This paper appeared in the March-April AWM Newsletter, 1995, Vol. 25, No. 2
Calculator Use and Gender Issues
In the spring of
1995 the College Board will require graphing calculators for the Advanced
Placement exams in calculus. Will the
requirement of calculators adversely affect the achievement of young women on
the exams? That is the issue raised in
the following statement from the November-December AWM Newsletter: "Young women may be placed at a disadvantage
if they are less at ease with the technology than the young men" (Vol. 24,
No. 6,1994, p. 9).
The increased use
of calculators in mathematics instruction does
have gender-related implications for confidence and achievement, but those
implications are not the ones suggested in the quotation above. Although it is a commonly held notion that
many women and girls are less comfortable with technology than their male
counterparts, research evidence supports this only with regard to computer use
in mathematics. Calculators, on the
other hand, seem to generate more positive feelings about mathematics, increase
confidence to do mathematics for both males and females, and improve
performance in in a variety of areas including problem solving [8]. In fact, results from some recent studies
indicate that with calculators female students perform as well or better than males. Consider the following:
• In a study of
high school students taking precalculus, Ruthven [9] found that among
calculator users women scored higher than men on symbolization tasks (converting
functions to algebraic form given their graphs) but the reverse was true for
the non-technology group. However, on
graph interpretation items -- for which technology did not give an advantage to
the treatment group -- males did better than females with or without
calculators.
• Boers and Jones [2] reported that graphing
calculators benefited females more than males when technology was required in a
college calculus course for mathematics/computer science majors. For the two years before calculators were
required, males had averaged slightly higher than women on the final exam. After the introduction of graphing
calculators, the women's scores improved so that their final averages for the
next two semesters were 10 and 9 points higher, respectively, than the men's
.
• In a study of over 200 college students
enrolled in precalculus, Dunham [3] found that men showed greater achievement
than women on visual items on a pretest.
After ten weeks of instruction with graphing calculators, both groups showed
significant gains in achievement on the posttest. However, gains for the women were greater, thereby eliminating
the gender differences that had been present on the pretest.
• Gender differences have been observed as
well when non-graphing models of calculators were in use. Bitter, Hatfield, and Mercer [1] reported a
positive influence on both performance and attitudes for middle school students
who used "fraction" calculators.
Overall, students made gains of one grade level or more when using calculators
on the Iowa Test of Basic Skills, but scores of the females increased to a
greater extent than those of the males.
The girls, who had scored lower on average than the boys without
calculators, performed equal to or better than the boys when both groups were
tested with calculators. Survey results
indicated that the students felt more competent and better able to understand
mathematics when using technology.
Motivating girls
and women to study mathematics is one of the great challenges the mathematics
community faces today. Many educators
and organizations like the MAA, the NCTM, and the National Research Council
have claimed that the use of graphing calculators will increase students'
interest and motivation and remove some of the barriers to learning mathematics
that have existed in the past. We are
now beginning to see evidence from research that the claims have merit. Recent studies have shown that, when compared
to non-technology users, students with graphing calculators engaged more willingly
in problem solving and stayed with a problem longer, had more flexible
approaches to problem solving, had greater overall achievement on graphing
items, and better understood connections among graphical, numerical and
algebraic representations. Moreover,
students reported greater confidence in their ability to solve problems when
calculators were available. (See the
research summaries in [4] and [5] for
specific studies and citations.)
But why would the use of calculators
benefit young women more than young men, even to the extent of giving females
an advantage over males in some cases?
The answers are not clear-cut, but there are at least four plausible
reasons why calculator-enhanced instruction might affect women's mathematical
achievement in this fashion. These
involve issues of confidence, spatial ability, algebra skills, and classroom
environment.
First, confidence consistently emerges as
a significant predictor of mathematical achievement for women, more so than for
men [6]. Anything that raises
confidence thus might have a greater benefit to women than men. Ruthven [9] has conjectured that women gain
confidence because graphing calculators provide feedback on algebraic work. That reduces anxiety and may result in
increased achievement. In other studies
[3,10,11] women have reported feeling more confident in their work because the
calculator provided a way to check algebraic solutions and confirm the accuracy
of answers.
Second,
gender differences in spatial ability have traditionally favored
males, and spatial ability is sometimes
a significant predictor for mathematics achievement in women. Since graphing technology requires students
to reason from visually-presented information, one might suppose that women
would be at a greater disadvantage with graphing calculators. In fact, it appears that using graphing
calculators can actually improve spatial ability. Shoaf-Grubbs [10] used traditional measures of spatial ability
with female students enrolled in college algebra. She reported that women in the graphing calculator section made
greater gains in spatial visualization skills than women in a non-technology
section. Despite an advantage for the
control group on pretests, the treatment group scored significantly higher on
the Card Rotation posttest and made larger gains on the Paper Folding test than
the control group. Ruthven [9] has
suggested that more exposure to graphical images via technology may have
improved the females' ability to visualize functions and graphs, thereby remediating
a deficiency in experience and leading to higher achievement for the women in
his study. Other researchers have shown
that spatial ability is amenable to training [7], so this may be a valid
interpretation. Even if ability to visualize does not improve,
the calculator provides an alternative source
of visual images for those who cannot create their own. Having the option of approaching a problem
both visually and algebraically is helpful as this woman notes: "In my
case, I can think about the problem more logically and realistically. Using the calculator has been a great
learning tool in that it uses illustrations, it is more interesting." [11,
p. 6]
Third, along with increased attention to
visual methods of solution, graphing calculator instruction reduces attention
to algebraic symbol manipulation.
