed that in one of her samples ,
females scored significantl y higher than males, but in her other sample,
no sex differences were found .
She concluded that students who took
2 - 3 years of mathematics in high school scored significantly higher
(E = -.44) on MARS than students who took 4 - 5 years of mathematics in
high school.
Also, students with higher MARS scores were less frequently
enrolled in calculus (E = - . 21) and received lower grades in mathematics
(E = -.29).
Higher MARS scores were
like of mathematics (E
=
positively
correlated
with
dis­
. 39) and feelings of anxiety about mathematics
(E = . 34) .
Morris, Kellaway. and Smith (19 7 8) conducted a study involving 106
college mathematics and psychology students .
They found that MARS (94 -
item version) scores were higher for psychology
mathematics
students
than
for
students (� = 2 . 24 , � < .05) and were inversely related to
performance as measured by final exam (E = -.37 ) and course grade
(E = -.30) for psychology students.
They found no sex differences in
MARS scores.
Boodt (19 7 9, 1980) administered the 98-item version of MARS to 228
remedial algebra students at a large metropolitan midwest university. She
found a significant reduction in the level of math anxiety ( over the
period of one semester) when students were grouped according to sex .
Lavroff (1980) randomly sampled 237 upper level students from 80
public colleges and universities in 50 states.
He concluded that math
anxiety (as measured by MARS) correlated more highly with choice of
academic major than sex , that math anxiety appeared to operate as an
27
� inhibi tor� in the choi ce of majors for student s who reported MARS scores
above the sample average , and that females were affected by math anxi ety
in the selection o f majors mo re than males ( wi th female education majors
repor t ing the highe s t math anxi ety scores ) .
Calvert ( 1 981 ) conduc ted a correla t i onal study involving 441 precal­
c ulus ma thematic s s tudent s .
She conc luded that mean MARS s c ores d iffered
by sex , females scori ng s igni ficant l y higher than male s .
She also found
an invers e rela ti onship be tween MARS scores and the level of mathematics
course previously completed , with students compl et ing only a general
mathema t i cs course having the highest MARS scores .
She did not find a
s igni f i cant dif ference among the leve ls of math anxiety experienced by
persons of different ages .
However , she did find that s tudents receiving
l ow grade s ( C , D , or F ) in the i r previous mathemat i cs course had higher
leve l s of math anxi e t y than student s who had received h igh grades ( A or
B) .
Sovchik , Mecon i , and Steiner ( 1 981 ) reported a sta t i s tical l y signif­
i cant: (.!. = 4. 29 , .E. < . 05 ) math anxiety reduc t ion ( as measured by MARS )
from pretest to pos t tes t in 59 students enroll e d i n a pres ervice elemen­
tary mathematics me thod s course .
They t ent atively concluded that taking
the mat hematics methods cours e reduced the math anxiety of these stu­
d ents .
Dew ( 1982 ) conduc ted a study involving 769 student s enrolled in
introduc tory classes at a southeastern university.
Dew ( reaffi rmed in
Dew, Galass i , and Galas s i , 1983 ) found sex-related differences on MARS
score s , wi th females scor ing higher .
But she j udge d the dif ferences to
be relatively small , a mean of 185 . 45 6 for males compared to 1 9 3. 89 1 for
femal es .
Dew computed a correlation of . 55 between the MARS and the TAl
(Test Anxiety Inventory . Spi e lberger , 1977 ).
28
She conc luded that math
anxiety was related t o t e s t anxi e ty , but not equiva lent to i t .
Dew,
Galas s i , and Ga las s i ( 1 984 ) further s t a t e d that math anXi e t y , as measured
by MARS (98 item s ) , wa s s igni f i cantly and inver s el y related for two tasks
( numerical compu t a t ions and word problems in a t e s t- like s i tuat ion ) .
They concluded that "math anxi ety had only a modes t relation to math
performance"
( p. 583 ) .
Resnick, Vi ehe , and Segal ( 1 98 2 ) found that 1106 co llege freshmen at
a privat e , non s ec tarian coeduca ti onal ins t i tu t i on had low l evels of math
anxi e ty , as measured by MARS (9'8 - i t em ve rsion ) .
They also re ported that
the re were no large sex di f ferences in degree of math anxie t y .
Math
anxi e ty was found mor e prevalent among s t udents enrol led in pre ca lculus
than among s tude n t s enrolled in the s t andard calculus sequence .
Correla­
t ions between MARS scores and grades ranged from . 005 to . 27 6 , al l non­
s ig n i f i cant .
Themes ( 1 9 8 2 ) conduc ted a s tudy involving 6 1 women , age range
1 8 - 60 , at a small , privat e Ohi o colleg e . She found no signi f i cant
correlat ion between MARS scores and grade point average in mathema t i c s ,
age , number of mathema t i c s cour s es comple t e d , and lengt h of time s ince
las t mathematics cour s e .
Sherman ( 19 8 3 ) compared the mathematics a t t i tudes of 63 g i rl s who
t ook two or three yea rs of high school mathematics .
Resul t s conf i rmed
that fear of mathemat i c s decreased in girls con t i nuing in mathema t i cs ,
and a t t i tudes toward s mathema t i cs be came more po s i t ive .
L i ng ( 1982 , 1 9 83 ) and rea f f i rm ed in Frary and Ling ( 1 9 8 3 ) repo r t e d
no s e x d i f f erences i n mean scores f o r the MAS
.
Their conclus i on was
bas ed on a s tudy invo lving 491 univers i ty s tudent s enrolled in mathe­
mat i c s courses ( large l y non t echni cal majo rs ) at a large , moderately
s el e c t i ve s t a te univers i t y .
They did report that higher leve l s of mat h
29
anxiety we r e as sociated wi th lower levels of mathemat ics compl eted in
high school, lowe r co llege grade point averag e s , and lower cour se grades.
F ina l l y , Fee-Fulkerson ( 1 982) and repor ted again in Fulkerson ,
Gal assi , and Ga lassi ( 1 98 4) found that math anxi e ty , as measured by }�RS ,
( 98 item s ) wa s not s i gnif icantly rela ted to ma themat ics performance , as
measured by solving mat hemat ical problems taken from the Scholas t ic
Apt itude Test.
They al so concluded that cognit ions do not vary as a
funct ion of math anxi ety or sex .
Subject s for the study were 71 stu­
dents , randomly selected by sex , from 5 8 2 students in large introductory­
level cla s s es conduc t ed at the Univer sity of North Carolina at Chapel
Hill .
In summary , the majority of studies found math anxiety to be s ignif­
icantly inversely re lated to performance in mathema tics as measured by
ach ievement t e s t s ( Be t z , 1 978) and as measured by mathemat ics course and
examina tion grade s (Drege r and Aike n � 1 957; Richardson and Suinn , 1 972 ;
Brush , 1 978; Morr is , Ke1laway, and Smith , 1 978; Calvert , 1 98 1; Frary and
Ling , 1 98 3) .
One study even obtained both s i gnificant and nonsignificant
relat ions be tween math anxiety and various math performance tasks (Dew ,
Galas s i , and Galassi , 1 98 4) ;
and two studi es found that math anxiety wa s
not signif icantly rela ted to math performance (Res nick , Viehe , and Segal ,
1 98 2; Fulker s on , Gala s s i , and Galas s i , 1 9 8 4) .
Mos t of the data sugges ted that math anxiety is a common phenomenon
among college studen ts (Dreger and Aiken , 1 957 ; Richard son and Suinn ,
1 97 2; Be t z , 1 97 8 ) . Howeve r , Resnick, Viehe , and Segal ( 1 982) ascertained
that from the results of their s tudy only a small number (2% of their
sample of 11 06) repor ted high levels of math anxiety .
So the prevalence
of math anxi ety may vary cons iderably from one college population to
another .
30
The studi e s agree that the more years of high school mathema t i cs
suc c e s s fu l l y complet e d . the lower the level of math anxiety ( Brush , 1978 ;
Calvert , 1 9 8 1 ; Re sni ck . V i ehe , and Segal , 198 2 ; Them e s , 19 8 2 ; Frary and
Ling , 1 9 8 3 ) .
However , in the study that corre lated the number of years
s ince the last mathem a t i c s course was comple t ed , Themes ( 1 982 ) reported a
lack of signi f i cance .
The l i t e ra ture s e ems to agree that the more t e chni cal the major , the
lower the lev e l of math anxiety reported ( Morri s . Ke l laway , and Smith ,
1 9 7 8 ; Brush , 1 9 7 8 ; Lavr of f , 1980 ; Resnick, Vieh e , and Segal , 198 2 ) .
However , the li t e rature wa s divided a s t o wh ether there are
related dif ferences in math anx iety .
sex­
Betz ( 1 9 7 8 ) , Calvert ( 19 8 1 ) , and
D ew , Gala s s i , and Galas s i ( 19 83 ) found math anxiety more prevalent in
women .
In one of her samples , Brush , ( 19 7 8 ) found sex- re la ted diff er­
ences in math anxie t y , wi th women being more math anxiOUS , but she found
n o sex- r e la t e d differences in another sample .
Richar d s on and S u i nn
( 19 72 ) , Resnick, Viehe , and S eg al ( 1982 ) , and Frary and Ling ( 1 983 ) found
no sex-related di fferences in math anxiety .
IV .
SUMMARY
This cha p t e r has d i s cu s s ed the his to r i ca l background of math anxiety
and presented vari ous d e s c r ip t ions of math anxiety .
It may be concluded
that math anxiety does exist in college popula ti ons and that math anxiety
can be measured by us ing Plake and Parker ' s revised vers ion of the Mathe­
mat i c s Anxiety Rat ing S c a le .
S everal s t udi es wer e reported whi ch sugge s t ed rela tionships be tween
math anxie ty and cho i ce of ma j o r in col lege , sex , performance i n mathe­
mat ics , and experience in mat hematics .
31
However , the studies frequentl y
d i s agreed on the nature of the relati onships .
Because further expl or­
a t i on of the pos s i b l e relat i onships between intens i ty of math anxi e ty and
several key vari ables would prove valuable , the ma jor hypo theses of the
present st ud y evolve d .
32
CHAPTER III
METHOD
Thi s chapter des cr i bes the s tuden t s part ic ipat ing in the s tudy. the
measuring ins t ruments used . the curri culum of cours es invo lved in the
s tu d y , and the procedures followe d .
I.
THE PARTIC IPANTS IN THE STUDY
P a r t i c i pants in the s tudy included s tudents enrolled in :
1.
College Algebra (Mat hema t i c s 1540 ) ,
2.
Preca l c ulus Mathemat i c s (Mathema t i c s 1700 ) ,
3.
S ingle Variable Calculus (Mathematics 18 40 ) .
4.
S tructure of the Number
Sys tem (Mathemati c s 2 1 1 0-2 1 2 0-
2 1 30 ) ,
5.
Teaching 'of Mathema t i cs :
Geometry and Analys i s , Grades 7 -
12 ( Curriculum and Ins truc t i on 3 7 5 2 ) ,
6.
Educa t i onal S ta t i s t i c s ( Curr iculum and Ins t ruc t ion 5 6 10 ) ,
and
7.
Eng li sh Com po s i tion (English 10 20 )
dur in g Winter Quart e r . 1985 , at The Univers ity of Tenne s s ee , Knoxville .
The s tudent s were about evenly divided be tween males and females ( 44 %
male s and 56% female s ) .
In par t i cular , however , the Technical Maj ors
Group was pred ominantly male , whi l e the Elementary Educ a t i on Maj ors Group
and the Graduate Stude n t s Group we re predominantly fema l e .
The o ther
three groups , Nontechni cal Ma jors , Mathema t i c s Education Maj ors , and the
33
Con t rol Group, were fairly evenly divided between males and females.
About 40% of the students were Technical Majors, 12% were Nontechnical
Ma jors, 25% were Educat ion Majors, 9% were Graduate Students, and 1 4%
were in the Control Group.
During the second week of school, adm inistrators read a common
int roductory statement to each class briefly explaining the study and the
stude nts' role in it .
Students agreeing to participate in the study
writ t en consent forms and indicated their age range (either under
signed
18 or 18 and older).
the study.
Students under 18 years old were not included in
(Copies of the consent forms are included in Appendix A . )
For consenting students to be included i n the study, they had to
meet these condit ions :
*
be 18 or older
(so that parental perm ission was not required).
*
have completed the RMARS on the init ial and final testing dates
(because only studen t s who completed the course were included in the
s tudy).
*
have completely and properly answered all questions on the SIQ
and the RMARS
(because only students for which all data was available
were included in the study).
*
have the ACT mathematics subtest score on their permanent record
(ex cept for Curriculum and Instruct ion 5610 students who, because they
were graduate students, did not have ACT scores on file).
*
never have par t icipated in a math anx iety treatment program
(because par t icipation in such a prog ram might affect their level of math
anx iety ) .
*
not be repeating their mathemat ics-related course
(because repeating a course might affect their level of math anx iety).
34
*
not represent the major typical of the mathematics-related cour se
(for example, an Engli s h major enrolled in Mathematics 1840--a Technical
Majors Group).
In addition, those in the Control Group were rejected if they were en­
rolled in a mathematics course.
Of the 600 students who initially consented to participate in the
study, data on only 173 were actually analyzed.
Almost one-half of those
who were not included in the study were rejected because they were not
present on the date the final testing was done.
Over 20% could not be
included in the study because they were in the Control Group (enrolled in
Engli sh 1020) but were also taking a mathematics cour se.
