Geometry of Inequality

Spring 2005

A math activity explores some of the causes of the 1992 "Rodney King Riots" in South Central Los Angeles

	Illustration: David McLimans

By Andrew Brantlinger

I taught a summer course last year to a group of students in a neighborhood school on Chicago's north side. They were there because they failed geometry during the regular school year. Most of the students were non-white, and 85 percent of the school's students were classified as low income. Many of the students in my class were not on track to graduate in four years and had histories of failing mathematics.

When I interviewed my students, many of them said they didn't see how mathematics related to their present and future lives outside of school. So, I chose to teach a lesson I hoped would help them connect geometry to issues of fairness and see how math could be relevant.

I began the lesson by asking my students if they had heard of Rodney King and the riots that took place in South Central Los Angeles in 1992. The five African-American students claimed they knew who Rodney King was, while many of the other students did not. One of my female African-American students explained that Rodney King "got beat by four white cops" and described a bit of what she knew about South Central. I added that the disturbances broke out in South Central and other neighborhoods in Los Angeles after a mostly white jury acquitted those four white police officers.

After this brief introduction, I asked the students to work in groups and come up with what they felt to be average ratios of people to movie theaters, liquor stores, and community centers in the United States. Obviously, a community's resources comprise more than simply theaters and liquor stores, and might also include parks, quality schools, libraries, diverse shopping areas, and adequate public services like water and sewage, not to mention access to good jobs. But the figures I had were from a National Public Radio story that aired shortly after the 1992 riots, and I was really struck by the disparity in South Central between the number of theaters and community centers on the one hand, and liquor stores on the other. I decided to use these statistics as the core of my lesson.

Initially, three of the four groups were reluctant to come up with estimates for the people-to-resource ratios. I think this was, in part, because I was asking them an unusual mathematics question—one with no exact answer. A few students insisted I had a "right" answer in mind, despite my reassurances to the contrary. In some sense they were correct; I did push them to justify estimates that seemed unreasonable to me.

Next, I asked the groups to use their people-to-resource estimates to make predictions about the number of movie theaters, community centers, and liquor stores in a "three-mile radius" in South Central circa 1992. Having used this activity with preservice teachers a few months earlier, I realized that estimates for the number of community places in South Central can be made without doing much mathematical thinking. I required my students to engage with the geometric issues that the problem presents. I hoped a better geometric understanding would improve students' critical understanding of the situation.

Because I also wanted my students to connect their everyday knowledge—of things like population distribution and size of city blocks—to the problem, I presented each of the four groups with a map of Chicago and asked them to draw a scaled-down circular region with a three-mile radius on it. Again, I wanted students to think mathematically, so I asked the class to figure out how many square miles and square city blocks would be in such a region.

Some students responded by drawing a square-mile grid on the map, while others used more ad hoc approaches to finding the area. As I went from group to group I heard students ask each other: "How big is a square mile?" "Where is a square mile on the map?" "Can we use A = πr² to find the area, or do we have to count squares?" When two of the groups asked me if A = πr² would give them the same result as counting the number of square miles inside the circle, I responded, "Try to find it both ways and see if they give you the same answer."

Approximating the number of city blocks in a circular region with a three-mile radius fostered a good discussion, in part because there was some degree of confusion. That is, my students were used to thinking about linear blocks as a measure of distance but they were apparently not used to thinking of square blocks as a measure of area. One group of students wanted to know if they could find the area of a square mile by counting the linear blocks on the perimeter of a square.

A student in a second group initially argued that the area of South Central would be 48 blocks because the diameter of the circular region is six miles and there are eight city blocks per mile. But one of her groupmates disagreed, stating, "No, it should be 96 blocks because you have to fill the circle up on both sides of the diameter." I asked this second young woman to show us the 96 blocks on the map. Shortly after beginning her count, she looked up, smiled, and claimed that 96 blocks would be far too few to fill up the circular region.

When I returned to this group later on, they explained that they used π(24)² to calculate the approximate number of blocks ( ≈1810) in the circular region. This solution—using a radius of 24 linear blocks instead of three miles—was slick. I had not considered it myself. When I asked them if they were sure of their answer, they showed me they could fill up a quarter of the circle with rectangles, which would give an area of about 450 blocks when combined, one fourth of 1800.

Working through the geometric aspects of the activity took the better part of a class period. At the end of the day, I asked all the students to jot down new estimates of how many liquor stores, community centers, and movie theaters they thought were in South Central circa 1992. I was a bit frustrated that several students were still reluctant to give estimates. I had assumed that this mathematical work would make answering this question easier. Four or five students insisted they would first have to count movie theaters, community centers, and liquor stores in their own neighborhoods to come up with an answer they felt comfortable with.

