Gender Differences 36
others using toys which involve numerical, spatial, and mechanical
relationships.
As their daughters advance to higher levels of
mathematics, Keinberg and Stenmark recommended that parents encourage
and support their daughters.
Allow the girls to talk about the problems
they are having and listen attentively.
Together, attempt to reach a
solution, find others with whom to study, or talk to someone who also
struggled with mathematics but were rewarded for perseverence.
Statements, such as 'I was never good at math either' or 'I can't do that
either' should be avoided.
When children are studying, it is not helpful to
give them correct answers, but to try to talk through the problem by
reviewing the facts given and the questions asked, and
find a logical way to solve the problem.
role model for their children.
by attempting to
Most of all, parents need to be a
If parents are willing to give up, even if the
topic is not related to mathematics, children will develop similar
attitudes, which will be reflected in their school work.
Teachers also need to be able to overcome this negative
socialization.
Jean Skolnick, Carol Langbort, and Lucille Day (1982), in
their book, timY.1C. Encourage
~
in Math and. Science, identified four
strategies for teachers to focus on in attempting to overcome the
negative socialization of students:
a)
building confidence,
b)
using
Gender Differences 37
manipulative materials,
c)
using different social arrangements,
being aware of gender-role bias.
and
d)
Skolnick, Langbort, and Day (1982)
believed that confidence is strongly linked to problem-solving skills.
Students who are excellent problem solvers are students who strongly
believe they are capable.
Unfortunately, girls tend to be socialized early
in life to believe they cannot do certain problems.
Thus they tend to give
up easily, are more discouraged, and do not get the same practice at
problems as do boys.
To help build confidence, Skolnick, Langbort, and Day
suggested different approaches for teaching.
First, they suggested that
teachers present and evaluate topics at many different levels.
This way
the students will have the opportunity to successful at their own level.
Secondly, they suggested that teachers give problems or activities which
can be approached in different ways and may have more than one right
answer.
This is valuable since not all students will think about a problem
in the same way; thus one approach is not necessarily better than another
nor is the approach considered right or wrong.
Problems with more than
one correct answer will allow the students who only find one answer to
still feel successful, while the higher level students can be challenged to
find all possible answers.
Students should also be encouraged to guess
and test ideas, which is also an important part of problem solving.
Girls
Gender Differences 38
are often afraid of guessing because they are afraid of being wrong.
Students need to be taught the importance of creating hypotheses and
testing them, and if their guess is wrong, they must understand how to
learn from mistakes.
Finally, students need to estimate.
If students
realizes they are close to an answer, their confidence will increase and
they will have a stronger deSire to find the exact answer.
Using manipulative materials is another strategy suggested by
Skolnick, Langbort, and Day (1982).
The manipulatives used do not have to
be expensive models ordered out of catalogue, instead they can include
easy to find materials such as playing cards, clay, mirrors, rocks, or sugar
cubes.
Because of socialization, girls learn to interact through verbal
means while boys learn through hands-on experiences.
When children
start school, girls are expected to understand and express mathematics
verbally or by writing, without ever experiencing it through some concrete
means.
Thus it is important, at both the elementary and secondary level,
to present concrete forms in order for the girls to fully understand the
abstract concepts.
Using different social arrangements is the third strategy
recommended by Skolnick, Langbort, and Day (1982).
Social arragements
can be independent, cooperative (single-gender and mixed-gender groups)
Gender Differences 39
and in the form of game playing.
Students, especially girls, gain
confidence from independent work because they are allowed to work at
their own rate and to create their own ideas.
Cooperative work allows the
students to share ideas and to interact with others.
Beginning with single
gender groups allow the girls to share with other girls who may also have
low confidence in mathematics.
There may also be certain mathematical
topics with which girls are not familar and this allows them to work with
others at their own level.
Mixed-gender groups are more successful at
later stages in activities.
Girls will have had a chance to gain self-
confidence before they begin working with boys.
When girls and boys work
together cooperatively, they will be able to learn from each other and to
consider each other equal partners.
learn strategies.
Game playing helps the students to
They learn to anticipate and to examine all possibilities
and consequences.
These techniques are not only valuable for problem
solving, but for logical thinking as well.
The final strategy presented by Skolnick, Langbort, and Day (1982) is
being aware of gender-role bias.
from observing role models.
gender as the student.
