This study is part of a longitudinal research project which investigated the cognitive and social development of rural children (ages 3-5, 6-8, and 9-11 years) in eight states of the U.S.A. This paper, however, reports only the cognitive development of 3- to 5-year-old subjects in rural Nebraska from 1976-1978. The longitudinal sample plus control cohorts added in 1977 and 1978 consisted of 40 3-year-old, 57 4-year-old, and 75 5-year-old children. Six Piagetian tasks from the Nebraska-Wisconsin Cognitive Assessment Battery (NWCAB) were used to collect data: (1) relations task 1 (RT1) - determines how the child seriates with one variable; (2) relations task 2 (RT2) - measures a child's ability to seriate with two variables; (3) classification task 1 (CT1) - assesses the child's ability according to his freely chosen criterion and according to a given specified criterion; (4) number-length 1 (NLT 1) - assesses the child's understanding of the conservation of number; (5) number-length 2 (NLT2) - assesses the child's mastery of conservation of length in the identity format; and (6) number-length 3 (NLT3) - assesses the child's mastery of conservation of length in the equivalent format. These tasks were administered to the three-year longitudinal sample in 1976, 1977, and 1978; to the two-year sample, in 1977 and 1978; and to the control-cohort in 1978 only. Among the results it was found that: (1) NLT2 and NLT3 proved too difficult for this age group (they were excluded from the data analysis); (2) scaled scoring on the NWCAB tasks for 3- to 5-year-old children reflected a progression from preoperational intuitive reasoning to a somewhat higher level of thinking. These findings tentatively support the Piagetian theory of cognitive structural change between the early and middle preoperational periods. (Author/MP)