A study had two aims: to explore the ability of pupils of grades 4-7 to give operational evidence of generalizing in selected numerical situations, and to study the effects of differing manners of verbalizing a generalization on the retention of the ability to use the generalizations. Pupils (18) from each of grades 4-7 in a public school were randomly chosen and given an individually administered discovery test consisting of the stimulus portions of instances of generalizations. For the exploratory part of the study, the number of instances required before the pupil gave correct responses, as well as the number of generalizations apparently formed, were recorded and analyzed by a grade-by-IQ level-by-sex analysis of variance and with respect to a linear model with independent variables age, IQ, arithmetic achievement, and mathematical interests. Performance on a follow-up test (one week later) based on instances of the generalizations on the discovery test was to provide information for the influence-of-verbalizing study. Indications are that most pupils can form generalizations of the type encountered, although pupils of lower IQ require more instances. With the number of instances needed as a criterion, the optimal grade level at which to offer generalizing tasks appear to be grade 6 or after. The plateau at grade 6 supports Piagetian thought, although it may be due to a plateau on computational proficiency. (Instruments and bibliography are included.) (Author/JS)