Jean Piaget's cognitive-developmental stage theory states that children in middle childhood are in the concrete operational stage. At this stage, children can solve problems logically, but they have not yet developed abstract thinking. Children in this stage grasp inductive logic but may struggle with deductive logic. Children may also grasp reversibility by understanding the relationships between various categories—for example, the child can know that her dog is a collie, a dog, and an animal at the same time. In the classroom, a child can know that the fraction three-fourths and 0.75 are the same amount.
The child can focus on things he/she can see but may have trouble grasping symbolic concepts. The child has a grasp of conservation, meaning that the child understands that one candy bar is the same as that same candy bar broken into smaller pieces.
The child in the concrete operational stage is less egocentric than a younger child. The child starts to understand that others may not see the world the same way he/she does and is able to start to feel empathy towards others. Children at this stage are starting to grasp how others may view situations, which is the beginning of abstract thought.
It is important that children in this stage of development grasp certain concepts such as addition, subtraction, multiplication, and division as these are key to understanding mathematical concepts requiring abstract thinking such as algebra and calculus. This stage in Piaget's theory lasts from approximately ages seven to eleven.