Not all constructions are of that type, however, nor should they be. Even when we are consciously working on a problem, we are not fully aware of all that we are learning. During all these activities, students construct valuable, but different kinds of, knowledge. We need to balance these times to meet our goals for students. Manipulatives make learners active.
Constructivist learners are lonely voyagers.
Rather, the phrase means that one person cannot simply and directly transmit knowledge by means of words into the mind of another person. So students do not construct knowledge alone, even though each has to modify his or her own ways of thinking and acting. Further, although inventing mathematical ideas together is important, so is learning to better communicate these ideas to others. We must rethink social relations among students and between student and teacher. For example, constructivist-oriented teachers must be skilled in structuring the social climate of the classroom so that students discuss, reflect on, and make sense of mathematics tasks.