Statistics in Social Context: Issues of Lesbians, Gays, Bisexuals and Transsexual in Teaching Statistics
Statistics in Social Context: Issues of Lesbians, Gays, Bisexuals and Transsexual in Teaching Statisticsby John Kellermeier.
Published in: (2002). Transformations, To appear Fall 2002.
Most students in the U.S. education system are taught mathematics and statistics using what Frankenstein (1994) calls "functional mathematics curricula... stripped of its relationship to the learner and to our society, concentrating instead on mechanical proficiency and rote memorization" (p. 22). This approach to mathematics education teaches students to view mathematics as a neutral knowledge system unconnected to such social and political realities as race, class, gender, and sexual orientation. Yet at the same time, mathematics and particularly statistical knowledge are used throughout our social and political discussions of race, class, gender, and sexual orientation. They are used to frame our discussions and to formulate our societal policies on these issues.
A functional mathematics curriculum does not prepare students to critically take part in these discussions and policy formulations. As an alternative to functional mathematics curricula, Frankenstein proposes
"Criticalmathematics literacy, on the other hand, involves the ability to ask basic statistical questions in order to deepen one’s appreciation of particular issues, and the ability to present data to change people’s perceptions of those issues. A critical understanding of numerical data prompts one to question 'taken-for-granted' assumptions about how a society is structured and enabling us to act from a more informed position on societal structures and processes." (p. 23)
A criticalmathematics curriculum would then weave a discussion of social issues into the learning of functional and mechanical mathematics thus preparing students to better participate as global citizens.
The typical introductory statistics course as taught throughout U.S. higher education introduces students to the fundamentals of probability and statistics using a functional curriculum that emphasizes an understanding of the mechanical techniques employed in probability calculations and in data analysis. However, I teach a course in which an additional hour of class time is devoted to learning about and discussing a particular social issue. These discussion sessions are based upon readings assigned from the literature on that social issue. Emphasis is placed both on the content of the readings and on the ways in which statistical knowledge is used in this content. The discussions are related to the learning of functional statistics through the use of word problems based on the readings.
The readings I use for a criticalmathematics curriculum for teaching statistics using lesbian, gay, bisexual, and transsexual issues are based primarily on Lesbian and Gay Stats by Singer and Deschamps (1994). This book is a collection of statistical information that gives “a series of snapshots of lesbians and gay men” (p. 4). It is organized into thematic chapters covering such issues as AIDS, the media, public opinion, violence, the workplace. Bisexuality is treated as a separate chapter and transsexuality is mentioned only once. In addition to Lesbian and Gay Stats, a variety of articles are used from the popular and academic press. These articles serve to further illustrate the statistics given in the book and, particularly in the cases of bisexuality and transsexuality, serve as the focal point for discussions.
A list of reading assignments from these sources is the following. This list of weekly assignments is based on a semester with 14 weekly discussion classes.
Class Topic
Readings
Introduction
Introduction, Singer & Deschamps, 1994.
Preface, Singer & Deschamps, 1994.
"A Statistical Battleground": Counting Lesbians and Gay Men in the United States, Singer & Deschamps, 1994.
Bisexuality
Bisexuality, Singer & Deschamps
Sexual orientation: A multivariable dynamic process, Klein, Sepekoff & Wolf, 1990.
Media and Public Opinion
Media, Singer & Deschamps, 1994.
Public Opinion, Singer & Deschamps, 1994
Major generational and gender gaps on issue of homosexuality, Moore, 1997.
Majority of Americans not fazed by Ellen’s coming out episode Saad, 1997.
Family and Relationships
Family/Relationships, Singer & Deschamps, 1994.
A descriptive empirical study of gay male stepfamilies Crosbie-Burnett & Helmbrecht, 1993.
Concerns and issues faced by families headed by a lesbian couple Hare, 1994.
Passing: Impact on the quality of same-sex couple relationships, Berger, 1990.
Violence
Violence, Singer & Deschamps, 1994.
VLGR discrimination and violence results, Vermonters for Lesbian and Gay Rights. 1987.
Survey details gay slayings around U.S., Dunlap, 1994.
Anti-gay violence and victimization in the United States: An overview, Berrill, 1992.
Sex and Transsexuality
Sex, Singer & Deschamps.
Orgasm in the postoperative transsexual, Lief & Hubschman, 1993.
