Writing Word Problems that Reflect Cultural Diversity

by John Kellermeier

Published in: (1992). Transformations, 3,(2), 24-30.
(1993). In S. McConnell-Celi (Ed.), Twenty-first Century Challenge: Lesbians and Gays in Education--Bridging the Gap, Red Bank, NJ: Lavender Crystal Press

Introduction

In many of our courses we use word problems, case studies and examples to teach and to illustrate our subject matter. All of these applications have an overt curriculum and a hidden curriculum. The overt curriculum is the subject matter we are trying to teach, while the hidden curriculum is the content of the applications. For example, I teach an introductory statistics course. To illustrate a particular concept in probability, I can use a word problem such as the following:

• An urn contains 4 red balls and 6 green balls. A ball is drawn from this urn and its color recorded. The ball is then replaced. This is repeated for a total of 10 draws. How many of these balls would you expect to be red?

The overt curriculum is the method for determining expected counts. The hidden curriculum is about urns and balls, a not very interesting topic at that. On the other hand I can teach the same overt curriculum with the following problem which uses information from a referenced source.

• In sixty-three percent of all rapes, the victim knows her assailant (Herman, 1991). If we interview 20 women who were raped, what is the probability that no more than 4 of them were raped by strangers?

In this case the overt curriculum is still the method for determining expected counts. However, the hidden curriculum is the fact that acquaintance rape accounts for 63% of all rape.

This is an example of how this hidden curriculum can be used to reflect cultural diversity and to incorporate issues of race, class and gender, particularly in those subject areas where such issues at first seem to have no relevance. Any time we use an application to illustrate our subject matter, the hidden curriculum provides an opportunity to bring issues of diversity into our classroom and to link these issues with our subject matter.

But why would we want to do this? Basically, the reasons I see for doing this are:

1. We live in a society in which diversity is used to marginalize people, a society in which power and privilege are based on a "norm" or standard of rightness. To overcome this, there is a need to expand acceptance and celebration of diverse peoples and cultures in our American society. This is important for those people who are in the "normative" groups as well as for those who are marginalized.


2. Students learn more easily when the subject matter is related to their lives. Students, particularly those marginalized by race, class, gender, sexual orientation, etc. are more willing and able to engage the overt curriculum if they can understand and see themselves in the hidden curriculum.


3. The demographics of North American society are changing to an increasingly diverse population. Additionally, global society is becoming increasingly interconnected through economic and informational networks. It is becoming more important for our students to appreciate and begin to value cultural diversity if they are to function as global citizens. This also means it is increasingly important for all educators to confront racism, sexism, and classism.


4. The inclusion of issues of race, class and gender breaks down the image of areas such as math and science as white male domains. This, in turn, serves to give increased access to these areas to students who have been marginalized by the traditional images of math and science.

In the rest of this paper I will give examples of word problems that reflect cultural diversity.

Using Diversity as a Background

The first type of word problem I will illustrate uses issues of diversity as a background. The first of these two problems use women's literature and the second uses names from diverse cultures as settings for questions about probability and statistics topics.

• An assignment for a literature course is to read five short stories by women: "Elethia" by Alice Walker, "Seventeen Syllables" by Hisaye Yamamoto, "Recuerdo" by Guadalupe Valdes Fallis, "Storyteller" by Leslie Marmon Silko and "Only a Phase" by Leslea Newman. The students will then be asked in class to write essays on three of the five stories, randomly chosen by the instructor. Suppose a student only reads "Elethia", "Recuerdo" and "Storyteller". Consider the following events:

A: The student has read at least two of the stories selected.

B: The stories by Alice Walker and Leslea Newman are among those selected for essays.

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?

• A sample of eight students were given a test designed to measure how much they knew about AIDS and HIV. Their names and scores were

Name	Score
Haji	92
George	88
Susan	91
Consuela	83
Rashida	86
Sola	84
Kyoko	92
Joshua	75

Find the mean, median, variance, and standard deviation of this sample.

Using Facts About Diverse Populations

The following problems use statistical information about diverse populations and issues of race, class, gender and sexual orientation as a basis for asking probability and statistics questions. The information presented in these problems is gleaned from a variety of sources such as journals, newspaper articles, Internet sources, and women's studies textbooks.

• U.S. Census data shows that 88.0% of black children live with their mothers (possibly also including their fathers), 37.6% live with their fathers (possibly also including their mothers) and 33.8% live with both of their parents (Thuban Consulting, 1994).

a. What percent of black children do not live with their mothers?

b. What percent of black children live with at least one parent?

c. What percent of black children do not live with either of their parents?

• Ten percent of all seats in national legislatures throughout the world are held by women. (Blum, Harrison, Ess, & Vachon, 1993, p. 23.) Suppose a committee of 18 national legislators meeting at an international conference represents a sample of all worldwide national legislators.

a. How many of these committee members would you expect to be women?

b. What is the probability that at least 3 of the committee members are women?

c. What is the probability that more than 12 of the committee members are men?

