The attainment of formal operations: a comparison of probability concepts in deaf and hearing adolescents

In a series of six experiments deaf and hearing adolescents were compared on attainment of formal operations in Piaget's theory as represented by performance on probability problems. Performance of deaf subjects provided a desirable control comparison, since their knowledge of probability concepts was most likely acquired outside school classrooms. The probability problems were usually binary choice situations that required no verbalizations and were designed to illuminate strategies, as well as to indicate conceptual stage. Two experiments, one a long-term training study of over two years' duration, used supplementary preadolescent subject groups. Most of the hearing adolescents and many of the deaf adolescents attained the formal operatory level for probability concepts according to the criteria described by Piaget and Inheldermtheir criteria can be criticized, however, as insufficiently demanding, although they do point up the difficulty of defining the place of computational abilities in formal operationsmresults from several experiments suggested a second and higher level of formal operatory attainment around the ages of 14 to 15. Further theoretical insights were obtained regarding the implicit rules that frequently appeared to guide subjects' choices; a surprising variety of strategies were reported. Analysis of choice tendendies showed consistent avoidance of calculations and selection of the choice with the greatest absolute rather than relative frequency (or area) even when these strategies produced systematic errors. Subjects were generally unable to combine probability information from two different sources. In the long-term training experiment spontaneous improvement was shown by children at formal operatory ages even without training, but not by younger children. Deaf adolescents performed as well as hearing adolescents on easy problems, but they made more errors on several types of more difficult problems; Deaf adolescents were also less consistent than the hearing in use of rules, and in several experiments they showed a two- to three-year performance lag.