CALIFORNIA STATE UNIVERSITY, NORTHRIDGE
THE RELATIONSHIP BETWEEN SELF-CONCEPT
AND MATH APTITUDE FOR NINTH GRADE FEMALES
A thesis submitted in partial satisfaction of the
requirements for the degree of Master of Arts in
Educational Psychology Counseling and Guidance
by
Vickie Lynne Deinhard
May 1985
The Thesis of Vickie Lynne Deinhard is approved:
Dr. Richard~ T1liel
(Chairman)
California State University, Northridge
ii
TABLE OF CONTENTS
PAGE
CHAPTER 1:
Introduction
1
Background of the Problem
2
Purpose of the Study and Hypothesis
8
Definitions, Terms and Limitations
of the Study
10
Review of the Literature
12
Review of Biological Research
13
Review of Sex-Role Research
14
Review of Socialiazation Research
17
Review of Self-Esteem Research
21
CHAPTER 3:
Methodology
27
CHAPTER 4:
Analyses and Interpretation of Data
31
Introduction
31
Results
31
Summary, Conclusions and Recommendations
35
Summary
35
Conclusions
36
Recommendations
37
CHAPTER 2:
CHAPTER 5:
BIBLIOGRAPHY
APPENDIX A:
40
Piers-Harris Childrens Self-Concept
iii
45
ABSTRACT
THE RELATIONSHIP BETWEEN SELF-CONCEPT
AND MATH APTITUDE FOR NINTH GRADE FEMALES
by
Vickie Lynne Deinhard
Master of Arts in Educational Psychology
Counseling and Guidance
This study explores one small aspect of the problem as
to why math scores for high school females sharply decline.
These scores decline below both the girls own former levels
of achievement and below the boys level of achievement.
The major
males'
focus
is
on the
relationship between a
self-concept and her math aptitude.
fe-
Because society
does not stress math as an important skill for females,
was hypothesized that
math,
have higher
females
who do go on to achieve in
self-esteems
society's conventions.
it
that
allow them to
ignore·
Ninth grade females were tested for
math aptitude using the Comprehensive Test of Basic Skills.
The Piers-Harris Children's Self-Concept Scale was chosen to
measure the females' self-esteem.
Although
findings
support
the
prediction
that
a
sta-
tistically significant correlation exists between math apti-
iv
tude
and
self-concept,
significant.
the
findings
are
not meaningfully
Age and self-esteem accounted for only 5% of
the variance associated with math aptitude.
The general conclusion is that other sociological factors beyond self-esteem must account for the decline in math
aptitude of high school freshmen girls.
v
CHAPTER ONE
INTRODUCTION
Todays women are fighting for equal pay,
opportunities in the working world.
positions and
A major concern in this
struggle is the gross under-representation of women in the
math, science and technical fields where so many of the high
paying
jobs
exist.
Why
this
under-representation occurs
has been the subject of many studies.
stated as discriminatory practices,
While most causes are
such as denial of equal
educational opportunities or an incapability of learning the
technical knowledge and skills,
three, surprisingly,
problem.
or any combination of the
they are not the primary causes of the
The disparity seems to exist because many women
choose to avoid math.
In 1973
Lucy Sells
(Sells,
1980:
Tobias,
1978)
did a
simple pilot study to test for what constituted an adequate
high school math background.
Her sample was the incoming
freshmen class at UC Berkeley (UCB).
From her study, Sells
found that 57% of the entering freshmen males had the 3. 5
years
of high
school math necessary for
the UCB calculus
series, while only 8% of the incoming females had the same
background.
tically
That meant that 92% of the females were automa-
disqualified
from
10
of
the
12
UCB
colleges
and
excluded from 22 of 44 possible majors because they lacked
1
2
the
math
background
necessary
to
take
The message seems simple and clear:
the prerequisites.
women need to take more
math.
However,
if women are voluntarily choosing to avoid a
subject, where's the problem?
are
choosing
to
interest them.
They don't like math, so they
concentrate
on
subject
areas
that
do
Why should they waste their time on a sub-
ject where they have little interest or capability?
The point
is,
it
is
difficult to make an intelligent
decision without first examining all relevant information.
Are women being given all of the pertinent information?
Are
they told they will have to prepare themselves for career
opportunities?
Are they told that all fields are becoming
more and more technical?
women
are
making
If this is not the case, then many
lifelong
decisions
based
on
incomplete
data, and technical fields are losing many people that might
become valuable resources.
achieve in math.
Women need to be encouraged to
They need to know the importance of math
skills in their everyday lives.
They also need to know that
being capable in math and being female is not an anomaly.
BACKGROUND OF THE PROBLEM
The odd twist to this problem is that the division between females and math does not appear at all during the elementary years.
Carpenter,
1981;
there are few,
achievement
Many researchers
up
Sells,
if any,
through
1980;
(Badger,
Fennema,
1981;
1980)
Fennema
report
&
that
differences between male and female
the
age
of
13.
Fennema
(1980)
3
hypothesizes that this is true because up to that point the
math curriculum and the number of math courses taken is the
same
for both
sexes.
It is during the high school years
when math courses become optional that females stop electing
to take them.
This is when females begin losing ground.
Once they
start
falling
behind,
the
gap between male
and female math achievement seems to get larger with each
successive
year
of
high
school
and
college
Parsons, Adler and Kaczala (1982) and Bleyer,
Elmore (1981)
education.
Pedersen and
all believe that the junior high years are a
critical period for the formation of attitudes toward math
and
for
courses.
their
influence
on
the
decision
to
take
further
It is during these years that the first differen-
ces in achievement appear.
The boys begin to have higher
expectancies and self-concepts of their math abilities and
girls begin showing higher levels of math anxiety.
Fennema and Sherman did a study published in 1978 that
showed
significant
sex-related
differences
in
two
areas.
The first was that males were overwhelmingly more confident
in their ability to learn math.
This was true even when the
achievement levels for males and females were the same.
The
second area was that males showed a much higher tendency to
rank math as
a male domain.
In other words,
although fe-
males were less likely to describe math as either a male or
female-type
activity,
males
were
much
more
inclined
to
describe it as a male-type activity which means they felt it
was an appropriate activity for them to be taking part in.
\.,
.
1
'
4
In 1980 Luchins and Luchins surveyed members of American
Women
Mathematicians
that indicated that
(AWM)
and
also
received
information
society sees math as a male activity 1
Many of the female mathematicians reported that their high
school peers treated them as if they were strange, and that
their male peers either did not like or were intimidated by
smart girls.
