This document reports the rationale, design, and execution of a longitudinal investigation of the intellectual achievement effects of a cognitively oriented preschool for disadvantaged Mexican-American children in San Jose, California. Seven groups of children ages 3-5 were studied. Two groups were exposed to two ten-week successive summer sessions of training prior to entry into kindergarten. Their program emphasized cognitively structured small group experiences with 4-5 children in each group. Group leaders were local Mexican-American high school students working under the supervision of experienced primary teachers. The other five groups were comparison groups; two were from outside the geographical area and three were from the school attendance area of the training groups. Seven hypotheses were tested through gathering and processing psychometric data from school-related achievement ability tests. Results were compared longitudinally across groups to determine the early advantage of specific cognitive training. All groups were tested at regular intervals and evaluations of in-school performance were made through kindergarten, first and second grades. In general, there were short-term gains but later, few differences existed between the training and comparison groups. An appendix provides samples of the training lessons plus information about project matters. (WY)