[EMAIL PROTECTED] wrote: > Although some children are capable of thinking abstractly enough to > understand stats, most below the age of 13 probably are not. The work of the > child psychologist Jean Piaget supports this assertion. Piaget described > different stages of thinking in kids. Children before the age of 7 tend to > think mostly with sensori-motor rhythms and habits but they are capable of > preconceptual thought that employs unstable mental images. For example, > show a five year old a ball of clay and ask them how much clay there is. > Then roll the ball into a sausage. They will probably say there is less clay > now because it is thinner than the ball. Then roll the sausage out into a > thin string. The child will probably now say that there is more clay, since > it is longer. The child fixates on particular aspects of the object with out > seeing that other aspects compensate for the changes. The clay may be longer > now but it is also thinner. The sausage may be thinner but it is also > longer. The young child's mind is incapable of grasping the equilibrium > between the aspects. This is very much a problem for children who are trying > to understand scientific sampling.
It would be worth reading recent research on child development (since Piaget). Children below 13 _are_ capable of abstract thought and reasoning, but both adults and children find absract concepts hard. You can change children's answers to these "conservation" tasks by changing the context in which they are asked. Part of the problem is the relationship between adult experimenter and child (e.g., work by Paul Light in the UK). [My favourite example is from my PhD superviser. As a student at Oxford she replicated the liquid conservation task in a variant using orange juice. The children had no problems realizing that the glasses contained equal ammounts.] A different example is in the use of analogy (which requires abstraction). Usha Goswami has shown that children can understand and employ analogies provided they use familiar relations. Similar findings occur with adults. You can show the same in perspective tasks (such as the mountains task used by Piaget). Children and adults both find it harder to take a different perspective. The most parsimonoius explanation is that it is computationally harder to shift perspective etc. (easy to show in computer models). Children have fewer cognitive resources (or are less skilled at marsahlling them) and therefore show bigger decrements in performance than adults (and the decrements are easier to detect). Thom . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
