Math Can Be A Dangerous Thing--
If It Is Being Done By Girls

Nadine Schiavo

Copyright 2001 by Nadine Schiavo
Included here with permission of the author

Do we really use history as a way to view ourselves and our future? If we look to the history of mathematics, women have been viewed as inferior. The Mathematics Teacher (2000) states:

Because women have been excluded from proper training, access to libraries, and networks of communication, it is not surprising that historically few women have entered the field of mathematics. Are times changing, are more women entering the once exclusive masculine "club" — professions of mathematics? The textbooks seem to say they slowly are, so why are the AP classes in mathematics predominately occupied by the male students in my school? Our female students who have well above the required grade of 88 to enroll in AP Calculus either reluctantly sign up for the course or enroll in a less rigorous Calculus course. The boys who barely make the grade of 88 plunge right into the AP Calculus course. The girls are uncertain, and the boys do not think twice about their decision.

Background Information

I examined the attitudes of mathematics course-taking behavior of junior and senior girls in a high school in suburban Northern Virginia. The population of the school is approximately 1400 students who represent all levels of academic achievement from basic to advanced placement. Fifty three percent of the student body are males, forty seven percent are females. Thirty-eight percent of our student body are enrolled in honors or advanced placement mathematics courses. There are twenty-two sections of honors courses ranging from Algebra 1 to Advanced Placement Calculus. Three of the twenty-two sections are taught by a male teacher, the other nineteen sections are taught by six female teachers. Our school is competitive with the other schools in the area with regard to the number of National Merit Finalists. We have had two to four finalists each year for the past five years. Three-fourths of the finalists were males, while only one-fourth were females. Females are as equally represented as males in sports, they dominate the school’s music program, but are noticeably missing in academic clubs. As moderator of the It’s Academic Team for the past nine years, I actively recruit females to join our club. Only twice did our TV team of four students include a female. This is the team that represents our school on the It’s Academic television show. The climate of the It’s Academic Club is very relaxed. We meet weekly for 45 minutes after school. Two heterogeneous teams are formed giving each student a chance to actively participate within their team. These teams offer a non-threatening environment for students to build on their knowledge of academic trivia. Both the females and males actively participate in the weekly activities, but the females are not comfortable enough to represent the school on television. The girls are not confident in their abilities even though they often out-perform the boys on their team.

The Cultural Inquiry Process

I began to investigate my puzzlement using the Cultural Inquiry Process (Jacob, l999) in my junior and senior level mathematics classes. The process consists of six steps and this paper will document my research and findings using those steps.

Selection of a Focus Group

I looked at the various student populations in my classroom. The focus group began to change as I continued to research my puzzlement. Initially, I considered a group of four female students who are in my Honors Calculus class. I thought I would focus on this group since they were the students whose choices in selecting mathematics courses I found particularly puzzling to me. As I continued to reflect on the topic, I identified another group of female students to include in my focus group. Struggling through the process of interviewing the initial focus group, it soon became clear to me that the difficulties they had in choosing mathematics courses are similar to the difficulties that my junior female students are now facing. Therefore, I decided to focus on the four senior girls in my Honors Calculus class and three of the junior girls in my Honors Analysis class. It made sense to me to share what I learned from the senior girls with the junior girls in my class. Since my puzzlement deals with the choices that females make in choosing mathematics courses and since the juniors will be faced with that decision this month, I decided to include them in my focus group. Based on my observations and casual conversations with the three junior girls, I knew they were having second thoughts about enrolling in the Advanced Placement Mathematics course.

I then began to think about their choices from a cultural perspective. The four senior girls were my students for the last three years. I had the pleasure of being their mathematics teacher in their sophomore, junior, and senior years. I knew these girls quite well and I was confident they would succeed in an AP course. All four girls were eligible and extremely well qualified to take Advanced Placement Calculus with another female teacher. However, they enrolled in my Honors Calculus course despite my recommendations and encouragement to enroll in the AP course.

