A 1-year postdoctoral research training program prepared one trainee in early childhood education during 1966-67. Flexible arrangements allowed this mature trainee to plan and follow his own program in consultation with the staff of the Research and Development Center in Educational Stimulation at the University of Georgia. Experimentation in ongoing school programs enabled the trainee to develop an inventory of early mathematics accomplishments for 5-year-olds, which was then used systematically by him in New York State as well as by others in Follow Through programs. Development of this group test of mathematics achievement is described, including the specification of detailed administrative procedures necessary with young children. The postdoctoral research training program was judged effective for its purpose, following the original proposal to provide a high level professional apprenticeship. Suggestions are made for improvement of the USOE research training program by expanding its scope to include establishment and support of advanced training centers to meet current retooling demands for high level educational personnel. (Author/DR)