De-emphasizing a traditional area of strength for women could lead to
lower achievement for them but, in an analysis of calculus exam responses,
Boers and Jones [2] found that the opposite had occurred. Males and females did prefer different
solution strategies, with men leaning more toward graphing solutions and women
more toward algebraic strategies. It
was the females' better performance on purely algebraic questions that gave
them their "edge" as they were able to use a full range of tools,
combining strength in algebra with new skills in graphical solutions.
Choice of solution method is further
complicated when its interaction with confidence is considered. Dunham [3] found that when given a choice of
strategies, low confidence females were the most likely group to use graphing
calculators and high confidence females the least likely. Analysis of interviews revealed that women
tended to use algebra wherever possible but they were happy to have a
calculator to "fall back on" when their algebra skills (or their
confidence in those skills) were not adequate.
Attitudes toward calculators didn't play a role in choice, in that most
students expressed confidence in graphing solutions and viewed calculators as
fast, efficient, reliable tools. But
the high confidence females were more likely to exhibit "algebraic
guilt," a feeling that they relied too much on "easy" calculator
solutions and would benefit more from learning algebraic techniques. The implication was, "Algebra is hard
so it must be good for you." High
confidence females also mentioned that using algebra gave them a greater sense
of personal accomplishment.
Finally,
past research on gender issues has shown that female students achieve
more in mathematics classrooms that promote cooperative learning over
competitive settings [6]. Recent
studies indicate that use of graphing calculators dramatically changes the
classroom climate [4,5]. Instructors
lecture less and students engage in more group work, investigation, and problem
solving. Thus a curriculum that fully
integrates technology may create a classroom environment that fosters and
encourages female students and is more conducive to their learning.
Further research is needed to determine
which, if any, of these factors accounts for female students' success with
graphing calculators. But whatever the
reason, it seems likely that young women will not be disadvantaged by the
requirement of graphing calculators for the AP calculus exams. Despite common notions that girls and women
are less comfortable with technology, most calculator users will agree with the
female college algebra student who wrote, " It is great to have a graph in
the palm of your hand and to be able to explore it and make comparisons. The graphing calculator should be introduced
as soon as possible to help overcome the common fears of math." [11, p. 6]
Perhaps an even stronger testament to the
power of technology is the one written by a student from the non-technology section
of Shoaf-Grubbs' study: "Although
I never used [a graphing calculator], I think that it should be used as a
tool/device because all of my friends who took the calculator section enjoyed
it very much. They also said that the
calculator decreased their anxiety about math." [11, p. 7] If word-of-mouth can generate such a
reputation for graphing calculators among women who haven't even used them,
think what benefits await women who do use the technology!
References
1. Bitter, G. G., Hatfield, M. M., & Mercer,
J. (1989). Arizona State
University/Scottsdale Unified School District Calculator Project: 1989-90. Report available from Technology Based
Learning and Research Community Services Center, Arizona State University,
Tempe, AZ.
2. Boers, M. A. M., & Jones, P. L. (1993).
Exam performance and the graphics calculator in calculus. In B. Atweh, C. Kanes, M. Carss, & G.
Booker (Eds.), Proceedings of the
Sixteenth Annual Conference of the Mathematics Research Groups of Australasia (pp. 123-128). Queensland University of Technology.
3. Dunham, P. H. (1991). Mathematical
confidence and performance in technology-enhanced precalculus: Gender-related
differences. (The Ohio State
University, 1990). Dissertation Abstracts International, 51, 3353A.
4. Dunham, P. H. (1993). Does using
calculators work? The jury is almost
in. UME
Trends, 5(2), 8-9.
5. Dunham, P. H., & Dick, T. P. (1994).
Research on graphing calculators.
Mathematics Teacher, 87,440-445.
6. Fennema, E., & Leder, G.C. (Eds.).
(1990). Mathematics and gender.
New York: Teachers College Press.
7. Ferrini-Mundy, J. (1987). Spatial training
for calculus students: Sex differences in achievement and in visualization
ability. Journal for Research in Mathematics Education, 18, 126-140.
8. Hembree, R., & Dessart, D. J. (1986).
Effects of hand-held calculators in precollege mathematics education: A
meta-analysis. Journal for Research in Mathematics Education, 17, 83-99.
9. Ruthven, K.
(1990). The influence of graphic
calculator use on translation from graphic to symbolic forms. Educational
Studies in Mathematics, 21, 431-450.
10.
Shoaf-Grubbs, M. M. (1993). The effect of the graphics calculator on
female students' cognitive levels and visual thinking. (Columbia University, 1992). Dissertation
Abstracts International, 54, 119A.
11.
Shoaf-Grubbs, M. M. (1995). The
long-term effects of the graphics calculator on female students' spatial
visualization skills and level of understanding in elementary graphing and
algebra concepts. Paper presented
at AMS-MAA Joint Meetings, San Francisco, January 4-7, 1995.
Personal Information
Penelope
H. Dunham, Ph.D.
Department
of Mathematical Sciences
Muhlenberg
College
Allentown,
PA 18104
610-821-3358
pdunham@max.muhlberg.edu
________________________________________________
Penny Dunham is a Visiting Assistant Professor of
Mathematics at Muhlenberg College, Allentown, PA, and a College Board
consultant for AP calculus. She has
conducted research, written, and spoken extensively on the integration of
technology with mathematics instruction.
She is also on the Board of Directors of Women and Mathematics
Education.