They felt their teachers paid more attention
to the boys and that their interest in math was not taken
seriously.
includes
This
all
information
of
the
reporting, however,
events
biases
was
that
all
self-report
accompany
that
and
so
sort
of
even if these women only perceived the
in this way,
their perceptions certainly influenced
their future actions.
By the time students reach their middle teen years, the
boys
start pulling ahead
study done by the
u.s.
in math achievement.
In a 1978
Department of Education and Science
(Badger, 1981) it was reported that 15 year old boys outperformed
girls
in all
15 math curriculum categories tested,
and significantly out performed them in 11 of the 15 categories.
Major performance discrepancies occurred in the two
general areas of spatial ability and problem-solving skills.
Fennema
males
this
and
Carpenter
outperformed
difference
the
( 1981)
reported that at age 17 the
females
increased
as
at
the
all
levels
number
of
tested,
math
and
courses
taken increased.
One possible explanation for the math achievement difference between sexes is the factor to which each sex attri-
5
butes its success.
success
in
math
When males were surveyed regarding their
(Parsons,
Adler,
Meece
&
Kaczala,
1982:
Wolleat, Pedro, Becker & Fennema, 1980), they usually attributed
it
to
internal
and
Females, by contrast,
and
unstable
This was
causes
true
stable
causes
such
as
ability.
attributed their success to external
such
as
effort
or
even for high achieving
easy
assignments.
females.
It seems
that males feel they have an innate ability to do well in
math, while females
feel that it is effort and not ability
that allows them to succeed.
If females believe they are
only achieving because of the effort they are putting out,
it would be
reasonable
anxious
as
the
degree
appears
they wait
for
for
of
them to become more
math
difficulty
and more
increases.
It
the day when their efforts will no
longer be adequate to keep up with the subject matter.
"The
frustrations,
confusion
and
tension
often
asso-
ciated with attempting math have finally been recognized as
symptoms
anxiety 1
of
"
a
severe
(Crawford,
and pervading problem,
1980,
pg. 8).
Crawford
namely
stated
1
math
that,
"math anxiety can be described simply as a fear of figuring,
a fear of doing anything mathematical"
mena is not restricted to the classroom.
(pg. 9).
This pheno-
It occurs for many
people in everyday life while paying bills, figuring tips or
computing interest rates.
Some people have nagging doubts
regarding their math skills, while others are immobilized by
the problem.
Suinn
and
Studies done by Rounds and Hendel (1980) and
Edwards
( 1982)
confirmed
that math
anxiety was
6
often associated with lower female math enrollment, learning
and performance.
According to Crawford (1980),
a person's
success with math has more to do with one's attitude and
feelings toward math than with one's innate aptitude for it.
The
lack
of
confidence
combined with
leads women to math avoidance.
math
anxiety
often
Even the women who have high
abilities and high performance levels in math are often not
free of associated anxieties.
Leder (1982) found that many
of these women had a high fear of success.
to be
associated with
succeeding
in
a
The fear seemed
traditionally male
field and being thought less feminine or of being socially
ostracized.
Women
who were
not
performing well
in math
exhibited a much lower fear of success, possibly because it
posed no threat to them.
Women's discomfort at being asso-
ciated with mathematicians may be partly explained by the
survey done by Brush (1980).
juniors
and
seniors
and
She surveyed 510 high school
found
that
both
sexes
described
mathematicians as having only masculine qualities.
The four most common decriptors were: responsible, wise,
rational and cautious.
Both sexes also felt that their own
self-image was closer to that of a writer than of a mathematician.
qualities
Since the stereotype of a mathematician included no
that are
typically considered feminine,
being a
mathematician or even associated with math does not appear
to be a role-appropriate activity for women.
The
mathematician
stereotype
exists
today
largely
because of the many math myths that people cling to (Ray &
7
Oxreider,
most
1982: Tobias,
debilitating,
1978: Tobias,
and yet most
1980).
Probably the
firmly believed,
myth
is
that some people can do math and some people can•t--you have
to have a
• math mind • •
from an •English mind•,
A •math mind•
1
is somehow different
history mind• or •musical mind•.
A
corollary to myth #1 is that people who do well in math are
smarter than people who do well in other subjects.
more
brains
to
learn math
than
to
learn other
It takes
subjects.
Because these people who do well in math have a •math mind•
and more brains they always find math easy. They don•t have
to struggle with it the way other people do.
These smarter
people with the •math mind• are men, of course, because men
are good at math and women aren•t.
The tragedy here is that people not only believe these
myths,
but they eventually pass them on as truths to their
children or students (Tobias, 1978).
Clinging to the myths
becomes a convenient excuse to explain failures,
eliminate
further effort and to avoid the subject all together.
Adding to the obscurity of the myths is the fact that
math has a language all of its own (Tobias, 1978).
its own vocabulary, rules of grammar and symbols.
It has
Often the
words and symbols will have meanings different from those of
common
English
usage.
To
fully
understand
the
subject,
people must be taught to properly use its language.
The final result of these stereotypes, myths and beliefs
is that fewer women than men elect to continue taking math
classes.
The problem starts in late high school and con-
8
tinues through the college years (Sherman & Fennema, 1977).
Tobias (1978) found that although girls accounted for 49% of
secondary school students in the
u.s.,
they made up only 20%
The college
of the students taking math beyond geometry.
and university population was made up of 45% women,
only 15% of the math majors were female.
did a
while
John Ernest (1980)
He found
study at UC Santa Barbara in 1976.
that
males made up 45% of the incoming freshmen class and yet 64%
Males were twice as
of the calculus enrollment was male.
likely as females to take calculus.
In addition, the attri-
tion rate of females from the calculus series and from math
The end result
as a major was higher than that for males.
of these situations is that women are choosing to avoid math
and
thus
they
are
greatly outnumbered
math and technical fields
(Meece,
Futterman,
1980;
1982;
Fennema,
in the
scientific,
Parsons, Kaczala,
Parsons,
Adler
&
Goff &
Kaczala,
1982).
The decision to
sequences,
not
the
career options
and
limit math training carries many conleast
of
inequities
which
is
the
in education.
limitation
of
Women cannot
expect high paying technical careers if they fail to prepare
themselves educationally for the technical field.
This ends
up as a great personal loss monetarily and career-wise for
many women in addition to the great loss of potential human
resources for the scientific fields.
PURPOSE OF THE STUDY AND HYPOTHESIS
While hundreds of studies show that a problem exists in
9
getting
females
to
continue
their
math
education,
more
research needs to be done regarding possible causes.
