Step 1: Understanding the Question:
The question asks to identify the specific stage in Erik Erikson's theory of psychosocial development where a child asserts their individuality, establishes initiative, and begins defining who they want to become.
Step 2: Detailed Explanation:
• In Erik Erikson's eight stages of psychosocial development, the third stage is Initiative vs. Guilt, which occurs during early childhood (ages $3$ to $5$ years).
• During this stage, children use their motor, language, and cognitive skills to actively plan and initiate activities, games, and social interactions.
• Erikson noted that during this stage, children become firmly convinced that they are a person of their own, separating from their parents' immediate identity and exploring their own potential and future self.
• Trust vs. Mistrust occurs in infancy and focuses on establishing basic security and trust in caregivers.
• Autonomy vs. Shame and Doubt occurs in toddlerhood (ages $1$ to $3$) and is centered on physical self-control and independence.
• Industry vs. Inferiority occurs in middle-to-late childhood, focusing on mastering social and academic skills.
• Thus, early childhood's active exploration of a personal identity through planful actions belongs to the stage of Initiative vs. Guilt.
Step 3: Final Answer:
The stage in which a child becomes convinced they are a person of their own and starts planning their future self is Initiative Vs. Guilt.