Final answer:
Preoperational children lack the cognitive ability known as 'class inclusion', which is the understanding that objects can belong to more than one category at the same time. This understanding develops in the later concrete operational stage, along with the principles of conservation and reversibility, which contribute to logical thinking.
Step-by-step explanation:
The concept you're asking about, where preoperational children lack the ability to understand that objects can be simultaneously part of more than one group or category, is known as the lack of the capacity for class inclusion. Jean Piaget referred to this developmental aspect in the context of his theory of cognitive development. According to Piaget, during the preoperational stage of development, children from approximately 2 to 7 years old have not yet developed this cognitive ability. This means that a child might not understand that a dog can be both an animal and a pet at the same time, which would be an example of understanding class inclusion.
Another key cognitive concept that develops later, around the concrete operational stage (7 to 11 years old), is the principle of conservation. This is the understanding that certain properties of objects remain the same despite changes in the object's appearance. It is also during this stage that children start to learn the ability of reversibility, meaning they recognize that objects can be changed and then returned back to their original form or condition. These developmental milestones contribute to a child's growing logical and mathematical abilities. They are able to make generalizations and understand relationships that are essential for rational thought.