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Published in:
(1995). NWSA Journal, 7(1), 98-108.
(1999). In I. Shor & C. Pari (Eds.), Education is Politics: Critical Teaching Across Differences, Postsecondary, Portsmouth, NH:
Boynton/Cook Heineman.
Over the past several years I have been working with curriculum inclusion issues as they apply to teaching statistics. I have done this by using the content of word problems as a vehicle for including issues of race, class, gender, and sexual orientation in an introductory statistics course (Kellermeier 1992, 1994). For example, in teaching a particular statistics concept, it does not matter whether we use as an example the percentage of red balls in an urn or the percentage of lesbians and gay men in a group of people. By using the later as the example, we can bring the issue of sexual orientation into the statistics classroom. This is precisely what I have done, using issues of race, class, gender, and sexual orientation in many of the word problems I have used in teaching statistics.
As part of this work on inclusion of diversity, I have regularly asked students to comment on the word problems as part of my course evaluation. The response from students has, for the most part, been positive. (see Kellermeier 1992, 1994) They see the issues discussed in the word problems as the important issues of their times. Many comment that the word problems make the course more interesting and in turn make them more willing to learn the statistics.
Yet, students often see this inclusion as more substantial than it actually is. Approximately 10-15% of students comment that the majority of the problems are about "women's issues" or about gays, lesbians, and bisexuals. In fact, a content analysis of all the word problems I use in a semester shows that only about one-sixth are about gender issues and less than 1% actually mention sexual orientation. Typically, some students see the small amount of inclusion of lesbigay issues as excessive. In particular, one or two students out of every class will comment that the few word problems using issues of gays, lesbians,and bisexuals are "just too much."
As a result, I decided to investigate what students' reactions would be if indeed there were a large number of word problems dealing with "queer" statistics. The word problems given as examples and exercises in the text (a manuscript text written by myself) include a very small number of lesbigay issues. The text, however, cannot easily be changed for one semester. Where I do have more immediate control of word problem content is on quizzes and tests. For two semesters of teaching an introductory statistics course I vastly increased the number of word problems on quizzes and tests that dealt with lesbigay issues. In the spring 1993 semester, there were a total of 39 word problems on quizzes and tests with 29 of them having lesbigay content (74%). In the summer 1993 semester, there were a total of 40 word problems on quizzes and tests with 37 of them having lesbigay content (93%). I should note that my students spend more time with quiz and test questions and in a less stressful setting than is typical in a statistics class. Quizzes are given as take-home assignments with students encouraged to work collaboratively. Tests are given in class but without a time limit. Additionally, students spend time reworking missed test questions for extra credit.
In what follows I will give examples of the word problems used in this course and an analysis of student evaluations. The word problems fall into three categories, (1) using lesbigay populations as a background, (2) using facts about lesbigay populations, and (3) using realistic data about lesbigay populations.
These word problems take typical statistics content and use lesbians, gays, and bisexuals as background.
Another Mother Tongue: Gay Words, Gay Worlds, by Judy Grahn
The Pink Triangle: The Nazi War Against Homosexuals, by Richard Plant
Gay Spirit: Myth and Meaning, edited by Mark Thompson
In the Life: A Black Gay Anthology, edited by Joseph Beam
Living the Spirit: A Gay American Indian Anthology, edited by Will Roscoe
Suppose a student in this course decides to pick the books randomly. Consider the following events:
A: Both books chosen are edited collections.
B: At least one book chosen is about people of color.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?
9 3 6 1 9 10 8
Find the following:
a. The sample mean
b. The median
c. The range
d. The sample variance
e. The sample standard deviation
a. What is the probability distribution of x?
b. What is the expected value of x?
c. What is the variance of x?
