• Concrete Operations
– Mental representation is used to solve
• Space-children at this age can find their way to
and from school
• Measurement skills
• Causality- children understand how physical
attributes effect an object. Number of objects on a
– Categorization- seriation- ordering objects
• Transitive inference-understanding the relationship of two
objects by knowing the relationship of each to a third object
– A child is shown three sticks. One green, one yellow and one
– She is shown that the yellow stick is longer than the green one
and the green one is longer than the blue one. She knows
without comparing them that the yellow one is longer than the
• Class inclusion-understanding relation between whole and its
– A child understands that when shown a bunch of flowers-10, 7
roses and 3 carnations- and asked which is more the roses or
the flowers, they understand that roses are part of the
subcategory of flower.
• Inductive and Deductive reasoning
– Inductive-Jere is a dog. My dog barks. So does your
dog. All dogs must bark. The problem is that they
may run into an exception.
– Deductive- All dogs bark. Spot is a dog. Spot barks.
Begin with class and then move to a specific.
• Developed by Alfred Binet
• Mental age divided by chronological age
multiplied by 100.
• 7 mentally, 6 chronologically=1.17
• 70 or <
• 130 or >
• No two children are alike
• No two children learn in the identical way
• An enriched environment for one student is
not necessarily enriched for another
• In the classroom we should teach children to
think for themselves
Marion Diamonds (2002)
Your brain is like a chandelier with ten different light
bulbs of different intensities.
• A second grade teacher has children read
a section of the story about a child who
lives on a farm. In this section, fall and the
harvest are described. After the children
have read part of the story, the teacher
asks comprehension questions: What did
the boy do when his father scolded him for
playing and not working? How did he feel?
What did he do next?