Approximately
15% did not fill out the instruments (SIQ and RMARS) properly.
The
remaining 15% were rejected because of age, grade, major, or other selec­
ting criteria di scuss ed previously.
In particular, of the 101 students in the Nontechnical Majors Group
who were initiall y tested, only 20 students were actually included in the
study.
In the Technical Majors Group, 224 students completed the initial
testing
(76 from Mathematics 1700 and 148 from Mathematics 1840). while
only 70 students were actually included (17 from Mathematics 1700 and 53
from Mathematics 1840).
Thirty-one of the 9 2 Elementary Education Ma­
jors, 13 of the 22 Mathematics Education Majors and 15 of the 27 Graduate
Students were actually included in the study.
Only 24 of the 129 English
1 020 students who initially completed the RMARS and the srQ became the
Control Group.
Other relevant data are summarized in Table 1.
35
TABLE 1
BREAKDOWN OF REJECTED CONSENTING STUDENTS BY CATEGORY
GROUP
INITIAL
1
2
3
4
5
6
7
101
2
51
18
2
0
8
0
20
TECHNICAL-1 700
76
2
26
11
0
0
20
0
17
TECHNICAL-1840
148
3
53
10
7
2
14
6
53
ELEMENTARY
97
0
38
11
3
2
2
10
31
MATH
22
2
4
2
1
0
0
0
13
27
0
6
5
1
0
0
15
0
12
7
NONTECHNICAL
ED
GRADUATE
129
CONTROL
*
0
0
ANALYZED
24
*:
For the Contr o l Group . 86 studen t s were enrol led in a mathemat i c s course . and were not inc lud ed in the stud y .
Key :
1:
under 18 yea r s of age
2:
did no t comple t e RMARS on final test ing da te
3:
did no t f i l l out RMARS/ SIQ completely
4:
did not have ACT mathematics subtest on pe rmanent rec o rd
5:
pa rt icipated in a math anxiety treatment program
6:
repeating mathema t ics-re la ted cour se
7:
untypical maj or
36
II .
THE MEASURING INSTRUMENTS
Rev i s ed Mathematics Anxiety Rating Scale ( RMARS )
A 2 4- item ve rsion of the Mathemat i c s Anxiety Rating Scale (RMARS ) ,
developed by Plake and Parke r , measure d the math anxiety of each parti c i­
pant. Each item on the RMARS repres ents mathemat i cal tasks and experi­
ences which potentially arouse anxi ety or apprehens ion. The student
indicates whether he is "not at all , " "a little , " "a fai r amount , "
"much , " or "very muc h" " frightened by it [ the task or experience] nowa­
days , "
Although the se re sponses const i tute ordinal data , the
i nvestigator followed the common practice of assuming they could be
conve rted to interval data by taking on the numeri cal value 1 for "not at
all , " 2 for "a li ttle , " 3 for "a fair amount , " 4 for "much , " and 5 for
"very much."
RMARS scores are the sums of these values ;
thus range from 24 to 1 2 0.
scores could
( Appendix A includes a copy of the RMARS. )
Plake and Parker ( 1 982 ) collected normative data on a sample of 17 0
students enrolled in introductory stat i s tics clas s e s at a large , ur ban ,
midwe st ern university.
The mean score for the sample was 59.8 4 , and the
standard deviation wa s 2 0 . 55.
The internal consistency ( coefficient
al pha ) reli abil ity was 0. 98.
To determ ine the vali dity of the RMARS ,
Plake and Parker admini stered both the RMARS and a 48 -item Mathemat ics
Achievement Test (MAT ) .
The MAT , d e rived from items on the ACT mathe­
mat i c s subt e s t , has a reliabi lity coe f f i c ient of 0. 91 as estimated by the
Kuder-Richard son formula 2 0.
The correlat ion coefficient between the
RMARS and the MAT was -0. 45.
Plake and Parker also reported that the
cor relation between
the RMARS
and the
MARS
wa s .97 .
They further
found that the di mensionality of the RMARS was s imilar to that of the
MARS , the ori ginal 98- item scale.
37
The princi pal components factor
anal ysis that they per formed indicated a two- factor solution :
Learning
Mathematics Anxiety (16 items) and Mathematics Evaluation Anxiety
(8 items) .
These factors accounted for 60% of the total variance.
Each
item had a factor loading of . 50 or greater on only one of the two
factors .
Student Information Questionnaire (SIQ)
The investigator developed the SIQ to determine for each participant
the (1) college major, (2) sex, (3) highest level of mathematics course
successfully completed , (4) score on the ACT mathematics subtest, (5)
grade received in current mathematics course, (6) lapse of time since
last successfully completed a mathematics cQurse, ( 7) self-rating of
mathematics ability, and (8) self-rating of mathematics anxiety .
(A copy
of the SIQ is included in Appendix A.)
In order to determine the level of each mathematics course on the
list from the SIQ, each mathematics course was assigned a code number
representing its position in the overall sequential arrangement of mathe­
matics courses .
(A copy of the code for the mathematics courses is
included in Appendix D).
Ill.
THE CURRICULUM OF THE COURSES INVOLVED IN THE STUDY
Except for those in the control group, all students who participated
in the study were enrolled in some sort of mathematics-related course.
This section outlines
the topics taught in each of the courses .
College Algebra (Mathematics 1540 )
The topics covered in College Algebra are:
sets, real and complex
number systems, exponents and radicals, fundamental algebraic operations ,
theory of equations, polynomial inequalities, relations, functions, and
38
graphs.
The prerequi s i tes for Coll�ge Algebra are ei ther ( 1) two years
of high school algebr a . or ( 2 ) one year of al gebr a and one year of
geome try.
Precalculus Mathema t i c s ( Mathematics 1700 )
The topics cover ed in Precalculus Mathematics are :
func t ion conc ept
and use of 'functional notat ion . propert ies of funct ions and their graphs ,
and polynomial , exponen t ia l , logari thmic , and trigonome tric funct ions.
The prerequ i s i tes for Precalculus Mathematics are ( 1 ) two years of high
school al gebr a and ( 2) the equivalent of a ha lf-year of trigonometry or a
concurrent Mathema t i c s 01 50 (Trigonometry) cour s e .
Single Var iable Cal culus ( Mathematics 1840 )
The to pics covered in Single Va riable Calculus are :
fun c tions ,
graphs , slope of a curve , defini tion of a derivat ive , limits , der ivatives
of algebrai c func tions , impl icit d ifferentiat ion , chain rule , differen­
tia l s , continuity , appli ca t ions of d e rivatives , and maxima and minima .
The pr erequi s i t es for Single Variable Calculus are
two years of high
school algebr a , one year of geome try . and one-half year of trigonometry
or the equivalent .
S tructure of the Number Sys tem (Mathemati cs 21 10-20-30 )
The topi cs covered in S t ructure of the Number Sys tem are :
theory . whole numbe rs , and in teger s .
set
The prerequi s i t es for S tructure of
the Number System are ( 1 ) one year of high school a lgebra and ( 2) at
lea s t sophomore st anding in elementary educa tion or the instruc tor ' s
consent.
39
Teaching � Mathematics :
and Instruction 3752)
Geometry and Analysis , Grades 7- 1 2 (Curricul um
The topics covered in this course are:
purposes , techniques , mater-
ials , and evaluation; directed observation in public sChools; and preparation of teaching plans and materials.
certification in mathematics.
This course is required for
Its prerequisite is admission to Teacher
Education.
Educational Statistics (Curricul um and Instruction 56 10)
The purposes of this course are:
(1)
To introduce some fundamental concepts of descriptive and
inferential statistics as app lied to educational problems ,
(2 )
To introduce the use of the hand-held calculator as a means of
computing statistical measures , and
(3)
To learn to apply the use of certain statistical measures to
educational problems, particularly, in research.
English Composition (English 1020)
English Composition is required for most students at The University
of Tennessee, Knoxville, regardless of major.
S tudents taking this
course were chosen for the Control Group because they represented different majors and because some of them were not concurren tly enrolled in
a mathematics course .
IV.
PROCEDURES FOR THE GR.OUPS
The RMARS and the SIQ were administered to students in their normal
classroom situation during the last part of class in the second week of
schoo l (Monday , January 14 - F riday , January 19 , 1985).
40
To facilitate
the students ' responding openly and honestly , the instructors did not
administer the instruments to their own classes.
Administrators were
selected from those mathematics graduate students and faculty who volun­
teered to ass ist the investigator.
They were scheduled according to
their availability at the times of the participating classes.
During the quarter the students met at their regular class times ,
following the normal cur riculum for each course in all of these sessions .
On Monday , February 25, 1985 (or the closest available date on which
no exam was given) , the RMARS was again administered to the students .
The same administrator conducted this retesting.
v.
S�Y
The purpose of this chapter was to describe the participants in the
study , to discuss the RMARS and the SIQ , and to outline the procedures
used with each of the sections of the courses involved in the study.
41
CHAPTER IV
RESULTS AND DISCUSSION
This chapter presents results of the analysis of the Revised Mathematics Anxiety Scale (R.�� ) scores, the changes in math anxiety levels
from pretest to posttest, and the degree of relationship between RMARS
scores and the six background and ex periential factors:
( 1 ) mathematics
background , (2) mathematics achievement , (3) mathematics performance , (4)
mathematics avoidance , (5) self-rating o f mathematics ability, and (6 )
self-rating of mathematics anxiety. (RMARS scores have been included in
Appendix B.)
1.
ANALYSIS OF THE REVISED MATHEMATICS ANXIETY RATING SCALE
Experimental Design � Statement o f the Hypotheses for the Two-Way
Analysis � Variance
The Revised Mathematics Anxiety Rating Scale was administered to al l
seven groups:
the Nontechnical Majors Group, the Technical Majors Group
enrol led in Mathematics 1700, the Technical Majors Group enrolled in
Mathematics 1840, the E lementary Education Majors Group , the Mathematics
Education Majors Group , the Graduate Students Group, and the C ontrol
Group.
The data were analyzed by an analysis of variance with the RMARS
score as the dependent variable and with tw o independent variables:
sex of the student, and (2) the group the student belonged to .
(1 )
Because
there were no males in the Elementary Education Majors Group and only one
in the Graduate Students Group , these gr oups were omitted from the two-
42
way analys i s .
Thus , a 2 x 5 factorial design resulted :
2 (male vs .
female) x 5 ( Nont echn i c a l Majors vs . Technical Maj o r s enrol l e d in Mathe­
matics 1700 vs . Techn i c a l Majors enrolled in Mathema t i c s 1840 vs . Mat he­
mat i cs Educat io n Maj o r s vs . Control ) .
This de s i gn de fine d ten combina­
t i ons :
1.
mal e Nontechnical Ma jors , MaRsN;
2.
female Non t echni cal Major s ,
3.
male Techn i c a l Majors enrolled i n Mat hema t i cs 1700 . MaRsT7 ;
4.
f emale T echnica l Majors enrolled in Mathem a t i cs 1700 , FeRsT7 ;
5.
male Techn i ca l Majors enrolled in Ma them a t i c s 1840 , MaRsT8;
6.
female T echni ca l Majors enrolled in Mathemat ics 18 40 , FeRsT8;
7.
male
8.
female Ma thema t ic s Education Maj o r s . FeRsM ;
9.
male C on t ro l ,
10 .
FeRsN;
Mathemat i c s Educat ion Ma j or s , MaRsM ;
MaRs e ; and
female C on t ro l . FeRs e .
The two-way ana l y s i s o f variance tested the f o llowing hypothes e s :
HoI ;
The re a r e no signif icant di fferences between male
and female means on the Revised Mathemat i c s Anxiety Rating Scale
acro s s ma jo r s .
Ho2 :
There a r e no significant differ ences among the RMARS
means for the Nont echnical Major s , the Technical Majors enrolled in
Mathemat ic s 1700 , the Technical Ma j o r s enrolled in Mathemat i cs 18 40 ,
the Mathema t ic s E d ucat ion Ma jors . and the Control groups .
Ho3 :
The i n t erac t ions are each zero .
Re sult s � the Two-Way Ana �ysis of Va rianc e .
Table 2 shows the mean
and the standard devi a t ion for each of the ten comb inat ions , and Table
summarizes the anal y s i s o f variance .
43
Result s show a sign i ficant group
3
TABLE 2
MEANS AND STANDARD DEVIATIONS OF SCORES ON THE RMARS
FOR FIVE OF THE GROUPS (MALES AND FEMALES)
MALES
GROUP
FEMALES
N
M
7
53.1 4
21. 19
Tech 1700
12
44. 92
11. 2
Tech 1840
40
51.85
13. 59
Math Ed
6
5 0 . 67
16.69
Control
10
55.9
16 . 5
Nontech
SD
N
M
SD
54. 54
24.68
47
15.89
13
47. 69
1 0.76
7
31.71
5.5
14
73. 93
22.32
13
5
Note : RMARS scores may range from 24 to 1 20; higher scores indicate
higher levels of math anxiety .
44
TABLE 3
SUMMARY TABLE FOR TWO -WAY ANALYS IS OF VARIANCE OF MEAN SCORES
FOR THE RMARS
SOURCE OF
VARIATION
df
SUM OF
SQUARE S
MEAN
SQUARE
F
2. 36
1
2 . 36
. 01
GROUP (G )
5 9 8 0 . 55
4
1 4 95 . 1 4
5 . 56
**
S X G
3256 . 4
4
81 4 . 1
3 . 02
*
ERROR
31 489 . 46
SEX ( S )
*
**
1 17
Sign i f icant a t . 05 level.