Male-to-female and female-to-male transsexuals: A comparison, Kockett & Fahrner, 1988.
Homosexual and bisexual identity in sex-reassigned female-to-male transsexuals, Coleman, Bockting & Gooren, 1993.
Politics and Law
Activism/Politics, Singer & Deschamps, 1994.
Civil Rights/Law, Singer & Deschamps, 1994.
Demographics and Social Activities
Demographics, Singer & Deschamps, 1994.
Health, Medicine and AIDS
AIDS, Singer & Deschamps, 1994.
Health/Medicine, Singer & Deschamps, 1994.
Physical health problems and concerns of lesbians, Trippet & Bain, 1993.
Homosexual and bisexual men’s perceptions of discrimination in health services, Kass, Faden, Fox & Dudley, 1992.
Seroprevalence of HIV and Risk Behaviors Among Young Homosexual and Bisexual Men, Lemph, Horozawa, Givertz, Nieri, Anderson, Lindegren, Janssen & Katz, 1994.
Workplace
Workplace, Singer & Deschamps, 1994.
Linking gay rights and unionism, Noble, 1994.
Hiring, firing, and promoting, Lee, & Brown, 1993.
Military
Military, Singer & Deschamps, 1994.
Americans deeply split over ban on gays in military, Saad, & McAneny, 1993.
Lift the ban, 1995.
After two years of "Don’t Ask, Don’t Tell, Don’t Pursue" discharge of suspected gay servicemembers reaches four year high, Sevicemembers Legal Defense Network, 1997.
New study faults Pentagon’s policy on gays, Shenon, 1997.
Youth
Youth, Singer & Deschamps, 1994.
Health and social issues of gay, lesbian, and bisexual adolescents, Dempsey, 1994.
Gay and lesbian youth: Contributing factors to serious attempts or considerations of suicide, Hammelman, 1993.
Education
Education, Singer & Deschamps, 1994.
And gladly teach: Lesbian and gay issues in education, Fassinger, 1993.
International and Religion
International,Singer & Deschamps, 1994.
Religion, Singer & Deschamps, 1994.
I begin each discussion class with a short reading quiz. The purpose for these quizzes are twofold, first to insure that the students actually read the materials prior to class and, second, to serve as a basis for class discussion. The first question on every quiz is: "What did you find to be the most interesting statistic from the readings for today and why?" Each student is asked to give her or his answer to this question. The resulting discussions often revolve around the use and validity of statistics and comparisons to previously discussed statistics.
When teaching statistics I give a variety of quizzes and tests that consist of word problems. All of the word problems used during the semester are generated from the readings assigned for the discussion class or from similar readings. Statistical information form the readings are either used directly or as a basis for simulating realistic data. The readings used are then cited. Students then get used to the idea that statistical information is always analyzed within a context.
The following are some examples of the word problems I have used. The word problems are ordered by the type of functional mathematics content within the problem. Collectively, they represent examples of word problems for an entire semester of an introductory statistics course.
Kinsey Study (1948)
Psychology TodayStudy (1970)
Playboy Study (1983)
National Opinion Research Center Survey (1991)
Janus Report (1993)(See Singer & Deschamps, p. 10-12.) Suppose a student in this course decides to pick the studies randomly. Consider the following events:
A: None of the studies chosen are from periodicals.
B: At least one study chosen is from the 1990s.a. What type of sampling is used in this situation?
b. List the samples in the sample space
c. List the samples in each of the events A and B.
d. What are the probabilities of each of the events A and B?
Level of Support Frequency of Answer Almost always 10 Often 23 Rarely 46 Never 13 Not out to relatives 8 a. What proportion of these fathers received support from relatives at least often?
b. What proportion of these fathers never received support or were not out to relatives?
c. What proportion of these fathers were out to relatives?
a. What percent of the respondents were white?
b. What percent of the respondents were people of color who favored extending civil rights laws to include homosexuals?
a. What percent of those interviewed were aged 18-49 and bothered by the coming out episode of the TV show "Ellen"?
b. What percent of those interviewed were aged 50 and over and bothered by the coming out episode of the TV show "Ellen"?
c. What percent of those interviewed were bothered by the coming out episode of the TV show "Ellen"?
d. What percent of those who were bothered by the coming out episode of the TV show "Ellen" were aged 50 and over?
