Here's why:
* "Approach" is a noun in this context, describing a method or strategy.
* "To" is a preposition, connecting the noun "approach" to the following phrase.
* "Writing" is a gerund, which functions as a noun.
* "Excited" is an adjective modifying the noun "student." However, since it's placed after the noun, it's functioning as a predicate adjective in this case, which essentially acts like a verb.
The sentence is grammatically incorrect, but "excited" is the part of the sentence that describes the action or state of being of the student.
Let me know if you'd like to explore other examples of verbs and their functions!