Throughout the "Overcrowding at Our School" project, the students had opportunities to insert their interests, goals, and purposes into the curriculum. For example, after several days of measuring classrooms and calculating areas, students formed small groups to pose their own problem about a particular aspect of the school space. Beatriz asked students to identify one issue dealing with overcrowding at the school and to discuss how they might use mathematics to find out more about the situation. As students posed problems that mattered to them, their desire to understand and affect the overcrowding increased their engagement in mathematics and enhanced the learning that occurred.
Angel, a tall and rather quiet African-American student, was not a frequent participant in problem-solving discussions before this unit. But when the class began to investigate overcrowding at their school, there was a notable shift in Angel's level of engagement. Angel was extremely concerned about the school's bathrooms.
She found it difficult to navigate among the other 10 or 12 people in the tight space. She noted that all females in the school, including 103 students and 15 teachers, had to share one rather small facility with only three working stalls, and a very small sink station. So when Beatriz asked Angel's group what aspect of the school space they wanted to investigate, the choice for Angel was obvious: "We want to know, why are the girls' bathrooms so small?"
Angel's group constructed a floor plan of the restroom, measured its dimensions, calculated the area, and then analyzed the bathroom space based on the number of stalls, the estimated wait time during peak use periods, and the space available for waiting. Angel spoke about how the opportunity to investigate an issue she cared about made her feel "mad curious" and drew her into the mathematics. She commented, "It was easier to do the math this way, instead of just learning it straight, like solving a problem, because we would actually really get into it, and that made it easier."
For other students, the opportunity to investigate real issues not only increased their engagement, but also pushed them to construct and apply important mathematical concepts.