Which stage in Piaget's theory is characterized by the ability to think mathematically?

The Concrete Operational Stage is characterized by the ability to think mathematically and logically about concrete events and objects. During this stage, which typically occurs between the ages of 7 and 11, children develop skills in logical reasoning, understanding the concept of conservation (the understanding that quantity remains the same despite changes in shape or arrangement), and can perform operations that involve tangible objects. This stage marks a significant advancement in cognitive abilities from the earlier stages, as children begin to think more systematically and can solve problems involving arithmetic in a concrete manner.

In contrast, the Sensorimotor Stage focuses on infants' interactions with the world through their senses and motor actions, while the Preoperational Stage is characterized by symbolic thinking and egocentrism but lacks the logical reasoning necessary for mathematical operations. The Formal Operational Stage, which follows, allows for abstract thinking and hypothetical reasoning, including advanced mathematical concepts, but it extends beyond the concrete manipulations seen in the Concrete Operational Stage.