The
problem cannot be corrected until there is more information
on
the
causative
factors.
This
is
not
to
say that
the
situation is uni-dimensional where one or two solutions will
answer
the
questions
for
everyone.
The
problem
of
encouraging females to take more math and thus realize the
importance
of
it
in
everyday
life
complex one with many variables.
revolving
around humans,
is
obviously
a
very
Like any problem situation
some variables
can be controlled
and some can't.
The
purpose
correlation
of
exists
self-esteem,
and
ticular
that
feel
this
paper
between
math
a
is
to
personality
achievement.
math
is
a
determine whether
factor,
Since
male domain,
males
a
namely
in
par-
( and presumably
they convey that belief in some way to females),
it would
seem that females who have a positive and realistic image of
themselves,
would
stand
a
better
chance of
shrugging off
stereotype ideas and pursuing their own interests.
one of those interests happens to be math.
Even if
It seems likely
then that most females who achieve in math also have high
self-esteem.
Many
studies
show
that
no
differences
in
achievement
exist for ages 5-13 and that the gap begins and gets larger
yearly at ages 14 or 15.
Because of that information, this
study will concentrate on females
are aged 14 and 15.
in the ninth grade,
who
This appears to be a crucial time for
10
formulating attitudes regarding math and making decisions as
to
whether
or
not
to
pursue
the
subject.
As
mentioned
before, it seems that "attitude" is actually more important
than "aptitude" in explaining female math performance.
is
also
a
time,
coincidently,
when
females
begin
This
shaping
their roles as women and start looking for their individual
niches in society.
To
obtain
as
testing
procedure
female
9th
much
at
grade
data
a
low
as
possible
anxiety
students
will
and
level,
be
to
keep
the
491
male
and
tested
using
the
\
1
Piers-Harris Children's Self-Concept Scale.
will be that the
tested,
rather
test
than
is
one
less
The assumption
threatening if everyone is
select group.
However,
only the
female test results will be used for the purposes of this
The
paper~
results
of
the
Piers-Harris
Children's
Self-Concept Scale will be compared to each 9th grade female
student's Comprehensive Test of Basic Skills
(CTBS)
score,
and her last semester math grade to see if any correlation
exists.
The
hypothesis
is
that
a
significant
positive
correlation exists between self-concept and math aptitude.
Girls who have high self-esteem scores will tend to also
have high math aptitude scores.
DEFINITIONS,
TERMS AND LIMITATIONS
OF THE STUDY
Two
terms that will be used frequently throughout the paper are
self-esteem
and
self-concept.
They
are
synonomous and will be used interchangably.
defined as:
assumed
to
be
Self-concept is
;>
11
The self-concept, or self-structure, may be thought of
as an organized configuration or perception of the self
which are admissable to awareness.
It is composed of
such elements as the perceptions of one's characteristics and abilities: the percepts and concepts of
the self in relation to others and as associated with
experiences and objects: and goals and ideals which are
perceived as having positive or negative valence.
(Rogers, 1951, p.l36)
This study was conducted at a single junior high school
in Simi Valley, California where the population is predominantly middle class whites.
The results, therefore, may not
be generalized to all 9th grade females.
Another limitation
is that the data were collected through self-report surveys
and tests and therefore contain all the biases endemic to
self-reports.
possible
by
The
biases
emphasizing
were
controlled
confidentiality,
as
honesty
much
as
and
the
importance of research.
The intent of this study is to signify a
relationship
which will help us understand why so many women avoid math
and
to
offer
insight
areas of research.
into possible
solutions
and
further
CHAPTER 2
REVIEW OF THE LITERATURE
The review of research includes three different areas of
investigation on math
overview of the
achievement.
approach
sex-related differences
recent
and then an
studies which link self-esteem and
Most research done on sex-related differences
the
problem
socialization angle -
from
far
biological stand point.
either
the
sex-role
or
the
fewer attack the problem from a
In all
fairness,
the few studies
available on biological explanations for differences may be
because of the problem of getting funding for such projects.
Studies that show one sex to be superior to the other are
not popular.
biological
All three areas,
factors,
were
sex-role,
reviewed
for
socialization and
contributions
and
added to them was the fourth category of self-esteem and how
it affects achievement.
The review of biological research is intentionally minimized and includes just three articles to give the reader a
flavor
of the different theories researched.
actually explain a
Biology may
part of the sex-related differences in
math, but it is the one area that cannot be readily changed
and at this stage, energies should be spent on the sex-role
and socialization areas.
The areas of sex-role and sociali-
zation are often hard to separate.
12
This explains why many
13
articles actually overlap the two areas.
These secttons are
more
the
extensive
because
they
point
out
many
factors
involved and the complexities of the problem.
REVIEW OF BIOLOGICAL RESEARCH
One
female
of
major
the
differences
math achievement
is
between
male
and
in spatial perception ability.
Because of the consistency of these differences it has been
suggested that the cause might be genetic.
of
the
research
resistant
to
(1981)
showed
environmental
that
factors.
Badger•s review
spatial
ability
To account
for
was
that
resistance it was proposed that spatial perception might be
carried by a
recessive
gene
on
the
X chromosome.
Males
receive only one X chromosome and thus there would not be
another
X
chromosome
trait
present
to
cancel
recessive spatial perception characteristic.
out
the
However, this
theory does not explain why the differences in ability begin
only at adolescence.
Attempts to explain that discrepancy
led to the next series of studies which suggested that spatial ability might also be linked to the change in hormone
level during the early teenage years.
Lee Dembart
recent
studies
(Jan.,
done
1984) of the L.A. Times reported on
at John Hopkins University by Camilla
Benbow and Julian Stanley.
Geschwind
study
which
Their work is based on a Norman
theorized
that
high
levels
of
testosterone (a male hormone) may cause the right hemisphere
of the brain to become dominant.
Math reasoning is believed
to
hemisphere
be
controlled
by
the
right
of
the
brain.
14
Geschwind • s
ability,
studies have shown a
left-handedness,
correlation between math
allergies
and
high
levels
of
Benbow and Stanley are continuing to work on
testosterone.
the testosterone and math ability connection.
The
final
study presented
in
this
section
also deals
with brain lateralization (Burton, 1978) but from a slightly
different angle.
Again, this research is based on the idea
that each hemisphere of the brain specializes in different
areas; the right side being dominant for math reasoning and
spatial
ability and
the
left
side
for verbal
and
logical
tasks.
It has been proposed that the early maturation of a
female•s left brain hemisphere (and verbal abilities) might
actually obstruct the development of their math and spatial
abilities.
