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What Are Students Doing?
Interacting with each other, as well as working independently, just as adults do.
Using textbooks as one of many resources. Students should know how and when to use manipulatives (such as blocks and scales) and technology (such as calculators and computers) as problem-solving tools.
Applying math to real life problems and not just practicing a collection of isolated skills. Lots of time is allowed for solving complex problems.
Seeking a best solution among several solutions to a problem. Students can explain the different ways they reach these solutions, and defend the choice of one over another.
Working in groups to test solutions to problems with each group member highly involved.
Communicating mathematical ideas to one another through exapmles, demonstrations, models, drawings, and logical arguments.
Working in teams to challenge and defend possible solutions. Students help each other to learn. |
What Are Teachers Doing?
Guiding students in exploring multiple solutions to any problems; challenging students to think deeply.
Moving around the room to keep everyone engaged in productive work.
Encouraging students to raise and discuss questions about math for which there are no textbook answers. Rather than simply answering these questions, teachers are helping students to gain mathematical competence and confidence by finding their own solutions.
Guiding students in making appropriate use of manipulatives and technology.
Promoting student use of inquiry and creativity. Students are moved to higher levels of learning by pursuing alternative approaches to solvving a problem or by proposing new problems that are variations on, or extensions of, a given problem.
Bringing a variety of learning resources, including guest presenters, into the classroom in order to increase learning options for all students.
Working with other teachers to make connections between disciplines to show how math is a part of other major subjects that students are studying.
Using assessment that focuses on problem solving and understanding rather than on memory and speed.
Helping all students to explore career opportunities that use the mathematics that they are learning. |