This became the foundation for my puzzlement: females are as able as males and they need mathematics just as much. Why wouldn’t they be represented equally in advanced placement mathematics courses at my school?

Information Known

The four senior girls have experienced much success in the mathematics courses they have completed. All four have been honor roll students since their freshman year of high school, and were eligible for Advanced Placement Calculus. They have consistently enrolled in honors level courses. They are active in sports, particularly basketball and cross country. They come from two parent households, both parents are college graduates and in all, but one case, their mothers work outside of the home. One of the four received an ROTC scholarship and an acceptance letter to Holy Cross College. The other three girls also got into their first choice college. One girl would like to become an architect, one a financial analyst and the other two are undecided. Scheduled parent-teacher conferences are held twice a year at our school, and appointments are made upon request. I have never talked to any of these girls’ parents.

The three junior girls also have experienced much success in the mathematics courses they have completed. They, too, are active in our school. One is a member of the student government, one is a swimmer who swims for two hours every day, and the third is a member of the chorus. This is the second year that I have taught two of the three girls, and the first year for the other girl. The mother of the student who is active in our student government comes to every parent-teacher conference. This is my second year as her daughter’s math teacher. She is always the first parent to arrive and always stays beyond the 20 minute school policy for the conference. I invite her to make another appointment with me, but she declines and says she will just be another minute or two. Ten minutes later she is still talking about her daughter’s GPA. The mother methodically goes to each of her daughter’s teachers and explains to each teacher what grade her daughter must get in their course to keep her GPA above a 3.6. She is putting enormous pressure on this child to keep her GPA above a 3.6.

The Advanced Placement Calculus teacher has taught in our school for fifteen years. She teaches two sections of AP Calculus with a total enrollment of forty-nine students, thirty-three boys and sixteen girls. Besides AP Calculus she teaches two sections of Topics. Topics is a fourth year mathematics course for basic, low track, senior students. A large portion of the learning in her classroom takes place in structured, small group work. She has four daughters all of whom graduated from this high school. Two of her daughters took AP Calculus and the other two took Honors Calculus.

I teach the Honors Analysis course that the three junior students are taking. I also teach Honors Calculus which is the course that the four senior girls are taking. This is my ninth year teaching at this school, and the second year that I have had the opportunity to teach the same students for three years. I have three children, two boys and a girl, who graduated from this high school. All three of my children took AP Calculus.

Cultural Questions

I read a fair amount of the research and strategies for achieving gender equity in the classroom and felt the culture of my classroom was female friendly. I incorporated teaching the "evaded curriculum" in my courses (Horgan, 1995). The term refers to what is not taught. Many topics that are central to the lives of girls and women are not included in the school curriculum. I often found interesting material on the role of women in mathematics and frequently shared this information with my students. I integrated into the curriculum stories about the contributions of women, as well as about men. I did not treat these female contributions as oddities. I performed a gender-bias audit of my classroom, and I felt comfortable with the outcome (Horgan, 1995).

Because of these experiences, I felt that "outside the school" was the key to ameliorating my confusion. So I looked to question 3.4 of the Cultural Inquiry Process (Jacob, 1999) to help me gain insight into my puzzlement. CIP 3.4.1 talks about how influences on students from outside school be contributing to the puzzling situation. I began the CIP study by interviewing the four senior girls. I asked the girls what effect outside influences, for example male peers and their parents, had on the course selections. I wanted to explore what message these girls are receiving about females and mathematics. I wanted to look at the messages they are receiving from their parents, in particular their father. Every year during Back to School Night at least two or three fathers tell me how either they or their wife or both were not very good at mathematics, and therefore I should not expect much from their daughter. I asked the four girls, in separate interviews, what impact their parents and peers had on their choices. I felt I needed to gain insight into my students’ perception of the other persons’ attitudes, expectations and beliefs. They all talked about the role their parents played in their course selections. They indicated that peers are the least important of all influences on their decisions.