Students learn what is expected of them
Usually the role model observed is the same
Through content relevance and the modeling of new
options, it is believed that girls will see new opportunities available to
Gender Differences 40
them which they never knew existed.
Content relevance involves relating
the mathematics which is being taught to different careers the students
may not have been aware of or relating the mathematics to real life
problems which may be solved by people in different careers.
The
modeling of new options presents problems in which women are portrayed
in nontraditional jobs and men are portrayed in nurturing roles.
Skolnick, Langbort, and Day (1982) presented many specific
activities to be used in the classroom in their book.
divided up into four categories:
The activities are
spatial visualization, problem solving,
logical reasoning, and scientific investigation.
These activites are gender
neutral so they are appropriate for the whole classroom.
They provide
alternate ways of presenting material which include more concrete
explanations for those who have trouble grasping the abstract.
Similar activites can be found in the Math!QJ: ~ Handbook
(Downie, Siesnick, & Stenmark, 1981).
In 1973, it was observed that
females were coming to college with insufficent mathematical
background.
Through extensive research, this handbook was published to
help girls learn mathematics through hands-on experience.
The activities
were designed to decrease students fear for math and increase their
problem solving skills.
Although the activites are appropriate for males
Gender Differences 41
and females, all pronouns in the book are either "she" or "her".
The term
"students", however, is used in place of "girls".
Conclusion
Researchers are still searching for an answer to the gender
difference question.
mathematical field.
Meanwhile, statistics show girls are lacking in the
Whether or not researchers ever agree on a solution
to the gender question, alterations need to be made in mathematical
education.
alter.
Genetic differences are impossible for parents and teachers to
Therefore, parents and teachers are challenged to alter
socialization.
Being aware of the gender difference problem and being
aware of the changes which can be made through socialization will be a
start towards encouraging girls to believe they are capable and that they
can succeed.
Gender Differences 42
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Luchins, E.H. and Luchins, A.S. (1980). Female mathematicians: A
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Gender Differences 49
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Developmental
Gender Differences 2
Gender Differences in Mathematical Ability:
An Empirical Look
In their review of the literature on gender differences, Maccoby and
Jacklin (1974) concluded that one of the four primary gender differences
is that boys excel in mathematical ability.
They believed that all gender
differences, including the gender difference in mathematical ability, are
the result of
a)
genetic factors,
b)
shaping of boy-like behavior and girl·
like behavior by parents and other socialization agents, and
c)
children's
spontaneous learning of behavior appropriate for their own gender through
imitation.
Maccoby and Jacklin reported that there was little difference
between male and female mathematical ability until adolescence;
however, the age at which gender differences appeared depended on the
measure used in testing.
Mathematics is not a unitary factor; the solving
of mathematical word problems is related to verbal ability while other
mathematical concepts, such as geometry, are related to visual-spatial
ability.
Because mathematics is not a unitary factor, it is difficult to
determine the factor which causes the gender difference.
Maccoby and
Jacklin were not able to give a definite reason for the mathematical
gender difference but did cite a number of theories and hypotheses.
Maccoby and Jacklin (1974) determined that a gender difference in
Gender Differences 3
mathematical ability did exist, however, the extent and reasons for this
gender difference could not be determined.
Following the publishing of
their findings, research continued to debate the genetic versus the
socialization theories of mathematical gender differences.
Although new
discoveries have been made, old theories disproved, and new theories
created, the research is stili inconclusive.
Vandenberg (1968; c.f. Maccoby and Jacklin, 1974) stated that visual
spatial ability was linked to heredity.
Visual-spatial ability was believed
to be linked to the X-chromosome causing visual-spatial ability to be
expressed at a higher rate in males than in females in a ratio of two-toone (see Maccoby & Jacklin, 1974, for a review).
There is little support
for mathematics being genetically related, however, there are many
theories for the relationship between visual-spatial ability and heredity.
Since mathematics is related to visual-spatial ability, it is believed that
mathematics is indirectly genetically linked.
The exact genetic basis for
visual-spatial ability is unknown, however, there is support for an Xlinked trait, hormones, or hemispheric specialization.
It is stili unknown
if these traits are independent or dependent, and if dependent, to what
extent they rely on one another (Thomas & Kail, 1991; Hier & Crowley,
1982; Geschwing & Galaburda, 1987; c.f. Halpern, 1982).
Camilla Benbow
----------~.-~-- . . ------~~~
._-_.
