By Elizabeth Van Cleef
A small group of teachers huddles around a table diagramming swimming pools on graph paper, trying to determine the relationship between the area and the perimeter of the square pools. The teachers attempt to see the problem through the eyes of their students. One person derives a formula – she works with high school students. Another creates a T-chart, a tool his fourth-grade students use often. The first grade teacher notes that eventually, as the area increases, the number of squares that make the pool becomes greater than the number of squares on the graph paper that form the perimeter. The group soon launches into an examination of each other's work in an attempt to see the connections between and across the grade levels.
The teachers are part of the mathematics curriculum committee from district 52 in Maine. This small rural district in central Maine comprising the towns of Leeds, Greene, and Turner, is a recent addition to the Alliance Schools initiative.
In the Fall of 2000, Alliance staff began collaborating with the district in an effort to create a process for improving the schools’ mathematics programs. Initial work focused on building awareness around critical issues in evaluating mathematics programs and initiating a change process. Committee members learned about ways to use school data for evaluation and planning. They also looked at data from the Third International Mathematics and Science Study and reflected on how they could use findings from the study to inform their own process. Central to this early awareness work, was the opportunity for members to do mathematics together and reflect on the experience of being learners of mathematics.
Drawing on these early meetings, the group began to outline a process to revise their district's mathematics curriculum. They decided to embark on an intensive study of the NCTM document, Principles and Standards for School Mathematics as an effective way to evaluate their own curriculum. The group believes that having a sound grasp of these standards will support their efforts to refine the curriculum document and, ultimately, to improve practice and student achievement in their district.
The swimming pool problem was part of the teachers’ exploration of the algebra strand. As they go through each strand in the document, the teachers work together on problems and then bring them back to their classrooms for their students to solve. The analysis of student work that follows gives them insight into how mathematical thinking develops from Kindergarten through twelfth grade, and how that should be reflected in the mathematics curriculum document. While the process the group has chosen is time consuming, the teachers feel it is the right one. One teacher comments, "the problems we have worked on together remind me of the work and thinking that my students must do in order to solve problems, and my work lets me think about the important math that I need to guide my students towards." Bringing the problems back to the students and then reviewing student work has been a key part of the process. Teachers are finding that students at all levels are able to grapple with the problems. The very different ways they approach the problems provides insight into the students’ mathematical understandings at different grade levels and how that can develop and become more sophisticated.
Ultimately, the group will use this work to guide their selection of mathematics curriculum materials. While they have much work to do before they are ready to select materials, the group is already considering how best to support colleagues, parents, and students in the process of change. They recognize that revising the program requires much more than selecting new curriculum.