Sign i f icant a t . 01 level.
45
269. 1 4
effect and a signifi cant in teraction e f fe c t , thus the null hypo theses for
the group effec t and the interact ion effect were re j e c t ed .
not ; however ,
show a signi f i cant sex effec t ;
Resul ts did
thus the null hypo thes i s
was not re jec ted for this effect .
Re sul t s of Scheffe' g Tes t .
Since the group and interact ion effect s
were the only sig nificant ef fects for the anal ys i s o f variance , Scheffe ' s
method was used t o compare the group means for males and females in 4 5
pai rwise cont rasts .
Figure 1 detail s t h e resul t s :
a significant d i f fer-
ence eXi s t e d petween the mean of the female Control Group and the means
_
of bo th the female Ma themat i c s Educ a t i on Group and the Technical Maj ors
Group enr olled in Mathemat i cs 1700 .
Di s cus s ion of the Resul t s .
It wa s found tha t there were no s ex-related difference s in math
1.
anxie t y .
This is in contras t wi th some s tudies ( B e t z . 1 9 78 ; Calvert ,
1 98 1 ; Dew, Gala s s i , and Galas s i , 1983 ) , whi ch found math anxiety more
prevalent in women , but not wi th others (Ri chard son and Suinn , 1 9 7 2 ;
Resni ck. V i eh e , and Segal , 1 9 82 ; and Frary and Ling , 1 9 8 3 ) .
One s tud y
has even obtained both s i gnif icant and nons igni f i cant sex di fferences
( Brus h , 1 9 7 8 ) .
2.
Ma th anxiety as measured by the RMARS was significantly di f-
ferent in only two of the 4 5 pairwi se contra s t s .
The math anxiety of the
females in the Control Gr oup was si gni f i c antly higher than the math
anxiety of bo th the female Mathemat i c s Educ a t i on Ma jors and the male
Techni cal Maj ors enrolled in Mathema t i c s 17 0 0 .
3.
The interacti on between group and s ex was found in the Ma the-
mat i c s Education majors and the Technical majors enrolled in Mathemat i c s
1 7 00 .
For the females , Mathemat ics Education ma jors had the lowe s t RMARS
46
MFe
3 1 . 71
T7Ma
44 . 92
T7Fe
47
MMa
50 . 67
T8Fe
47 . 69
T8Ha
5 1 . 85
l\TMa
53 . 14
!-ire
54 . 54
CMa
55 . 9
CFe
73 . 9 3
No t e : Those means unde r l i ne d by the same l i ne are not s igni ficantly
d i f fe rent (2 < . 05 ) .
MFe and T7Ma are signif icantly lower than CFe .
Key :
MFe :
T 7Ma :
T7Fe :
T8Fe :
MMa :
T8Ma :
NMa :
NFe :
CMa :
CF e :
Mathema t ic s Educ a t i on
Techni cal Ma thema t i c s
Techn i c a l Ma them a t i c s
Technical Mathema t i c s
Mathema t i c s Educ a t i o n
Technica l Mathemat i c s
Nont echni c a l Mal e s
Nont echn i c a l Fema les
Control Ma les
Control F ema les
Females
1 7 00 Males
17 00 Females
1840 Females
Male s
1 8 40 Mal e s
S che f fe ' s compari s ons of males and fema l e s on RMARS means
Figure 1 .
f o l l owing a signi f i ca n t two-way ana lys i s of var iance .
47
scores of all the f ive groups , wi th the Technical majors enrolled in
Mat hema t i cs 1700 having the secon d lowes t score s .
For the male s , how-
eve r , Techni cal Maj or s enro lled in Mathemat i c s 1 7 00 had the lowest RMARS
score s , wi th the Mathema t i c s EduG a t i on maj ors having the second lowe s t .
F o r both males and female s , t he Control Gro up had the highe s t RMARS
scores , followed by the Non t e chnical
Maj ors Group and the Technical
Ma j o r s enro lled in Mathemat i cs 1840 .
Experimental Des ign and S ta t em�nt o f the Hypotheses for the One-Way
Analysi s of Variance
Because the El emen t ary E�uc a t i on Majors and the Graduate Students
lacke d enough males t o be included in the two-way Ana l ys i s of Varianc e , a
one-way Ana lys is of Var iance di sregard ing the s ex variable was performed .
The data were subsequent l y analyzed by an analys is of variance wi th group
a � the only independent variqple and the RMARS score as the dependent
variable .
All seven groups . � re thus included :
1.
Nontechnical Maj o r s . : RsN;
2.
Techni cal Maj ors �nrolled in Mathemat i cs 1700 , RsT7 ;
3.
Technical Maj o rs enrol led in Mathemat i cs 1840 , RsT8 ;
4.
Elementary Educ a t i o n :Major s , RsE ;
5.
Mathematics Educ a ti o n Maj o r s , RsM ;
6.
Graduate S tudent s , R$G; and
7.
Contro l , RsC .
The analys i s of variance t e s ted the following hypot he s i s :
Ho2 b :
There are no signi f i cant differences among the
RMARS means for the Nontechnical Major s , the Technical Ma jors enrolled in Mathema t i c s 17 00 , the Techni cal Maj ors enrolled in Mat hem at i c s 184 0 , the E lemen tary Educ a t i on Ma jors , the Mathemat i c s Educat i on Majors , the Graduat e � tudent s . and the C ontrol Group .
48
Results of the One-Way Analysts of Variance.
Table 4 shows the mean
and standard deviation for each of the seven groups , and Table 5 summarizes the analysis of variance . Results show a significant group effect ;
thus the null hypothesis was rejected.
Results of Scheffe ' s Test .
Scheffe's method was used to compare the
means of the 7 groups via 21 pairwise contrasts;
in Figure 2.
results are summarized
A significant difference existed between the means for the
Control Group and the means of (1) the Technical Majors enrolled in
Mathematics 1700. (2) the Technical Majors enrolled in Mathematics 1840,
and (3) the Mathematics Education Majors .
Discussion of the Results.
Math anxiety as measured by the RMARS
was significantly different in three of the 21 pairwise contrasts . The
math anxiety of the Control Group was significantly higher than the math
anxiety of (1) the Tech nical Majors enrolled in Mathematics 1700 , (2, the
Technical Majors enrolled in Mathematics 184 0 , and (3) the Mathematics
Education Majors.
Students enrolled in the less rigorous mathematics-related sequences--Curriculum and instruction 5610, Mathematics 211 0-20-3 0, and
Mathematics 154 0--had more math anxiety than students in the more rigorous mathematics-related sequences--Mathematics 1840, Mathematics 1700,
and Curriculum and Instruction 3752.
These students also had (1) poorer
mathematics backgrounds, (2) lower scores on the ACT mathematics subtest
and (3 ) longer lapses of time since their last mathematics course.
The
observation that students with the less technical majors display higher
levels of math anxiety supports what has been suggested in the literature
(Morris. Kellaway, and Smith, 1978; Brush, 1978; Lavroff , 1980; Resnick.
Viehe, and Segal, 1982 ) .
49
TABLE 4
MEANS AND STANDARD DEVIATIONS OF SCORES ON THE RMARS
FOR EACH OF THE SEVEN GROUPS
GROUP
N
MEAN
NONTE CHNICAL
20
5 4 . 05
22 . 95
TECHNICAL 1700
17
45. 53
12 . 26
TECHNICAL 1840
53
50. 83
12 . 98
ELEM ED
31
5 8 . 06
15 . 32
MATH ED
13
40. 46
15 . 1
GRAD
15
60. 47
2 3. 94
CONTROL
24
66. 42
2 1. 69
STANDARD DEVIATION
No te : RMARS scores may range from 2 4 to 12 0; hi gher score s indicate
higher levels of mat h anxie ty .
50
TABLE 5
SUMMARY TABLE FOR ONE-WAY ANALYSIS OF VARIANCE OF MEAN SCORES
FOR THE RMARS
Sum of
Squar es
df
G r ou p
8967 . 99
6
1494 . 67
E r r or
49803 . 33
166
300 . 02
Sourc e o f
Vari a t i on
**
Signif icant at . 01 leve l .
51
Mean
Square
F
4 . 98
**
M
No t e :
d i f f erent
T8
T7
4 0 . 46
4 5 . 53
50 . 8 3
N
E
G
C
54 . 05
58 . 06
6 0 . 47
66 . 42
Tho s e means und e r l i n e d by the
(2 < . 05 ) .
M.
T7 .
same l i ne
are not signi fic ant l y
and T8 a r e sign i f ican t l y lower than C .
Ke y :
M:
Mat hema t ic s Educa t i on
T7 :
Techni cal Mathemat i c s
1700
T8:
Techni cal Ma t hema t i c s
1840
N:
Non technical
E:
Elementary Educ a t i on
G:
Gradua t e
C:
Control
F igure 2 .
Sch e f f e ' s compari son of groups on RMARS
s igni ficant one-wa y ana l y s i s
of variance .
52
fol l owing a
II.
CHANGES IN · MATH ANXIETY LEVELS
The RMARS was both a pretest (during the second week of class) and a
posttest (seven weeks later) of the Nontechnical Majors Group, the Tech­
nical Majors Group enrolled in Mathematics 17 00, the Technical Majors
Group enrolled in Mathematics 1840, the Elementary Education Majors
Group, the Mathematics Education Majors Group, the Graduate Students
Group, and the Control Group.
A t-test for correlated groups was used to
analyze the data, defining 14 combinations:
1.
pretest Nontechnical Majors ,
PrRsN;
2.
posttest Nontechnical
3.
pretest Technical Majors enrolled in Mathematics 17 00, PrRsT7;
4.
posttest Technical Majors enrolled in Mathematics 17 00, PoRsT7;
5.
pretest Technical Majors enrolled in Mathematics 1840, PrRsT8;
6.
posttest Technical Majors enrolled in Mathematics 1840, PoRsT8;
7.
pretest Elementary Education Majors ,
8.
posttest Elementary
Education
9.
pretest Mathematics
Education Majors ,
Majors,
PoRsN;
PrRsE;
Majors,
PoRsE;
PrRsM;
1 0.
posttest Mathematics Education Majors, PoRsM;
11.
pretest
Graduate Students,
PrRsG;
12.
posttest Graduate Students,
PoRsG;
13.
pretest Control, PrRsC; and
1 4.
posttest Control, poRse.
The t-test for correlated groups tested the following hypotheses:
Ho4 :
There are no significant differences between pretest and
post test means on the Revised Mathematics Anxiety Rating Scale
within each major.
53
HoS :
Ther e are no signif icant diff erences between RMARS pr e-
t e s t and pos t t e s t means for males and females within each major .
Res ults of the t- test
-
Table
--
6
li s t s the mean and s t andard deviat ion of the pre- and pos t-
test for each of the seven groups ,
and summar izes each group ' s t- tes t s
for corre lated groups . Res ul t s show a signi f i cant dif ference be tween the
pre test and pos t t e s t means for two of the seven group s :
the Techni cal
Majors enrolled in Mathematics 17 00 and the T e chnical Ma jors enro lled in
Mathemat i c s 1840 .
Table 7 li s t s the mean and s tandard deviation of the males for 10 of
the 14 combinations (PrRsE , PoRs E , PrRs G , and PoRsG were omi t ted because
of small s ize) , and summarizes the t-test for the males.
Resul ts show a
signi f i cant difference be tween the pretest and pos t t e s t means for two of
the f iv e groups :
the Technical Majors enrolled in Mathematics 1700 and
the Technical Ma jors enrolled in Mathema t i c s 1840 .
Table 8 li s t s the mean and s tandard deviat ion of the females for
each of the 14 combinat ions , and summarizes the �- tes t for the females .
The res ult s show no s igni fi cant dif ference between the pretest and posttes t means for any of the seven group s.
Di s cuss ion of the Resul t s
1.
Math anxi ety as measured by the RMARS s i gnificantly decreased
wi thin the Technical Majors Group enrolled in Mathema t i cs 1700 and the
Techni cal Ma jors Group enrolled in Mathemat i c s 1840 , and it signi f i cant ly
decreased for males within bo th of the Techni cal Majors Groups .
Howeve r ,
t he decrease wa s not signifi cant for the fema les wi thin the Technical
Major s Groups.
54
TABLE 6
THE t
TESTS
FOR DIFFERENCES BETWEEN PRETEST AND POSTTEST MEANS
OF THE RMARS FOR EACH OF THE SEVEN GROUPS
GROUP
N
PRETEST
POSTTEST
DIFFERENCE
NONTECH
20
5 4 . 05
51 . 5
2 . 55
. 94
t
TECH
1700
17
4 5 . 53
41
4 . 53
2 . 24
*
TECH
1840
53
50 . 83
48 . 42
2 . 41
2 . 04
*
ELEM ED
31
58 . 06
57 . 45
. 61
. 25
MATH ED
13
40 . 46
41 . 77
-1 . 31
- . 66
GRAD
15
6 0 . 47
57 . 33
3 . 14
1 . 09
CONTROL
24
6 6 . 42
66 . 08
. 34
. 14
*
Signi fi cant a t . 05 level .
