Voltolini, 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.
Piaget describes an experiment in which children describe the nature of toy mountain constructed on a table. Young children will describe only what they see from where they stand. They do not tend to walk around the mountain, seeing things from all points of view. This is because the child's very conception of the mountain changes from one perspective to another. They do not see it as the same mountain, when view from different directions. This same phenomen is seen frequently even in adults who lack the intellectual capacity to think abstractly. For example, a convenience sample is pretty much just a snap shot from where a person stands. To "walk around the mountain" would require an abstract conception of the subject matter. How do the phenomena look from the extremes of their ranges, the midranges, etc. Experimentalists do sample in the more abstract manner because they realize the relativity of perspective while being able to conserve the abstract identity of the phenomena. They give equal weight to all the aspects as they come in and out of focus while walking around the mountain. Piaget says that it is only when the child is able to employ lattice structures in assimilation can she think abstractly. Lattice structures are logical frameworks that reveal all possible combinations. Cochran and Cox discuss lattice structures when they pioneered the factorial design in their book Experimental Designs, 1950. With lattice structures the person is capable of imagining all logical possibilities, such as revealed in factorial designs. These patterns tend to start showing up in childrens thought at about age 12 to 13 but because of something Piaget called horizontal and vertical decalage, such formal operational thinking is not found in all people nor is it employed in all areas of thinkings until much later in life and maybe never in most people. Poeple romanticize snap shots just as children fixate on the concrete here and now. In an intermediate state called concrete operational thinking, people recognize formal operations such as factorial designs but they are incapable of seeing them outside concrete contexts. These people tend to use abstractions without fully grasping their nature. Their minds are very much like naive engineers who plug parts together without really understanding the principles that govern the nature of the parts and whole. We find many such mediocre intellects among adults in statistics, people who use statistics without an understanding of the underlying abstractions that define the methods. They tend to be concretistic and oriented to practical applications, since they are bound by the immediate concrete issues in life. Even intelligent children below the age of 13 would be unlikely to work beyond concrete operations. In a sense the adult professional worlds are divided along the constraints of concrete and formal operations. The masters degree prepares a person to apply fixed operations to concrete circumstances, in recipe manner. The PhD degree trains people to think in terms of possibilities and underlying principles... they use abstraction to create new methods. The PhD is trainned to invent new operations by inspecting the abstract possibilities, and not limiting her mind to recipes. At least in good PhD programs. If you must teach statistics to children, be careful. Stick with teenagers. And remember that there is nothing commendable about helping to certify people who lack the intellectual abilities to understand statistics. With the availability of software packages that make it very easy to analyze data, many adults with compromised intellects have bought themselves degrees without comprehending the deeper nature of statistics. They do a great disservice to the public. I read a paper a few years ago concerning the ages of the best mathematicians and statisticians when they did their best work. Brilliance in number theory tends to occur early in life, on average... in the twenties. Brilliance in statistics, however, tends to be a middle age accomplishment. The article suggested that statistics is far more complex than number theory and a degree of intellectual and emotional maturity is required for significant accomplishments in statistics. It may not take much intelligence or maturity to feed numbers to a computer, but the proper practice of statistics is not for children, either those young chronologically or in terms of mental maturity. So carefully consider your goal before trying to teach or to create a trend in teaching children statistics. Really we already have enough of them making a mess of things, with masters degrees and software in hand. Why compound the problem? William Chambers "VOLTOLINI" <[EMAIL PROTECTED]> wrote in message 002301c26a30$ebe93960$de89fea9@jcvoltol">news:002301c26a30$ebe93960$de89fea9@jcvoltol... > Are kids prepared to learn statistics ? Why to teach statistics for kids ? > > I was discussing these questions with some collegues and several of them > said that kids are NOT prepared for statistical abstraction and then..... I > would like to to know about your opinion. This is not a question about "how" > but "why" to teach ! > > It seems to me that sometimes statistics can be used in classroom using real > life examples more easily than math. > > Maybe this is a question for a specialist in theory of education (any > available?) > > > Regards...... > Voltolini > > > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ > Prof. J. C. VOLTOLINI > Grupo de Estudos em Ecologia de Mamiferos (ECOMAM) > Universidade de Taubate, Departamento de Biologia > Praca Marcelino Monteiro 63, Bom Conselho. > Taubate, SP. CEP 12030-010. BRASIL. > Tel: 0XX12 - 2254165 (Lab. Zool.) ou 2254277 (Depto. Biol.) > E-Mail: [EMAIL PROTECTED] > http://www.mundobio.rg3.net/ > http://www.sobresites.com/ecologia/institui.htm > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ > > "Tutto di noi � un angelo con un'ala e > possiamo volare soltanto se ci abbracciamo" > > . > . > ================================================================= > Instructions for joining and leaving this list, remarks about the > problem of INAPPROPRIATE MESSAGES, and archives are available at: > . http://jse.stat.ncsu.edu/ . > ================================================================= . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
