At what stage of childhood development does logical thinking and mathematics typically begin to emerge?

The development of logical thinking and mathematical abilities generally begins to emerge during the Concrete Operational stage. This stage, according to Jean Piaget's theory of cognitive development, occurs roughly between the ages of 7 and 11 years. During this time, children start to think more logically about concrete events and can perform operations that involve tangible objects.

They begin to understand the concept of conservation—recognizing that quantity doesn’t change just because its shape does—and can categorize and organize objects based on multiple criteria. These cognitive advancements allow for the application of logical reasoning to solve mathematical problems, laying the groundwork for more complex operations.

In contrast, the preoperational stage, preceding Concrete Operations, is characterized by symbolic thinking and egocentrism without yet mastering logical thought processes. The formal operational stage, which follows, involves abstract thinking and hypothetical reasoning, but it is not where foundational logical or mathematical skills first develop. The sensorimotor stage, which occurs before the preoperational stage, focuses on physical interaction with the environment rather than logical reasoning or mathematics.