new material. Teaching in small steps requires time, and the more effective teachers spent more time presenting new material and guiding student practice than did the less effective teachers. In a study of mathematics instruction, for instance, the most effective mathematios teachers spent about 23 minutes of a 40 -minute period in lecture, demonstration, questioning, and working examples, In contrast, the least effective teachers spent only 11 minutes presenting new material. The more effective teachers used this extra time to provide additional explanations, give many examples, check for student understanding, and provide sufficient instruction so that the students could learn to work independently without difficulty: In one study; the least effective teachers asked only nine questions in a 40 -minute period. Compared with the successful teachers, the less effective teachers gave much shorter presentations and explanations, and then passed out worksheets and todistudents to solve the problems. The less successful teachers were then observed going from student to student and having to eyplain the material asain. training, Imaginative teachers have found ways to involve all students in answering questions. Examples include having all students: - Tell the answer to a neighbor. - Summarize the main idea in one or two sentences, writing the summary on a piece of paper and sharing this with a neighbor, or repeating the procedures to a neighbor. * Write the answer on a card and then hold it up. - Raise their hands if they know the answer (thereby allowing the teacher to check the entire class). - Raise their hands if they agree with the answer that someone else has given. Across the classrooms that researchers observed, the purpose of all these procedures was to provide active participation for the students and also to allow the teacher to see how many students were correct and confident. The teacher may then reteach some material when it was considered necessary. An alternative was for