Concept Images , Computers , and Curriculum Change

It seems self-evident that the way to teach mathematics is to start from simple concepts familiar to the learner and to build more complex ideas through a sequence of activities growing steadily in sophistication. It is a salutary experience to learn that a curriculum carefully built in this way can cause serious difficulties in learning. The problem arises because the human mind does not operate in a logical manner. Instead evolution seems to have given us a powerful patterning mechanism that recognizes implicit regularities in a given context and leads to each of us forming our own personal concept image of a mathematical concept. By presenting mathematics to a learner in a simplified context, we inadvertently present simplified regularities which become part of the individual concept image. Later these deeply ingrained cognitive structures can cause serious cognitive conflict and act as obstacles to learning.