As far as I know, we can analyze the sentence in the following way.   



The sentence originates from the following sentence:



I spend the whole day ON studying math. 



So studying math is a gerund which is a complement or an object of the preposition ON. It seems that ON is often omitted. From a generative perspective, you can say that there is a phonetically null counterpart of ON. 



In the above, studying is a verbal gerund so it takes math as its complement or an object without such preposition as OF. 



In a sentence like the following, we often omit IN. This is the same as the above case. 



I have difficulty (in) studying math. 



I hope my explanation can answer your question. 

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2019. 10. 12. 오후 9:31, Greg Campbell <[log in to unmask]> 작성:



> 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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