The group that was taught to count by tens did better than those who counted in the ordinary way. The poorest results came from the group that did not count past ten-those who grouped objects into tens and ones and only later in the process used the normal number names. Two studies examine preschool children's knowledge of the effects of the physical processes of addition and subtraction on the relative amounts of two sets. Results indicate that children are very competent at these elementary problems though they often do not use numbers. They can select the set with more elements when the two initial sets are equivalent in number and operations are performed on one or both sets and when the initial sets are unequal but small in absolute size or very different in size.
Most children recognize the inverse relationship of addition and subtraction.
The effects of both grade level and distraction setting on problem-solving performance were highly significant. The results suggest that distractors play a key role in nonverbal problem solving. Much more research, however, is needed if the role of distracters in nonverbal problem situations is to be clearly understood .