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.
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.