Neutral Discouraging Discouraging Discouraging Neutral Discouraging Encouraging Neutral Neutral Neutral Discouraging Encouraging Encouraging Discouraging Neutral Discouraging Neutral Encouraging Neutral Discouraging Neutral Discouraging Neutral Discouraging Neutral Discouraging Discouraging Discouraging Neutral Encouraging Encouraging Neutral Neutral Discouraging Discouraging Discouraging Discouraging Neutral Discouraging Neutral Neutral Discouraging Neutral Discouraging Neutral Neutral Neutral Discouraging Encouraging Neutral (Data simulated from Vermonters for Lesbian and Gay Rights, 1987.) Organize these data in a table and draw a bargraph.
14, 1, 5, 11, 2, 9, and 6.
(Data simulated from Hare, 1994.) Find the following:
a. The sample mean
b. The median
c. The range
d. The sample variance
e. The sample standard deviation
a. Find the probability distribution of x.
b. What is the expected value of x?
c. What is the variance of x?
d. What is the standard deviation of x?
a. What is the probability that at least 13 of these couples agree that both partners should have an equal say in the relationship?
b. What is the probability that at least 13 of these couples agree that both partners do have an equal say in their relationship?
a. Out of a sample of 100 heterosexual teenagers, what is the approximate probability that at least 30 will have attempted suicide?
b. Out of a sample of 100 lesbian and gay teenagers, what is the approximate probability that at least 30 will have attempted suicide?
a. Do these data provide sufficient evidence to conclude that the majority of transsexual youths attempt suicide?
b. Determine a 95% confidence interval for the proportion of transsexual youths who attempt suicide.
a. Do these data provide enough evidence at the 0.05 level of significance to conclude that there is a difference in average age when MTF and FTM transsexuals have sexual reassignment surgery?
b. Determine a 90% confidence interval for the difference in average age when MTF and FTM transsexuals have sexual reassignment surgery.
a. Do these data provide sufficient evidence to conclude that there is a difference in the proportion of lesbian and gay male youths whose self-esteem is affected positively by “coming out?” Use a significance level of 0.01.
b. Determine a 99% confidence interval for the difference between the proportion of lesbian and gay male youths whose self-esteem is affected positively by “coming out.”
Yes
No
No Opinion
White
325
510
44
Non-white
53
55
6
(Data simulated from Hugick, 1992.) Do these data provide enough evidence to conclude that race and opinions on the acceptability of homosexuality are related? Use significance level 0.05.
My experience with teaching this course using lesbian, gay, bisexual and transsexual issues as a theme has been positive. Even though students often seem to not be aware of it, their ability to question, understand, and confront information given in statistical form is much greater than in other statistics classes I have taught without a social issue discussion section.
During course evaluations I administer at the end of the semester, I ask students to comment on the question:
How well did the readings and discussions of lesbian, gay, bisexual, and transsexual issues help you understand probability and statistics and how they are used?
Over three semesters of using this evaluation I have gotten mostly positive feedback from students. Out of 40 students who have completed evaluations, only seven have said that the readings and discussions have not helped them with their understanding of probability and statistics. For example, one student commented,
It did not relate to the regular class. It seemed like a whole other class.
At the same time many of these student still expressed a value in the discussion class. An example of this is the student comment,
I don’t really think I related the math to the discussions but I still enjoyed the discussion for my own personal growth.
Positive answers to the evaluation generally fell into one of three statements. The three statements and some examples of student comments are as follows.
The discussions classes demonstrated to students the utility of learning statistics.
It helped me see that this class had a point.
It helped me relate what we did in class to the purpose statistics serve.
They helped me bring meaning to the course.
The discussion classes showed me what all the problems in class were used for.
Using real issues made learning statistics more interesting, more understandable and more fun.
It gave real issues and real situations that are occurring or have occurred. It’s interesting to learn these things that were discussed.
The readings made the work more interesting when they were applied to a social context.
I found it made the “statistics” part easier to understand and more real.
The discussion classes helped to make the mathematical part of statistics more real. I think that this “real life” connection made learning the mathematical statistics more fun and easier.
The discussions classes helped students to develop criticalmathematics skills in statistics.
It put them into perspective & taught me how to take them with a grain of salt.
They made me question what the one number in a statistic means.
