Piaget's Concrete Operational Stage: 8 Logical Operations

Group Operations: Concrete

1. Formation of a Hierarchy of Classes

• a) 7-8 years: Can include classes.
• b) 8-9 years: Can classify to represent flowers in clusters. For example: What will a large branch be? If you cut all the flowers in the garden, would any remain? Can a daisy be in the "Flowers" category without changing the sign? If you take all the daisies from the box, would any flowers remain?
• c) They have difficulty in representing objects that involve mental representation. For example: If all animals died, would any birds remain? If all animals die, would some animals remain? Can these two cells be under the same sign? Children cannot respond to these problems until 10 or 12 years of age.
• d) In the absence of specific references, Piaget found that 75% of children aged 9 years denied that Genevans are Swiss.

2. Seriations: Orderly Relation

• a) 7-8 years: Are able to coordinate the comparison of a pair of sticks and build an ordered series.
  • Easier when it comes to size and color depth.
  • Ability to coordinate weight by 10 years.
  • 9-10 years: Can solve difficult problems in oral form.
• b) Problems of verbal order for children from 9 to 10 years lead to a return to the intuitive thinking of the preoperational period.
• c) Can solve order problems when they have physical objects.
• d) The mastery of these two operations (classification and order) allows the acquisition of the concept of number.

3. Substitutions

4. Symmetric Relations

• a) 6 years: Understand that a distance does not change, whatever the direction.
• b) Around 8 years: Understand that two siblings are each other's brother. They begin to understand the relationship of friends, fellow players, and factors of a product.

5. Multiplication of Classes

• a) There are numerous examples using classifications in pairs. Riddles such as: "A yellow flower that starts with 'R'", "No pairs between 10 and 20", "A continent of 13 letters to the south of Ecuador".
• b) Children at 9 years are usually able to classify objects by color, shape, and context.

6. Multiplication of Series

It is possible to identify a square area in a street plan.

7. Concept of Time

• a) The child must understand that a sequence of increasing age corresponds to a decreasing series of dates.
• b) The concept develops very slowly until the age of 9 or more.

8. Family Tree

• a) We can group individuals and objects, making one term cut across several. For example, the class of triangles, or pairs of points between 10 and 20.
• b) In this way, we can make a family tree.
• c) Also, the classification of forms results in a family tree lesson.

A) The 8 "group operations" of logic become accessible to children during the period of concrete operations. Thought that conforms to them obeys certain laws:

• Law of composition or closure
• Law of inversion
• Law of association
• Law of identity
• Law of tautology. Regarding numbers: the law of iterations.

B) In the domain of the 8 groups, children are able to keep all quantities that they did not have access to in the previous period. Thus:

• 7-8 years: Number, length, and solid
• 9 years: Area
• 10 years: Weight
• 11-12 years: Volume