REVIEW OF SEX-ROLE RESEARCH
Research in this area explores possible connections between the sexual roles that individuals live within and their
mathematical
performance.
Specifically,
it is
looking at
how differences in female and male sexual roles might also
explain differences in female and male math achievment.
One of the factors that confounds this problem is that
differences
do not
always
exist.
A study done on eighth
grade students (Smead & Chase, 1981) showed that there were
no
differences
in
sex-role
expectations.
Girls had high
expectations for themselves and for girls as a whole with
regard
to
math
achievement.
However,
reached the lOth and 11th grades,
by
the
time
they
the picture had changed
15
(Sherman
Fennema,
&
1977}.
The girls
fidence in their ability to learn math,
that
math
would
be
useful
to
them,
now had
less
con-
fewer expectations
and
perceived
their
parents as being less positive toward them as math learners.
Within a 2 to 3 year period they went from being very confident, to being insecure in the same subject area!
Part
attitudes
UCSB
of
of
survey
teachers,
that
change
the
teachers
(Rapport,
63%
in attitude might be due
surrounding those
1978)
to
girls.
the
In a
of elementary and high school
felt that girls did better in English
(none
felt that boys did better) and 41% felt that boys did better
in math (none felt that girls did better).
Maybe girls are
reacting to what they feel is expected of them.
The stu-
dents themselves were surveyed for subject preference and no
sex differences were found.
This
indicates that boys are
not achieving in math because they like it better.
Girls might also be reacting to what they see their role
models doing.
often admit
Elementary teachers (who are usually female)
to
disliking math
(Kogelman
&
Warren,
1978).
Many of these teachers actually get someone else to teach
the subject for them.
Girls get the message that it's okay
to dislike and avoid math - you can always get someone else
to do it for you.
to
do
well
in
It might even be socially undesireable
math
and
appear
to
be
too
intelligent.
Imitating the same sex parent could also produce differences
in
math
oriented
abilities
toward
(Hilton
quantitative
&
Berglund
tasks
like
1974).
their
Boys
are-
fathers
so
16
they can handle money and finances
for a career.
and
social
careers,
later
Girls are more oriented toward verbal tasks
skills.
(Sherman
1978; Fennema,
1981).
Because girls
they do not
life
and prepare themselves
1980;
are
not guided
towards
see math as being useful to them in
Fennema,
&
1974;
Kogelman
&
Warren,
Fennema & Becker,
and Pedro, Wolleat,
In addition, the sex role attitudes are more impor-
tant to a girls learning of math, than to a boys learning of
math (Fennama & Sherman, 1978).
more by significant others,
Girls seem to be influenced
and thus are more likely to do
what is expected of them to please others.
Despite the fact that most children are taught to model
the behavior of same sex persons,
crosssex
identification
intelligence
interests
of
(Tobias,
the
seems
1978).
opposite
studies have shown that
to
Boys
sex
be
related
and
girls
actually
intelligence and creativity tests.
to
higher
who pursued
scored
higher
on
A possible explanation
for this is that intelligent children find society's rules
oppressive and ignore them.
At any rate, women who do well
in math were shown to embody the best of masculine and feminine characteristics.
The
final
sex-typing
section on
of math.
sex-role research deals with the
For many
reasons,
regarded as being the domain of males.
math
is
generally
Burton (1978) found
that the characteristics of notable scientists were not part
of the tradi tiona! female role.
technical
fields
Those who excelled in the
were highly intelligent,
channeled
their
17
energies into one direction (their careers), were extremely
independent,
and capable of spending much time apart from
others without
guilt -
qualities
that
are
not
ordinarily
women
and
math,
stressed for females.
Many
stereotypes
exist
regarding
one
being that female mathematicians are less feminine than nonmathematicians
(Ernest,
has
been
disproved many times but is still commonly believed.
When
506 high
school
1980).
students were
That
surveyed,
notion
32% of them felt
that boys are better at math while only 16% felt that girls
are better.
math
an
Weissbrod,
Male adolescents in particular are apt to find
inappropriate
1980).
activity
Obviously,
for
girls
at least a
(Tobias
&
few teachers and
administrators also feel it is an inappropriate activity for
girls
by virtue of the
fact
that one researcher
(Tobias,
1978) found that a tie clasp was offered as first prize each
year for the math competition.
In addition to math being
stereotyped as a male domain (Fennema, 1980: Bander & Betz,
1981),
it
has
also
masculine-typed males
math anxiety scales.
duals
who
have
been
and
found
females
that
androgynous
and
usually scored lower on
This is probably because these indivi-
adopted
masculine
or
androgynous
charac-
teristics feel they are the very ones who are "supposed" to
be doing math.
REVIEW OF SOCIALIZATION RESEARCH
Is
it
adulthood,
possible
habits
that
while
and beliefs
preparing
young
women
for
are passed on that actually
i1
'
18
stifle
their math potential?
Are
fail or to lag behind in math?
they
in
fact
taught to
Those questions and others
were investigated by the studies that are examined in this
The common element in these studies is that some-
section.
how socialization techniques
math.
affect women 1 s
achievement in
This section has been given greater emphasis and put
after biological research and sex role research because it
appears
to
have
Socialization may
the
most
bearing
explain why the
on
female
the
math
problem.
achievement
enigma is not universal and why the significant discrepancy
seems to surface during early adolescence.
Home conditions and environment seem to be very important to math attitudes and learning (Tsai & Walberg, 1983).
Again,
the math
attitudes held by
females
seem to have a
great affect on their math learning so the viewpoints presented at home regarding math will probably have a
bearing on their math achievement.
influential
daughters
in
the
their daughter 1 s
1980).
Fathers were found to be
mathematical
(Kirschner,
achievement
of
their
1982) while mothers had an affect on
degree of math anxiety
(Wilhelm
&
Brooks,
Those parents who had confidence in their own abili-
ties and were confortable using math,
attitude toward the
who were
beliefs
daughter.
very
direct
not
subject.
Parents,
comfortable with math,
which
tended
to
projected a positive
raise
the
especially mothers,
modeled behaviors and
anxiety
level
of
a
Even though parent support has been shown to be
important
to
female
math
achievement,
many
parents
19
reported not noticing or encouraging their daughter's early
math
interest
& Cohn,
(Fox
1980).
Some
parents
actually afraid to encourage their daughter • s
were
interest in
math for fear that it would make her different and lead to
social ostracism (Tobias, 1978).
There are conflicting accounts regarding the amount of
influence exerted by role models on math achievement.
