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nd the pendulum’s weight).
By disjunction: “It’s either this or that” (e.g. it’s either the length or the weight).
By implication: “If it’s this, then that will happen” (the formation of a hypothesis).
By incompatibility: “When this happens, that doesn’t” (the elimination of a hypothesis).
On top of that, he can operate on the operations -- a higher level of grouping. If you have a proposition, such as “it could be the string or the weight,” you can do four things with it:
Identity: Leave it alone. “It could be the string or the weight.”
Negation: Negate the components and replace or’s with and’s (and vice versa). “It might not be the string and not the weight, either.”
Reciprocity: Negate the components but keep the and’s and or’s as they are. “Either it is not the weight or it is not the string.”
Correlativity: Keep the components as they are, but replace or’s with and’s, etc. “It’s the weight and the string.”
Someone who has developed his or her formal operations will understand that the correlate of a reciprocal is a negation, that a reciprocal of a negation is a correlate, that the negation of a correlate is a reciprocal, and that the negation of a reciprocal of a correlate is an identity (phew!!!).
Maybe it has already occured to you: It doesn’t seem that the formal operations stage is something everyone actually gets to. Even those of us who do don’t operate in it at all times. Even some cultures, it seems, don’t develop it or value it like ours does. Abstract reasoning is simply not universal.
Reference
A: Cleverly, J. Phillips, D.C. Visions of Childhood Influential Models From Locke to Spock. Teachers College Press, New York. 1986.
B: Oxford, R. (1997). Constructivism: shape-shifting, substance, and teacher education applications. Peabody Journal of Education, 72, 35-66.
C: Ewing, J. Kamii, C. (1996). Basing teaching on paiget's constructivism. Childhood Education, 72, 260-264.
D: Elkind, D. The Hurried Child, Growing Up Too Fast Too Soon. Addison-Wesley Publishing Company, New York. 1988.
E: Understanding Psychology. Random House, New York, 1986
F: Taylor, J. (1996). Piagetian perspectives on understanding children's understanding. Childhood Education, 72, 258-259
G: Building an Understanding of Constructivism, (http:Hwww.sedl.org/scimath/coml2ass/vOlnO3/2.bLmij. 6/18/01.
H: Boeree, G. Jean Piage . (http:Hwww. crystal inks. com/pi aget. htm). 6/18/01.
I: Smith, L. (Sept-Oct 1996). With knowledge in mind: novel transformation of the learner or transformation of novel knowledge. Human Development, 39, 257-263.
J: Papert, S. (1992). The Children's Machine: Rethinking School in the Age of the Computer. New York: Basic. 137-156.
K: Siegler (1991). Piaget's Theory of Development. 17-57.
L: Youniss, J. (Nov-Dec 1995). The skill useful classic concept of development. Human Development, 38, 373-379.
M: Beilen, H. (Mar 1992). Piaget's enduring contribution to developmental psychology. Developmental Psychology, 28, 191-204.
By disjunction: “It’s either this or that” (e.g. it’s either the length or the weight).
By implication: “If it’s this, then that will happen” (the formation of a hypothesis).
By incompatibility: “When this happens, that doesn’t” (the elimination of a hypothesis).
On top of that, he can operate on the operations -- a higher level of grouping. If you have a proposition, such as “it could be the string or the weight,” you can do four things with it:
Identity: Leave it alone. “It could be the string or the weight.”
Negation: Negate the components and replace or’s with and’s (and vice versa). “It might not be the string and not the weight, either.”
Reciprocity: Negate the components but keep the and’s and or’s as they are. “Either it is not the weight or it is not the string.”
Correlativity: Keep the components as they are, but replace or’s with and’s, etc. “It’s the weight and the string.”
Someone who has developed his or her formal operations will understand that the correlate of a reciprocal is a negation, that a reciprocal of a negation is a correlate, that the negation of a correlate is a reciprocal, and that the negation of a reciprocal of a correlate is an identity (phew!!!).
Maybe it has already occured to you: It doesn’t seem that the formal operations stage is something everyone actually gets to. Even those of us who do don’t operate in it at all times. Even some cultures, it seems, don’t develop it or value it like ours does. Abstract reasoning is simply not universal.
Reference
A: Cleverly, J. Phillips, D.C. Visions of Childhood Influential Models From Locke to Spock. Teachers College Press, New York. 1986.
B: Oxford, R. (1997). Constructivism: shape-shifting, substance, and teacher education applications. Peabody Journal of Education, 72, 35-66.
C: Ewing, J. Kamii, C. (1996). Basing teaching on paiget's constructivism. Childhood Education, 72, 260-264.
D: Elkind, D. The Hurried Child, Growing Up Too Fast Too Soon. Addison-Wesley Publishing Company, New York. 1988.
E: Understanding Psychology. Random House, New York, 1986
F: Taylor, J. (1996). Piagetian perspectives on understanding children's understanding. Childhood Education, 72, 258-259
G: Building an Understanding of Constructivism, (http:Hwww.sedl.org/scimath/coml2ass/vOlnO3/2.bLmij. 6/18/01.
H: Boeree, G. Jean Piage . (http:Hwww. crystal inks. com/pi aget. htm). 6/18/01.
I: Smith, L. (Sept-Oct 1996). With knowledge in mind: novel transformation of the learner or transformation of novel knowledge. Human Development, 39, 257-263.
J: Papert, S. (1992). The Children's Machine: Rethinking School in the Age of the Computer. New York: Basic. 137-156.
K: Siegler (1991). Piaget's Theory of Development. 17-57.
L: Youniss, J. (Nov-Dec 1995). The skill useful classic concept of development. Human Development, 38, 373-379.
M: Beilen, H. (Mar 1992). Piaget's enduring contribution to developmental psychology. Developmental Psychology, 28, 191-204.
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