Doing away with repetitive drills means that classrooms can become places where kids explore interesting problems using important mathematical ideas. Students learn effectively as they record measurements of real objects, describe properties using statistics, and explore the properties of a function by examining its graph. In a geometry unit, a teacher engages the students in sighting and projecting, locating and orienting, reasoning spatially, drawing and constructing, measuring and calculating. Such exercises, over time, enable students to depend less on the teacher to tell them whether they are right or wrong. The students find opportunities to develop confidence in using mathematics.
Students explore alternate solution methods, and find possible extensions of problems.
They're encouraged to pose questions that require elaboration and allow for extensions of that dialogue.