Imagine a Title I school in which around 80 percent of the students qualify for free and reduced-price lunch. Now picture, at this Spokane, Washington, school, a leadership team that could no longer ignore the need for a focus on mathematics instruction. Why? Quite simply, because fewer than half of the 480 students at this school, Sheridan Elementary, were meeting the mathematics state standard.
In spring 2005, the state standardized assessments showed that 73 percent of our students were performing at or above grade level in reading. There was simply no reason for only 46 percent of those same students to be performing at or above grade level in math. After one year of intentional collaboration around student achievement in math, the percentage of our students at or above grade level leapt to 56, earning Sheridan an Academic Improvement Award from the Washington Office of the Superintendent of Public Instruction. Math achievement continued to rise in the following school year, with 65 percent of students at or above grade level in spring 2007. How did we do it?
Choosing to Collaborate
The Spokane Public Schools has made teacher collaboration a priority, adjusting school start times and setting aside one hour each week from 8:00 to 9:00 a.m. for staff members to come together. Schools can use the time to meet as a whole staff, break into grade-level teams, or use any other configuration that might help staff members work together.
The work in Sheridan Elementary's math collaboration took place in grade-level groups in which we considered state standards and familiarized ourselves with the state assessment test and item specifications. Through conversation, supported with research, we identified math problem solving as our target area.
Solving the Problem-Solving Problem
John Van de Walle (2004, 2006) heralds math problem solving as the activity through which students develop true understanding. The Sheridan staff decided to implement a regularly scheduled problem-solving time.
As the school's instructional coach, I met regularly with other instructional coaches in the district and collected strategies that had worked in other schools. I brought these ideas back to Sheridan to help us discuss and plan instruction during grade-level meetings.
Our first steps were to concentrate on the structure and expectations of the problem-solving sessions. We arranged to have four to five adults (for example, resource teachers, instructional assistants, tutors, and volunteers) in each classroom for 30 minutes, three times a week. This enabled us to place four to six students in small groups with an adult leader, much like literacy groups. At the beginning of each session, the teacher and I led a whole-group demonstration; then the class practiced together; finally, the students broke into problem-solving teams.
We made sure that the problems we chose were clearly related to the targeted standards. For example, for the standards related to understanding decimal representation in money and using mathematics to define and solve problems, 4th grade students were given the following problem:The total cost of a glass of juice and an ice cream cone is $2. If the ice cream cone costs $1 more than the glass of juice, how much does each item cost?
The adults received the problems ahead of time so that they would have time to become familiar with them before class. To help the group leaders prepare, we took 15 minutes on Monday mornings to discuss with them the learning goals and the difficulties students might have.
Slowing Students Down
Research indicates that students often rush through reading a problem and begin solving without fully understanding it (Johnson, 2000). The 3rd, 4th, and 5th grade teams agreed on a process that would make students spend more time considering the problem before beginning to solve it (Chapin, O'Connor, & Anderson, 2003; Hyde, 2006).
- I need to find out . . . (a brief description of what they need to do).
- I know . . . (a list of important information that the problem provides).
- Solve . . . (the steps undertaken to solve the problem, with all pictures or numbers labeled).
- Answer . . . (a complete sentence that answers the question posed in the problem).
Discussing Thought Processes
Simply guiding students through problems was not enough for our problem-solving teams. We wanted to enable students to discuss their thinking, strategies they used, and connections they made in mathematics (Chapin et al., 2003; Johnson, 2000). The 3rd, 4th, and 5th grade teachers had a goal of asking more higher-order thinking questions, which fit nicely with our goal of conducting classroom discussions of problem-solving activities.
- How could you verify . . .
- How would you explain . . .
- What alternative would you suggest for . . .
- What would happen if . . .
These discussions enabled teachers to identify student misconceptions that were not evident on paper. As students explained their thinking and answered probing questions, they learned to correct their own mistakes.
The problem-solving discussions engaged even our most challenging students. The questioning strategies set a higher expectation for deeper thought. Students also took greater pride in their finished products because of the opportunity they had to present their own work to the class. The next step was to encourage students to self-assess and reflect on their learning.
Assessing Together
Students assessed themselves using a rubric with a four-point scale in which a score of three or higher indicated expected grade-level performance on the problem. We began by introducing students to the rubric and scoring some papers in front of the class. Then we scored some papers as a class, and eventually students began scoring their own papers in their small teams. This practice was woven into the ongoing math conversations.
A 4th grade teacher took the rubric one step further by adding an opportunity for reflection. Her students received a half sheet of paper that had a place for the score and some lines for them to reflect on why they deserved that score. We found that students were honest with themselves and quickly became familiar enough with the tool to closely gauge an appropriate score.
When we began focusing more on student reflections in mathematics, students became more engaged in building a deeper understanding of mathematics (Stiggins, 2006). Students could understand their goals, where they were according to the learning goals, and what they needed to do to achieve those goals.
Making Time for Change
Thanks to the time spent collaborating within grade-level teams and between grade levels, our teachers have changed their instructional practices. These changes didn't occur because of a prescribed program or a day spent in a professional development class. Real improvement like this happens when teachers pool their practical knowledge by working in teams (Schmoker, 2006).
The Sheridan staff identified a need, discussed instructional strategies, and used data to determine effectiveness or to adjust instruction. The collaborative time spent together was focused on student work and data that guided teachers' conversations toward instructional practices. This collaborative atmosphere is integral to our school environment.
Our teams have continued to monitor their goals and identify new ones. For example, the 3rd grade team has begun exploring ways to encourage student reflection during the entire math period, not just the problem-solving sessions. The 4th grade team is planning for its students to be more involved in identifying academic goals. The 5th grade team has decided to focus on differentiation throughout math instruction.
The key for all the teams is collaborating around a common goal and basing their conversations on authentic student work and data. These reflective practices build our school into a true collaborative learning community and help us to provide a meaningful education to all students.