I also wanted to explore what messages these girls are receiving from males in general. I couldn’t help but recall a statement made during a college campus visit just four years ago. My daughter and I were visiting a Jesuit college, and our tour guide was a priest. As we passed by the College of Arts and Sciences, he said to the prospective students (who just happened to be all females), "The reason why I became a priest is because you don’t have to take any math in college. Like you ladies, I did not like math." I wonder if he told the boys the same thing. His comment led me to believe that gender remains a thorny issue in the college mathematics classroom. I couldn’t help but wonder if my students view mathematics as a male domain, did they view mathematics as being useful, both immediately and in their future? I wonder what messages the female students will get in their college classroom about mathematics.

After talking with the girls, it became apparent, much to my surprise, that I needed to consider two cultural questions. In addition to considering CIP 3.4.1 (Jacob, 1999), I also needed to focus on CIP 3.2, and in particular the culture of my classroom. Through these interviews I learned what influences I, as their teacher, had on the girls' choices. I also learned during the interviews about how comfortable the four senior girls have been in my classroom during the last three years. I wondered if might I be making the culture of my classroom so comfortable that I am encouraging these girls not to take learning risks.

Gathering Information

I gathered information first by conducting interviews with the four senior girls and then by administering a survey on Mathematics Course-Taking Behavior.

Student interviews: Influences outside the school community. I interviewed the four senior girls on the same day but at separate times. I wanted to know what role their parents played in helping them select their level of mathematics courses. In a study conducted by Parsons’ and her colleagues, she found that parents indicated they considered boys and girls to be equal in math ability. However, they also held a contradictory view that math is more difficult for girls. She found that parents considered math to be less important for girls than it is for boys. Fathers encouraged their sons to take advanced mathematics courses, while they often discouraged their daughters. Fathers considered themselves better in mathematics than mothers considered themselves to be, although mothers rated themselves higher in overall high school performance (Chipman, Brush & Wilson, p. 305). I found it interesting that all four girls had similar experiences with their parents. They told me that their parents were more interested in their GPA than in the level of the academic course. Their parents were aware of the minimum GPA that the state schools in Virginia required, and as long as they kept their GPA up to that standard then they left the course selection to their child. One girl did comment that she felt if she took non- academic courses, like weight training, then her father would probably get involved. The decision on what level of an academic course to take, basic, regular, honors or advanced placement, was left up to the child. The girls I interviewed were either an only child or had just female siblings so I was not able to gain any insights on the parental encouragement of their sons and daughters that Parsons mentions in her study.

Student interviews: Teacher influences. Because I teach the tenth, eleventh and twelfth grade advanced students, I am especially interested in making special efforts to encourage able, young women who might be wavering to persist in mathematics. One of the students commented to me that she remembered how I would tell the class how I too struggled with some of the concepts they find difficult. She said that it helped her to know that I sometimes had trouble in math. She said that it is a case of, "If you could do it, maybe I can too." It became clear to me that when I shared my remembered perplexity and frustration with my students, I was helping them gain confidence in their own abilities in my classroom. Another girl said she felt comfortable with me since I admitted that I too got baffled by concepts. She was afraid that the next teacher may be a "whiz at math" and she would get lost in the class. When I shared that anxiousness is a healthy response to frustration, I was hoping to mobilize them to help their learning, but was I also making them afraid to take learning risks? I then began to question the culture of my classroom. Am I making the girls too dependent on me, am I stifling their confidence, am I failing to permit my female students to develop a real sense of pride in their own ability to do mathematics, are my math classes too female friendly? Elizabeth Fennema points out:

