WHAT MAKES CERTAIN ARITHMETIC WORD-PROBLEMS INVOLVING THE COMPARISON OF SETS SO DIFFICULT FOR CHILDREN

Arithmetic word problems with an unknown reference set, such as ''John has 7 eggs. He has 4 eggs fewer [more] than Peter. How many eggs does Peter have?'' are considerably more difficult for children than problems with an unknown compare set (second sentence: ''Peter has 4 eggs more [fewer] than John.'') Six experiments with 1st graders and kindergartners investigated reasons for this finding. Experiments 1-4 revealed that neither difficulties in processing the personal pronoun nor the use of key word strategies could explain the difficulty differences. Experiment 5 showed that most 1st graders were not aware that the difference between 2 sets can be expressed by either ''In Set x there are n more objects than in set y'' or ''In Set y there are n fewer objects than in Set x.'' Experiment 6 indicated that this lack of access to flexible language use is what makes compare problems with an unknown reference set so difficult.