55
TABLE 7
THE t TE STS FOR DIFFERENCE S BETWE E N PRE TE ST AND POSTTE ST
OF THE RMARS FOR FIV E OF THE GROUPS (MALE S ONLY )
MEANS
PRETE ST
POSTTE ST
DIFFERENCE
7
53 . 14
49 . 57
3 . 57
1 7 00
12
44 . 9 2
3 9 . 92
5
2 . 11
*
TE CH 1 8 40
40
5 1 . 85
49 . 2
2 . 65
1 . 92
*
UATH ED
6
50 . 67
52 . 67
CONTROL
10
55 . 9
55 . 3
GROUP
N
NONTECH
TE CH
*
S igni f i cant a t . 05 level .
56
t
.72
- . 47
-2
.6
. 14
TABLE 8
THE � TESTS FOR DIFFERENCE S BETWEEN PRETEST AND POSTTEST MEANS
OF THE RMARS FO R EACH OF THE SEVEN GROUPS ( FEMALES ONLY )
GROUP
N
NONTECH
13
DIFFERENCE
t
PRETEST
POSTTEST
54 . 54
52 . 54
2
.6
47
43 . 6
3.4
. 79
1 . 69
. 71
. 25
TECH 1 7 00
5
TECH 1 8 40
13
4 7 . 69
46
ELEH ED
31
58 . 06
57 . 45
. 61
ED
7
3 1 . 71
32 . 43
-0 . 72
GRAD
14
6 1 . 14
5 7 . 79
3 . 35
1 . 09
CONTROL
14
7 3 . 93
7 3 . 79
. 14
. 06
MATH
57
-.6
2 . The RMARS scores be tween pre- and pos t t e s ting decreased in all of
the groups except the Mathemat i cs Educ a t i on Group , whose RMARS scores
i nc�eased nonsigni f i can tl y .
The Mathematics Educ a t i on Group was uniq ue wi th respect to the way
in whi ch the mathemat i cal cont ent was presented .
Ins tead of concent ra-
ting on the learning of mathemati cs . the emphas i s was on the ways of
pre s ent ing the mat e rial .
Thi s format is in sharp contras t to the other
mathemati cs-related courses that these st udent s have taken .
I I I . CORRELATION OF THE RMARS AND THE
SIX BACKGROUND AND EXPERIENTIAL FACTORS
One of thi s study' s go al s was to determine whether math anxi ety
correla tes wi th the six background and experiential factors :
mat i c s background , ( 2 ) mathematics achievement ,
( 1 ) mathe-
( 3 ) mathematics perfor-
mance , ( 4 ) mathema t i c s avoidanc e , ( 5 ) sel f- rating of mathemat i c s abi l i t y ,
and ( 6 ) self-rating o f mathema t i c s anxiety.
Several Pearson prod uc t
moment correlat ion coef f i cients were calculated to compare the RMARS wi th
the se
six backgr ound and expe rient ial factors .
The following null
hypothe s i s was tes ted :
Ho6 :
The correlation c oe f f ic i ents are equal to zero .
F o r each s tudent in the s tudy the following data were avai lable :
pre t e s t RMARS scores , highe s t level of mathemat i cs course succes s ful ly
completed , lapse of t ime s i nce last suc c es s fully compl eted mathemat i c s
cour s e , t h e self- rat ing of mathema t i c s abi l i ty on a scale from 1 ( terrible) to 10 ( excellent ) , and the self-ra t i ng of mathema t i c s anxi ety on a
scale f r om 1 ( highly anxi ous) to 10 ( not anxi ou s ) .
In addi t i on , the
grade received in current mathematics-related course was avai lable ( except for Control Group members , who were not taking a mathemati c s
58
course). Fina lly, the score on the ACT mathematics subtest was available
for all students except those in the Graduate Students Group, who are not
req uired to have their ACT scores on their permanent records .
Six Pearson product moment correlation coefficients were calculated
for the Nontechnica l Majors Group, the Technical Majors Group enrolled in
Mathematics 17 00 , the Technical Majors Group enrolled in Mathematics
,
1 840, the Elementary Education Group, and the Mathematics Education
Group.
Five Pearson product moment correlation coefficients were calcu­
lated for the Graduate Students Group and the Control Group.
matrices are presented in Tables 9, 1 0, and 1 1 .
Corre lation
Tables 12 , 13, and 14
show the mean of the six background and experiential factors for the
groups as a whole, by male, and by female.
Results of the Correlational Analysis
In 90 of the 1 04 correlations , &MARS correlated as anticipated with
the six background and experiential factors .
As expected, &MARS general­
ly correlated negatively with five of them--mathematics background , math­
ematics achievement , mathematics performance , self-rating of mathematics
ability, and self-rating of mathematics anxiety ; and positively with one
of them--mathematics avoidance .
Specifically, as an individual had a
higher level of math anxiety as measured by the RMARS, that individual
could be expected to have successfully completed only lower level mathe­
matics courses , have a lower score on the ACT mathematics subtest, have a
poorer grade in a mathematics-related course, have more likely a near­
"terrib le " self-rating of mathematics ability, and have more likely a
near-"high" self-rating of mathematics anxiety.
Furthermore, the higher
the level of math anxiety, the longer the time lapse since the last
successful completion of a mathematics course .
59
TABLE
9
/
CORRELATIONAL MATRIX FOR THE VARIABLES SHOWN IN THE TABLE AND RMARS SCORES FOR GROUPS SHOWN
GROUP
VARIABLE
(J'\
0
NONTECH
1 7 00
TECH
TECH
1840
ELEM ED
MATH ED
BACKGROUND
- . 34 2
- . 07 9
-. 212
- . 35 3 *
- . 318
ACHI EVEMENT
- . 356
-. 179
- . 076
-. . 47 4 **
- . 234
PERFORMANCE
- . 206
.112
. 01 2
- . 127
- . 838 **
. 268
. 12 7
. 17
AVO IDANCE
ABILITY
- . 61 1 **
ANXIETY
- . 53
*
**
S ign i f icant at
S ig n i f i cant at
**
. 04 7
. 002
GRAD
- . 766 **
CONTROL
- . 38 6 *
- . 46
*
- . 618 **
. 592 **
'. 224
- . 55 2 **
- . 31 2 *
- . 58
**
- . 531 *
- . 88 6 **
- . 54 6 **
- . 104
- . 369 **
- . 43 7 **
- . 52 4 *
- . 857 **
- . 58
. 05 level
. 01 level .
*
10
TABLE
CORRELAT IONAL MATRIX FOR THE VARIABLES
TABLE AND RMARS
SCORES FOR MALE S
SHOWN IN THE
IN GROUPS
SHOWN
GROUP
VARIABLE
1700
TECH
NONTE CH
BACKGROUND
-.515
-.327
ACHI E VEMENT
-. 307
-. 491
PERFORMANCE
-.768
AVO IDANCE
-. 31
AB IL I TY
-.23 5
ANXIETY
-. 38
*
**
*
1840
CONTROL
MATH ED
-.268
-.57
-. 629
*
-.14 7
-. 209
-. 768
**
.229
-.03 7
- . 919
. 16 8
.166
-.054
.798
**
-. 246
-.331
*
-.425
-. 775
**
-.33
*
-.077
-.111
. 159
S ignificant at .05 level
S ignificant at 01 level
•
TECH
•
61
*
**
TABLE 1 1
CORRELATIONAL MATRIX FOR THE VARIABLES SHOWN I N THE
TABLE AND RMARS SCORES FOR FEMALES IN GROUPS SHOWN
GROUP
VARIABLE
0\
N
TECH 1 7 00
NONTECH
TECH 1840
EUM ED
MATH ED
CONTROL
GRAD
BACKGROUND
- . 25
. 57 9
. 31 3
- . 35 3
*
ACH IEVEMENT
- . 38 2
. 57 4
. 13 4
- . 47 4
**
PERFORMANCE
- . 04 8
- . 09 7
. 29 7
- . 127
. 42 9
- . 64 9
**
UNDEFINED
. 04 7
- . 586
. 617
**
. 55 5
- . 789
**
- . 36 9
- . 36 2
- . 27
. 658
**
. 08
ABILITY
- . 70 5
**
- . 92 5
**
- . 34 4
- . 58
**
- . 01 7
- . 893
**
- . 49 4 ..
ANXIETY
- . 585
*
- . 764
*
- . 42
- . 437
**
- . 21 9
- . 856
**
- . 813
AVOIDANCE
*
**
S igni f icant a t . 05 level
S igni f icant at . 01 level .
. 2 57
*
TABLE 12
MEANS OF THE VARIABLES SHOWN IN THE TABLE FOR GROUPS SHOWN .
GROUP
VARIABLE
BACKGROUND
ACHIEVEMENT
0'\
LV
NONTECH
4 . 95
17 .4
TECH 17 00 TECH 1840
ELEM ED
MATH ED
GRAD
CONTROL
6.4
5.38
6.24
8.62
5.68
16 . 08
1 8.82
21 . 7 7
16 . 03
24.62
17.71
PERFORMANCE
2. 73
3.06
2.1
3 . 21
3 . 27
3 . 37
AVOIDANCE
7.93
1 . 85
1. 77
2.32
1 . 17
35.43
ABILITY
5.9
6 . 76
1 . 26
5.91
1 . 85
5 . 17
5
ANXIETY
5.8
6 . 12
5 . 74
5 . 42
8
4.93
4 . 38
5.1
Not e : Background ranged f rom 1 ( general mathema t ic s ) to 21 (9 mathema t ic s courses
beyond Mathema t i c s 1840)
A chievement ranged from 7 to 34
Performance ranged from 0 ( F) to 4 ( A )
Avo idance ranged from 1 quarter ( prev ious quar t er ) to 90.5 quarters
( about 22 ye ars )
Abi l i ty ranged from 1 ( terrible) to 1 0 ( excel lent )
Anxiety ranged from ( highly anxious ) to 1 0 ( not anxious )
\ .
TABLE 1 3
MEANS OF THE VARIABLES SHOWN IN THE TABLE
FOR MALES IN GROUPS SHOWN
GROUP
VARIABLE
\
BACKGROUND
NONTECH
5
TECH 1700 TECH 1840
MATH
ED
CONTROL
6 . 42
8 . 52
15 . 33
5.2
18 . 8
ACHIEVEMENT
1 7 . 71
19 . 92
21 . 88
24 . 17
PERFORMANCE
2 . 86
3 . 13
2 . 66
2 . 67
AVO IDANCE
7 . 29
1 . 42
2 . 03
2
7
ABILITY
5 . 86
7 . 08
7 . 33
7 . 33
5.1
ANXIETY
5 . 57
5 . 75
5 . 33
6 . 67
5.5
Not e : Background ranged from 1 ( genera l mathenatics ) to 2 1
(9 mathematics cour s e s beyond Mathemat i cs 18 40 )
Achievement ranged from 7 to 34
Performance ranged from 0 ( F) to 4 ( A )
Avo idance ranged f rom 1 quarter ( prev i ous quart e r ) t o
90 . 5 quar t e r s ( about 22 years )
Abi li ty ranged from 1 ( terrible ) t o 1 0 ( excellent )
Anxiety ranged from 1 ( highly anxiuos ) to 10 ( not
anxious )
64
TABLE 1 4
/
MEANS O F THE VARIABLES SHOWN I N THE TABLE FOR FEMALES I N GROUP S SHOWN
GROUP
VARIABLE
0\
VI
NONTECH
TECH 1 7 00 TECH 1840
5.8
ELEM ED
MATH ED
GRAD
8 . 92
5 . 68
16 . 71
6.5
2 1 . 46
16 . 03
CONTROL
5.5
BACKGROUND
4 . 92
ACHIEVEMENT
17 . 23
PERFORMANCE
2 . 65
2.9
2 . 81
3 . 27
3 . 79
3 . 39
AVOIDANCE
8 . 27
2.9
1
2 . 32
1 . 57
34 . 64
3 . 75
ABIL ITY
5 . 92
6
7 . 06
5 . 97
8 . 29
5 . 18
4 . 93
ANXI ETY
5 .92
7
7
5 . 42
9 . 14
4 . 86
3 . 57
18
25
16 . 93
Not e : Backgr ound ranged from 1 ( general ma themati c s ) to 2 1 ( 9 ma thema t i c s courses
beyond Mathema tics 18 40 )
Achievement ranged from 7 to 34
Performance ranged from 0 ( F) ' to 4 ( A )
Avoidance ranged from 1 quarter ( previous qua r t e r ) t o 90 . 5 quarters
( about 22 yea r s )
Abi li ty ranged from 1 ( terrible ) to 1 0 ( exce llent )
Anxiety ranged from 1 ( highly anxious ) to 10 ( not anxious )
Fourt een of the 104 correla t i ons took an unexpec ted direct ion ; these
correla t i ons , however , we re not stat i s t ically s i gn i f i cant .
Thi rteen of
the four t een correlat i ons occurred in the Technical Ma jors Groups and the
Mathema t i c s Educat i on Ma jors Group-- the more r i gor ous ma themat i cs- related
cour s e s-- five on the factor of mathematics performanc e , two on mathe­
mat ics avoidanc e , two on mathema t i c s achievement ( females only) , three on
mathema t i c s background ( females only) , and one on self-rating of mathe­
mat ics anxi e t y .
Groups � � Whole .
A st rong pat t e rn of s i gn i f i cant correlat ions
emerged for the fac to r s of self-rating of mathema t i c s abi li ty and self­
r a t ing of ma themat i c s anxiety .
The other correla t i ons we re no t signifi­
cant for mo r e than three of the groups .
