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Trust the Child. In a very real sense, parents using the Pittsburgh Plan are making a sincere effort to get out of the way. We are creating an environment for learning . . . . but we are not trying to teach. We are providing plenty of emotional support . . . . but we are not dominating the sessions. We are committed and constant . . . . but we are not applying pressure. By following these rules, we avoid the unintentional but very real impediments to learning that accompany most efforts to teach. In effect, we are trusting the child to learn!
When we allow a young child to learn actively, we are not just loading data into the memory of a computer; we are actually building the computer. Not only are we helping the child learn facts; we are also helping him learn to organize those facts effectively so that they can be retrieved and used when needed. And the organization of knowledge has an even more important consequence; it determines how well the child will be able to see connections and understand relationships between various facts. So when a young child learns a fact, he is doing more than just burning it into his memory; he is establishing a network of connections between that fact and his other knowledge, a network that will determine how well he can use his knowledge.
What does this mean for our purposes? When a child struggles to extract a rule or connection, he integrates it into his mental framework. In so doing, he alters and strengthens that framework, a good thing (he now has a stronger CPU in his computer). And, the new rule will be connected to his existing knowledge in a sensible way, because it was necessary for him to establish those connections in order to extract the rule. By making him work, we help him strengthen his internal architecture, and we also ensure that his new knowledge is well-integrated with the rest of his knowledge.
A child that has learned inductively will tend to have multiple perspectives, i.e., different angles and views of the same underlying concept. This will allow him to draw connections and see relationships that a more didactic learner might miss. Also, a child that learns inductively is free to tackle material using his own strengths. One child might think spatially about a math problem, while another might think logically, in a series of steps. One young reader might prefer a phonics approach to an unfamiliar phrase while another might lean more heavily on context. Each child is free to fit new information into his already-well-developed mental framework, instead of being locked into a rigid approach and a predetermined set of connections that is imposed on him – a set of connections that may well be much harder for him to internalize, since the didactic way in which they are presented may not enlist the aid of his innate language learning apparatus.
By now you see that the Pittsburgh Plan does not prescribe very much at all about the way that a child should learn. This is mostly left up to the child! The parents and the Plan materials provide a good deal of behind-the-scenes guidance, and erect a carefully structured learning environment that is designed to make maximum use of the child’s abilities. But we are agnostic when it comes to theories as to how the human mind learns math. We do not really care which method a child uses; we just want to make sure that we do two important things: (A) provide a rich variety of materials that engages the child’s full learning apparatus and ability; and (B) get out of the way so that we do not block creative learning by our preconceptions.
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