The problem is that unlike the math

The problem is that unlike the mathematician, the student may easily become addicted to the automatic symbolic manipulations. If not challenged, the pupil may soon reach the point of no return, beyond which what is acceptable only as a temporary way of looking at things will freeze into a permanent perspective. When it happens, there is not much chance that the student will be able to explain his or her decisions. If asked for justification, he or she may become as confused as a centipede who has been required to tell how it moves its legs. Thus, to fight pseudostructural conceptions it may be not enough to reform the teaching method in the ways proposed above. It seems very important that we try to motivate our students to actively struggle for meaning at every stage of the learning. We must make them active sense-seekers who, as Davis (1988, p. 10) put it, would 'habitually' "interpret situations, interpret their actions, think of the meanings of symbols and meanings of symbols and operations