Neo-Piagetian theories of cognitive development criticize and build upon Jean Piaget's theory of cognitive development.

Overview The neo-Piagetian theories aim to correct one or more of the following weaknesses in Piaget's theory: Piaget's developmental stage theory proposes that people develop through various stages of cognitive development, but his theory does not sufficiently explain why development from stage to stage occurs. Also published in Turkish: Mansoor Niaz has argued that Piaget's stages were merely a heuristic for operationalizing his theory of equilibration. Piaget's theory does not sufficiently explain individual differences in cognitive development. The theory does not account for the fact that some individuals move from stage to stage faster than other individuals. The idea of rigid universal stages of cognitive development is incorrect. Research shows that the functioning of a person at a given age varies significantly from domain to domain (such as the understanding of social, mathematical, or spatial concepts), that it is not possible to place the person in a single stage.

To correct these weaknesses of Piaget's theory, various researchers, who are known as neo-Piagetian theorists, produced models of cognitive development that integrate concepts from Piaget's theory with newer concepts from cognitive psychology 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 one stage to the next and individual differences in developmental rate. Juan Pascual-Leone was the first to advance this approach.

Pascual-Leone argued that human thought is organized in two levels. This is outlined in the Theory of Constructive Operators (TCO).

The first and more basic level is defined by mental power or capacity. 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 - the memory span - that one can keep in mind simultaneously at a given moment. Therefore memory span can be understood as the quantum of action of thought.https://www.researchgate.net/publication/288034156_Memory_span_as_the_quantum_of_action_of_thought

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 2–3 years of age and it increases by one unit every second year until it reaches its maximum of 7 units at 15 years of age. He studied 8,10,12 and 14 year olds and then adults and found that the development of short-term memory is because of capacity growth. He claimed that Piaget's, classical seven stages – pre-operational, intuitive, early concrete, late concrete, concrete-to-formal transitional, early formal and late formal thought – require a mental power of 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 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.

The theory of Robbie Case Based on Pascual-Leone, several other researchers advanced alternative models of capacity development. Robbie Case rejected the idea that changes in processing capacity can be described as a progression along Pascual-Leone's single line of development.Case, R. (1985). Intellectual development: Birth to adulthood. New York: Academic Press. Instead, he maintained that processing capacity development recycles over a succession of four main stages and that each of them is characterized by a different kind of mental structures. These stages correspond to Piaget's main stages of sensorimotor, preoperational, concrete operational and formal operational thought. Each of these four stages involves its own executive control structures that are defined by the medium of representation and the type of relations that are possible at the stage.

Executive control structures Executive control structures enable the person to: represent the problem situation; specify the objectives of problem solving; conceive of the strategy needed to attain the objectives.

Case maintained that there are four types of executive control structures:

sensorimotor structures from 1 to 18 months of age (i.e., perceptions and actions such as seeing and grasping). There are 3 substages in this structure. 4–8 months- Children find joy in objection movement and being able to control the movement. 8–12 months- This is the substage children divide their attention between actions and reactions. 12–18 months- In this substage the reversible relationships between an objects actions and reactions are introduced. inter-relational structures from 18 months to 5 years of age (i.e., mental representations that stand for actual objects in the environment, such as words or mental images); dimensional structures from 5 to 11 years (i.e., mental representations that are connected together by a consistent relation such that every particular case can be related to every other case, such as the mental number line where every number can be related to every other number); vectorial structures from 11 to 19 years (i.e., relations between the dimensions of the previous stage, such as ratios and proportions which connect two or more dimensions with each other).

Case also argued that development within each of these four main stages evolves along the same sequence of the following four levels of complexity (thus, structures of increasing complexity can be handled at each of the four levels): operational consolidation (when a particular mental unit specific to each of the four main stages above can be contemplated and handled, such as an action in the sensorimotor stage, a word in the relational stage, a number in the dimensional stage, etc.); unifocal coordination, (when two such units may be interrelated); bifocal coordination, (when three such units may be interrelated); elaborated coordination, (when four such units may be interrelated).

According to Case, this expansion of the capacity of short-term storage space is caused by increasing operational efficiency. That is, the command of the operations that define each kind of executive control structures improves, thereby freeing space for the representation of goals and objectives. For example, counting becomes faster with age enabling children to keep more numbers in mind.

Successive stages are not unrelated, however. That is, the final level of a given stage is at the same time the first level of the following stage. For instance, when the concept of number is well established at the final level of elaborated coordination of the relational stage it enables children to view numbers as related to each other and this is equivalent to the first level of operational consolidation of the following dimensional stage. Thus, when the structures of a given stage reach a given level of complexity (which corresponds to the level of elaborated coordination) a new mental structure is created and the cycle starts up from the beginning.

Central conceptual structures Case recognized that variations may occur in the organization and development of different domains, due to differences in how meaning is organized in each of the domains. Specifically, Case recognized that there are central conceptual structures. These are "networks of semantic notes and relations that have an extremely broad (but not system-wide) domain of application and that are central to children's functioning in that domain."Case, R., Okamoto, Y., Griffin, S., McKeough, A., Bleiker, C., Henderson, B., & Stephenson, K. M. (1996). The role of central conceptual structures in the development of children's thought. Monographs of the Society for Research in Child Development, 61 (1-2, Serial No. 246).

Case and his colleagues identified central conceptual structures for quantities, space, social behavior, narrative, music, and motor behavior. Each of these structures is supposed to involve a set of core processes and principles which serve to organize a broad array of situations; for example, the concept of more and less for quantities, adjacency and inclusion relationships for space, and actions and intentions for social behavior. Thus, these are very broad structures in which many executive control structures may be constructed, relative to an individual's experiences and needs.

For example, in the central conceptual structure that organizes quantities, executive control structures to solve arithmetic problems, to operate balance beams, to represent home locations according to their street address etc., may be constructed. In short, central conceptual structures function as frames and they provide the basic guiding principles and raw conceptual material for the construction of more locally focused concepts and action plans, when the need for them arises.

Learning the core elements of a central conceptual structure opens the way for fast acquisition of a wide array of executive control structures, although this does not generalize to other conceptual structures. It remains limited within the one affected, indicating that there may be variations both within and across individuals in the executive control structures that can be constructed within each central conceptual structure. These variations depend on the environmental support provided to each structure and on the individual's particular preferences and involvement.

The theory of Graeme S. Halford