Intere s t ingly, the Graduate
S t udent s Group sign i f icantly correlated wi th all the fact or s that they
were mea sured o n , and the Control Group signi fi cantly correlated wi th all
the f ac t or s that they were measured on except mathemat ics avoidance .
In
parti cular , for the groups as a who le , the RMARS c o rrelated neg a t ively
wi th s i gn i f icance at the . 05 level wi th :
1.
self- rating of mathemat i cs abi li ty in all groups ;
2.
sel f-rat ing o f mathemati cs anxie ty in al l but the Technical
Maj ors enrolled in Ma thematics 17 00 ;
3.
mathemat i c s background in the Elementary Education Maj or s ( all
f emale ) , the Graduate S tudents ( al l female except one ma le) , and
the Control Group ;
4.
ma themat i c s achi evement in the Elementary Educ a t i on Group ( all
femal e ) and the Control Group ;
5.
and
mathemat ics performance in the Mathemat i cs Educa tion Maj ors
G r oup and Graduate S tudents Group ( al l female except one male ) .
66
RMARS correla t e d po s i t ively wi th s i gnificance at the . 05 leve l as an
ind i cator of mathema t i c s avo idance for the Graduate S tudent s .
Males .
emerged .
of males .
For the ma le s , n o cl ear patt ern of sign i f i cant correla t i on s
No correla t ion wa s s i gnificant for more than two o f the groups
( I t should be no t e d again that the Elementary Educa t ion Ma jors
and the Graduate S tudent s could not be included in this anal ys i s becaus e
they had too few ma le s . )
Interesti ngly, the Control Group signific antly
correlated wi th all the fac t o rs they were mea sured on except s e l f-rating
of mathema t i c s anx iety .
In part i cula r , the RMARS corre lated negat ively
wi t h s ignif i cance at the . 05 level with :
1.
se lf- rat ing of mathem a t i c s abi lity in the Techni cal Ma j ors
enrolled in Mathemat i c s 18 40 and the Control Group ;
2.
self- ra ting of mathem a t i c s anxiety i n the Techni c a l Maj o rs
enrolled i n Mathema t i c s 18 40 ;
3.
mathema t i c s backgr ound in the Control Group ;
4.
mathemat i c s ach i evement in the Technical Maj o r s enro l led in
Mathema t i c s 1 7 00 and the Control Group ;
5.
mathemati c s perf ormance in the Non t e chnical Maj o r s Group and the
Mathema t i c s Educa t i on Group .
RMARS correlated po s i t ively wi th s i gnificance at the . 05 level as an
ind i cat o r of mathema t i c s avo idance in the Control Group .
F emales .
For the females , f ive of the seven correla t i ons were
signifi cant for self- ra t i ng of mathematics abi lity and se lf-ra ting of
mathematics anxie t y .
The o t her correlation s we re not s ignif i cant for
mor e than two of the gr oups of f emales .
Intere s t ing ly, the Graduat e
S tudent s Group signifi can t l y correlated wi th a l l the fac t o r s they were
67
measured on .
In par t i cular . the RMARS correlated negat ively wi th sig-
n i f i cance at the . 05 leve l wi t h :
1.
sel f- rat ing of mathemat i cs abi l i ty i n the Nontechnic a l Majors ,
the Techni ca l Maj o rs enrolled in Ma thema t i cs 1700 . the E l ementary Educat ion Ma j ors , the Graduate S tudents Group , and the C ont rol Group ;
2.
self- ra t ing of mathema t i cs anxiety in al l but the Techni cal
Maj ors enrolled in Mathema t i cs 1840 and the Ma themat i cs Educat i on Ma j ors ;
3.
mathemat i cs background in the Elementary Educa t i on Majors and
the Graduate S tudents Group ;
4.
mathemat i cs achievement in the Elementary Education Maj ors ;
5.
mathema t ics performance in the Graduate S tudents Group .
and
RMARS correlated posi tively with s i gn i f icance at the . 05 level as an
ind i cator of mathema t ics perf ormance for the Nontechnical Ma jors and the
G raduate S tudents Group .
Discussion of the Results
-
--
In summary , higher levels of math anxiety a�e asso ci a t ed wi th six
factors , br i e f ly li sted here and then d iscussed in more detail .
1.
mathemat i cs background
2.
math emat ics achievement
3.
mathemat ics performance
4.
mathemat i cs avoidance
5.
sel f- ra t ing of mat hemat i cs ab i li ty
6.
self-rating of ma themat i cs anxiety
1.
Higher levels of math anxie t y are associated wi th the successful
completion of the lower level mathema t i cs courses ,
68
( a)
for the group , as a whole , and males wi thin the Cont rol
Group ;
( b)
for the group , . as a whole , and for females wi thin the
Graduate S tudents Group ( only one male ) ; and
( c)
for the t o t a l Elementary Educat i on Maj o r s Group ( al l
females ) .
Thi s suppo rts wha t has been suggested in the l i t erature ( Be t z , 1 9 78 ;
Hendel , 1 9 80 ) .
Hendel f o und a correlat ion o f - . 31 be tween scores on the
MARS and number of s eme s t e rs of high schoo l math in a sample of adult
women .enrolled in a math anxiety treatment program .
B e t z found stat i s­
t i cally s igni f i cant corre l a t i ons ranging from . 19 to . 43 be tween math
anxie ty and number of years of high school math in three groups of
freshmen and sophomores enrolled in mathema t i c s or psychology courses .
2.
Higher level s of math anxiety are associat e d wi t h lower ACT
mathemat i c s subt e s t scor e s ,
(a)
for the group , as a whole , and for males wi thin the Con­
trol Group ;
( b)
fo r the t o t a l Elementary Educ a t i on Maj or s Group ( al l
females ) ; and
( c)
for the males wi thin the Techni cal Majors enroll ed in
Mathema tics 1 7 00 .
B e t z ( 1 9 78 ) also found a mo derate rela t i onshi p be tween math anxiety and
ACT Mathema t i cs scores .
She found correla t i ons that ranged from . 17 to
. 42 .
3.
Higher levels of math anxi ety are associat ed wi th lowe r grade
received in current mathema t i cs- relat e d cour s e ,
( a)
fo r the group , as a whole , and for males wi thin the Mathe­
mat i c s E d uc a t i on Majors ;
69
( b)
for the group , as a whole , and for females wi thin the
Graduat e S tudent s Group ( al l fema les except for one male ) ;
and
(c)
for males wi thin the Nont e chni cal Maj ors Group .
B e t z ( 1 9 78 ) , Dreger and Aiken ( 1 9 57 ) , Hendel ( 1 980 ) , Richardson and Suinn
( 1 9 7 2 ) , and Dew ( 19 8 2 ) all found s imilar resul t s .
4.
Higher levels of math anxiety are assoc iated with longer lapse
of time s ince las t suc cess ful l y comple ted mathematics course ,
(a)
for the group . as a wh ole , and females in the Graduate
S tudent s Group ;
5.
( b)
for males wi thin the Cont r o l Group ; and
( c)
for female s wi thin the Nont echnical Majors Gr oup .
Higher levels of math anxi e t y are a s s ociated wi th lower se lf­
r a t ing of mat hema t i c s abili ty ,
(a)
for the groups , as a who l e , and males , and females wi thin
each group in the Control Group ;
( b)
for the group , as a whole , and males wi thin the Techni cal
Maj o r s enrolled i n Mathemat i c s 1840 ;
( c)
for the groups , as a whole , and females wi thin each group
in the Technical Maj o r s enrol l ed i n Mathema t i c s 1700 , the
Nontechnical Maj o r s , and the Graduate Students Group ( only
one male) ;
( d)
for the group , a s a whole , in the Ma thematics Educa t ion
Group ; and
( e)
for the total Elemen tary Educa t i on �mj ors Group ( al l
female s ) ,
70
6.
Higher levels of math anxiety are a s s o c i a t ed wi th higher self­
ra� ing of mathema t i c s anxiety .
( a)
f o r the group . as a whole , and mal es wi thin the T echni ca l
Ma j o r s enrolled in Ma themat i c s 18 4 0 ;
( b)
for the groups , as a wh ole , and f emale s wi thin each group ,
in the Nontechnical Majors Group , the Gradua t e S tudents
G r oup ( all females except one ma l e ) and the Control Group ;
( c)
f o r the group , as a whole , i n the Mathema t i c s Education
Maj ors Group ;
( d)
for the total Elementary Educa t i on Ma jors Group ( all
f emale ) ; and
( e)
for females within the Technical Majors enrolled in Mathe­
mat i c s 1 7 00 .
IV .
SUMMARY
Thi s chapt e r pre s en t s and discusses the re s ul t s of the analysis of
the Revised Mathematics Anxiety Rat ing Scale , the change s from pre- to
po s t te s t RMARS score s , and the correlation coef f i cients relat ing the
RMARS to the s i x ba ckground and experi ent ial factor s .
71
CHAPTER V
SUMMARY , CONCLUS ION S ,
AND
SUGGESTIONS
The purpose of this s tudy was to inve stigate the preva lence and
inten s i ty of math anxi e ty in co llege s tudent s ( as a whole , by maj or , and
by sex) , to det ermine the s t a b i l i t y of math anxi ety over time , and to
determine those background and experiential factors re lated t o the occur­
rence of math anxiety in c o l l ege stud ent s .
Data gathered on college
s tudents in mathema t i cs , educ a t io n , and English classrooms were u t i l i zed .
S t udents comple t ed two ins trument s :
1.
the revi sed vers ion of the Ma thematics Anxiety Rat ing S c a le
( RMARS ) , a scale developed by Plake an,� Parker ( 19 8 2 ) which wa s des i gned
to provide an effic i en t index of ma th anxiety , and
2.
'
the S tudent Inf orma t i on Ques tionnaire ( SIQ ) . deve loped by the
inves t i ga tor to mea sure the factors of college ma j o r , sex , mathemat ic s
background , mathemat ic s achievement , mathema tics performance , ma thema t i cs
avo idance , self-rat ing of ma thematics abi lity , and se lf-rating of mathe­
ma tics anxiety.
I.
ANSWERS TO RESEARCH QUESTIONS
As a whole , math anxiety wa s not very prevalent in the seven groups
of co llege studen t s part i c i pa t i ng in the study during Wi nter Quarter ,
1 9 8 5 , at The Univers i ty of Tenne s see , Knoxvil le .
intense in three group s :
and Control Group .
Ma th anxi ety was mos t
E l ement ary Education Maj ors , Gradua t e S tudent s ,
However , even the Control Group , whose pre t e s t RMARS
72
s c o res we re the highe s t of all of .the group s , were on the average only
" frightened " by the i tem s " a li ttle " to "a fair amount " of the time .
Thi s is also the ca se for the Gradua te S tuden t s and the Elementary Educa­
t ion Ma j or s .
The re sponses of the Nontechnical Ma jors and the Techni cal
Maj or s enrolled in Ma thematics 1840 averaged "a li ttle . "
And the average
responses for the Technical Ma jors enrolled in Mathematics 1 7 00 and the
Mathemat i c s Educa t ion Ma j o r s we re "not at all , " Als o , math anxiety was
not any more prevalent in one sex than anothe r .
Math anxi ety was fairly stable over a short period of time ( seven
weeks ) .
Only the math anxiety of both of the Technical Maj ors Groups
s i gni f i cantly decrea s e d .
S e l f- ra t in g of mathematics abi lity wa s the factor that was mo s t
related t o the occurrence o f math anxiety for all o f the groups .
Bow­
eve r , for the E l ementary Education Majo r s , the Graduate S tudent s . and the
Control Group , all of the fact ors were rela ted to the occurrence of thei r
mat h anxi ety .
The resul t s sugg e s t e d these answers to the research ques tions mot ivat ing this s tudy , briefly li sted here and then d i s cussed in mo re de tai l :
I,
Math anxi ety is related to choice of col lege ma jor .
2.
Males and females do not differ i n the ir math anxiety levels .
3.
Ma t h anxiety levels change very l i t t le over a shor t time
interval .
4a .
Math anxiety is relat ed to mathema t i c s background in the
E lemen tary Educa t ion Ma j or s , the Graduate S tudent s , and the Con­
t r ol Group .
4b.
Mat h anxiety is rela ted to mathema t i cs achievement in the
Elementary Educ a t i on Maj ors , the C ontrol Group . and the males in
the Techni cal Ma j ors enrol led in Mat hema tics 1700 .
73
4c .
Ma th anxi e ty i s rela ted to mathema tics perf ormance in the
Mathemat i c s Ed uca t i on Ma jors , the Graduat e S tudent s , and the
males in the Nont echni cal Ma jors Group .
4d .
Math anxi ety i s rela ted to mathema t i cs avoidance in the Gradua t e
S tudents Group , t h e females i n the Nontechni cal Ma j ors Group ,
and the males in the Control Group .
4e.
Math anxi e ty is rela ted to se lf-rating of mathema t i c s abi l i ty in
all seven groups .
4f .
Math anxi e t y , as measured by the RMARS , is relat ed t o s e l f­
rating of mathema t i c s anxie ty in all of the group s , except the
males in the Technical Majors enro lled in Mathema t i c s 17 00 .
1.
Math anxiety is related t o choice of colleg e ma j o r .
