Diversity Content as a Gateway to Deeper Learning: The Statistics of Sexual Orientation
Michele DiPietro, instructor in the Department of Statistics and associate director of the Eberly Center for Teaching Excellence, Carnegie Mellon University
Carnegie Mellon University
Academia has embraced queer studies as a legitimate
area of scholarship, but course offerings in this field
are still predominantly in the humanities. Yet the current
debate about civil rights for LGBT people is framed
around questions like, "Does nature or nurture cause
sexual orientation? Can people change their sexual orientation?
How many people are gay, transgendered, or in a same-sex
relationship?" These questions can be statistical or
scientific in nature, with answers that require researchers
to gather data, synthesize information, draw conclusions,
and generalize those conclusions to a larger population.
To address the gap between queer studies and statistics, I decided with the support of my dean to develop a first-year seminar on the statistics of sexual orientation. To my knowledge, this is the first and only course specifically devoted to LGBT content to originate in a department of mathematics or statistics. My goal in designing the class, which I have taught since 2004, was to equip students with the statistical and critical thinking tools they would need to take informed positions in ongoing debates. I created the course on a gamble: I had a hunch that diversity content and statistics would act synergistically and reinforce each other. I hypothesized that the controversial nature of LGBT content would act as a "hook" and motivate deeper learning.
In traditional introductory statistics classes, every homework problem starts with a random sample from a population. But there is no such thing as a random sample of LGBT people, because there is no "master list" to draw from. Thus statistical studies of LGBT people require other sampling methods that tend to be less efficient statistically but that reflect how research is carried out in real life. I hoped that the course's research-based, scientific perspective would allow students to clearly articulate competing theories and hypotheses about the LGBT population, and evaluate the evidence for or against each theory.
The course covers content similar to that of a traditional course, but I introduce each statistical topic as a tool needed to answer a specific question related to LGBT issues. For example, the question of how many people are LGBT introduces the concepts of sampling and estimating proportions. Furthermore, because many LGBT people will not self-identify in surveys, the question raises the problem of bias and how one can identify, reduce, or estimate it. Similarly, the "nature versus nurture" question introduces hypothesis testing. I also use specific studies to introduce various tests (T-test, ANOVA, Chi-Square). Because the course content centers on diversity as well as statistics, I use a variety of assessments to measure students' learning, including mathematical problem sets, journals, concept maps, and student presentations. Below I describe three sample activities.
Minimal groups. I start the course with an activity borrowed from Isbell and Tyler (2003). I project an image of dots on the overhead screen and ask students to estimate the number of dots. After I reveal the correct number, I ask students to identify themselves as "overestimators" or "underestimators." Students then fill out a questionnaire, rating on a one-to-ten scale the extent to which overestimators and underestimators display certain qualities (for example, intelligence, laziness, creativity, thoughtfulness, dependability). I collect the data, summarize it in a table, and return it to the students, directing them to study the table for patterns that emerge. Invariably, both overestimators and underestimators discover that they rated their own group more favorably than the other group across all dimensions. Later in the course, we learn techniques to quantify this bias, but the pattern is so striking that students notice it immediately even without deep statistical knowledge. Students think of themselves as open-minded and unprejudiced, and they are horrified to discover that a simple distinction based on how many dots they estimated immediately elicits strong yet unconscious in-group versus out-group biases. This experiment highlights the need for students to become more informed about issues related to diversity and stereotypes, and it sets the stage for productive attitudes toward learning.
"Gaydar." I give students a set of photographs and ask them to classify the people pictured as gay or straight. I then reveal the subjects' sexual orientations, and students count their classification mistakes. Students learn to use the Chi-square test to analyze their data, and they also reflect on the implications of labeling people based on superficial features.
Paper analyses. In addition to the readings I assign to anchor statistical and LGBT topics, students read and analyze five scientific papers espousing theories that are often cited by opponents of LGBT rights (for example, that gay men have shorter life spans). I scaffold their analysis with a checklist that helps them become critical consumers of research. Students scrutinize each study's experimental design, measures collected, controls used, conclusions, authors' reputations, and other factors, and then decide whether they believe the study's conclusions. In some cases, we examine how the popular press represents these studies, and students realize that the media often magnify the studies' claims to the extreme. In their journals, students report that they have started to apply this analytical process to other scientific papers and even to the news.
Students usually start the course with precious little knowledge of both statistics and LGBT issues. Their initial concept maps have very few nodes and include many misconceptions. By the end of the semester, however, students display several kinds of learning gains.
Statistical knowledge. As expected, students learn a lot about statistics. Their end-of-semester concept maps are more meaningful and sophisticated than those they create at the beginning of the course. By the semester's end, students are able to apply basic statistical techniques to solve standard problems. They are also able to read social science articles critically and with alertness to standard sources of experimental or survey bias.
Intellectual development. Students' journal entries document a developmental transition. To use Perry's terminology (1968), most students start the course--and college--in a "dualistic" stage, where they see knowledge as black and white with very little gray in between, and where they would not even consider questioning sources. In contrast, students' later entries come from a position of "multiplicity," with students perceiving knowledge as theory or opinion which they feel empowered to critique or challenge. Their learning becomes personal as they enter a dialogue with sources and with each other. Several students' final journal entries reflect "relativistic" positions: the understanding that not all opinions are equal, and that it is possible to evaluate a position based on evidence. These students make extensive reference to the studies they read throughout the course and are comfortable citing statistics to defend their positions.
Intercultural competency. I have witnessed three dimensions of development in intercultural competency. Students become increasingly comfortable putting themselves in other people's shoes, most notably the shoes of transgendered people. These students' positions move from abstract ("I don't believe in transgenderism") to personal ("I wonder how I would feel if my dad told me he decided to transition"). Entries also show a decrease in stereotyping of, or even discomfort with, LGBT people. Finally, some students begin educating others (friends, roommates) about LGBT issues, especially about the harm of using homophobic language.
It seems my gamble paid off. LGBT content does indeed support deeper statistical learning. Likewise, a solid statistical toolkit helps students engage the complexity of LGBT debates instead of settling for simplistic answers.
Isbell, L., and J. Tyler. 2003. Teaching students about in-group favoritism and the minimal groups paradigm. Teaching of Psychology 30 (2): 127-130.
Perry, W. 1968. Forms of intellectual and ethical development in the college years: A scheme. New York: Holt, Rinehart, and Winston.