• The amount of time spent in domestic labor (housework and child care) by wives who are employed outside the home is normally distributed with a mean of 42 hours (Shinkle, 1994). Suppose this time is normally distributed with a standard deviation of 9.7 hours.

a. What proportion of such women work more than 50 hours a week on domestic labor?

b. What amount of domestic labor puts such a women in the lowest 10%?

• While blacks constitute about 12% of the U.S. population, only 6% of management jobs in the broadcast industry are held by African-Americans (Chideya, 1995, p. 6). Suppose a sample of 45 managers from the broadcast industry is taken.

a. How many of these managers would you expect to be African-American?

b. What is the probability that less than 6 of the managers are African-American?

• The annual incomes of African American single mothers in a large metropolitan area have a mean of $12,100 and a standard deviation of $5,800 (Andersen, 1993, p. 115.) . If 100 such women are sampled what is the probability that there average annual income will be above $13,000?

• Eighty percent of gay, lesbian, and bisexual people have been verbally harassed because of their sexual orientation (Berrill, 1992). Suppose a sample of 19 gay, lesbian and bisexual people is taken.

a. How many of them would you expect to have experienced verbal harassment because of their sexual orientation?

b. What is the probability that more than 12 of them have experienced verbal harassment because of their sexual orientation?

• Two job fields account for over half of all women who worked in the paid labor force. 52% of all women work in clerical and service work. Suppose 210 women are selected from all women in the paid labor force.

a. How many of these women would you expect to work in the clerical or services fields?

b. What is the standard deviation of the number of these women who work in the clerical or service fields?

c. What is the probability that at least 100 of these women work in the clerical or service fields?

• In the U.S. 28% of births are to unmarried women (The World’s Women 1995: Trends and Statistics, 1995, p. 19). If you believe the rate of births to unmarried women in your community is no higher than that, how many births would you have to sample in order to estimate the rate accurately to within 0.01 at confidence level 99%?

• The U.S. military reports that 10% of the armed forces are women (Blum, Harrison, Ess, & Vachon, 1993, p. 61). Out of a sample of 122 military personnel from a particular installation, 19 were women.

a. Do these data provide sufficient evidence to conclude that the proportion of women at this installation is higher than the proportion throughout the entire armed forces?

b. Find a 90% confidence interval for the proportion of women among the military personnel at this installation.

Using Realistic Data About Diverse Populations

This next group of problems also use facts or information about diverse populations. In these problems, however, the information is uncovered by the process of doing the problem. The sample data given in these problems is not "real data" in this sense that it is taken from actual studies. Rather, it is "realistic data" simulated on the basis of the results of actual studies.

• The number of seconds required to perform a six-week vacuum aspiration abortion was recorded for a sample of six such abortions. The results were as follows:

84, 100, 80, 98, 85, and 84.

(Data simulated from Jewett & Peltier, 1989). For this sample find:

a. The mean and the median

b. The range, the variance, and the standard deviation.

• A random sample of college faculty were asked their gender (coded as M for male and F for female) and their faculty rank (coded as INS for instructor, AST for assistant professor, ASO for associate professor and FPR for full professor). The results are as follows:

Sex	Rank	Sex	Rank	Sex	Rank	Sex	Rank	Sex	Rank
M	AST	M	ASO	M	FPR	F	INS	M	ASO
M	AST	F	INS	M	FPR	F	FPR	F	AST
M	ASO	M	ASO	M	ASO	F	AST	F	INS
F	INS	M	AST	M	AST	M	ASO	F	AST
F	ASO	M	INS	M	INS	M	INS	F	INS
M	FPR	M	ASO	F	INS	M	AST	M	AST
M	INS	M	INS	M	FPR	F	INS	F	INS
M	AST	F	AST	M	INS	M	AST	F	AST
F	INS	M	ASO	F	INS	M	INS	M	INS
M	INS	F	AST	F	ASO	M	INS	M	AST

a. Organize these data in a contingency table.

b. Determine the cell proportions for gender classes.

c. Draw a bargraph for these data.

• Gay men, bisexuals and lesbians who experience violence against them because of their sexual orientation sometimes face a further problem if they choose to report the incident to the police, namely that the police themselves may be discouraging in the pursuit of the matter. To study this, 50 lesbigay people who had reported such violence to police were asked whether the attitudes of the police had been encouraging, discouraging or neutral.

Neutral	Discouraging	Discouraging	Discouraging	Discouraging
Neutral	Discouraging	Encouraging	Neutral	Discouraging
Neutral	Neutral	Discouraging	Encouraging	Neutral
Encouraging	Discouraging	Neutral	Discouraging	Neutral
Neutral	Encouraging	Neutral	Discouraging	Discouraging
Neutral	Discouraging	Neutral	Discouraging	Neutral
Neutral	Discouraging	Discouraging	Discouraging	Neutral
Neutral	Encouraging	Encouraging	Neutral	Neutral
Neutral	Discouraging	Discouraging	Discouraging	Neutral
Discouraging	Neutral	Discouraging	Neutral	Encouraging

(Data simulated from Vermonters for Lesbian and Gay Rights, 1987.) Organize these data in a table and draw a bargraph."