-~
Gender Differences 4
has been a leader in the search for a genetic reason for the mathematical
gender difference.
Benbow (1990) believed it to be important for girls to
realize that genetically they may not be as intelligent as boys so that they
may accept and adjust to the situation.
Many feel that it is dangerous to
state such opinions from controversal research (Kolata, 1980).
Other researchers think that boys have been socialized over time to
have a greater interest in mathematics than have girls.
This socialization
begins in the home by the parents when the children are young with simple
things such as toys.
Boys are given mathematical and science related toys
such as erector sets and microscopes, while girls are given dolls and
eventually parents will have a greater desire for their sons to go to
college than for their daughters.
Parents tend to discourage inappropriate
gender behavior in boys more than in girls by allowing girls to act as
tomboys but considering it wrong for boys to act feminine (Lansky, 1967).
The socialization theory is favored more than the genetic theory.
Support
for the socialization theory is summarized in six hypotheses stated by
Halpern (1992):
1.
Females maintain more negative attitudes toward mathematics.
2.
Females perceive mathematics to be less important for career
goals than males do.
Gender Differences S
3.
Females have less confidence in their ability to learn
mathematics.
4.
Mathematics is a male-stereotyped cognitive domain.
S.
Females receive less encouragement and support for studying
advanced mathematics.
6.
Females take fewer mathematics courses than males; therefore,
they score lower on tests of mathematical reasoning ability.
The majority of researchers believe in a combination of genetics and
socialization.
Scarr (1987) discussed how genetics may influence our
interest, while the environment limits our experiences.
The question
about reasons for gender differences in mathematics is still unanswered.
Because it is possible to alter socialization, as opposed to genetics,
society is encouraged to create an environment in which females are given
the opportunities to be mathemtically equal to males.
Hyde and his colleagues (Hyde, Fennema, & Lamon, 1990) believed
that the actual gender differences are very small and in some cases do not
exist, depending on how the mathematical categories are classified.
They
found females to be slightly superior in computation, males to be slightly
superior in problem solving, and no gender difference relating to
understanding of concepts.
Miller and Crouch (1991) found that even
Gender Differences 6
though males score higher on achievement tests, females actually have a
higher GPA in mathematics classes than do males.
The extent of the
gender difference, or lack thereof, depends on the subjects and
measurements used in testing.
The purposes of this study were to explore:
elementary grades versus high school grades,
b)
a)
gender differences in
gender differences in
high school English grades versus mathematics grades,
c)
gender
differences in English achievement scores versus mathematical
achievement scores.
It was expected that there would be no gender
difference in elementary grades while the females would score higher
than males in high school.
This was expected because few gender
differences were found until adolescence (Maccoby & Jacklin, 1974),
however, in high school girls were found to have a higher GPA than males
(Miller & Crouch, 1991).
On achievement tests, it was expected that
males would score higher than females on the mathematical section while
females would score higher than males on the English section.
This was
expected because of the belief that males are more superior in
mathematics, while females are more superior in English (Maccoby &
Jacklin, 1974).
Gender Differences 7
Method
Subjects.
The subjects in the experiment were 190 seniors at a
public high school in a rural district of northwestern Indiana.
The
students came mostly from white, middle class families and had a mean
age of 17.7 years (32 were 17 years old, 38 were 18 years old, 4 were 19
years old, and 1 was 20 years old).
Approximately 39% of the students
participated.
procedure. The surveys (see Appendix A) were handed out in the
English classes of the high school and were returned to the English
teachers when completed.
The survey was voluntary and the only
identification information required was gender and age.
The students
were asked to record their English and mathematical grades for
kindergarten through the twelfth grade and their SAT scores.
Results
The means of the mathematics and English grades for elementary and
high school and SAT scores can be found in Table 1. The grades in Table 1
are on a four point grading scale.
There were no significant gender differences found in mathematical
elementary grades, mathematical high school grades, mathematical SAT
scores, or English SAT scores.
Although no significant differences were
Gender Differences 8
found in these categories, females did have a higher mean in the
mathematical elementary grades.
The males had a higher mean in the
mathematical SAT and Verbal SAT.
There was a significant difference in
English elementary grades and English high school grades.
Females
(M =3.45) had significantly higher English elementary grades than males
(M=2.99), £=5.831, Q.<.05.