In a
study done by Parsons, Adler and Kaczala (1982) the results
showed that parental role modeling had very little affect on
their children's math-related self-perceptions, actual performance or plans to continue in mathematics courses.
The
authors of the study felt, however, that parents may contribute to sex differences in math through their expectancies
rather then through their
role modeling,
since parents of
sons thought that math was a more important subject for them
than did parents of daughters.
an L.A.
models
Times article,
and
social
Lee Dembart (Mar., 1984) in
pointed to the lack of female role
support
to
representation of women (12% of
3.5% of
u.s.
explain
u.s.
the
gross
under-
scientists are female,
engineers are female) in the technical fields.
Kogelman and Warren (1978) stated that while young girls are
struggling with
their
identities,
they may weigh the evi-
dence and decide to label math as being masculine.
fail
to
parents,
The
receive
reinforcement
and
support
from
If they
teachers,
peers and society they will probably reject math.
lack of reinforcement is
avoid the subject.
interpreted as permission to
Several researchers (Fennema & Sherman,
20
1977;
Tobias,
often
cultural
1978;
Ernest,
conditions
1980)
make
have
the
pointed
study
of
out
that
math
seem
inappropriate for females.
Another proposal has been that different learning styles
and practices might account for sex-related math differences.
Armstrong
(1981)
found that thirteen year old girls
started the high school math program with the same math abilities
as
the
boys,
and
visualization abilities.
with
no
differences
However,
in
spatial
by the end of the high
school years, males were superior at one and two step word
problems.
Even though math background and the courses taken
were controlled, Armstrong hypothesized that the differences
occurred because of different learning techniques
(females
may have been using different and/or less successful strategies to solve the word problems) and math experiences outside
of
school
(males
may have extracurricular activities
which foster their math abilities).
7th graders
(Fox
&
Cohn,
In a study of bright
1980) it was shown that the math
achievement gap between the sexes is narrowing except in the
case of mathematically precocious students--there the males
retained a tremendous edge over the females.
boys
reported
studying
math
and
science
Many of the
with
interested
teachers or parents while also working informally with math
puzzles,
games
and books.
The girls,
however,
were
less
eager to pursue math and science activities and enjoyed more
social interests instead.
It is often hard to distinguish between the sexual role
21
aspects and the socialization aspects with respect to their
effects
on math
inter-related.
achievement because the two ideas
are so
There does seem to be substantial evidence
though that many sources in our society give young women the
impression that they cannot or should not succeed at math
and,
worst of all,
completely ignore
that there
is
these messages
no real
which
reason to.
come
from
To
so many
directions within the environment, a young women would have
to possess a firm sense of her own identity and what is most
important for her.
That thought then leads to the signifi-
cance of self-esteem with respect to academic performance.
REVIEW OF SELF-ESTEEM RESEARCH
Having good self-esteem means having the confidence in
onesself and ones • abilities to pursue the goals that are
interesting
others.
or
important
regardless
of
the
support
of
This would seem to be particularly vital for young
women who are more concerned and affected by the opinions
and support of significant others than young men are.
Many
researchers feel that a correlation does exist between selfesteem and academic achievement.
Karen Prager (1982) did research on identity development
and
self-esteem in young women.
Her results
showed that
achievement of an identity is important to self-esteem development in women.
of
She also found that non-traditional areas
identity development were becoming more
the adjustment of women.
environment,
influential
in
Possibly because of the changing
women are beginning to see the importance of
22
goals other than interpersonal ones.
women are
involved
in a
It seems that even if
male-oriented
career,
they
still
value and identify with those characteristics normally associated with being feminine
(Plas & Wallston, 1983).
results
young women
are
pursuing
important
math
they
for
will
suddenly
These
who worry that by
begin
exhibiting
male
characteristics.
Another important ingredient toward good self-esteem is
an inner-locus of control
(Starr,
1979).
Starr feels that
females need a strong inner-locus of control and high selfesteem to overcome the existing social and educational climate.
No
causality
in
either
direction
has
been
established, but internal locus of control, high self-esteem
and academic achievement (particularly math achievement) are
correlated.
The mistake that many young women make is to
relinquish that internal locus of control and to attribute
their
success
to
effort
or
luck
rather
than
to
ability
(Parsons, Adler & Kaczala, 1982; Blumenfeld, Pintrich, Meece
& Wessels, 1982).
The next point is so obvious that it may seem trivial,
but it is worthy of exposure: people do the things they feel
confident
in
and
(Fennema, 1980).
avoid
subjects
that
cause
them
anxiety
As stated earlier, males are significantly
more confident of their ability to learn math, so that even
if the subject causes anxiety,
this confidence allows them
to overcome the anxiety while girls drop out.
positive experiences
Additionally,
lead to positive self evaluations and
23
vice
versa
(Coopersmith,
experiences
with
The
cornraderie
the
the
an
positive
seems to be instrumental to success within that area.
classmates,
creates
shared
that
the
subject
Having
atmosphere
of
any
1959).
encouragement
of
teacher can be extremely essential to the growth and developernent of a healthy math attitude.
Several studies (Lamke, 1982; Bander & Betz, 1981) state
the desirability of androgyny in adulthood but continue to
propose stereotype sex-role behavior for healthy adjustment
during adolescence.
to
be
Research shows that a woman is supposed
androgenous
appropriate
difficult
roles
to
as
an
adult
in adolescence.
determine
if
the
and
yet
fulfill
sex-
This conflict makes it
adolescent
is
progressing
through stereotypical behavior as a result of the developmental
process
or whether
the
child
roles that society approves of.
math is
not a
is
simply
fulfilling
In either case,
pursuing
traditional activity for adolescent females
and thus not likely to enhance their self-esteem through any
sense
of
conformity.
Somewhere
between
adolesence
and
adulthood, these young women need to slowly start acquiring
positive
masculine
traits
to
associated higher self-esteem.
the
growth
process
is
the
achieve
androgyny,
and
its
It is sad that nowhere in
importance
of
androgyny
ever
femininity
and
stressed.
Yanico
and
Hardin
(1981)
tested
the
masculinity scores of female engineering and horne economics
majors.
The engineering majors scored higher on masculinity
24
characteristics but there was no difference between the two
groups on femininity scores.
or
masculine
esteem.
typed
Individuals with androgynous
characteristics
also
had
higher
self-
Hetherington and Parke (1979) and Berzonsky (1981}
agree with Lambke that for a young women to establish positive
self-esteem
she
appropriate activities.
needs
to
participate
in
sex-role
Following the traditional feminine
route seems to aid her in building a positive self identity.
