Final answer:
Children typically begin to identify with a parent of the same sex during early childhood, around 3 to 6 years of age. This identification process consolidates as they reach school age, from 6 to 10 years old, when they further develop their gender roles and self-concept.
Step-by-step explanation:
Children tend to identify with a parent of the same sex during the phallic stage of psychosexual development, according to Freudian theory, which is around ages 3 to 6. However, modern psychological understanding suggests that this identification can continue and solidify as they further develop their self-concept and gender roles throughout their early and middle childhood years. By the time they are around 6 years old, children begin to more clearly define their group memberships and might show signs of identifying with same-sex role models, which can include but isn't limited to parents.
As they reach school age, around ages 6 to 10, children become increasingly aware of societal norms, including gender roles, and often seek to emulate and identify with role models of the same sex. This period is critical for the development of self-esteem and behavioral patterns, and children at this age are already forming a sense of identity that includes gender identification.