Children see that on Saturdays their mom spends the day inside cleaning and doing the laundry while their dad does outside work such as mowing the yard and changing the oil. What theory suggests that children learn gender roles through this type of modeling?

Social Theory

Explanation:

Social theory is a phenomenon that states that people tend to learn more quickly by observing, imitating and modeling other people and their surroundings.

A child would learn a trait that his father practices more efficiently rather what is taught to him. So the above example where children observe their parents tending to different activities on the weekends develops clear gender roles in their minds. This would fall in the category of social theory rather than cognitive theory.