If the findings by Protinsky and Farrier (1980) are correct
that
young
esteem,
female
adolescents
experience
a
drop
in
self-
it would seem logical that teenage girls will per-
form better on tasks they believe to be sex appropriate as
they try
to
regain their self confidence.
These
results
seem to conflict with the studies done with women showing
that
androgynous
and
positive
masculine
traits
(such
as
decisiveness and goal orientation) are associated with very
high self-esteem.
One possible explanation is that during
adolescence, females develop confidence and gain approval by
conforming to the expectations that society has for females.
Once their identity is established, they feel secure enough
to
break
away
adopt
the
best
their
needs.
from
of
The
conforming
masculine
sad
to
and
situation
society's
feminine
is
that
dictates
traits
to
the passive
and
suit
and
dependent behaviors that are reinforced during the teenage
years are actually detrimental to academic and career success.
This final
section deals with the relationship between
(l.
25
high
self-esteem and
academic
achievement.
Yarworth and
Gauthier (1978) did a study on self-concept and extracurricular
activities
that
was
based
on
the
assumption
of
a
correlation between self-concept and academic achievement.
In his
review of the
literature,
Leviton
(1975)
not only
found a consistent correlation but also found that many studies showed that self-concept is an antecedent to academic
achievement.
However,
the exact point in which this rela-
tionship exists does not appear to be consistent.
nection between
self-esteem and
the math and
The con-
verbal
test
scores for sixth graders was studied by Primvera, Simon and
Primavera (1974).
They found a significantly high correla-
tion between high test scores and high self-esteem for the
girls.
The authors hypothesized that this may be because
girls get more approval from teachers in elementary school
thus
affecting
self-esteem.
deteriorate in
junior high.
This
Finally,
trend
Fink
starts
(1962)
to
studied
the relationship between self-concept and academic achievement for ninth graders.
He found an unquestionably signifi-
cant correlation for boys but it was considerably less for
girls.
Fink recommended further research to sort out the
findings for girls.
It seems obvious by now that the math avoidance and lack
of achievement by females is not a simple problem requiring
one solution.
of
studies
tested,
and
To make the issue more complicated, results
vary
the
according
various
to
definitions
populations
used,
studied.
factors
Biological
26
factors
may
cause
part
of
the
problem
in
the
form
of
recessive genes or changes in sex hormones but again, those
are not factors that can be readily changed or controlled.
Certainly
society
has
created
although no longer useful,
an
image
of
women
(that
still exists) portraying them as
conforming, dependent and bascically social people.
Because
parents and teachers want their daughters and female students to be approved of, they foster these traditional feminine traits even though they are detrimental to career and
academic success. Finally, there appears to be a correlation
between self-esteem and math achievement, although the relationship is not a definite one for females during the adolescent years.
The intent of this paper is to further clarify the relationship between a ninth grade female's self-esteem and her
math performance.
Each female student's Piers-Harris Self
Concept Score will be analyzed along with her age, her CTBS
math scores and her math grade to see if a positive correlation existed and to determine the possibility of predicting
math performances using self-esteem scores.
CHAPTER 3
METHODOLOGY
This was a
correlational study designed to investigate
the degree of relationship between a ninth grade female's
sel £-concept,
her
math
aptitude
and
her
math achievment.
Although no cause-and-effect conclusion was possible, it was
expected that a positive correlation would exist between the
three stated variables for high school freshman females.
To collect data for this project,
all ninth grade stu-
dents (male and female) at a Southern California junior high
school were tested.
A briefing session was held for all of
the ninth grade math teachers to dispense testing materials
and instructions.
tions
Each teacher received a set of instruc-
to read aloud to the
received
the
same
students
information
prior
so that all students
to
the
test.
Each
teacher then administered the test to his or her math students.
The test was given during one 55 minute period on a
day chosen by each individual teacher.
This particular sample group was chosen because of their
availability and convenience.
All ninth grade students were
tested so that it did not appear to the students to be a
selective process.
In an effort to encourage the students
to be as candid as possible, the testing situation was made
as
anxiety-free as
possible.
It was
27
assumed that if all
28
students were being tested,
the situation would not appear
threatening to any one particular group.
Afterwards,
only
the test results from females was used for this project.
addition
to
all
males,
two
excluded from the data base.
other
general
groups
In
were
Those students that were new
to this particular junior high school this year were deleted
because the necessary Comprehensive Tests of Basic Skills
(CTBS)
scores
were
not
available
English-as-a-Second-Language
because
language
grade
they
were
to
receive
girls were
included
not
for
(ESL)
students
proficient
valid
included
test
in
them.
enough
scores.
in
All
Also,
all
were
dropped
the
English
other
the data base.
ninth
Of the 188
females, 5 were eventually dropped during the sta-
tistical analysis because of missing data on their tests.
The
instrument
used
to
measure
self-concept
was
the
Piers-Harris Children's Self-Concept Scale (see Appendix A).
It
is
a
self-report questionaire containing 80 statements
concerning how
selves.
children
and
adolescents
feel
about
them-
Students filling out the survey were asked to indi-
cate whether each statement is true or false for them.
To
save time in data reduction and analysis, students responded
true or false on computerized scanning sheets.
No differen-
ces in test validity have been found for the Piers-Harris
between the computerized scanning sheet and pencil and paper
tests.
The Piers-Harris yields several scores with regards to
self-concept.
One
is
a
total
score
of
the
80
items
29
answered, giving an overall index score of self-concept.
It
has also been broken down into six different clusters which
yield scores for smaller components of self-concept.
clusters
are:
behavior,
intellectual
and
school
These
status,
physical appearance and attributes, anxiety, popularity, and
happiness
and satisfaction.
The
statistical analysis was
done with the overall Piers-Harris score only.
l\1ath aptitude was determined by using the two math sections of the CTBS.
This test was given to these students in
April of their eighth grade year.
three math scores.
measures
math
The CTBS actually offers
One measures math computation: another
concepts
and
applications:
the
third
is
a
total score of the other two sections.
These scores were
analyzed
to
individually
and
all
together
determine
the
strongest relationship between the variables.
The eighth grade Spring semester math grade was used as
an indicator of each girl's math achievement. It is realized
that grades are subjective and in no way can they give an
objective measure
of
each
girl's math
achievement.
were, however, the best achievement indicator
They
available and
so were used cautiously.
Age was converted from years and months to a comparison
of
11
months older 11 than the youngest student.
In other words
the youngest student was assigned a base of
age.
