The purpose of the study was to examine the informal and more formal mathematical notions of children of ages four to six, and to evaluate the interaction between these two sets of notions. Two groups of problems were given to 60 children. The first included 14 Quantity Tasks in the form of stories which were illustrated by manipulable items. The second set, the Arithmetic Tasks, required the child to count as high as he could, to count backward, to count by tens, to tell what number comes before and after a given number, and to identify cardinal numbers and ordinal positions. Results showed that part of the difficulty children had with tasks appeared to involve misinterpretations of the word "more," that there were few misinterpretations in tasks where the number of items used was very small or where there existed a vast difference between the number of items in the groups, that a range of formal notions was found, and that an interaction of formal and informal notions could be defined. (Author/DT)