Answer: Vygotsky's theory of cognitive development
Explanation: Vygotsky's Cognitive Development Theory is the theory that states about the constructive behavior of the children to obtain the cognitive factors. Instruction ,guidance and interaction on social base is considered as the feature of the theory which enhances the learning , solving problem and other skills.
The situation mentioned in the question describes about the Vygotsky's theory because Dr Smith believes in improving the knowledge through instruction in 9-year old .