Those
assigned a
students
value of
older received a
11
2 11 ,
who were
11
1
11
one month
11
0.. for their
older were
relative to the base,
etc.
then
two months
Grades were also converted to
30
numerics for data analysis.
The base of "1" was assigned to
"F" and correspondingly "A" became "5".
Once all of the data had been collected and coded onto
the
conputerized
scanning
sheets,
analysis was done by computer.
the
actual
statistical
CHAPTER 4
ANALYSES AND INTERPRETATION OF DATA
INTRODUCTION
The purpose of this study was to establish a connection
between a ninth grade female's
lity and performance.
self-~steem
and her math abi-
The analysis and interpretation of
the data were directed toward supporting the theory that age
and self-esteem could be used to predict math achievement.
RESULTS
For
background
deviation,
descriptive
variance,
variables
information,
the
minimum
maximum
are
and
mean,
presented
standard
for
in
the
six
Table
I.
Intercorrelations for the measures are provided in Table II.
The strongest correlations,
as would be expected, were
between the two math sections of the CTBS test and between
each math section and the total CTBS math score.
The next
group of strong correlations exist between math grade,
the
two CTBS math tests,
All
and the CTBS total math score.
three correlations are significant at the p
<
• 001
level.
Despite the strong correlations, math grade was not chosen
as either a predictor or criterion variable because of the
subjective nature of the variable.
vely
with
the
other
five
measures
Age correlated negatiwhich
finding of the review of the literature.
3 1
supported
the
32
TABLE I
Analysis of Condescriptives of Math Grade, Aptitude, Age and
Self-Esteem for 9th Grade Females
MGRADE
SCORE
MEAN
3.303
58.851
STD DEV
1.142
VARIANCE 1.303
AGE
MCOMP
CAPPLID
CTOTAL
19.755
31.532
34.096
65.404
10.048
4.500
7.032
7.933
14.238
100.972
20.250
49.450
62.932
02.723
MINIMUM
1.000
24.000
7.000
10.000
4.000
13.000
MAXIMUM
5.000
77.000
35.000
40.000
45.000
85.000
Where:
MGRADE
SCORE
AGE
MCOMP
CAPPLID
CTOTAL
N = 188
-
Math Grade
Piers-Harris Score
Age in months
CTBS Math Computation Score
CTBS Math Concepts and Applications Score
Total CTBS Math Score
The Population Sample
TABLE II
Intercorrelations Between Measures of Math Grade, Aptitude,
Age, and Self-Esteem for 9th Grade Females
SCORE
.26658
AGE
-.12859
MCOMP
.44061
CAPPLID .40603
CTOTAL
.45793
-.06802
.16857
.16130
.17802
-.15907
-.13509
-.15772
.71461
.91682
.92910
Where:
SCORE
AGE
MCOMP
CAPPLID
CTOTAL
N = 183
-
Piers-Harris Score
Age in months
CTBS Math Computation Score
CTBS Math Concepts and Applications Score
Total CTBS Math Score
The Population Sample
TABLE III
Hierarchical Multiple Regression Summary: Age and Self-Esteem Predictors for Female 9th
Grade Students with the Math Achievement Criterion
PREDICTOB
VARIABLE
F
SIGNIF
R2
R
R.::
CHANGE
SIMPLE
R
OVERALL
F
SIGNIF
5.11999
.007
AGE
4.11607
.044
.15772
.02487
.02487
-.15772
SCORE
5.43323
.021
.23020
.05299
.02812
.17802
-------------
---
--
.
- - - - - - -'------
-
Where:
AGE
- Age in months
SCORE
- Piers-Harris Score
N = 183 - The Population Sample
w
w
34
To determine whether age and self-esteem could be us.ed
to predict a 9th grade females math ability,
multiple regression was run.
a hierarchal
Age and the Piers-Harris score
were entered on step number 1 as predictor variables.
The
total CTBS math score was chosen as the criterion variable.
The multiple regression summary is given in Table III.
The multiple R for age and Piers-Harris score was .23.
The overall F of 5.12 is significant for P < .001.
The two
predictors accounted for 5% of the variance associated with
math
achievement.
score was
The
contribution
of
the
Piers-Harris
just slightly more than that of age (. 02487)
the criterion.
to
CHAPTER 5
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
SUMMARY
The aim of this study was to determine-the relationship
between a ninth grade female's self-concept, her math aptitude and her math achievement.
The hypothesis was that a
positive correlation exists between math aptitude and selfesteem so
that
girls
with high
self-concept
scores would
tend to also have high math aptitude scores.
A correlational study was devised to determine the relationship
girls.
high
between
age,
self-esteem
and
math
aptitude
for
Ninth grade girls from a Southern California junior
were
Children's
tested
for
self-esteem
Self-Concept Scale and
using
for
the
Piers-Harris
math aptitude using
the Math Computation and Math Concepts and Applications sections of the CTBS test.
putation score,
Age,
self-esteem score, math com-
math concepts and applications score, CTBS
total math score and math grade were entered into a multicorrelation matrix.
chosen
as
aptitude
predictor
and
a
Finally, age and self-esteem score were
variables
hierarchal
for
multiple
the
criterion
regression was
of
math
run
to
determine the success of predicting math aptitude from age
and self-esteem.
five measures
Age correlated negatively with the other
in the correlation matrix and age and self-
35
36
esteem were statistically significant as predictors for math
aptitude.
CONCLUSIONS
The negative correlations of age with the other measures
indicate
that
as
females
approach
the
middle
teen
years
their math grade, math aptitude and self-esteem all decline.
This substantiates the findings of other research projects
on high school females.
gical
female
factors
become
teenager•s
(although
still
It is assumed that various sociolovery
important
developement,
undefined)
are
at
and
this
that
detrimental
stage
these
to
a
of
a
factors
female • s
progress in math.
Additionally, although age and self-esteem were shown to
be
statistically significant
predictors
of math aptitude,
they are not practically significant predictors.
Because of
the large N size necessary for multiple regression studies,
even very small
changes
cant.
it
However,
is
appear to be statiscally signifinecessary to
uses of this information.
look at the practical
Age and self-esteem account for
only 5% of the variance in math aptitude.
That means that
95% of the variance is caused by factors other than age and
self-esteem.
Because society seems to hold math less impor-
tant for females and perhaps even socially unacceptable for
them, it was hypothesized that females with high self-esteem
would be able to
ignore
the dictates
of society and show
higher math aptitude scores than the general female population.
The
data
of
this
study as
analyzed did not prac-
3
39
revel in their perceived inadequacies, they will continue to
do so.
This
then denies
society of a vast technological
resource, and dooms many women to limited success as well as
success in limited areas.