Females (M=3.10) also had significantly higher
English high school grades than males (M=2.36), £=14.63, Q.<.001.
Gender Differences 9
Table 1
Means of grades and SAT scores by gender
Variables
Males
Females
Significance of F
Elementary
Math
3.17
3.42
.179
English
2.99
3.45
.021
Math
2.87
2.88
.954
English
2.36
3.10
.001
Math
561
500
.195
Verbal
479
448
.267
High School
SAT Scores
'i
I
Gender Differences 10
Discussion
The purposes of this study were to explore:
elementary grades versus high school grades,
b)
a)
gender differences in
gender differences in
high school English grades versus high school mathematics grades,
and
c)
gender differences in English achievement scores versus mathematical
achievement scores.
It was expected that there would be no gender
differences in elementary grades, while females would have higher grades
at the high school level in both mathematics and English.
It was also
expected that males would have a higher achievement score in
mathematics, whereas females would have a higher score on the English
achievement tests.
It was expected that there would be no gender differences in the
elementary grades in either mathematics or English.
However, there was
a significant difference in the elementary English grades in favor of the
females.
Although Maccoby and Jacklin (1974) reported few gender
differences until adolescence, they also reported that females have a
greater verbal ability than males.
Maccoby and Jacklin also reported that
males have a greater mathematical ability than females, however, Hyde,
Fennema, and Lamon (1990) found males to have a greater mathematical
ability in problem solving only.
They found no gender difference in
Gender Differences 11
understanding of concepts and female superiority in computation.
Elementary mathematics places little emphasis on problem solving which
may help to keep the gender differences balanced in the elementary school.
The expectation that females would have higher grades in high
school was supported by the data, however, a significant difference was
found in English grades only.
Miller and Crouch (1991) found that females
usually have higher GPAs than males.
It is not surprising that a
significant difference was found in English, since females also tend to
have greater verbal abilities than males (Maccoby & Jacklin, 1974).
One
reason females tend to have higher GPAs in any subject at the high school
level is that they are more responsible and more attentive to their grades.
Although females are more responsible at the high school level, the
mathematical classes are beginning to increase in difficulty.
At
adolesence, males begin to surpass females in mathematical ability
(Maccoby & Jacklin, 1974) which may account for the close means for
male and female mathematics grades.
The final expectation was that males would have a higher
.mathematical achievement score whereas females would have a higher
English achievement score.
The results showed that males scored higher
on the achievement tests in both mathematics and verbal, however, none
Gender Differences 12
of the scores were significant.
Because there were few subjects on which
to calculate the data for achievement tests, no significant difference was
found for the mathematical section.
61 points in favor of the males.
However, the mean score differed by
If there had been more subjects, there
may have been a significant difference in favor of the males.
This
supports the research of Miller and Crouch (1991) which found that males
have higher mathematical achievement scores than females.
This research had its limitations.
The number of participants who
agreed to participate were few in number.
Because this was a
retrospective survey, of those students who did participate, few students
were able to provide complete surveys.
It should also be noted, that even
though males and females responded evenly, females tended to be more
complete in their memory of grades.
It can also not be certain that the
students were honest in their responses.
To receive more accurate and
complete data, it would be helpful to have the students obtain a copy of
their transcripts or to receive this information from the school systems.
Another option, which is time consuming, is to follow the students from
kindergarten through the senior year of high school.
The significant
differences observed or not observed in this sample may have been
different if more subjects had participated.
The larger the sample, the
Gender Differences 1 3
more accurate the results.
It is important to look at many different areas before creating a
conclusion concerning gender differences in mathematics.
Few
researchers compare achievement scores to grades in their investigations.
They tend to draw conclusions from one or the other.
If more research
were done in comparing achievement scores to grades it may be possible
to see that grades depend more on social factors while achievement
scores tend to be more genetically based.
Researchers have also found
that when different measures are used the degree of the gender difference
is altered.
To be more consistent, researchers should use more than one
measure to determine gender differences, before drawing conclusions
which may be invalid.
Researchers should also consider the different
parts of mathematical ability, instead of looking at mathematics in
general.
Males may be considered superior in mathematics in general,
however if you separate mathematics into problem solving, computation,
and understanding of concepts, males may not always be considered the
superior ones.
Gender Differences 14
References
Benbow, C.P.
(1990).
Gender differences: Search for facts.
Amerjcan
Psychologist, 45, 988.
