Can anyone lend some input to what we have in the following sentence: 

I spent the whole day studying math. 

A student submitted it wanting "studying" to be the object complement, which it definitely isn't. One colleague is seeing "studying math" as potentially functioning adverbially (how you spent the day), and another sees "studying" as a second verb (lacking the helper verb) taking "math" as a direct object. It strikes all of us as a pretty common sentence pattern, yet we can't seem to pin it down. I know we're potentially missing something obvious, but any input is appreciated!

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