The math
anx i e ty of the Control Group ( no t enrolled in any mathema t i cs cour s e s )
was higher than t h e ma th anxiety o f t h e Gradua t e S tudent Group , whi ch was
higher than the Elementary Educa t i on Maj ors , f o l l owed by the Nontechnical
Ma j ors , the Technical Ma jors enrolled in Mathemat i c s 18 40 . the Techni cal
Maj ors enrolled in Mathemat i c s 1 7 00 , and finally the group wi th the lea s t
math anxie ty-- the Mathema tics Educ a t i on Group .
So s tudents in the less
mathematically rigo rous groups had more math anxi ety than s tudents in the
more mathemat ically rigorous groups .
s ignif i cant .
higher
(!
=
Three of the di f f erences we r e
The math anxiety of the Control group wa s signi f i cant ly
4 . 98 , � < . 01 ) than that of the Technical Maj o r s ( both) and
of the Mathema t i c s Educ a t ion Maj ors .
These group s had the be s t mathe­
mat i c s background s , highe s t ACT ma themat i cs s ubtest score s , and shortest
lapse of time since la s t success ful comple t i on of a mathemat i c s course .
2.
Males and females do not di ffer in their math anxi ety levels . By
comparing males and females in the same group , the number of mathema t i c s
74
cour s e s previously comple te d was actually being controlled , as the pre­
requi s i t e s for each cour s e had to be met by all s tudent s , regardless of
s ex .
3
val .
.
Math anxiety levels change very li t t le over a short time inter­
The math anxiety of all the group s , except the Ma thema tics Educa­
t ion Maj or s , slightly decreased from the beg inning of the quarter to a
point seven we eks la t e r , s i gn i f icantly for th e Technica l Maj ors enrolled
in Mathemat ic s 17 00 (� = 2 . 24 , £ < . 05 ) and Mathematics 1840 (� = 2 . 04 ,
£ < . 05 ) and for males wi thin the Technical Ma j o r s enrolled in
Mathema t i cs 17 00 (� = 2 . 11 , £ < . 05 ) and Mathemat ics 18 40 (� = 1 . 92 ,
£ < . 05 ) .
The ma th anxiety of the Mathema t i c s Educat ion Maj o rs ( had the
lowe s t level s of math anx i e ty ) increa sed nons ign i f i cant ly.
4.
The f ollowing r e la t i onships were found be tween math anxie ty and
the s ix background and experiential fac t or s :
( a)
Math anxiety is related to mathemati c s background in the
Elementary E ducat i on Maj ors (E = - . 35 3 , £ < . 05 ) , the Graduate S tudents
(E = - . 76 6 , £ < . 01 ) , and the Control Gr oup ( E = - . 386 , £ < . 05 ) .
The
higher the leve l of math anxiety , as measured by the RMARS , the lower
the level of mathematics cours e successfu l l y comple t ed .
These three
g r oups had poor backgrounds in mathema t i c s , on the average compl e ting
only up through high school algebra .
( b)
Math anx i e ty is related to mathema tics achievement in the
El ementary E ducat ion Maj o rs (E
=
- . 47 4 , £ < . 01 ) , the Con trol Group
(E = - . 46 , £ , . 05 ) , and th e males in the Technical Ma jors enrolled in
Mathemat i cs 17 00 (E = - . 49 1 , £ < . 05 ) .
The higher the level of math
anxie ty , as measure d by the RMARS , the lowe r the score on the ACT mathe­
mat ics subt e s t .
The scores of the Elementary Educat i on Ma jors and the
75
Control Group we re the lowe s t of all of the group s , wi t h an average of
16 . 87 .
( c)
Ma t h anxiety i s related t o mathemat i cs per formance in the
Mat hema t i c s Educ a t i on Maj o r s (� = - . 83 8 , 2 < . 01 ) , the Graduat e S tudent s
(� = - . 618 , 2 <
. 01 ) , and the males in the Nont echnical Maj o r s
(� = - . 768 , 2 <
. 05 ) .
The great e r the math anxi e ty , as measured by the
RMARS , the lower the grade received in the current mathem a t i c s-related
c our s e .
(d)
Math anxi e t y is re lated to mathemat ics avoidance in the
Graduat e S tudent s Gr oup (� - . 59 2 , 2 < . 01 ) , the fema l e s in the Non tech­
nical Maj o r s Group (� = . 65 8 , 2 < . 01 ) , and the males in the Con t ro l
Group (� = . 79 8 , 2 < . 01 ) .
the RMARS ,
The greater the math anxi e t y , as measured by
the longer t he lap s e of time since they l a s t succes s fu l l y
completed a mathemat i c s cour s e .
The s e groups had not suc c e s sfully com­
p l e ted a mathema t i cs cour s e for a t leas t two year s , wi t h the Graduate
S tudent s Group no t being enro l l e d in a mathema t ics cour s e for the longe s t
period o f t ime , a n average o f eight and one- hal f year s .
(e)
Math anx i e ty is rela ted to s e l f-ra t i ng o f mathematics
abi l i ty in a l l s even groups :
1.
Nont echnical Maj ors (� = - . 61 1 , 2 <
. 01 ) ,
2.
Techni ca l Maj or s enrolled i n Mathemat i cs 17 00
(� = - . 55 2 , 2 < . 01 ) ,
3.
Techni cal Maj o r s enrolled i n Mathem a t i cs 18 40
(�
=
-
. 312 , 2 < . 05 ) ,
4.
Elementary Educa tion Majors (� = - . 58 , 2 <
5.
Mat h emat i c s Education Maj o r s (� = - . 53 1 , 2 < . 05 ) ,
6.
Graduat e S tudent s (� = - . 88 6 , 2 < . 01 ) , and
7.
Con t r o l Group (� = - . 546 , 2 < . 01 ) .
76
. 01 ) ,
The greater the math anxi ety , the l ower the s e l f- rating of mathematics
abi l i ty .
( f)
Math anxie ty , as measured b y the
RMARS ,
is re lated to
s e l f- rating of mathema t i c s anxiety in all of the groups , except the
Technical Majors enrolled in Mathematics 1 7 00 :
1.
Nontechnica l Ma j ors (� = - . 53 , 2
2.
Techni cal Maj o r s enrolled in Mathematics 1840
(� = - . 36 9 , 2
<
<
. 01 ) ,
. 01 ) ,
3.
Elementary Educa t i on Maj o r s (� = - . 43 7 , 2
4.
Mathema t i c s Education Ma jors (� = - . 524 , 2
S.
Graduate S tudent s (� = - . 85 7 , �
6.
Control Group (� = - . 58 , �
<
<
. 01 ) ,
<
<
. 05 ) ,
.01 ) , and
. 01 ) .
The greater the math anxi e t y , as measured by the RMARS , the greater the
s e l f-rat ing of mathematics anxiety .
II .
1.
CONCLUSIONS
Math anxiety showed rela t ively l i t tle relationship to math­
ema t i cs performance .
Of the 16 correlations between math anxiety and
mathemat ics performance , five
( th o s e in the Technical Ma jors Groups and
the Mat hema tics Educa tion Maj o rs Group) indicated that higher lev e l s of
math anxiety were associated wi th higher mathematics- course grade s .
Thus
improving mathemat i cs performance wi l l require programs that do mo re than
reduce math anxiety .
In fact , mo derate levels of math anxi ety may ac­
tually improve one ' s mathemat i cs performanc e in those groups .
2.
Math anxiety showed a mo derate relationship to mathema ti cs
background , mathemat i cs achievement , and mathematics avoi dance .
s hould be not ed that the relationship i s leas t pronounced in the
77
It
Technical Ma j o r s Groups and the Ma thematics Educ a t i on Majors Group , whose
overall math anxi ety wa s no t very high, and who had rela tively st rong
backgroun d s , high achievement scores ( ACT mathemat i c s subte st ) , and no
prolonged avoidance behavi ors .
The relat ionship is mos t pronounced in
the Elementary Educ a t ion Majors Group , the Graduat e S tudents Group , and
the Control Gro up , whos e prior mathema t i c s background and achievement are
inadequat e and who have avoided taking mathemat i c s courses .
Because the
Graduate S tudents Group wa s mainly composed of re- entry student s , such
student s would appear to bene f i t mos t from treatment of math anxi ety .
3.
The s tudents wi th the more techni cal ma j o r s generally displayed
lower levels of math anxie ty than the s tudents wi th the less technical
maj ors .
Al s o , the higher one ' s level of math anxiety . the lower one ' s
s e l f- rat ing of mathematics abi l i t y .
Thus , math anxiety appears to be
related to inherent mathemat i cal abili t i e s of s tudent s .
4.
The RMARS seemed to adequately measure one ' s level of math
anxie ty as perceived by ones e l f for al l gr oups except for the Technical
Maj o r s enrolled in Mathematics 17 00 .
There fore the da ta does not support
the not ion that the RMARS is an inadequate measure of math anxiety for
s tudent s taking cal culus .
S.
S ex- re lat ed differences in math anxi ety may exi s t , but they are
p robably much sma l l er than has been sugges t ed previous l y .
This is proba­
bly due' in part t o this st1.1.dy ' s comparis on of mal e s and females with
s imilar mathematics backgrounds and experiences .
However , more hopeful­
l y . it might repr e s ent a de crease in sex-re lated di fferences over the
pas t de cade .
6.
Richardson and Suinn ( 19 7 2 ) reported a t e s t-retest reliabi li ty
of . 8 5 for the MARS , Suinn , Edie , Nicolet t i , and Spinelli ( 19 7 2 ) reported
78
one of . 78 , while Dew ( 1 9 8 2 ) repo rted one of . 87 .
The correlation
between the RMARS and the MARS was . 97 (P lake and Parke r , 1 9 8 2 ) .
the test-ret e s t reliabi l i ty of the
MARS
S ince
is re la t ively high and the corre­
lat i on between the RMARS and the MARS is relat ive ly high , it follows that
the test-retest reliabi l i ty of the RMARS is relat ivel y hig h .
S ince there
exi s t ed sign i f i cant di f fe renc e s in math anxiety be tween the C on trol Group
and both Techn i ca l Majors Groups . it is reasonable to conclude that the
reduc tion of math anxiety in the Technical Majors Groups could be attrib­
uted primarily to the unique elements of these group s :
prerequis ites , and po s i t i on in the sequenc e .
cour s e cont ent ,
Speci f i c a l l y , the content
of bot� the Technical Ma jors Groups wa s directly re lated to Calculus .
Prerequ i s i t e s for the Technical Majors Groups are iden t i c al and are as
fol lows :
( 1 ) two years of high schoo l algebra , and ( 2 ) one year of high
school geomet ry .
The corequi s i t e for the Technical Maj o r s Groups is one
half year - of high school t r igonometry .
Mathematics 1700 i s offered for
s tudents who in tend to take Mathema tics 1840 but score less than 26
the ACT mathemat ics subte st .
on
Both Mathema t i c s 1100 and Mathematics 1840
are beginning courses in a six-quar ter Calculus sequenc e .
the following conclus i on wa s made .
As a re sult ,
The unique element s of the Technical
Ma j ors Groups , in and of themselves , effect ively red uc e d math anxiety .
III .
1.
SUGGESTIONS FOR FURTHER RESEARCH
There is a need to identify the reas ons for the d i sparity of
male and female enrollment in the Technical Majors .
S ince males and
females did not differ in their math anxiety levels , atten t i on should be
focused on cultural factors , not only at the college level . but
especially at the junior-high schoo l level ( before the d i ff erential
c ourse- taking by sex begins ) .
79
2.
There i s a need t o conduct long- term pro ject s in whi ch math
anx i e ty is mea sured on a regular ba s i s ( i . e . ev ery quart e r ) for a period
of year s .
In par t i cular , a study should be conduc ted to plot the math
anx i e ty of the Elementa ry Education Ma j o r s and the Mathematics Educat ion
Maj o r s whi le they are in college as s tuden t s and after gradua t i on while
they are teaching mathema t i c s .
Furthermo re , the math anxiety of thes e
" teache r s " could be compared to the math anxi ety of their student s .
Als o , a s t ud y should be conducted t o track the Technical Maj ors Croups to
d e t e rmine whe ther the i r reduction in math anxiety remained s table over a
l onger t ime period .
3.
The re is a need t o identify other background and experi ent ial
fac t o rs effecting the level s of ma th anxi e t y , including amount o f time
s pe n t in s tudying mathematics outside of the clas s room .
4.
There i s a nee d t o analyze the RMARS by item to determine
whe ther there is a common subset of i tem s to wh i ch s tudents respond wi th
"much" and "very much " a s a whole , by maj o r , and by sex .
80
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A t t i tudes Scal e s : ins truments desi gned to measure a t t i tudes toward
the learning of mathematics by females and males . Journal for
Research in Mathema t ics Educat ion , l, 324- 3 2 6 .
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--
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cogn i t ions and per formance in math anxious student s : a fai lure of
c ogni tive theory? Journal of Couns eling P sycho logy, 1l ( 3 ) , 37 6382 .
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&
Wa rren , J . ( 197 8 ) .
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Mind over ma th .
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--
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9 6 0A .
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Rx
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Na t ional
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( 1 9 74 ) . Psychology of � differences .
Mac coby , E . E . , & Jackl i n , C . N.
Palo Alt o : S tanf o rd Unive r s i ty Pres s .
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Ra t ing Scale :
predi ct ing anxi ety experi ences and academic
performance in two groups of s tudent s . Journal of Educational
P s ycholo gy, 70 ( 4 ) , 589-59 4 .