"
'
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APPENDIX A
Piers-Harris Children's Self-Concept Scale
Here are a set of statements. Some of them are true of you
and so you will circle the ~· Some are not true of you
and so you will circle the no. Answer every question even
if some are hard to decide, but do not circle both ~ and
E£• Remember, circle the ~ if the statement is generally
like you, or circle the no if the statement is generally not
like you. There are no right or wrong answers. Only you
can tell us how you feel about yourself, so we hope you will
mark the way you really feel inside.
1.
My classmates make fun of me •••••••••••••••••••• yes no
2.
I am a happy person ••••••••••••••••••••••••••••• yes no
3.
It is hard for me to make friends ••••••••••••••• yes no
4.
I am often sad •••••••••••••••••••••••••••••••••• yes no
5.
I am smart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . yes no
6.
I am shy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . yes no
7.
I get nervous when the teacher calls on me •••••• yes no
8.
My looks bother me •••••••••••••••••••••••••••••• yes no
9.
When I grow up, I will be an important person ••• yes no
10.
I get worried when we have tests in school •••••• yes no
11.
I am unpopular •••••••••••••••••••••••••••••••••• yes no
12.
I am well behaved in school ••••••••••••••••••••• yes no
13.
It is usually my fault when something goes wrong yes no
14.
I cause trouble to my family •••••••••••••••••••• yes no
15.
I am strong ••••••••••••••••••••••••••••••••••••• yes no
16.
I have good ideas ••••••••••••••••••••••••••••••• yes no
17.
I am an important member of my family ••••••••••• yes no
18.
I usually want my own way ••••••••••••••••••••••• yes no
19.
I am good at making things with my hands •••••••• yes no
45
46
give up easily ••••••••••••
.......... .......... yes
20.
I
21.
I am good in my school work ••••••••••••••••••••• yes no
22.
I
23.
I
24.
I
25.
I
... ................ . ....... yes
can draw well •• . .. .. . ... . ... .... . .. . .. . . .. .. .. yes
am good in music •• .. . . .. .. ...... ... . . .. ... .. . . yes
behave badly at home •• .. . . . .... . . . .. .... . .. ... yes
26.
I
am slow in finishing my school work ••
27.
I
am an important member of my class •••
no
28.
I
am
no
29.
I
have pretty eyes •••••••••••••••••••••••••••••• yes no
. 30.
I
can give a good report in front of the class •• yes no
do many bad things.
no
no
no
no
no
yes no
. .... ... . yes
nervous •• . .. .... .. . .. . .. . . .. .. . . . ..... . . . .. yes
........ . .. yes
sister(s) ... . .... .. . yes
31.
In school I am a dreamer •••••••••••••
32.
I
33.
My friends like my ideas •••••••••••••••••••••••• yes no
34.
I
often get into trouble ••
no
35.
I
am
no
36.
I
am
37.
I worry alot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . yes no
38.
My parents expect too much from me •••••••••••••• yes no
39.
I
like being the way
40.
I
feel left out of things ••
41.
!'have nice hair ••
no
42.
I
no
43.
I
44.
I
45.
I
46.
I am among the last to be chosen for games •••••• yes no
pick on my brother(s) and
. ......... .... . .... .. . yes
obedient at home ••••• . . . .. . . . .. .. . .. ... .. .. yes
lucky ••• . ... .. . . ... . . . ... . ... .. . . .. .. .. . . .. yes
I
am ••
.... .. . ............. . yes
no
no
no
yes no
.............................. yes
often volunteer in school. . ... ... .... ...... ... yes
wish
were different. . .. .... .. .. ... . .... . .. .. yes
sleep well at night ••• . . . .. ... .. . . . .. ... ..... . yes
hate school ••••••••••• . .. . .. .. .. . . . . . .. ... . ... yes
I
no
no
no
no
47
47.
I am sick alot....... . . . . . . . . . . . . . . . . . . . . . . . . . . . yes no
48.
I am often mean to other people. • • • • • •.• • • • • • • • • • yes no
49.
My classmates in school think I have good ideas. yes no
50.
I
51.
I have many friends ••
no
52.
I
no
53.
I
54.
I
55.
I
56.
I
57.
I am popular with boys •••••••••••••••••••••••••• yes no
58.
People pick on me ••••••••••••••••••••••••••••••• yes no
59.
My family is disappointed in me ••••••••••••••••• yes no
60.
I have a pleasant face .. .... .
61.
When I try to make something, everything seems
am unhappy •••••••••
•
• •
•
•
•
•
• •
•
•
•
•
w • •
e • e e e e e e e o o
yes no
............ ............... yes
am cheerful •••••••• . . .. .. .. .. . .. ... .... . . .. . .. yes
am dumb about most things •• . . .. . . . .... ... .. ... yes
am good looking •• . . . .. .. ... .. . .. .. .... .. .... .. yes
have lots of pep.
........ ........... .. yes
get into a lot of fights. . .. . ... . .. .. ... . . ... . yes
. .... .. .......... .. yes
no
no
no
no
no
to go wrong. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . yes no
am picked at home ••
. . ... .......... ....... ..... yes
no
62.
I
63.
I am a leader in games and sports ••••••••••••••• yes no
64.
I
65.
In games and sports, I watch instead of play.
66.
I
67.
I
68.
I
69.
I
70.
I
71.
I would rather work alone than with a group ••••• yes no
72.
I
73.
I have a good
am clumsy •••••••••
yes no
yes no
.... ................ yes
am easy to get along with. . .. ... . .... .. .... . .. yes
lose my temper easily •• . .. .... . .. . ... .. . . . . .. . yes
am popular with girls. . .. . ... .. ...... .. .. . . .. . yes
am a good reader •••••• . . .. ... . .. . ..... .... .. .. yes
forget what I learn •••••••
.................. .... yes
figure •••••• .. . .. . . .. . . .. . ... ... .. yes
like my brother (sister)
no
no
no
no
no
no
no
48
74.
I
75.
I
76.
I
77o
I
78.
I
79.
I
80.
I
.............. ........... yes
am always dropping or breaking things. ... . . .. . yes
can be trusted •••••••••••••••••• ... . . . .. . ..... yes
am different from other people •• ... ... ....... . yes
think bad thoughts. ... ... ... .... ... . .... . .. . .. yes
cry easily •••••••• . ... ... ... . ... ... ... .. .... .. yes
am a good person •• . .. .. .. . . . . ... . .. ..... . .. ... yes
am often afraid ••••
no
no
no
no
no
no
no