Rules versus cognitive structure as bases for children's performances on probability problems

The present study compared two hypotheses about children's solutions to Piaget and Inhelder's (1975) two-set alternative choice probability problems. The first was that children follow rules that specify a temporally ordered sequence of tests and decisions (Siegler, 1981). One prediction of rules is that children who know strategies that combine variables within sets (e.g., ratio or subtraction strategies) will only use them on problems that require such strategies (conflict problems), whereas lower level (nonconflict) problems will be solved by directly comparing the values of variables between sets. The second hypothesis was that once children develop knowledge of within-set solutions to probability problems, they apply them to both conflict and nonconflict problems. The results supported the latter hypothesis. The majority of children who solved conflict problems using within-set strategies explained at least one nonconflict problem by referring to within-set combinations. Results were discussed in terms of their implications for cognitive development and for instruction.