Piaget's Cognitive
Operations
[Concrete Operations Stage]
7-11 Years of age

Reversibility
Ability to perform mental inversions, or to mentally undo a sequence of actions. This enhances ability to figure out mathematical problems, and draw conclusions about observed outcomes on the basis of prior relationships--not just concrete or tangible appearances. This evidences sensitivity to distinctions between what seems to be and what really is.

Decenter
The child can focus on multiple features of an object at the same time. Takes into account all relevant perceptual data and can focus on both the height and the width of the glass at the same time.

Reciprocity
Ability to recognize that a change in one feature is balanced by an equal and opposite change in another. The length in one row is compensated for by the density of the other row.

Conservation
The ability to recognize that two equal quantities remain equal even if one is changed in some way--as long as nothing has been added or taken away. Is not evident all at once, but emerges gradually over three stages. Gradually acquires the ability to conserve number, length, mass, area, weight, and volume of objects and substances--although not all the properties of objects and substances at one time, because these abilities emerge in sequence.

The Concept of Number
One to one correspondence. May do a lot of re-counting at first.

Classification
An understanding of "more than" and "less than" and of the fact that one number is included in another. That # 2 is part of # 3, which in turn is included in #4. Ability to understand that there is a hierarchical relationship between subordinate and superordinate classes. This has far-reaching implications in understanding of the social world and the multiple roles people play, and it also enhances the ability to learn such subjects as geography

Seriation
The ability to arrange objects in an orderly series--it demonstrates systematic, planful thinking on the part of the child. Helps the child construct a logical view of reality. Able to engage in transitive reasoning.

Transitive reasoning
The ability to recognize a relationship between two objects by knowing their relationship to a third.

Information Processing

Selective Attention
The ability to focus on relevant aspects of the environment and to disregard irrelevant aspects.

Memory
Ability to pay attention to a task enhances children's capacity for memory. Child can build upon what she already knows, and this aids her ability to solve problems and acquire new knowledge.

Organization
The grouping of items to be remembered into groups or clusters of information. Can remember more words in a list because of the ability to organize.

Metamemory
An intuitive understanding of how the memory works--acquired during middle childhood school years.

Metalinguistic Awareness
Enables the child to think about language which increases the child's communicative competence.

Communicative Competence
An ability to think about what one is being told and to judge whether the message being conveyed is clear. Acquire ability to understand complex grammatical sentences and, as well, more precise meaning of words and their correct use.

Syntax
The underlying grammatical rules that specify the order and function of words in a sentence, develops throughout the middle childhood years as the child becomes better able to understand the connections between words.

Understanding Metaphors
Language also becomes increasingly nonliteral--to understand that some words have a literal as well as a nonliteral meaning. A metaphor relies on the use of a word or a phrase out of context to suggest an unexpected similarity. Sweet and bright, for example.

Humor
Love to engage in play on words and to tell jokes that involve double meanings.