$27,700 $29,100 $30,900 $32,200 $33,000 $34,500 $28,500 $29,100 $31,000 $32,300 $33,100 $34,600 $28,700 $29,500 $31,000 $32,400 $33,400 $35,700 $28,700 $30,400 $31,100 $32,500 $33,700 $35,900 $28,900 $30,700 $32,200 $32,500 $34,100 $37,000 a. Draw a line graph for these data.
b. Organize these data in a table and draw a histogram.
a. Is there sufficient evidence to conclude that these two couples spend different average amounts of money on food per day while on vacation? Use significance level 0.10.
b. Find a 99% confidence interval for the difference in the average amount of money these two couples spend on food per day while on vacation.
These word problems use statistical information about lesbians, gays, and bisexuals as a basis for the statistical content of the word problems. The information for the first five of these problems was taken from a report by Vermonters for Lesbian and Gay Rights published in the Vermont newspaper Out in the Mountains (June 1987).
Level of Education Percentage High School Graduate 8% Some College and 2-year Degree 16% College Graduate 45% Masters and Ph.D. 31%
Assume these percentages are accurate for all the readership of this periodical.
a. What percent of the readership has a 4-year college degree or higher?
b. What percent of the readership does not have a post-graduate degree (Masters or Ph.D.)?
c. What percent of the readership does not have at least a high school diploma?
a. How many of those sampled would you expect to have experienced some such harassment or violence?
b. What is the probability that at least 15 of them would have experienced some such harassment or violence?
c. What is the probability that at least 5 of them had never experienced some such harassment or violence?
a. How many of these people would you expect to have experienced housing discrimination?
b. What is the probability that no more than one has experienced housing discrimination?
The next two problems use information from a news article out of The New York Times (Schmalz, 1993).
a. How many of council members do you expect would support lesbigay equal employment rights?
b. What is the probability that at least 15 of the council members support lesbigay equal employment rights?
c. What is the probability that more than 4 of the council members are against lesbigay equal employment rights?
The last two problems use information from the Internet email list GAYNET (Richardson, Cheney)
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?
In these word problems statistical information about lesbians, gays, and bisexuals is uncovered by the process of doing the problem. The data used in these problems are not real data taken from research but are realistic in the sense that they were simulated using real statistics as a basis. For example, the first two problems use data taken from the Vermonters for Lesbian and Gay Rights report (1987).
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 Organize these data in a table and draw a bargraph.
a. Determine a 95% confidence interval for the percentage of lesbians, gay men, and bisexuals who encountered employment discrimination.
b. Determine a 95% confidence interval for the proportion of lesbians, bisexuals, and gay men who experience harassment or violence.
The VLGR report stated that of those reporting violence to police, 17% found the police encouraging, 35% found the police discouraging and 48% found the police neutral. In order to simulate data I assumed a sample size of 50. With this sample size, there would be 8.5 Encouraging, 17.5 Discouraging, and 24 Neutral. These numbers are rounded off so that in the data given, there are 8 Encouraging, 18 Discouraging, and 24 Neutral. The second problem came from report statements that 44% of those surveyed experienced employment discrimination and 80% experienced harassment or violence. Assuming a sample size of 133, this would mean numbers of 59 and 105 respectively.
The next problem uses the information that of those who believe homosexuality cannot be changed, 57% also consider homosexuality an acceptable lifestyle (Schmalz 1993).
This next problem uses information posted on the Internet email list GLB-NEWS (Morin). This posting states information from polls taken by the National Opinion Research Center at the University of Chigago in 1977 and in 1991. In 1977, 67% believed sex between consenting adults of the same sex was "always wrong." In 1991, 71% said the same.
a. Do these data provide sufficient evidence to conclude that the attitudes of Americans on this issue have changed between 1977 and 1991? Use significance level 0.01.
b. Find a 95% confidence interval for the difference between the proportions of Americans who believed that sex between consenting adults of the same sex was "always wrong" in 1977 and in 1991.
The data for this last problem were taken from a posting on the Internet email list GAYNET (Herbert). This posting stated that "between 1980 and 1990 women constituted 23% of those discharged for homosexuality. Also, women constitute about 11-12% of the military."
The school where I teach is a four-year state college in the State University of New York system. The student body is primarily white. Only two students in each of the classes were students of color. The statistics course is taught in the mathematics department. It is the course that most students take to fulfill the general education requirement in mathematics skills. Consequently, it is taken by a wide variety of majors, in particular those majors that do not require a mainstream calculus course. The gender breakdown in this course is usually about 50% females and 50% males.
