Siegler and Liebert (1975) used two instructional conditions and a control condition. In
the conceptual framework condition, children were taught about factors, levels, and tree
diagrams. In the conceptual framework plus analogs condition, children were also given
practice and help representing all possible solutions to a problem with a tree diagram. All
students were provided with paper and pencil to keep track of their Wndings. Few students
in the control condition (0% of fifth graders and 10% of eighth graders) were successful in
producing the complete set of 16 factorial combinations. Students exposed to 20–25 minutes
of instruction were more successful in the case of eighth graders (50% produced all
combinations) but not fifth graders (0%). In contrast, in the conceptual framework plus analogs
condition which included 20–25 min of instruction and practice, the majority of fifth
graders (70%) and all eighth graders were able to engage in the manipulation and isolation
of variables necessary for success on this task