We didn't have time for students to count in their neighborhood, so I provided them with data from Evanston, a mixed-income suburb that borders Chicago to the north. When we revisited the South Central problem the next day, I put up an overhead that stated that Evanston was a "fairly typical community" with an area of 8.5 square miles and approximately 75,000 people, seven liquor stores, eight community centers, and three movie theaters. (I used the Evanston yellow pages to estimate the numbers.) The students were able to quickly figure out that approximately three Evanstons would fit into the area of South Central and that a little more than three Evanstons would have about nine or 10 movie theaters, 26 community centers, and 27 liquor stores.

As my students read these results to me I told them, "I see this activity as a critique of our society as a whole, and our government, and not of the people who live in South Central." I said, "According to National Public Radio at the time of the riots, there were zero community centers and zero movie theaters." This surprised them.

Then I asked the class to guess how many liquor stores they thought were in South Central at the time of the LA riots. They called out a range of numbers from five to 100.

When I stated that the actual number of liquor stores was 640, Dele* let out an "Ooooh... " and Maya exclaimed, practically shouting, "What!?"

José said, "Oh man, that's cool," and laughed.

Dele said, "All they want them to do is drink."

Then he added, "All they do is drink."

Upon hearing this second comment, I repeated that I did not intend for this activity to be a critique of the people who lived in South Central. "Look, there are no jobs," I claimed.

"That's why they be on the streets," responded Dele.

Later on, when students were writing up their individual responses to the activity, Dele's groupmate Tony asked me how I thought the overabundance of liquor stores in South Central was connected to the riots. I explained that I meant there was probably good reason to rise up, considering the lack of alternatives and the gross resource inequities between what people in South Central had compared to, say, people in Evanston. Tony looked me in the eyes and nodded, but I don't remember him responding to me verbally.

Potential Pitfalls

When I reflect on my South Central lesson, I see two pedagogical problems. First, I had not expected this lesson to potentially reinforce the dominant worldview that the problem with South Central is the people who live there. My students know that some white teachers buy into prevalent myths that blame working-class blacks, Latinos, and whites for poverty and other social ills. In hindsight, it makes a lot of sense that Tony asked me to re-explain where I stood on the root causes of the riots.

The next time I do this activity, I will bring in additional resources to clearly set up the sociopolitical context of the problem and hopefully avoid the possibility of reinforcing negative stereotypes. Excerpts from an article by Mike Davis called "Who Killed Los Angeles?" that discuss the root causes of the riots—like economic disinvestment and racist government policy—would be helpful in this regard.

Second, I shied away from opening up the political whole-class conversation that might have happened at the end of the lesson. The students reacted to the shocking numbers, but then I spoke at them about my beliefs. While I did make an attempt to open up the floor, I should have asked them to discuss what they thought were the root causes of the riots and what they thought about Dele's two conflicting comments: "All they want them to do is drink," and, "All they do is drink." I also wish I had asked Dele who the "they" he was referring to really are.

Instead of pushing my students to enter the conversation, I rushed on to the planned end of the activity in which I explained Brazilian educator Paulo Freire's notion of "reading and writing the world." I ended the activity asking the class to write individual responses to the (perhaps leading) questions: "Is this activity a meaningful way to begin to read the world using mathematics?" and, "Does the use of mathematics help one understand more deeply aspects of our reality?"

In truth, the problem of opening up a political conversation was not entirely due to my lack of pedagogical expertise; three of my students made it clear to varying degrees that they expected me to teach the depoliticized form of mathematics they were used to. One of my African-American students repeatedly opted out of critical activities like this one, choosing instead to work alone on geometry worksheets. I wondered if her actions meant she doubted my assertion that math could be socially relevant.

Despite its problems, I believe this activity was a powerful experience for many students. Many students did seem to think we should discuss issues of fairness in school. Typical written responses to the activity read, "We should have more jobs and more community centers; then you wouldn't have to worry about the riots," and, "The government should put more money in [South Central]."

Finally, I think Dele spoke for many of his fellow students when he told me they were learning "more about real facts" in critical activities like this one than in decontextualized geometry activities. This intrigued me because I have heard many mathematics educators claim that traditional mathematics is as close to the truth or "real facts" as students will ever get. Clearly, Dele did not see it this way.

Andrew Brantlinger (abrant@northwestern.edu) is a secondary mathematics teacher and a graduate student at Northwestern University. "South Central" was adapted from an activity developed by University of Illinois-Chicago professor Eric Gutstein.

* All students' names have been changed.

Spring 2005