83
Natki n , G . L . ( 1 9 6 7 ) . The trea tment of mathemat ical anxiety through
mediated t rans fer of a t t i tude toward mathemat i cs ( Do c t oral
di s s ertation , Indi ana Univer s i ty , 1 9 66 ) . Dis sertat ion Abs trac t s
Int ernat ional , 27 , 41 3 7 A .
P lake , B . S . , & Parker , C . S . ( 19 82 ) . The deve lo pment and valida t i on o f a
rev i s ed version of the Mathemat i cs Anx i e ty Rat ing Scale .
Educ at i onal and Psychological Mea surement , � ( 2 ) , 551-557 .
Res ni ck. H . , Viehe , J • • & Segal , S . ( 19 8 2 ) .
Is math anxiety a local
phenomenon? Journal of Coun s e l i ng P sychology. l! ( 6 ) , 39-4 7 .
Ri chard son , F . C . , & Suinn , R . M .
S ca l e : psychometric dat a .
( 6 ) , 551-554 .
( 1 9 7 2 ) . The Mathemat i cs Anxiety Rat ing
Journal o f Counsel ing Ps ychology, l!
Ri chard son , F . C . , & Wo olfolk, R . L . ( 19 80 ) . In I . G . Sarason ( Ed . ) , Te s t
anxi ety :
theory, re search , and applicat ion . Hillsdale , N. J . :
Laurence Erlbaum As sociate s .
---­
Round s , J . B . , Jr . , & Hendel , D . D . ( 19 80a) . Measurement and
dimensionali ty of mathema t i c s anxiety . Journal of Couns eling
P sychology, �, 138- 1 4 9 .
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Abs t racts Internat ional , 34 , 7054A-7 0 5 5 A .
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and u s er ' s manual . Journal for Research in Mat hema tics Educ a t i on ,
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84
Suinn , R . M . , E d i e , C . A . , Nicole t t i , J . , & S p i ne l l i , P . R . ( 1 97 2 ) .
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Suinn , R . , and Richardson . F . ( 1 9 7 1 ) . Anxi e t y management training : a
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( 1 9 8 2 ) . Three methods of reduci n g ma th anxie ty in women
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Ab s t ra c t s Interna t iona l . 44 , 97A .
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Math mys t ique :
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Time , 109 , 36 .
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Co .
Overcoming ma th anxiety.
Wagner , J . L .
( 1 9 80 ) . Math anxiety :
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William s , D . A . ,
�; 73 .
&
King , P . ( 1 9 80 ) .
85
New York :
W . W . Nor t on
&
prevent ion and cure . Curr i culum
Do male s have a math gene ?
Newsweek .
APPENDICES
APPENDIX
A
MATERIALS USED IN THE STUDY
INFORMATION ABOUT THE USE OF A REVISED VERSION
OF
THE
MATHEMATICS ANXIETY RATING S CALE
AT THE UNIVERSITY OF TENNES SEE
Dur ing the Win t e r Quart er , 1985 , C & I 37 5 2 , C & I 5 6 1 0 , Math 1540 ,
Mat h 1 7 00 , Math 18 4 0 , Math 21 10-20-30 , and English 1020 , wi ll be involved
in a resear ch s tudy about math anxiety . The aim of thi s research is to
gain insights into the study of math and math anxie ty . Each person
pa r t i Ci pa t i ng in the study will be requi red to compl e t e a revised vers i on
of the Mathema t i c s Anxiety Rating Scale (RMARS ) and a s tudent informa t i on
que s t i onnaire . The ��S is a twenty- four i tem scale on wh ich you state
how anx ious you feel concerning various mathematical s i tua t ions . Al so ,
each pe r s on par tici pa ti ng in the s tudy au thorizes the Univer s i t y of
Tenne s s ee to release hi s /her ACT-ma themat i c s score to the re s ea rcher .
As a result of your part i c ipat ion in the s tudy, you wi l l probably
have a greater unde r s tanding of your own feelings and att itude s regard ing
the study of mathemati c s . I t is reas onable to as sume tha t you wi ll not
experience any ne ga t ive effects from the study.
Par ti c i pat ion in the s tudy is volunt ary . Refusal to par t i cipate
wil l no t involve any penalt y . Als o , you may di scontinue par t i c i pat ion at
any t i me during the quarter wi thout any penalty .
No student wi l l be identif ied in any way in the publication of the
r e s earch . All of your responses wi l l be held in confid ence by the
res earcher and your res ponses will have no e f fect on your grades .
If you
have any ques t ions regarding the s tudy , please contact Patty Lets inger ,
Ayr es Hall , 403 C .
I have read the above explana t i on and g ive m y consent t o parti cipate
in the research stud y .
NAME :
SOCIAL SE CUtUTY NUMBER :
DATE :
P le a s e check the ap propriate blank :
I
am
18 years of age or older
I
am
under 18 ye ars of age
88
NAME
T01,'
Sco<.
REVISED MATHEMATICS ANXIETY RATING SCALE (RMAAS )
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0
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Ixpendi tu,ts.. u
PiCki"9 UP tho mllll \.x\ bool< to
bevin
...o,I<.ing on
• homework assilP'\ment.
Being 9'•• n , homowo<k usiqnmonl of many difficult
problems whic:ll is clue til. nu t d. .. m.. ting.
TOTAL
89
Wailing to 9" • INt" lut rllu,_
'"
....;c!I you
IXI)OICIId 10 dO poorly_
Goltin9 reKy
.0' "
III
A
1.1111
0
0
.-
to 'Iudy lor I .....tIt 'HI.
....J
a
Lislening 10 a teeturl in & marl'> d.1os&.
8eing ;iwn I H;x>p'. qUI: In I """th clan.
.....;
A 'ait
.......ftl
"'lid!
V...,
--
0
C
:J
,
c
a
0
c
....1
.�
0
0
0
a
!J
G
,
Hiving to .... . 11. t.bI•• in tN bold< 01 a matl'l
0
0
0
0
0
Being told ho.... 10 i....crpr.1 pro.,.btlily .1oO ffmenlL
a
0
0
0
0
.boo lt.
TOTAL
ToUI Seo...
90
STUlDENT INFORMATION QUESTIONNAIRE
P l e a s e compl e t e each of
NAME :
the following s t a t ement s about your s e l f .
��__________________��____________��_
last
( pl e a s e pr int )
middle
first
S O CIAL SECURITY NL�ER :
SEX :
FEMALE
MALE
COLLEGE :
MAJO R :
Place a check beside e a ch o f the cour s e s that you have suc c e s s fully
compl e t e d :
(wi th a grade of ' c ' or bet t e r )
( A ) IN JUNIOR HIGH O R
MIDDLE SCHOOL OR
( B)
IN COLLEGE
HIGH SCHOOL
MATH 0 1 50 ( TRIG )
MATH 1540 ( ALGE B�
MATH 17 00 (PRECALCUL�
GENERAL MATHEMAT I C S
ALBEGRA I
GEOMETRY
ALGEBRA II
TRIGONOMETRY--
MATH 1840 ( CALCULUS )
OTHER ( SPEC IFY )
ANALYS I S
PRECALCUL�
ADVANCED MATH
CALCULUS
L i s t all mathemat i c s cour s e s you are enrolled in thi s quar t e r :
I la s t succe s s fully compl e t ed ( wi th a grade
cours e :
FALL 1984
1983
1982
'c'
or be tter) a mathematics
WINTER 1984
SUMME R 1 9 8 4
S PRING 1984
OTHER ( S PECIFY )
_
_
Place a circle around one numb e r to show how you ra te your mathematics
abi li ty :
2
1
4
3
5
6
7
8
9
10
EXCELLENT
TERRIBLE
Place a ci rcle ar ound one numb er to show how you rat e your anxi ety about
mathema t i cs :
1
2
3
4
5
6
7
8
9
10
NOT ANXIOUS
HIGHLY ANXIOUS
Have you ever par t i c i p a t e d i n ( or are curr ently par t i ci pa t i ng in) a math
a nx i e ty t r eatment program?
YES
NO
Are you repea t i ng th i s cour s e becaus e you previously received
t D ' OR
'F' ?
YE S
NO
91
a
grade of
APPEND IX
B
STATISTICAL DATA
TABLE 1 5
STATISTICAL DATA - NONTECHNICAL MAJORS ( n
SEX
RMARS
PRETEST
RMARS
POSTTEST
MATHEMATICS
BACKGROUND
MATHEMATICS
ACHIEVEMENT
43
33
37
53
54
47
82
54
41
46
28
39
55
24
38
49
95
81
31
1 00
9
3
3
2
8
8
4
4
3
5
5
4
4
10
4
8
4
3
4
4
19
17
8
23
23
17
12
12
14
10
23
20
7
27
21
23
21
19
24
8
MATHEMATICS
PERFORMANCE
==
20)
MATHEMATICS
AVOIDANCE
SELF-RATING
OF
MATHEMATICS
ABILITY
SELF-RAT ING
OF
MATHEMATI C S
ANXIETY
6.5
14 . 5
1
22 . 5
6.5
6.5
10 . 5
6.5
6.5
10 . 5
1
6.5
6.5
4
6.5
3
4
10. 5
6.5
18 . 5
7
5
5
6
5
5
5
5
7
8
8
8
6
5
4
9
6
4
8
2
6
8
9
3
1
4
1
4
6
5
9
9
6
8
7
7
3
2
9
9
---_._-,-
'"
w
M
F
M
M
F
F
F
M
M
F
F
F
F
M
F
F
M
F
F
F
31
49
62
42
72
37
90
63
48
56
32
37
38
34
48
35
92
97
27
91
3
2
2
4
4
1
4
2
3
2.5
1
4
2
4
3
4
2
3
4
0
TABLE
16
STATISTI CAL DATA -- TE CHNICAL MAJO RS ENROLLED IN MATHEMATICS
1 7 00
( 0 - 17 )
SELF-RATING
OF
RMARS
SEX
POSTTEST
OF
MATHEMATICS
MATHEMAT I C S
MATHEMATICS
MATHEMATICS
MATHEMATI CS
MATHEMAT I C S
BACKGROUND
ACH I EVEMENT
PERFORMAN CE
AVOIDANCE
AB IL ITY
ANXIETY
A
6
M
3J
30
6
26
)
F
55
49
59
8
20
4
1
6
5
60
5
19
4
1
8
3
53
43
5
16
4
1
8
7
38
71
42
5
6
22
3.5
1
6
7
22
2
5
3
5
5
5
27
4
3
8
11
3
5
10
1
1
1
8
7
6.5
M
M
\0
�
PRETEST
RMARS
SELF-RATING
F
F
M
54
F
52
39
M
51
42
29
40
F
32
34
5
15
2
M
M
M
28
31
8
21
2
1
6
7
26
47
28
30
5
3.5
3.5
1
1
8
6
26
14
6
3
1
36
43
8
4
26
18
2
9
3.5
3
2
7
M
40
57
6
6
M
46
37
8
16
4
1
7
6
M
59
59
8
20
3
1
6
6
M
10
5
5
8
6
TABLE 1 7
STATISTICAL nATA -- TECHNICAL MAJO R S ENROLLED I N MATHEMATI C S 1 8 4 0
RMARS
SEX
\.0
IJl
PRETEST
RMARS
POSTTEST
MATH EMATICS
BACKGROUND
MATHEMATI C S
ACHIEVEMENT
(n
'"
53 )
MATHEMATICS
PER FORMANCE
MATHEMAT I CS
AVOI DANCE
SELF-RAT I NG
OF
MATHEMAT I C S
ABILITY
SELF-RATI NG
OF
MATH EMAT I C S
ANXI ETY
F
31
34
4
1
8
8
76
60
9
9
24
M
M
17
3.5
1
6
4
68
52
9
13
1
1
6
1
H
17
69
9
21
4
1
7
1
M
51
43
9
18
1
1
8
7
F
41
45
10
20
1
1
7
10
M
49
48
9
24
3
1
1
2
M
F
35
36
71
9
25
3
1
1
10
10
9
22
25
2.5
3.5
1
6
7
4
1
9
9
23
20
3
3.5
1
7
1
20
17
3
0
4
6
7
M
59
35
F
F
64
47
29
51
51
M
M
M
33
66
53
53
9
M
35
64
64
59
M
50
37
9
6
9
9
26
23
25
1
5
4
7
5
4
4
3
3
1
8
6
1
2.5
1
7
6
1
5
M
50
45
9
13
2.5
1
8
1
M
49
43
10
12
2
1
1
6
M
38
34
9
26
2.5
1
8
6
M
59
65
5
19
3.5
21
6
5
F
M
54
55
34
9
9
24
3
1
8
25
1
1
8
10
30
8
TABLE 1 7 ( continued)
SEX
\,0
'"
M
M
M
M
M
M
F
M
M
F
F
F
M
M
M
M
M
F
F
M
M
M
M
RMARS
PRETEST
33
63
50
56
67
52
29
36
62
45
57
47
72
39
55
58
33
35
44
69
54
37
46
RMARS
POSTTEST
MATHEMATI CS
BACKGROUND
MATHEMATI C S
ACHIEVEMENT
40
42
49
51
60
77
30
37
60
39
46
49
62
44
39
55
35
44
39
72
50
9
9
9
9
9
5
9
10
9
9
9
8
8
9
5
9
9
7
9
5
8
9
9
21
21
27
22
23
27
25
25
22
24
17
26
22
22
19
24
16
8
24
21
21
23
26
50
36
MATHEMATICS
PERFORMANCE
2
3
4
2
2.5
2
1
3
4
3
3
3.5
1
4
1
2
2
3
3
3
3.5
2
3
MATHEMATICS
AVOIDANCE
1
1
1
1
1
3
1
1
1
1
1
1
4
1
6.5
1
1
1
1
2
6.5
1
1
SELF-RATING
OF
MATHEMATICS
ABILITY
SELF-RATING
OF
MATHEMATICS
ANXIETY
7
7
9
8
7
7
8
7
9
7
4
8
8
7
7
7
8
7
8
6
7
8
7
6
5
4
6
6
8
10
5
5
6
7
8
3
8
9
5
5
5
7
3
2
7
8
TABLE 17
RMARS
SEX
\.0
-..J
PRETEST
RMARS
POSTTEST
( con tinued )
SELF-RATING
SELF-RATING
MATHEMAT I C S
ANXIETY
OF
MATHEMAT ICS
MATHEMAT I C S
MATHEMATICS
MATHEMATICS
OF
MATHEMATICS
BACKGROUND
ACHIEVEMENT
PERFORMANCE
AVOIDANCE
ABILITY
1
1
8
6
8
4
M
52
53
9
21
3
M
44
41
9
27
3
M
M
65
37
F
61
M
31
M
68
72
9
27
4
3
9
23
2
3.5
1
38
44
1
8
2
9
22
3
1
8
6
36
69
9
19
27
4
4
1
8
8
1
9
6
9
TABLE
18
STATI STICAL DATA -- ELEMENTARY EDUCATION MAJORS
(n
a
31 )
SELF-RATI NG
OF
RMARS
SEX
P
F
F
F
\0
00
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
PRETEST
11
47
55
64
64
35
71
67
47
46
79
42
34
80
96
47
52
60
59
40
56
75
76
RMARS
POSTTES T
55
74
43
65
56
31
102
72
39
52
61
48
28
69
99
53
44
63
46
47
52
60
79
SELF-RATING
OF
MATHEMATICS
MATHEMATICS
MATHEMATICS
MATHEMATICS
MATHEMATICS
MATHEMATICS
BACKGROUND
ACHIEVEMENT
PERFORMANCE
AVO IDANCE
ABILITY
ANXI ETY
4
3
5
6
5
9
4
3
5
9
6
10
7
6
4
6
4
6
6
5
4
6
7
11
7
14
6
13
20
10
23
22
23
11
27
19
9
6
21
13
21
17
19
22
17
18
2
2
3
3.5
2
4
4
3
4
4
3
4
4
4
4
4
3.5
4
4
4
4
3
2.5
2
6.5
6.5
3
1
1
6 5
4
3
1
1
1
3
1
4
1
1
1
1
1
1
1
2
.
