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Children in these classrooms had a great deal of freedom in deciding how to solve problems and also in deciding what strategies to report about their problem solutions. It is clear that children often have a variety of strategies to use to solve problems, and strategy use is a matter of preference. For some reason, did the girls prefer to use and report strategies that would have an influence on the development of their understanding?
This choice may have inhibited the development of fluency with more abstract strategies. Perhaps girls chose to use strategies that could make their ideas clear e. It was obvious in the classrooms that teachers wanted to know what the child had done, and children were equally eager to make sure that the teachers understood. Modeling strategies are easier to report and to understand than are invented algorithms. Or did the girls simply prefer reporting the less abstract strategies?
Sowder supported this idea when she suggested that although the girls may have understood invented strategies as well as the boys did, they may have just preferred less abstract strategies. Many believe that student preferences are important, but in this case, it may have been that using such strategies inhibited the development of more abstract strategies.
In summary, it is clear that cognitive science methodologies are providing tools for us to gain deeper understanding of the complexity of gender differences. We are just beginning to understand differences in mental activities between girls and boys and to assess their impact on learning. Feminist Perspectives. I am no expert on feminist theories and their accompanying research paradigms, but it seems to me that people working in feminist perspectives share one common component.
Feminist scholars argue very convincingly that most of our beliefs, perceptions, and scholarship, including most of our scientific methodologies and findings, have been and are dominated by male perspectives or interpreted through masculine eyes. According to feminist scholars, this perspective has resulted in a view of the world that is incomplete at best and often wrong.
A basic assumption of feminist work is that there are basic differences between females and males that are more prevalent than the obvious biological ones. These differences result in males and females interpreting the world differently. Many of these scholars present convincing arguments about how the world influences males and females differently. It appears irrelevant whether these differences are inherent or environmentally caused, and most feminist writers that I have read are basically uninterested in whether or not such differences are genetic or related to socialization.
It is enough that the differences exist. For those who are just thinking about this idea for the first time, I recommend that you find a little book called The Yellow Wallpaper Gilman, Feminist scholars work in many areas and almost all of them are outside mathematics education.
Some are trying to interpret a basic discipline of science such as biology or history from a female, rather than a male, point of view. They argue that almost all scholarship, including the development of what is called science and mathematics, has been done by men from a masculine viewpoint, utilizing values that are shared by men, but not by women. Those major bodies of knowledge that appear to be value-free and to report universal truths are in reality based on masculine values and perceptions.
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Jim Schuerich has suggested that a feminist science is better than a value-free science. Each of them has demonstrated quite conclusively that research on male-only populations has produced results that were not only incomplete but wrong. Similar approaches to history and literature have resulted in deeper, richer understanding. The idea of masculine-based interpretations in areas such as history or literature, and even in medical science, is not too difficult to illustrate nor even to accept.
For example, how many even knew who Sacajawea was or her contributions to the opening of our American West until very recently. Did you know that was her image on the new dollar coin? Many conclusions in medical research have been based solely on male subjects; their inaccuracy is easy to illustrate. History has been presented as if most of our ancestors were male and as if important things in the public arena happened predominantly because of and to males. The use of male names by female writers in order that their writing be accepted, or even published, is commonly known. Does the prevalence of the idea of a masculine or feminine world-view apply to what mathematics is and if so, how?
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Can mathematics be seen as masculine or feminine? Is not mathematics a logical, value-free field? The idea of a masculine or feminine mathematics is difficult to accept and to understand, even for many who have been concerned about gender and mathematics. One way to approach the problem of a gendered mathematics is not to look at the subject, but to examine the way that people think and learn within the subject. Do females learn math differently than do males? Should we develop special instructional programs for females?
It is beyond the scope of this paper to explicate these ideas, but we should consider this.
Earlier I alluded to the idea that most mathematics classrooms appear to be organized to be more appropriate for boys than for girls and even quoted some research that supports that idea. Others have interpreted discussions arising from the belief about a female world-view and applied the ideas to describing female-friendly instruction.
Others have argued for single-sex schools oriented to the mathematics instruction of females. Running through these suggestions, it seems to me, is a basic belief that females learn differently and perform differently in mathematics than do males. This belief is dramatically different than the belief of a universal way of human thinking espoused by the cognitive scientists.
