However, when questioned on the paths taken to arrive at the conclusion, highly gifted students may be unable to explain the sequence of thinking they followed. They may get a visual image of an intricate set of relationships and be unable to translate their thinking process in such a manner that others can follow it. Often the gifted student who has difficulty putting calculations on paper is at risk of being suspected of cheating. Because of the differences in speed and quality of learning, gifted students need a curriculum that combines acceleration and enrichment. Acceleration includes progressing through material at a faster pace with less repetition or at an earlier age.
Enrichment is the modification of the density, depth, diversity, and complexity of the curriculum.
One of the most widely held and damaging myths about gifted children is that acceleration will jeopardize a student's social and emotional well-being. Parents are often told that while their child is different than other children the same age, he or she must learn to fit in. Yet researchers have repeatedly found no evidence that well-conducted acceleration causes emotional and social harm. In fact, some form of acceleration is essential if the student is to be with children of similar ability so that learning can continue. Without such interactions, such students are at risk for the emotional problems that can arise from social isolation and the prolonged severe underachievement described below.