They brought real-life situations and gave me the ability to criticize statistics fed to me by the newspapers, TV, etc. (the media) instead of taking it as a given.
It helped me to look beyond the numbers and ask where they came from, who did the research and why they did the research.
Another benefit of the discussion class was that it helped to create a classroom community. Once a week we sat in a circle where we could see everyone’s face and talked about the issues we were reading about. This created an environment where students came to know each other as individuals and became more comfortable talking with each other. This helped to create a community which was taken back into the “regular” classroom where the students sat in the chairs in traditional rows facing a board. In this setting they still knew each other as individuals. This meant that they were more likely to talk, interact and help each other to learn. One student expressed this quite well in here last journal of the semester.
I wasn't sure if you wanted us to write a journal for this week, but I decided to write one regardless. I wanted to be sure to tell you how much I have enjoyed this class. Besides learning a lot about statistics, how they are found, and how they are reported, I learned how to be part of class that is a lot closer and friendlier than other classes. I have thoroughly enjoyed that feeling. Sitting around in a computer lab or in a classroom or even in a hall waiting has not been as exciting as it was this semester. I never knew what to expect: D. might be talking about anything and everything, C. could come sliding into class with a laundry basket, P. might be cracking jokes about a serious (or at least fairly serious) topic, S. would be sitting at her desk amusedly watching everyone else. I really liked all of these things. I think I enjoyed the class a lot more because of the atmosphere, an atmosphere that you helped to create from the first day of class by making us talk to each other. Thank you for that. I personally believe that you have created a wonderful math class.
Lastly, for many students learning about and dealing with issues of lesbians, gays, bisexuals and transsexuals was an opportunity for personal growth. For some this meant dealing with their own homophobia and transphobia. An example of this is expressed in end-of-the-semester comments when students were asked what was the most important thing they learned from the discussion classes. The first of these comments is from a straight male and the other from a gay male.
I learned that homophobia is the problem whereas being gay/lesbian/bisexual is not the problem.
I became aware of my own gender prejudices vis-à-vis transsexuals/transgenderists.
During the spring of 1996, I administered a homophobia index questionnaire to students at the beginning and at the end of the semester to determine if the course would decrease levels of homophobia. With a sample of eleven students who took the index both before and after the class, a hypothesis test for decrease in homophobia showed statistically significant results ( t = 2.25, p = 0.024). Thus the discussion classes help students to lower their levels of homophobia.
For some students the discussion classes helped in dealing with issues of gay, lesbian, or bisexual identity, either their own or that of their family members.
During the semester, I have a transsexual guest speaker and a gay, lesbian and bisexual panel come into the discussion class. This last semester two of the students in the class chose to come out to their fellow students and take part on the panel. For both of these students this was a profoundly empowering event. For one student in particular this was the first public coming out as a bisexual. This experience gave her the confidence to put together and be a member of a gay, lesbian and bisexual a panel of for one of her other classes, a class on diversity issues in social work.
In a previous semester, I received the following journal from a student showing the extent to which the discussion classes had enabled her to reach out to a gay family member.
Upon my return [from Spring Break], I had a pleasant surprise. My Uncle M. is gay and he has had a boyfriend for three years. My parents are not very receptive to their lifestyle so I have only met my Uncle M. once and have never met J. At the beginning of the semester I wrote them a letter saying that I recognize both of them as being a part of my family. I also explained to them that I was taking this course and hoped to learn more and understand more about the gay/lesbian lifestyle.
I received a letter from my "Uncle" J. when I got back from Spring Break. It was very exciting. I had not heard from my Uncle M. so I figured I had overstepped my boundaries in addressing his sexuality. Not only was I well within the boundaries they both received my letter as being the "most powerfully moving letter related to their sexuality that they ever received." My Uncle J. was so excited that I understood their lifestyle as being just different and not bad or wrong. They told me that I am the only family member that has addressed this issue in a positive way and accept them for who they are. I am glad that I have formed this new bond with my uncles. I want you to know that it was this class that encouraged me to reach out to them.
Overall I found the use of a discussion of lesbian, gay, bisexual, and transsexual issues to be beneficial to teaching students in an introductory statistics class. Not only does their criticalmathematics literacy increase, but the discussion sessions help to create a sense of community that carries over into the learning of the functional mathematics curriculum. For many students the study of these issues also provides an opportunity for personal growth.
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