To scholars with this conviction, it is not enough that scholars identify important research questions that are studied objectively using a positivist approach. Thus, the world can, and will be, interpreted from a female perspective. Scholars who work within this belief system often use women subjects as co-investigators, have females reporting their own experiences, and use females as the main subjects under investigation who also help to interpret results.
There are not many of these studies available currently in mathematics education, but I predict that we shall see increasing numbers of them as the importance of female voices is recognized. Those that are available indicate that females often have a very negative view of mathematics, how it is taught, and mathematicians.
It is too early to be able to assess the impact that studies using feminist methodologies will have on our understanding of the relationship between gender and mathematics, both the identification of the problem and its solutions. But, it appears logical to me that as I try to interpret the problem from a feminist standpoint, the focus used in my earlier work changes.
I do not interpret the challenges related to gender and mathematics as involving problems of females e. Instead, I begin to look at how a male view of mathematics has been destructive to females. I begin to articulate the problem that lies in our current views of mathematics and its teaching.
I am coming to believe that females have recognized that mathematics, as currently taught and learned, restricts their lives rather than enriches them. I must say at this point that the current reform movement has strong feminine overtones and that is an anathema to many people. Whatever our own value position about feminism and mathematics, I believe that we need to examine carefully how feminist perspectives can add enriched understanding to our knowledge of mathematics education. And, indeed, we should be open to the possibility that we have been so enculturated by the masculine-dominated society we live in that our belief about the gender neutrality of mathematics as a discipline may be wrong or, at the very least, incomplete.
Perhaps we have been asking the wrong questions as we have studied gender and mathematics. Could there be a better set of questions, studied from feminist perspectives, that would help us understand gender issues in mathematics? What would a feminist mathematics be? Is there a female way of thinking about mathematics? Would mathematics education, organized from a feminist perspective, be different from the mathematics education we currently have? Perhaps my beginning to believe that the decision by females not to learn mathematics or enter mathematics-related careers because mathematics has not offered them a life they wish to lead is an indication that my old view about learning and teaching mathematics, as well as about gender and mathematics, was immature and incomplete.
What Do I Know? Throughout this paper, I have been expounding on the complexity of dealing with gender and mathematics. Nothing appears to be simple and listing what I really know is difficult. That females participate in mathematics-related careers less than do males is one of the few accepted facts.
Sex differences in education - Wikipedia
That differences exist in the learning of mathematics seems clear also, although many scholars believe either that the differences are diminishing or that any differences that exist are unimportant. But I caution everyone about such simplistic statements. What mathematics is being measured in tests where gender differences are either shown or not shown? How was the information about values obtained?
Too often research dealing with these issues provides an incomplete picture at best and only helps to perpetuate the belief that females are somehow inadequate in relation to learning and doing mathematics. Dilemmas for Practice.
Student Gender and Inclusive Education. Balance or Bias?
Many of these appear logically to apply equally to girls and boys. But a closer examination reveals that nothing to do with gender is simple. Consider the reform recommendation that has to do with encouraging students to communicate their mathematics thinking by presenting their ideas and convincing peers of their correctness by arguing, questioning, and disagreeing. It is widely believed that those who enter into this kind of debate will learn better. But will girls enter into this kind of communication as willing as do boys? Many teachers have reported informally that girls will not for a variety of reasons.
Perhaps this even helps to explain some of the gender differences we reported in the CGI study. Will boys tend to dominate such discussions and not listen as well as girls? Another major reform recommendation has to do with the use of technology in the classroom. Others at this conference have discussed this as it relates to girls and boys.
It is clear that boys have more experience with technological toys than do girls. Does this reflect interest? Does this mean boys have more knowledge? How do teachers take these ideas into consideration? The Standards recommend that mathematics be situated in problem-solving contexts that are socially relevant. Unfortunately many textbooks and teachers are more aware of contexts that are from male dominated fields such as projectiles for parabolic equations, or sports for statistics. One interesting study that I did not review earlier suggests that gender differences in problem solving skills were eliminated when girls were familiar with the context in which the problem was situated Marshall, But will boys willingly participate in problems from female-dominated fields?
Should classrooms be competitively organized or organized around cooperative activities? Certainly the most visible reward in most mathematics classrooms is grades that are highly competitive.