Student surveys. I administered the Fennema-Sherman Mathematics Attitude Scales survey (Fennema & Leder, 1990) to my Pre-Calculus and Calculus students. The survey was administered to 91 students, thirty-three females and fifty-eight males. There were no significant differences between the females’ and males’ responses to the "Reasons and Factors about Work" portion of the survey. The girls and boys perceived the usefulness of mathematics, in both daily life and in relation to career plans. I found a relationship between the students’ perceived usefulness of math and their intention to take a mathematics course, but not on the degree of course difficulty within the discipline. Since the instrument was given to students in honors level courses, perhaps there is a relationship between the perceived usefulness and enrollment in a fourth year of mathematics. Difference between the two groups occurred with reference to the "Reasons to Study Mathematics" portion of the survey. The females tended to check "somewhat important" to the question about taking advanced math because their friends are also taking advanced math, while all of the boys checked "not important." Another difference was the question about mathematics being easy to learn. The boys felt mathematics was easy to learn and the girls felt that was not always the case. An interesting result had to do with the "Mathematics as a Male Domain" and the "Self Confidence" portions of the survey. Both sexes generally responded that math is a subject appropriate for everyone. This proved not to be a barrier to females’ participation and achievement in math. I found consistency when reporting sex differences in confidence in one’s math ability. The boys were consistent in giving themselves higher ratings of math ability than girls did. They considered math courses to be easier, and the boys had higher expectations of success in future math courses. I thought it was interesting to note the male and female responses to the question about support. The boys listed their teachers and their dad as people who encouraged them. The girls listed their teachers and their parents, not singling out their dad. Also, several females wrote, "No one really," to the question about support of significant others.

Interventions

The interventions had to do with actively recruiting females for higher level mathematics classes. I sought after females in my Honors Analysis course, and in particular the three junior females I included as part of my focus group, to take the AP Calculus course. I wanted to encourage these students to enroll in optional math courses. I knew I needed to convince these students that they would be successful, and that advanced mathematics on an AP level is something that they could do. I learned during my interviews with the senior girls that despite their good grades, these students had lower estimates of their future chances of achieving a satisfactory grade in advanced mathematics than did the males. To increase the girls’ positive self-concept of their mathematical ability, I proposed four interventions.

Sadker and Sadker (1995) point out that boys and girls take almost the same number of mathematics courses, including algebra and geometry. Then their roads diverge, with more boys studying AP calculus and more girls dropping out. While girls are staying with math longer, it is often a matter of endurance without enjoyment. Girls are more anxious and less confident about their math ability. The majority of my interventions dealt with their increasing their confidence. I focused on creating an atmosphere of inclusiveness in the classroom. I switched from having the students just call out an answer to my questions, to a kind of acknowledge-and-response pattern. I noticed the males in my classes tended to speak more, have more confidence, and seemed to learn through argument with me. At times I felt they just wanted to talk. Now I make an extra effort to call on the students, involve the females by allowing more time before I choose someone to answer a question. I found by waiting another few seconds, I am encouraging more girls to speak up. The boys tend to speak freely and spontaneously, while the girls needed to reflect on the questions. I am very aware of whom I am calling on. By providing them with a number of participatory experiences, I am giving them the confidence to express their ideas and become more confident of their performance. Once I started to increase the wait time before calling on students, the girls seemed to enjoy the opportunity to become involved in class discussions. This little bit of extra attention is proving to be effective in drawing out the females in my class.

My colleagues and I are often frustrated by the constant interruptions to our schedule and shortened class periods. These short class periods, sometimes as short as ten minutes, are a wonderful time to teach math history, my second intervention. We look at the contributions that females have made in the discipline. We also use this time to talk about the people behind the mathematics. It helps me present math as a human endeavor. I share with them my own experiences with math anxiousness. I do not think my gender is necessarily enough to positively affect my students’ persistence, but my gender in combination with certain kinds of shared experiences may be having a positive influence on them.

