Past tense vs past progessive tense

Question

I was her biological teacher for 3 years she had been studying there

Or

I was her biological teacher for 3 years she had studied there

Also, in written situation it is best to write 3 years or three years?

Answer 1

Before we get to verb tenses, there are actually a few other grammar problems with your sentences:

• As folks have noted in the comments, "I" (the first-person singular pronoun) should always be capitalized.
• "biological teacher" does not make a lot of sense. The word "biological" when referring to a person or position implies that someone is related to someone else through biology (e.g. "biological parent" vs. "adoptive parent"). I suspect what you meant here was the name of the school subject, which is always "Biology". Note that when used as the name of a school subject or class, this is also a proper noun, so it should always be capitalized, too, so what you presumably wanted to say was "Biology teacher".
• If you are talking about the specific three years during which she was studying (she was only there for three years, and those are the specific three years you mean), then you need to use the definite article ("the") before "three years" ("the three years she had been studying here"). If instead you are saying you had been a teacher for 3 years, and during that time (coincidentally) she was also studying there, then you don't need "the", but you do need a comma and an appropriate preposition between "three years" and the following verb ("three years, while she had been studying there"). The current form (no definite article, no preposition) is not grammatically correct.

(for the following I'm assuming you meant to say that you were here teacher for the specific three years that she was there)

Now, as for verb tenses:

I was her Biology teacher for the three years she had been studying there.

This is actually the past perfect continuous (or past perfect progressive) tense. This is actually fine, and I would say is probably the most natural/correct way to say this, as it implies that the action (her studying) was taking place over some period of time, that it happened in the past, but it then finished.

I was her Biology teacher for the three years she had studied there.

This is actually the past perfect tense. It says that it took place in the past, but that it had already happened before some other thing in the past which we're talking about. In this case, it sounds a bit odd, because the only other thing in the past mentioned is the time you were her teacher, so what this actually seems to say is that she had already finished studying there before you were her teacher for the 3 years she studied there (which doesn't make a lot of sense).

However, if there is some larger context where you were already talking about some other past event which happened after all of this, the past perfect might make sense, to emphasize that her studying (and your teaching) happened before that other event instead. To make this clear it would be better to use the past perfect for both verbs, though ("I had been her Biology teacher...")

Note that in most cases where you can use a perfect tense (such as the past perfect continuous), you can usually also use the non-perfect tense (in this case past continuous), it just won't tell the listener quite as much about the relative timing of when things started or ended:

I was her Biology teacher for the three years she was studying there.

And in general, any time you're using any past tense, you can usually also just use the simple past, but this tells listeners the least amount of information about when things happened (it just says it happened some time in the past, nothing else):

I was her Biology teacher for the three years she studied there.

In this case, both of these are perfectly fine, too.

As for whether to use "3" or "three" in this case, there is no hard rule for this. Many style guides recommend spelling out numbers up to ten, and using digits for any numbers larger than ten (sometimes people will also spell out larger "round" numbers, such as twenty, fifty, etc). Because of this, if you're writing more formally (such as academically or for publication), it's generally good to spell out small numbers, as it can make things sound more professional. For more casual use, in general, nobody really cares much either way, though.