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Introduction and Implementation Strategies for the Interactive Mathematics Program: A Guide for Teacher-Leaders and Administrators
How the IMP® Classroom Is Different
IMP's rich curriculum and its focus on understanding require changes in the classroom. The discussion below looks at several aspects of this change:
The IMP curriculum requires an expanded role for the teacher.
Because the curriculum goes beyond mechanical skills, the teacher's role must expand as well. Not simply an imparter of facts, the teacher must also be a keen observer, a sympathetic listener, and a skilled facilitator to ensure that students progress in their learning. The teacher asks challenging questions and provokes students to do their own thinking, to make generalizations, to discern connections and relationships, and to go beyond the immediate problem by asking themselves "What if?" The teacher uses his or her expertise to provide the "glue" needed to help students tie ideas together and to clarify any misconceptions that may arise.
One facet of the teacher's role that does not change is the maintenance of a positive learning environment that conveys confidence in students' capabilities. Teachers continue to set high standards and have high expectations for every student.
The IMP curriculum requires a more active role for the student.
Just as the role of teachers changes, so does the role of students. In many traditional classrooms, a student's task is to mimic the work presented by the teacher and to find numerical answers to similar problems. But in a world that is ever changing, students need to be equipped to handle problems they have never seen before, and to handle them with confidence and perseverance.
To meet this need, the IMP curriculum is designed to give students a more active part in their learning. They work with complex and realistic situations, rather than with problems fitting a rigid format. They construct new ideas by moving from specific examples to general principles. They progress beyond simply finding numerical answers; they use those answers to make decisions about real-life problem situations. They generate probing questions for each other and challenge each other's ideas. They must justify their reasoning by explaining to the teacher and to their peers what approaches they tried, what worked, and what didn't.
The IMP curriculum involves extensive oral and written communication.
Many students think of math class as the one place where they don't have to write a complete sentence or say anything more complex than a single answer. The IMP classroom is a radical departure from this image.
Through POWs, daily homework, and in-class activities, IMP students are constantly communicating in writing about mathematics. Many assignments ask them to synthesize ideas, which may mean summarizing a week or more of concept development in their own words. Students are sometimes asked to write reports as if they were professional consultants hired to give advice about a problem. During class, students are talking with each other about mathematics and making oral presentations about challenging problems.
By communicating their ideas to others, both orally and in writing, students reach deeper levels of understanding. Questions from classmates require student presenters to refine and clarify their thinking. Such opportunities to explain, defend, and convince others of their ideas help IMP students to develop and hone communication skills that will be important to them in school and on the job.
In the IMP classroom, students learn both teamwork and independence.
IMP students spend much of their in-class time working together in teams; the curriculum promotes this type of interactive learning through its use of complex problems. In or out of class, they are encouraged to talk and do mathematics with other students, with teachers, and with parents. They learn to share ideas, build on each other's efforts, communicate, and take risks.
At the same time as students are expanding their ability to work productively with each other, they are also gaining independence as learners and thinkers. Because the curriculum demands a more active role from them, they demand more from themselves. The result is a classroom in which students take individual and joint responsibility for their own learning.
In IMP, teachers assess student learning according to a variety of criteria.
Assessment in the IMP classroom is an ongoing, daily process. Neither timed tests nor multiple-choice or short-answer questions are adequate for assessing what teachers value most - real understanding of and ability to use mathematical concepts. Assessment in IMP is varied and is designed to help students understand what is important in mathematics.
Therefore, assessment of individual students in IMP is done using a variety of tools, including daily homework assignments, oral presentations, contributions to the group or whole-class discussions, Problems of the Week, in-class and take-home unit assessments, end-of-semester examinations, student self-assessments, and student portfolios.
The IMP curriculum incorporates the new technology of graphing calculators.
The IMP curriculum incorporates graphing calculators as an integral part of the development of mathematical ideas. These calculators are always available to students, and the students decide when to use them. They come to regard the calculator as simply another tool to use, like paper and pencil, in working on problems.
This technology enables students to see mathematics and problem-solving in a different way. They can focus on ideas and not get bogged down by tedious computation; they can do experiments, trying hundreds of examples; they can formulate conjectures and test them quickly; and they can solve problems based on real-world situations. They use the technology to create simulations, develop mathematical models, and create graphics.