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Mountainview High School, with a student body of about 1,700 students, graduated its first senior class at the end of the 1992-93 school year. A year before Mountainview opened, the district convened a "cadre" of teachers, administrators, and parents to plan the new school's academic program. Carol Jennings had been teaching in the district for years and was a well-known figure among mathematics teachers throughout the district and across the state. Her reputation for leadership and innovation-in her classes as well as at the state and national levels-made her a natural choice to head the new mathematics department.
Carol and the other members of the school's leadership team chose the "Five I's"-Interactive, Integrated, Interdisciplinary, Individualized, and International-as themes to guide each subject area's curriculum. In the mathematics curriculum, the new school was to have a program that would give all of its students access to the mathematics knowledge they would need to meet the district's developing mathematics proficiency list. The program was to be integrated, blending the traditionally separated disciplines of algebra and geometry, along with less traditional disciplines like probability, data analysis, and statistics. It would ask students to solve meaningful and realistic problems and tackle extended projects. It would group students heterogeneously, rather than track students based on prior achievement or some measure of "ability." It would stress cooperative learning and use of technology. And, sensibly, it would be based on curriculum materials already written.
A set of innovative integrated curriculum materials was chosen for the seventh and eighth grades. For the high school, they chose a three-year, problem-centered, "interactive" curriculum that was being written and implemented in another state. It became known as "INT," integrates mathematics "strands," links content to real-world applications, and does so in a classroom setting that encourages cooperative group work and use of technology, problem solving, and emphasis on written and oral communication. Teachers and students described the difference of the INT content as: more student-oriented than teacher-oriented; more integrated with regard to topics; more challenging than traditional math classes; more demanding in terms of writing; and more demanding in terms of thinking.
At the same time, an "alternate sequence" of Algebra I, Geometry, Algebra II/Trigonometry, Pre Calculus, and AP Calculus was offered at Mountainview. Some of the most innovative texts available were used in these classes, and many of the mathematical problems from the INT courses made their way into the "traditional classes."
The role of teachers in the INT I classes were similar in several ways. The teachers would assume the familiar position at the front of the room, speaking while students listened, but they would do so for only about five minutes. Then the teachers moved physically and pedagogically away from the center, joining the students as mathematical sense-makers and assuming the roles of problem poser, discussion participant, and observer.
The students played a central role in the INT classes. The focus in these classes was on the students' efforts, individually and in small groups, to make sense out of problem situations and their classmates' struggles to understand these efforts. Making presentations to their peers, the students assumed prominent positions as leaders of, and participants in, discussions with each other and with the teacher. A good portion of their time was spent working in groups of about four students. During this time, the students either reviewed homework or wrestled with new problems.
Pushed together in threes and fours, students' desks provided large work surfaces as they sit facing each other. In addition, none of the students had textbooks; rather, they referred to their three-ring binders and folders, which contained packets of copied materials. In their groups, the students worked through problems from the packets. When students had questions, they would either talk to the teacher individually or pose the questions before the entire class, generating class discussion.
For assessment measures, students were assigned daily homework, worked on "problems of the week" (although a bit less frequently than once per week), were given assessments (some of which are included in the packets of materials), and took "matrix finals" each semester. Additionally, teachers evaluated the extent of student's participation to class discussions and group work, attention to others, and how often they presented problems to the group. Students were also given a number of opportunities for self-assessments.
The development of alternatives to traditional assessment schemes raised several important issues at Mountainview. The first was the degree to which each component was actually used by individual teachers. Some teachers did not implement all of the assessments consistently, if at all. Additionally, tensions arose because the alternative assessment schemes were perceived by some students, parents, and teachers as being "subjective" and therefore less fair.
The 14 Mountainview mathematics teachers were grouped into teams made up of those who taught the various sections of each course. Team planning sessions for each course were a regular part of these teachers' already crowded schedules. In their meetings, the teachers discussed pedagogical issues such as how to determine the appropriate size of groups; how to incorporate the use of graphing calculators in subsequent problems for which students will use the same graph-interpret-predict approach; what sequence teachers will follow for the next few problems in the unit; and how to assess student work.
Despite these structures for discussions between teachers, there did exist breakdowns in communication between teachers in the department who were deeply divided on fundamental issues of mathematics curriculum and pedagogy.
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