5
5
7
5
6
7
4
4
6
9
7
7
8
8
2
7
6
6
6
8
5
5
5
6
5
6
3
6
6
7
3
8
10
7
5
8
5
1
8
2
6
7
7
7
5
2
TABLE 18
RMARS
SEX
\0
\0
PRETEST
RMARS
POSTTEST
( continued)
SEL F-RATI NG
OF
SELF-RATING
OF
MATHEMATICS
MATHEMATICS
MATHEMATICS
MATHEMATICS
MATHEMATICS
MATHEMATICS
BACKGROUND
ACHIEVEMENT
PERFORMANCE
AVOIDANCE
ABILITY
ANXIETY
F
82
55
5
16
3
1
5
5
l"
56
36
7
10
1
6.5
6
4
F
53
50
7
13
3
3
4
3
Ii'
SO
60
5
18
3
1
6
4
F
48
47
6
19
2.5
2
5
7
F
64
73
5
21
3.5
1
6
4
F
43
76
6
14
2
1
7
4
F
41
44
5
17
4
3
8
7
TABLE 1 9
STAT I STICAL DATA -- MATHEMATICS EDUCATION MAJORS ( n
SEX
.....
a
a
M
F
M
M
F
M
F
F
F
M
F
M
F
RMARS
PRETEST
36
30
81
51
31
53
24
32
28
35
36
48
41
RMARS
POSTTEST
MATHEMATICS
BACKGROUND
30
31
81
38
26
63
24
36
30
41
35
63
45
17
18
14
13
16
16
13
15
19
19
15
13
21
MATHEMATICS
ACHIEVEMENT
20
29
20
24
26
34
26
21
26
30
22
17
25
MATHEMATICS
PERFORMANCE
3
4
1
3
4
3
3
4
4
3.5
3.5
2.5
4
-
13)
MATHEMATICS
AVOIDANCE
SELF-RATING
OF
MATHEMATI CS
ABILITY
SELF-RATING
OF
MATHEMATICS
ANXIETY
1
3
1
4
1
1
3
1
1
1
1
4
1
7
9
7
7
8
7
8
8
9
8
7
8
9
5
9
6
6
10
9
10
9
9
8
7
6
10
TABLE 20
STATISTICAL DATA -- GRADUATE STUDENTS ( n
SEX
�
0
....
F
F
F
F
F
F
F
F
F
F
M
F
F
F
F
RMARS
PRETEST
RMARS
POSTTEST
MATHEMATI CS
BACKGROUND
112
50
42
47
55
68
29
66
91
44
51
93
59
73
27
89
45
47
42
52
73
33
49
80
64
51
84
42
79
30
4
5
10
11
4
4
11
5
3
8
5
4
5
4
13
MATHEMATICS
PERFORMANCE
3
4
3.5
4
4
4
4
3
2
3
3
3
3
3
4
=
15)
MATHEMATICS
AVOIDANCE
58 . 5
44 . 5
30 . 5
6.5
49
46 . 5
25
26 . 5
90 . 5
22
46 . 5
38 . 5
14 . 5
18
14 . 5
SELF-RATING
OF
MATHEMATICS
ABILITY
3
7
7
6
6
3
8
4
1
6
5
2
5
5
9.5
SELF-RAT ING
OF
MATHEMATICS
ANXIETY
1
7
4
8
8
1
9
4
1
8
6
1
5
1
10
TABLE 2 1
STATISTICAL DATA -- CONTROL ( n
SEX
M
F
F
0-
0
N
M
F
F
F
F
F
M
M
M
F
F
M
M
F
F
M
F
M
F
M
F
RMARS
PRETEST
RMARS
POSTIEST
MATHEMATICS
BACKGROUND
66
102
36
58
75
104
98
53
59
64
33
42
86
77
65
45
65
92
34
88
82
60
70
40
47
102
38
37
87
101
93
66
49
60
32
56
74
83
86
56
44
93
38
91
84
60
57
52
3
9
9
5
4
4
4
11
5
2
12
8
5
5
2
9
2
4
3
4
4
5
4
6
MATHEMATICS
ACHIEVEMENT
19
12
12
21
17
16
15
23
14
10
27
22
22
18
18
20
14
22
21
7
13
19
17
26
�
24 )
MATHEMATI CS
AVOIDANCE
SELF-RATING
OF
MATHEMATICS
ABILITY
SELF-RATING
OF
MATHEMATICS
ANXIETY
10 . 5
1
1
10 . 5
6.5
6.5
1
4
1
6.5
1
6.5
1
1
4
1
10 . 5
10 . 5
4
6.5
15
1
11
1
3
4
8
4
1
4
4
7
5
4
8
5
7
5
4
6
3
6
8
3
5
5
4
7
2
2
7
3
5
1
1
5
5
1
7
7
3
6
10
8
3
1
5
1
9
2
3
8
APPENDIX
C
HUMAN SUBJECTS APPROVAL
THE U N I V E R S I TY OF T E N N ESS E E. K NOXVI L L E
K NOXVI L L E
37996-0'.Q
OFFICE OF TI-IE VICE P�VOST
FOR RESEARCH
November 6 , 1 984
.1 '1' £ .1. � . '5
"" E l.. e:: P� O "" E 9 " 4 l.466
Pat r i c i a P re s t on Lets i n g e r
1 2 1 Ay r e s H a l l
CAMPUS
De a r Ms .
Lets i nger:
T h e pro j e c t wh i ch you s u bm i tted e n t i t l ed , " A Study o f t h e R e l a t i o ns h i p
be twe e n L e v e l o f Mathema t i c s Anx i ety a n d Se l e c ted C og n i t i ve V a r i a b l e s , " C R P
#A- 283 , h a s b e e n re v i ewe d .
Th i s p ro j e c t comes w i th i n the g u i de l i n e s wh i ch p e rm i t me to c e rt i fy
t h a t t h e p roj ect i s exemp t from rev i ew by t h e Comm i ttee on Res e a rc h
P a rt i c i p a t i o n .
T h e re s po n s i b i l i ty of the p roj ect d i rec t o r i n c l u d e s the f o l l ow i n g :
1.
P r i o r a p pro va l from t h e Dea n fo r R e s e a rc h mu s t be o bta i ne d be fore
a ny c ha n ge s i n the p roj e c t a re i n s t i t u t e d .
2.
A s ta teme n t mu s t be s u b m i tted ( Form D ) at 1 2 -mo n t h i n te rv a l s
a t te s t i ng to t h e c u rrent s t a t u s of t h e p ro j e c t ( p rotoco l i s s t i l l
i n e ffect , proj ec t i s t e rm i nated , etc . ) .
T h e Comm i ttee wi s he s you s u c ce s s i n you r re s e a rc h e n d eavors .
)l;ILv
Ma r l a Peterson
De a n for Re sea rc h
s cw
cc :
D r . C . W . Mi n k e l , Ac t i n g V i c e Provost fo r R e s e a rch
Dr . T. W. H i p p l e
D r . Don a l d J . Des s a rt
D r . J a n e t R . Hand l e r
104
APPENDIX D
CODING FOR MATHEMATICS BACKGROUND
STUDENT INFORMATION QUE ST I ONNAIRE
Please comple t e each of the fol lowi ng statements about yourse lf .
NAME :
last
first
middle
( pl ease print )
SOCIAL SECURITY NUMBER :
SEX :
MALE
FEMALE
COLLEGE :
MAJO R :
Place a check beside each o f the courses that you have succes sfully
(wi th a grade o f ' c ' or be t te r )
compl e t ed :
( A) IN JUNIOR HIGH OR
MIDDLE SCHOOL OR
HIGH SCHOOL
GENERAL MATHEMATI C S
2
ALBEGRA I
-3
GEOMETRY
ALGEBRA 114
TRIGONOMETR�
9
ANALYS I S
PRECALCUL�9
ADVANCED MATH""":9
11 CALCULUS
( B ) IN COLLEGE
1
MATH 0 1 5 0 ( TRIG )
8
MATH 1 5 4 0 ( ALGEB�5
MATH 1 7 00 ( PRECALCUL'US) 10
-MATH 1840 ( CALCULUS )
­
12
OTHER ( SPE C IFY )
MATH 1 5 50
6
MATH 1560
7-
L i s t all mathematics courses you are enro lled in thi s quarter :
I la s t succes sfully comp l e t ed ( wi th a grade
cours e :
or be t t e r ) a mathema t i c s
'c'
SUMMER 1 9 84
SPRING 1 9 8 4
FALL 1984
1982
OTHER ( S PECIFY )
1983
WDlTER 1984
Place a circle around one number to show how you rate your mathemat i c s
abi l i ty :
2
1
TERRIBLE
3
4
5
6
7
8
9
10
EXCELLENT
Place a ci rcle around one numb er to show how you ra t e your anxi ety about
mat hematics :
1
2
3
HIGHLY ANXI OUS
4
5
6
7
8
10
9
NOT ANXIOUS
Have you ever pa rticipated in ( or are current l y par t i c i pating in) a math
anxiety treatment program? YES
NO
Are you repeating thi s cour s e becau s e you prev i ously rec e ived a grade of
' D ' OR ' F ' ? YE S
NO
1 06.
VITA
Patricia (Patty) Ann Pre s ton wa s born in Washing ton , D . C . on
November 17 , 1953 , and at tended public schoo l s in Cha rle s t on , Wes t
Virgini a , At lanta , Georgia , S t . Louis , Mis s ouri , Arling t on , Virgini a , and
Dye rsbur g , Tennes see .
She att ended Lambuth Colleg e , the Univers i ty of
Tenne s s ee , Martin, and Jackson State Community College , and was gradua ted
f rom the Univers i ty of Tennessee , Knoxvi lle , with a B . S . degree in
Mat hemat i cs Education in 197 4. She was a graduate teaching a s s i s t ant in
the Mathematics Department at the University of Tennessee , Knoxv i l le , and
received her Master of Mathemat i cs degree in 197 5 from the Univer s i t y of
Tennessee , Knoxvi lle .
From 197 5 to 197 7 , she wa s a mathema tics teacher at Seven Ri lls
I nd ependent Schoo ls , C incinna t i , Ohi o , where she taught at all levels
f rom eigh th through eleventh g rad e .
In 197 8 , she ent ered the Graduate School of the Univers i ty o f
Tennessee , Knoxvi l le , where she was a graduat e teaching as s i s tant i n the
Mat hemat i cs Department .
She received the Doctor of Philo sophy degree
wit h a major in Mathemat i cs Educat i on in June 1986.
She i s a member o f P i Lambda The ta honorary society, Nat ional
Counci l of Teachers of Mathema t i cs , Association for Women in Ma thematics ,
and the Mathematical As sociati o n of Amer i ca .
Patty is married t o Wad e C . Le t s inge r , and they have three ch i ldren ,
Robin Mi chele , 9, Michael Todd , 7 , and Ann Mari e , 1.
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