The third intervention is to share with them the processes that I go through in solving a complicated problem. More often, girls rather than boys say to me, "I would never have been able to do that kind of problem on my own" or "I would have never thought of that." Another example of a confidence issue. Too often teachers just share the finished product, the problem done completely and correctly. It appears to the students that we just arrived at the solution painlessly. I think, at times, students need to see all the crumpled papers I put in the wastepaper basket. They need to understand that mathematicians do not arrive at a solution the first time or the first way. On occasion I do not solve all the problems before class. Instead, I show students how I start a given problem, make an error, and begin the solution over again. I think my female students need to watch women teachers solve (and fail to solve) problems. They need models of thinking that are human and imperfect, but attainable.

The fourth intervention has to do with making my students aware of the social barriers that women in mathematics have had to overcome in order to achieve their success. I also wanted to a share with them the enjoyment women have experienced in their mathematics careers. As Yusuf (1995) points out, "Gender differences in mathematics performance are predominately due to the accumulated effects of sex-role stereotypes in family, school, and society" (p. 187). I have incorporated two field trips into my sophomore and junior year curriculum. The National Cryptography Museum in Laurel, Md. is one of the places that I took the students. They are the world’s largest employer of mathematicians. My students spent the day with a mathematician and then a historian. They experienced some of the fun things that mathematicians do, like decoding secret messages. They also learned about the role many female mathematicians played during the wars. Women were very instrumental in breaking codes of the enemy. The second trip is sponsored by American University in Washington, DC. I took six female students to American University for Sonya Kovalevsky Day. The motivation for the day is to encourage young women to continue their interest in math and science. Sonya Kovalevsky was the first woman in modern history to be awarded a doctorate in mathematics, the first to hold a chair position in mathematics, and the first ever to hold a position on the editorial board of a major scientific journal. Besides learning about Ms. Kovalevsky, the day involves interactive workshops, seminars, group problem solving activities, and the communication of ideas. This gives my students an opportunity to meet other high school girls in the area who are also interested in mathematics.

I feel my intervention strategies will help to increase the students’ confidence, but are the girls confident enough to move on to another teacher? I still was not sure. I needed to address how I could help the girls "find their wings" to leave my classroom and feel confident with another teacher. I discussed my conversations, which I had with the senior girls, with the AP Calculus teacher. She shared my concern. We arranged for two after school meetings with all prospective students who qualify for AP Calculus. She went over the course outline, the course requirements, and reassured all in attendance that if they were willing to work hard they all would succeed. The AP teacher explained to the students that due to the sophistication of the course, much of the work is done in small cooperative groups. Students work on the assignments at their own pace. She invited the prospective students to talk to her about any concerns that they may have. My second approach was to talk to our new Academic Dean. I shared my concerns with her, and they quickly became her concerns. She is looking into arranging students’ schedules so that they do not have the same mathematics teacher three years in a row. We are a department of thirteen teachers, and at least two teachers teach each level of mathematics courses in our department. She feels that for most students this will be possible when scheduling classes.

Results of My Interventions

I started this project focusing on the three junior girls whom I identified as being very able to perform in an AP Calculus course. I was concerned that they were feeling threatened by the rigor of the course and would consider a less rigorous course. As I was working through the Cultural Inquiry Process (Jacob, 1999), I soon realized that my efforts were applicable to many more students, both male and female. So the interventions that I used were applied to all of my students. I was able to connect with the majority of my students and we agreed on the appropriate course for next year.

I individually talked to each student prior to their placement in a mathematics course for next year. This gave me an opportunity to discuss such topics as under-confidence, self-assessment, setting lower goals, and avoiding risks. It also gave me an opportunity to discuss with appropriate students under-preparation for schoolwork. In the past, the teachers in our department made a decision on placement based solely on their grade. We then informed the student of our recommendation and the student either agreed or opted for a less rigorous course. The students made the final decision. I found by spending a little extra time and talking to each student individually I was able to connect with the students’ anticipation, fear, or in some cases over-confidence. I realized that what students think they can do, rather than what they can actually do, determined their choice of courses. I assured them that occasional failure is good therapy, that it is OK to suddenly get stuck on a problem. All but one of my students agreed with me on their placement for next year. I feel those students who were hesitant are somewhat more confident in knowing that they can be successful. The one student who chose not to go into AP Calculus was one of the three junior girls that I initially focused on for this paper. She is the student whose mother is pressuring her to keep her GPA above a 3.6. I explained to her that she may not make the ‘A’ but a high B is well within her reach. We went over the calculations for GPA’s in an honors versus AP course. After talking this over with her mother, they decided against my recommendation and she enrolled in the honors course.

