The gym roars with 50 different conversations. Around the walls, and throughout the room, students stand before their projects. Most are pasted on poster board, others on reused pizza boxes. Over the din, the girls describe their work to fellow students, teachers, and a handful of “willing listeners”—volunteer adults (parents, mostly) who have come to find out what the kids have learned.
Along the back wall, the 5th- and 6th-grade classes present their findings from the school waste audit. The 1st- and 2nd-grade students have studied how hard it is to live on the “welfare diet”—the contents of the average food bank recipient’s weekly allotment—and have created graphs to show what they, and their families, have eaten that week. The older girls have prepared individual projects. Melanie, 7th grade, wondered if children with autism received the same amount of funding as children with other disorders, and her results are strikingly demonstrated on a bar graph. Mi-sun, 9th grade, used a line graph to demonstrate that Korean students, among all nationalities, are most likely to commit suicide. Andrea, 7th grade, used a scatter plot to investigate the correlation between GDP and carbon dioxide emissions. On a table, the results of the 6th-grade class’s collective research is illustrated, with labeled bags of rice offering a three-dimensional representation of what the world eats every day: China has a huge pile; Iceland just a few grains.
The lights flicker on and off, and the conversations die down. “We’re halfway finished,” Michelle calls out. “It’s time to switch! Those of you who were presenting should now listen, and those who were listening should now present!” The noise picks up again.
The Social Justice Data Fair has been held at the Linden School in Toronto for the past several years. It is an opportunity for our math students to use data management skills to study issues they’re concerned about. The fair is an example of how our independent, girl-centered school for students in grades 1 to 12 tries to include topics of social justice in our curriculum. Compared with other Toronto-area private schools, our school is quite culturally diverse, and we enroll students from many nontraditional families. Most of our families support learning math through the lens of social justice. (Parents have commented how much they enjoy having their daughters bring math class conversations to the dinner table.)
We, like all teachers, feel the pressure to cover a packed curriculum in a limited amount of time. In Michelle’s case, data management accounts for only a few expectations in her 7th-grade curriculum—what one would expect to cover in a few classes. Preparing students for the data fair takes several weeks, putting the crunch on other important topics. There is increasing evidence, however, that case studies enable students to form meaningful connections with their mathematics and lead to greater learning—especially for girls. The Ontario curriculum, which we follow, also encourages making real-life connections, and this helps justify our program.
The Social Justice Data Fair really “came into its own” by its second year. For the first year, not all classes participated. Some teachers needed to see how it worked before committing to participate. This type of initiative requires all the participating teachers to create meaningful course content beyond their textbooks. It has been exciting to see how each teacher supports students to make those connections in age-appropriate and grade-relevant ways.
Start by Asking Questions
We teach girls, and girls have historically received messages that they are not good at math. These messages are often self-fulfilling. A social justice pedagogy, in addition to introducing social justice topics into the curriculum, must reduce barriers to learning for all students. It must engage students as agents of change in the world, and encourage them to view their skills—in math and elsewhere—as tools for enacting that change.
The traditional school curriculum takes today’s social and environmental conditions mostly for granted. The world just is; students are not encouraged to approach it with a curiosity about how it got to be this way. Social justice math, on the other hand, begins with our curiosity about the world and especially about the world’s unfairness. Thus a key part of the curriculum at the Linden School is promoting the habit of thoughtful questioning. In math classes, we use the inquiry process to reinforce the idea that knowledge is built from evidence that the students collect themselves. For example, we teach principles of geometry by conducting experiments.
“What do you know about triangles?” Beth asks her grade 5/6 split.
“They have three sides,” blurts out one student.
“And three angles,” adds another, “and if all the angles are the same, it is an equilateral triangle.”
After this, the students find it harder to come up with ideas.
“Are there any other rules that triangles have to follow?” Beth prompts. “For example, do the angles have to be a certain size?”
The students are not sure about this. Slowly, Brianna raises her hand. “It depends on how big the triangle is. If it is bigger, the angles can be bigger.”
“Well, let’s find out. Today, I want each of you to run an experiment on triangles. Just like you would in science. Think of a question you wonder about triangles, then find an answer. How will you do that?” Beth turns and writes four words on the board: Question, Hypothesis, Observations, Conclusion. “Those are the steps you’ll need to follow today.”
“Not ‘Procedure’?” asks Natane.
“No, not today.”
“Yes!” That means less writing. Natane pulls out a piece of paper.
The students are familiar with the scientific method. Through years of in-class investigations and annual science fair projects, we hope they see that the process of science allows anyone at all to ask a question and to find an answer. Experiments, run by people from all walks of life, formally and informally, form the basis of everything we know about the world around us. It is not a stretch, then, to apply this idea to math. Later, when we prepare for the social justice data fair, the girls are primed to use math to answer their own questions.
Keisha is constructing different triangles to see what will happen when she adds up the angles.
On her third triangle, she shouts, “Hey, do they always add up to the same thing? I’ll try a bigger one.” She does, using her ruler to draw a triangle that covers the whole of a new page. Double-checking with her protractor, she writes down the size of each angle. “Again!” she shouts. The girls around her laugh.
“So,” says Beth, “why do you think that happens?”
By the end of the class, Keisha isn’t quite sure why her angles always add up to 180 degrees. That’s not important, at least not yet. What’s important is that she asked a question and found an answer. And the answer, most importantly, didn’t come out of the textbook or from the teacher. Social justice education is not just about recognizing problems; it’s also about helping students recognize their own power to find answers. They need to trust in their own authority—not just ours.
