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Neo-Piagetian theories of cognitive development
Piaget's theory of cognitive development has been criticized on many grounds. One criticism is concerned with the very nature of development itself. It is suggested that Piaget's theory does not explain why development from stage to stage occurs. The theory is also criticized for ignoring individual differences in cognitive development. That is, the theory does not account for the fact that some individuals move from stage to stage faster than other individuals. Finally, another criticism is concerned with the nature of stages themselves. Research shows that the functioning of a person at a given age may be so variable from domain to domain, such as the understanding of social, mathematical, and spatial concepts, that it is not possible to place the person in a single stage.〔Greenberg, D. (1987). (Chapter 19, Learning ), Free at Last, The Sudbury Valley School. The experience of Sudbury model schools shows that a great variety can be found in the minds of children, against Piaget's theory of universal steps in comprehension and general patterns in the acquisition of knowledge: "No two kids ever take the same path. Few are remotely similar. Each child is so unique, so exceptional" (Greenberg, 1987). Retrieved June 26, 2010.〕 To remove these weaknesses, a group of researchers, who are known as neo-Piagetian theorists, advanced models that integrate concepts from Piaget's theory with concepts from cognitive and differential psychology.〔Demetriou, A. (1998). Cognitive development. In A. Demetriou, W. Doise, K. F. M. van Lieshout (Eds.), ''Life-span developmental psychology'' (pp. 179-269). London: Wiley.〕〔Demetriou, A., Mouyi, A., & Spanoudis, G. (2010). The development of mental processing. Nesselroade, J. R. (2010). Methods in the study of life-span human development: Issues and answers. In W. F. Overton (Ed.), ''Biology, cognition and methods across the life-span. Volume 1 of the Handbook of life-span development'' (pp. 306-343), Editor-in-chief: R. M. Lerner. Hoboken, NJ: Wiley.〕〔Demetriou, A. (2006). Neo-Piagetische Ansatze. In W. Sneider & F. Wilkening (Eds.),''Theorien, modelle, und methoden der Endwicklungpsychologie. Volume of Enzyklopadie der Psychologie'' (pp. 191-263): Gotingen: Hogrefe-Verlag.〕〔Morra, S., Gobbo, C., Marini, Z., Sheese, R., (2007). ''Cognitive development: Neo-Piagetian perspectives.'' London: Psychology Press.〕
==The theory of Juan Pascual-Leone==
Initially, neo-Piagetian theorists explained cognitive growth along Piagetian stages by invoking information processing capacity as the cause of both development from the one stage to the next and individual differences in developmental rate. Juan Pascual-Leone was the first to advance this approach.〔Pascual-Leone, J. (1970). A mathematical model for the transition rule in Piaget’s developmental stages. ''Acta Psychologica, 32'', 301-345.〕 Specifically, he argued that human thought is organized in two levels. The first and more basic level is defined by mental power or capacity. That is, this level involves processes that define the volume and kind of information that the individual can process. Working memory is the functional manifestation of mental power. The capacity of working memory is usually specified in reference to the number of information chunks or units that one can keep in mind simultaneously at a given moment. The second level involves mental content as such. That is, it involves concepts and schemes about the physical, the biological, and the social world, and the symbols we use to refer to them, such as words, numbers, mental images. It also involves the mental operations that we can carry on them, such as arithmetic operations on numbers, mental rotation on mental images, etc. Pascual-Leone proposed that the increase of the number of mental units that one can represent simultaneously makes the persons able to handle more complex concepts. For instance, one needs to be able to hold two mental units in mind to be able to decide if one number is bigger than another number. To be able to add them, the person needs to be able to hold three units, that is, the two numbers plus the arithmetic operation to be applied, such as addition or subtraction. To be able to understand proportionality, one must be able to keep in mind five units, that is the two pairs of numbers to be compared and their relation.
According to Pascual-Leone, mental power is equal to 1 scheme or unit of information at the age of 2–3 years and it increases by one unit every second year until it reaches its maximum of 7 units at the age 15 years. He claimed that the classical Piaget's stages of pre-operational, intuitive, early concrete, late concrete, transitional from concrete to formal, early formal, and late formal thought require a mental power of 1, 2, 3, 4, 5, 6, and 7 mental units, respectively. Having a lesser degree of mental power than required by a task makes the solution of this task impossible, because the necessary relations cannot be represented and computed. Thus, each increase in mental power with age opens the way for the construction of concepts and skills up to the new level of capacity. Falling short or exceeding the mental power that is typical of a given age results in slower or faster rates of development, respectively.
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