In both semesters during which I used large numbers of lesbigay content word problems, I did not announce to students that this content would be used. Neither of the two classes asked any questions about the information presented in the word problems about lesbigay issues. In the first class I had no discussions about these issues with the students. In the second class, taught in the summer, the length of the class period required a five to ten minute break each day. During this break, on a few occassions I had conversations with students about the topics of the quizzes. However, these conversations were never carried into the entire class.
At the end of the semester, the students were asked as part of the course evaluations to respond to the following question:
Please comment on the word problems you did as part of this course. Specifically, what do you remember of what the problems were about? What do you think of the word problem content?
As is usual with student evaluations, the students were told that I would not have access to these evaluations until after I had submitted grades for the semester.
The students in the statistics course taught during the spring semester of 1993 consisted of traditional college-age students with nearly all of them being first and second year students. There were 29 females and 4 males. This ratio was considerably different than the usual 50/50 ratio and seemed to be due to random enrollment patterns. Out of the 33 students, 30 submitted evaluations and 24 of those mentioned the lesbigay content. By my own reading of these comments I found 15 positive, 3 negative and 6 ambivalent comments. This last group consisted of comments such as the following:
The problems would become a little more enjoyable if you didn't always put in lesbian and homosexual terms in it. I don't mean that it was bad, but some variety would be nice.
The content of the problems is a touchy topic with some people and in a way I do see why every question had to be about "it" but I did not have a problem with them.
The most positive comments spoke of an additional learning benefit from the lesbigay word problem content. Such comments included the following:
I think the word problem content was good material because I became more informed to this issue and I understand it more. It has a very positive effect on me.
Knowing that these statistics are approximately correct, I feel that their content brought added value to the course.
The second statistics course was during a five week summer school session. The students in this course were older than those during the spring semester with half being 24 years or older. There were no first-year students and only one-third were sophomores. Exactly half of the 20 students were female. There were a total of 18 students submitting evaluations with 16 commenting on the lesbigay content. Of these, 9 were positive, 3 were negative and 2 were ambivalent. There did seem to be an undercurrent of discontent from a couple of the students, mostly expressed to other students. In speaking of this, one student wrote:
I think it's scary how upset people in class have gotten over the use of non-sexist, non-heterosexist questions in the course--it's a pretty sad (but unfortunately not surprising) statement about our society. I am always glad to see efforts made that try to equalize the imbalances that exist in education.
However, the majority of the class was positive about the lesbigay word problem content. Again, there were comments which indicated the positive effect that these problems had on students. Two students wrote:
It took me a while to get used to reading material about gays and lesbigays. But now I don't think of the content as being out of the ordinary because of reading it so often.
If anything, being exposed to those problems day after day I got a feeling that this is not the faceless community we see in the media but a living part of this society.
Overall, I felt that the use of lesbigay word problem content in these two courses was successful. First, the majority of the students in both classes reacted favorably to the content of the word problems. For at least some of the students, these word problems heightened their awareness of lesbians, gays, and bisexuals and the homophobia they face.
Secondly, for those students who are out, who are coming out now or who will come out in their futures, these problems will help them see a positive reflection of themselves, one that they may not often see in other classes.
Thirdly, for me, I found an appreciation of the use of a thematic approach to word problems. Because of this experience, my next venture is to combine thematic word problems with a discussion of the theme as well. Unfortunately, the need to cover the required statistical content in three credit hours makes this difficult. I have designed an introductory statistics course, Statistics in Social Context, that adds one credit hour to allow time for the discussion of the issues raised in the word problems.
In the end, it seems that the best way to deal with students' complaints of inclusion as "just too much" is to do more inclusion. Once lesbigay issues are repeated often enough, they become commonplace. Then, as these issues become commonplace in the classroom, students may be better prepared to accept, support, and appreciate gays, lesbians, and bisexuals out of the classroom as well.
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