• A recent sample of 35 husbands was asked how many hours a week they spend on housework. Their answers were as follows.

0	1	3	4	6	7	8
9	9	9	10	11	11	12
12	13	13	13	13	13	14
14	14	14	15	15	16	16
16	17	17	18	20	33	40

(Data simulated from Shinkle, 1994). Fill in the following and draw a boxplot for these data.

Minimum:

Lower Hinge:

Median:

Upper Hinge:

Maximum:

Using Facts That Make a Point About Diverse Populations

The following problems also use statistical information about diverse populations as a basis for asking a probability and statistics question. However, these problems also show how probability and statistics are used to make a point about these populations.

• Data from 1990 shows that 44% of black children, 38% of Hispanic children and 15% of white children live in poverty (Andersen, 1993, p. 127). Does this mean that most poor children are black or Hispanic? In a typical community the children might be 12% black, 10% Hispanic and 78% white (Nadeau, Niemi & Levine, 1993).

a. What percent of children in this community are poor and black?

b. What percent of children in this community are poor and Hispanic?

c. What percent of children in this community are poor and white?

d. What percent of children in this community are poor?

e. What percent of poor children in this community are white?

• Recent studies suggest that among college women who have been raped, that is forced to have sexual intercourse against their wills, only 27% realize it, that is consider that they were raped (Sweet, 1985). The same studies show that 12% of college women have been raped.

a. What percent of college women who have been raped do not realize it?

b. Out of all college women, what percent have been raped and do not realize it?

• The average annual household income for black families is $21,161 and for white families is $38,909 (Chideya, 1995, p 117). Suppose these salaries are normally distributed with standard deviations of $6,345 for black families and $6,989 for white families.

a. What percent of black families earn more than $25,000 per year?

b. What percent of white families earn more than $21,000 per year?

From working these problems students learn that most poorchildren are white (56% in the community given in the problem), that 9% of college women have been raped and do not realize it, and that a much higher proportion of white families earn over $25,000 per year than do black families (98% to less than 27% ).

The problems given in this paper were developed for an introductory statistics class. A similar approach to the incorporation of issues of diversity can be used in any classroom where word problems, case studies or applications are used.

At the end ofeach semester, students are asked to give written comments on the word problems they had done, what they remembered about the subjects of the word problems and what they thought of them. Students overwhelmingly liked the diversity of problems. In the words of one student, "I liked the subjects because they related to real life and something we could all understand and relate to." Another said "they were relevant to real life." Students recognized that word problems were about racism, sexism, sexual orientation, politics, etc, what one student called the "major issues occurring today." This was also received positively. Another student said, "We dealt with real statistics from many diverse areas and it made us think about them for a few seconds."

A negative comment made by one of the students illustrates the overwhelming need for an inclusive curriculum. This student commented "There were too many problems dealing with bisexual, lesbian stuff." In reality, out of about 275 word problems assigned for this course one was about a lesbian and one about bisexuality. Additionally in two problem specifically mentioned heterosexuals. Thus about 1% of all word problems had any mention of sexual orientation. When these few problems can be seen as "too many" it is clear that there is a need for all our students to be exposed to a diverse curriculum.

References

• Barile, M. (1992). Disabled women: An exploited underclass, Canadian Woman Studies, 12(4) 32-33.
• Blum, A., Harrison, J., Ess, B., & Vachon, G. (1993). WAC Stats. New York: The New Press.
• Chideya, F. (1995). Don’t Believe the Hype: Fighting Cultural Misinformation about African-Americans. New York: Plume/Penguin.
• Herman, D. (1991). The rape culture. In Cochran, J., Langston, D. & Woodward, C. (Eds.), Changing Our Power: An Introduction to Women Studies (pp. 276-289). Dubuque, Iowa: Kendall/Hunt.
• Jewett, S. (Producer), & Peltier, M. (Producer, director, writer, editor). (1989). Abortion: For Survival [Video]. Los Angeles, CA: The Fund for the Feminist Majority.
• Langston, D. (1991). Women and work: Two jobs for less than the price of one. In Cochran, J., Langston, D., & Woodward, C. Changing Our Power : An Introduction To Women Studies. Dubuque, IA: Kendall/Hunt, p. 134.
• Nadeau, R, Niemi, R. & Levine, J. (1993). Innumeracy about minority populations. Public Opinion Quarterly, 57(3), 332-347. Exercise 2.51, 7.52. Example 7.10.
• Shinkle, F. (1994, January 30). The chore wars. St Louis Post-Dispatch, C1.
• Sweet, E. (1985, October). Date rape: The story of an epidemic and those who deny it. Ms. 14, 56-58.
• Thuban Consulting, 1994, Selected summary of social characteristics of the population by sex and race: March 1994. [web site]. http://www.Thuban.com/census/tables/sum1_)94.html. [Accessed 29 June 1998].
• Vermonters for Lesbian and Gay Rights. (1987, June). VLGR discrimination and violence results. Out in the Mountains. 7.
• The World’s Women 1995: Trends and Statistics. (1995). New York: United Nations.

©2009 John Kellermeier