When can children understand abstract symbols and complex problems?

Children typically begin to understand abstract symbols and complex problems during the concrete operational stage of cognitive development, which usually occurs between ages 7 and 11. However, the ability to grasp more abstract concepts and solve complex problems continues to develop into adolescence, particularly during the formal operational stage starting around age 12. Individual differences in cognitive development can lead to variations in when children achieve these skills. Factors such as education, environment, and personal experiences also play significant roles in this process.