Mental imagery in mathematics

Abstract

At the elementary school level, teachers need to help each child form a basis for trusting his own thinking. For example, the authors recently asked numerous sixthgrade children for the sum of ½ + ⅓. Many of the children, even those from “culturally advantaged” schools, were unable to find a correct answer or even to attack the problem with understanding. Furthermore, many of those producing correct answers were unable to relate the process to anything very meaningful. What is worse, the children had no place to go to construct a sensible answer for themselves . They were completely dependent on their teachers to remind them about common denominators before they could proceed. If a major objective of education is, in fact, “to enable a child to get along without his teacher,” then there is still much work to be done.