A Lesson

If you’ve been checking up on me, you’ve probably noticed that I’m a bit behind on my blogs. I blame the weather. All this rain and grey skies—it’s totally ruining my creative energy. Remind me never to move to Seattle.

Enough of that: This is supposed to be an introduction to my project. Rose Ellen wrote a very nice intro to our group project; allow me elaborate on what this project has become for me.

As I mentioned in an earlier blog, it all started with an Ed. D student named Eliza. In mere passing she’d mentioned Social Justice Math to me. Initially, I was not intrigued. I thought it sounded like socio-Marxist mathematics. Unsurprisingly, that’s what a lot of people think it is.

As I dug in deeper, I came to appreciate it as something more—as a way to see the world as it truly is using real-world statistics and mathematics. Teaching mathematics in this way is very contextual: It makes math real.

For our project, we chose to drive around Newark and see what popped out at us. Jin drove. Rose-Ellen took pictures, and I looked out the window. As we drove around the lower-income areas we kept seeing the same few things: liquor store, Western Union, Church, Fast-food joint, grocery/tienda, and used car place. Every few blocks: Rinse and repeat.

At first it started out as a joke, an open query: Just how many check places were there in Newark? Or in the central ward? Were there more in different wards? And what could that mean? By the end of the trip, however, I knew that we had a potential lesson.

The lesson or ongoing project would start with an assignment:

“In a group, travel 1 square mile around your neighborhood and make a chart of each kind of business. Be sure to keep a tally of each kind. Be sure also to record the addresses for each kind of business.”

For Newark, teachers could assign different square miles if students were older, didn’t live in Newark, and/or had access to a car. Further, I see this lesson as being appropriate for grades 8 and up. The idea here would be to encourage students to cull data. To elicit further interest, teachers would explain to teachers that this was a part of a new investigation called: “What Makes a Neighborhood.” When pressed what such an investigation would cover, teachers could say that it would allow them to learn about the places in which they live.

In the next class, students would bring the data they culled together. Here they would determine the average number of each business per square mile per ward. Taking this idea a step further, teachers would ask students: “Now that you have this statistic, how many of each business is in each ward? And further, what is the ratio of people per ward to each business type?” Challenged in this way, the teacher would facilitate a discussion with the students on different ways to approximate areas, and in particular, unusual areas like Newark’s wards. A variety of methods would be introduced: among these would be Pick’s Theorem. For homework, students would determine an area of each of the wards using different approximation techniques. After class (or during if they have access to computers) students would also post the results of their discussions onto a class webpage. They should also be developing a class map using Google maps. On this map, they can post the location of each kind of institution/service/business.

In class 3, the teacher would facilitate a discussion with students on the different areas determined for each ward. The teacher would then pose another question: Given the number of square miles in each ward, what are good approximations of each number of businesses? Students discuss in groups and then discuss in a teacher-facilitated discussion. Here the idea of ratio, rate, and proportion is discussed as students instruct others on how to determine the approximate number of services/businesses available in each of the wards. For homework, each student would look at the number of businesses and types of each per ward and discuss in a journal the equity of said distribution. Students would also note the distribution of certain institutions in the different wards—e.g., banks, gyms, hospitals, supermarkets—and discuss this equity, as well. In particular, students would assess if people in the different wards require better access (e.g., more, but less costly transportation, or a better distribution of services per ward), to institutions and services that are unavailable in the different wards.

During the fourth lesson period, the teacher might ask her students to discuss what they wrote about in their journals, directing the class in particular to the notion of distance, time, and money required to arrive at certain institutions: e.g., banks, gyms, hospitals, or supermarkets. As a final activity, student will use the map they have been developing to determine the most effective route from their home to each service/institution. Using www.njtransit.com, they will also determine if they can take a bus there, how much walking is required of them, and how much money the trip will require. After this activity is completed, the class will come together, and report their results. From these, averages will be determined. These will go on their webpage. Students can also write about their discoveries in their math journals. They should discuss how they feel about the costs, and speculate how this affects the constituents in their community.

If time is provided, the project could be extended to the suburbs, and this time to encompass 5-square-mile blocks of similarly affluent neighborhoods. Here, as before, students would record the different number of businesses/services/institutions represented in that block. If students do not possess cars, this part of the project could be altered in the following ways:

1) It could be developed into a field trip, wherein different groups of students would go with an assigned parent or teacher to a different part of a very affluent suburb and canvas the neighborhood in a way similar to the listing above; or

2) This project of three to four lessons could be developed at the same time by another or several mathematics classes in affluent suburbs in the state.

At the beginning of the project, students would be told that they would be working on a social project with students at these other schools and that each class would be developing their own web pages to illustrate that learning. Similar in scope to the 3-day activities posted above, classes in the affluent suburbs would be responsible for accumulating data about affluent areas. Ideally, these classes should look at 5 square-miles. If this is unrealistic, however, the teacher can partition a suburb into square-mile blocks and assign each to each pair. Those students can then do the same activities as their urban counterparts: cull data on neighborhood businesses, determine the type and number of each kind per 5-square miles and use this approximation as a way to estimate the number of and type of each business for each suburb. As determined, this information would go up on each class web page. Students from all classes would be required to look at each for each stage of the project.

With the data available on each class webpage, each teacher should require their students to compare life in the suburbs to life in the urban areas (using their data as a metric). Out of this activity, students should analyze the different ratios, distances, number of institutions, costs, and distances/times from home to each institution developed by the classes. Students should determine numeric and symbolic ways to compare these times and draw generalizations from the data. After completing these activities, students should discuss their findings in a teacher-mediated discussion. The teacher should bring up the notion of access, and ask students about the fairness of each situation. She should ask them if there are ways to ameliorate the inequalities in access, and provide them with ideas if the class has none. For homework, students should reflect on the ideas discovered from this project and what might do to affect their community positively in regards to the lessons learned from the project.

And that, I think would be a really cool and interesting project. Certainly a lot more interesting than anything I ever did in math class.