Geschwind, N. and Galaburda, A.M.
(1987). Cerebal lateraljzatjon:
Biologjcal mechanisms associations,
a..rui pathology.
Cambridge, MA: MIT Press.
Halpern, D.F.
(1992).
Jersey:
£ax. differences in cognitive abilitjes. New
Lawrence Erlbaum Associates.
Hier, D.B. and Crowley, W.F.
(1982).
Spatial ability in androgen-deficient
men. I.b..a.~ England Journal Qf Medicine, 306, 1202-1205.
Hyde, J.S., Fennema, E., and Lamon, S.J. (1990). Gender differences in
performance:
A meta-analysis.
psycho log ical Bu lIetin, 107, 139-
155.
Kolata, G.B.
(1980).
Math and sex:
Are girls born with less ability?
SCience, 210, 1234-1235.
Lansky, L.M.
(1967).
The family structure also affects the model:
role attitudes in parents of preschool children.
sex-
Merrill-palmer
Quarterly, 13, 139-150.
Maccoby, E.E. and Jacklin, C.N. (1974).
Stanford:
I.b..a. psychology Qf ~ differences.
Stanford University Press.
Gender Differences 15
Miller, C.J. and Crouch, J.G.
(1991).
Expectancy and problem context.
Gender differences in problem solving:
~
Journal Qf Psychology, 125,
327-336.
Scarr, S. (1987). In J.Arnoff, A.1. Rabin & R.A. Zucker (Eds.) I.hii
emergence
21 personality
Thomas, H. and Kail, R.
(1991).
(pp. 49-78), New York:
Springer.
Sex differences in speed of mental
rotation and the X-linked genetic hypothesis.
Intelligence, 15,
17-32.
Vandenberg, S.G.
intelligence?
(1968).
Evidence from twin studies.
Parkes, Genetic
Plenum Press.
Primary mental abilities or general
In J.M. Thoday & A.S.
alli! enyironmental influences Q1l behavior. New York:
Gender Differences 16
APPENDIX A
Student Letter and Survey
Ball State University
Teachers College
Department of Educational Psychology
Dear Seniors,
I am doing my Honors Thesis at Ball State University and would appreciate your help in
collecting data. My thesis involves researching the development of achievement in
mathematics and language. I would appreciate your cooperation in filling out this survey as
completely and accurately as possible. Any item for which you do not have information or
any item which is not applicable should be left blank. Your participation is strictly
voluntary and the only identification I want is your gender and age. When you are finished
with the survey, please return it to your English teacher.
317·285·8500
Muncie, Indiana
47306-0595
DEVELOPMENT OF ACHIEVEMENT
Jenny Lou Coffer--Ball State University
Circle one:
female
male
Age: ___________________
PART I--MATH GRADES
Please fill in the math grades you received and the gender
of the teacher for the following grades.
grade
1
grading period
2
3
4
final
gender of
math teacher
K
1
2
3
4
5
6
7
8
Please fill in your grades from high school under the
appropriate math class.
In the parentheses, state the year
taken (9, 10, 11, or 12) and include the gender of the
teacher.
subject
(year)
1
)
basic math
pre-algebra
(
)
algebra I
geometry
algebra II
trigonometry
)
grading period
2
3
4
final
gender of
math teacher
(Math grades continued)
analytic geo
)
calculus
)
other:
I
PART II--ENGLISH GRADES
Please fill in your English grades for the following classes
and the gender of your English teacher for each class.
grade
I
grading period
2
3
4
final
gender of
English teacher
K
1
2
3
,
i
'
4
5
6
7
8
I
,I
::
Please fill in your English grades from high school under
the appropriate English class.
Include the gender of the
English teacher for each class.
II
subject
Freshmen English
General
'I
Academic
Gifted
1
grading period
2
3
4
final
gender of
English teacher
(English grades continued)
Sophomore English
General
Academic
Gifted
Junior English
General
Academic
Gifted
Senior English
General
Academic
Gifted
PART III--STANDARDIZED TESTS
Please fill in the scores for the test which you have taken
and for which you have a record of scores.
ISTEP (Score(s) and date(s) taken):
SAT Scores:
Verbal: _________________
Math: _________________
ACT Scores:
English: ________________
Math: __________________
Composite: _____________
Plans fOllowing graduation (include intended major if
attending college): _____________________________________________