I encouraged students to have their parents come to the parent-teacher conferences that are held in the spring. Typically, those parents of students who succeed all the time would come to the spring conferences. As a result of how I handled placements for next year, I did notice a few more parents coming to the conferences. This gave me an opportunity to discuss with them how the role that parent attitudes related to their children’s math attitudes and achievement.

It is interesting to note that the parent of the junior girl who decided not to enroll in AP Calculus did not come to the parent-teacher conference. She had attended all conferences in the past.

Conclusions

After working through the Cultural Inquiry Process, I now understand there is more to placing a student into an AP course besides prior grades they received. This process helped me to understand how low self-esteem and low self-confidence affect girls’ decision making when selecting a higher level mathematics course. The process also forced me to examine the culture of my classroom. Might I not be fostering a spirit of taking learning risks within my classroom setting? The research provided me with insightful information on how to modify my personal behavior to counteract some of the negative motivational messages that some girls receive. I realized that strategies for achieving gender equity must begin on the first day of the school year. As I continue to monitor my interventions during next year, I hope to see an increase in the number of girls selecting Advanced Placement Mathematics.

I was unable to convince the student that a B+ in an Advanced Placement course is more highly valued by college admissions than an A in an honors course. Perhaps, the time to address this issue is Back to School Night in September. I apparently need to explain to the parents of my students that the tougher courses improve standardized test scores, so that even if their students’ GPA slips a bit, a high SAT score will compensate.

I also feel that my anxiousness to maximize the potential of all my students must be shared with their parents. After the interviews with the girls I realized that some parents unintentionally convey low expectations to their daughters. While I know that all parents want their children to succeed, I learned that some parents may be conveying their own math anxiety to their children. My new dilemma is how to get parents to work with me and share my goal. I realize that my further research will now take a different path. A path that uncovers ways on how to deal with parents and engage them in achieving gender equity for their children.

In conclusion, I think the point that Myra and David Sadker (1995) make about male courses and male careers is worth noting. They suggest that gender lines guarding male domains, mathematics and sciences, are vanishing, but harmful remnants remain. The Sadkers point out that even Mattel’s Talking Barbie Doll admitted, "Math class is tough." They felt it was OK for Barbie to say this, since Math class is tough. They also felt that Barbie should not admit it unless Ken does too. And he doesn’t!

References

Chipman, S. F., Brush, L. R., & Wilson, D. M. (Eds.). (1985). Women and mathematics: Balancing the equation. Hillsdale, N. J.: Lawrence Erlbaum.

Fennema, E. & Leder, G. C. (Eds.). 1990. Mathematics and gender. New York: Teacher College Press.

Horgan, D. D. (1995). Achieving gender equity: strategies for the classroom. Needham Heights, Ma: Allyn and Bacon.

Jacob, E. (1999). Cultural Inquiry Process [Online]. Available: http://classweb.gmu.edu/classweb/cip/

Sadker, M. & Sadker, D. (1995). Failing at fairness. How our schools cheat girls. New York: Touchstone.

Simon, M. (2000, December). The evolving role of women in mathematics. The Mathematics Teacher, 93, 782-786.

Yusuf, Mian M. (1995). Mathematics and multiculturalism. In J. M. Larkin & C. E. Sleeter, (Eds.), Developing multicultural teacher education curricula (pp. 187-201.) Albany, New York: State University of New York Press.