Which stage of Piaget's Cognitive Development Theory does an individual begin to understand mathematical reasoning?

In Piaget's Cognitive Development Theory, the Concrete Operational stage is where individuals typically begin to understand mathematical reasoning. This stage occurs roughly between the ages of 7 and 11 years old. During this period, children develop the ability to think logically about concrete events. They gain a better understanding of the concept of conservation, which allows them to comprehend that quantity does not change despite changes in the shape or arrangement of objects. Additionally, they start to grasp the use of operations such as addition and subtraction, and they can solve problems involving physical objects and real-life scenarios effectively.

Children in this stage are also able to classify objects into different sets and can understand the relationships between them, which underpins their growing mathematical skills. In contrast, the other stages either occur before this stage (like the Sensorimotor and Preoperational stages) or address more abstract and hypothetical reasoning (such as in the Formal Operational stage). These characteristics illustrate why the Concrete Operational stage is key for the development of mathematical reasoning in children.