Kotovsky and Simon (1973) identified 4 basic subprocesses in their computer simulation of adult and adolescent performance on Thurstone letter series completion problems. In the 1st experiment, children from grades 1-6 were pretested on those problems, and then trained on 2 of the 4 processes as an attempt to experimentally support a correspondence between the computer subroutines and human cognitive processes. A posttest administered in the experimental and control conditions revealed a significantly greater improvement for experimental subjects, although both groups made significant gains. The children''s distributions of errors were consistent with Kotovsky and Simon''s predictions. In the 2nd experiment, children from grades 3 and 5 took 4 series completion tests without intervening training. The additional practice was sufficient for grade 5 subjects to make improvements similar in magnitude to those produced by training. Grade 3 subjects, however, made no gains. Results are related to Tulving and Pearlstone''s (1966) distinction between the availability and the accessibility of memory traces.