Something similar is happening in the 7th-grade classroom, where students are learning about percent. Michelle is encouraging students to present different strategies for solving problems. This reinforces the idea that questions can be approached in different ways, that the person doing the inquiry doesn’t uncover the answer so much as she constructs it.
“Who can calculate this percent?” asks Michelle, referring to a problem on the board.
Mahera comes up to the board and writes her solution.
“Is this correct?” Michelle asks the class.
“No, you did the steps in the wrong order,” suggests Marla.
“Yes, it’s right, but I do it a different way,” says Nicole.
“What do others think?” prompts Michelle.
A lively conversation follows, where students discuss the validity and merit of different ways of approaching the problem.
After Michelle gets the students’ attention again, she continues the lesson. “Now it’s your turn. Come up with your own percent questions.”
Making Meaning Out of Numbers
The Social Justice Data Fair takes place in April, after nearly a full year of practicing inquiry skills in math and in other classes. To prepare for it, the girls start, once again, by asking questions. The 5th/6th-grade class started with a question that had bothered some of the students: Why do the garbage, recycling, and compost get all mixed up in the school containers? After gathering the contents of all of the school’s containers, we took the waste up to the roof—the location of our urban school’s playground—and, amid some squealing, began the messy, smelly task of sorting and weighing it. The girls were particularly interested in locating “forbidden” trash like disposable Starbucks containers, which are no longer allowed into the school. They also wanted to know how much of the total waste was food packaging, which is discouraged under our Litterless Lunch program. After determining the total masses of categories of waste (like paper and aluminum), as well as measuring the amounts of waste that were sorted incorrectly by the school community, we had an interesting set of primary data. We added this information to the results of our school survey, which gathered information about our population’s habits and attitudes when it came to generating and dealing with their garbage. From there, the students used further questions and a variety of graphs to answer them. Which floor generated the most waste? Were we producing more waste than in previous years? Did the location of bins have an effect on how well sorted they were?
The upper grade students, who work independently on their projects, start by selecting an appropriate topic. Some girls find it easy to come up with their topic; they arise out of issues they’re passionate about. The 7th-grade class had learned about national and per capita carbon dioxide emissions when we studied scientific notation, and many students were affected by the Copenhagen Climate Conference, so we had quite a few projects on this topic. Alina and Brigit were both concerned about species extinction, so Alina focused on tigers and Brigit chose elephants. We help students who have trouble choosing something by brainstorming topics as a group, looking in the newspaper for ideas, and describing projects from previous years. The goal is for each girl to be excited about using math to dig deeper into a topic that interests her.
Once the students have selected a topic and have had it approved, the next step is to develop a thoughtful research question. We discuss as a class what makes an investigable question, and then students work to hone their questions into ones that are clear, specific, and can be answered using quantitative data. The students keep in mind that they must produce at least two different types of graphs, and this affects the questions they pose. Sometimes the question development process takes some time, since students must do some preliminary research to find out what kind of data are available. After some research, 7th grader Nicole’s concern about homelessness in Toronto turned into two questions: What diseases most commonly affect Toronto’s homeless population (bar graph)? And what reasons do homeless people have for not sleeping in a shelter (pie chart)?
The next step is collecting data. Students decide whether it is more appropriate to gather primary or secondary data for their topic and question. For example, Helen, a 7th grader who loves green sea turtles, worried about their declining population. Michelle, her teacher, suggested some online resources, and Helen learned about the age distribution of turtles in the Pacific. Then she analyzed her data to determine what types of graphs would best represent it. From there, she looked for trends and outliers, and was ready to start compiling her work for presentation.
Fair Day Arrives
The day before the fair, we have a dress rehearsal. The students practice presenting their projects to their classmates, and get feedback. Michelle had planned to act as facilitator for her class, to prompt discussion and to ensure that the space was safe for students to risk asking questions and risk making mistakes. To her delight, no facilitation is necessary: She just sits back and watches math happen.
Heidi stands by her bear-shaped project board. “I learned a lot from this project, but I still want to know if stopping climate change would help the polar bear populations grow again, and I also wonder if polar bears will adapt to having less ice by changing their habits,” she concludes her presentation. “Are there any questions?”
A half-dozen hands shoot up. “I really liked your presentation, by the way. I love your board! I was wondering, why did you decide to use a bar graph to represent the populations?” asked Melanie.
“Why did you focus on those regions?” Alina wants to know.
“It’s neat how you made the bars different colors,” comments Alisa.
“Do you know how they find those numbers?” asks Nita.
Michelle sees students proudly sharing the product of several weeks of hard work, including background information, graphs, and analysis. She is familiar with the projects, and she has worked with the students to develop good research questions, find data, and use spreadsheet software to create graphs. But what impresses her are the discussions that follow the presentations. Students engage each other on the topics they researched, and on the math they used to analyze their data. They use their data management skills to justify their choices and defend their conclusions. We want students to feel that they have legitimate questions and comments to share about the math, about the thinking that their classmates were sharing.
Before students leave the gym on the afternoon of the fair, they are asked to hand in their “passports”—a brochure in which they’ve answered a series of questions about the student presentations they attended. The last question is “What did you learn?”
Kayla: “There are more females than males living with low incomes.”
Madison: “Black men are more likely to be executed than white men.”
Georgia: “8th graders from Singapore have the highest test scores in mathematics.”
Meirion: “Green sea turtles are going extinct.”
Zaketa: “The average North American purchases 4,000 calories of food each day, but throws 30 percent away.”
Nita: “There is too much social justice to fit in this box!”