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The context is a letter to a prospective employer. Which of the forms is correct?

1. I am a Cambridge graduate and have taught history at a school ten years ago.

2. I am a Cambrige graduate and taught history at a school ten years ago.

The first one sounds more natural to me, though the second one should theoretically be more correct, since the activity of teaching happened in the past and is not prolongued into the present. Native speakers, help please. Thanks.
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Do not use present perfect ("have taught") with a specific time reference ("ten years ago").

The first is incorrect.
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Thanks for your reply, in fact I made a mistake when asking. What I wanted to use was a non specific time reference:

1. I am a Cambridge graduate and have taught history in the past.
2. I am a Cambridge graduate and taught history in the past.

What about these two? Thanks and sorry.
Anyone?
Hi,

'In the past' seems redundant.

Why not just say this?

I am a Cambridge graduate and have taught history.

Best wishes, Clive
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Thank you Clive. I think that a time reference is necessary in this case. The idea is that I taught history for 4 or 5 years, about 20 years ago. After that I performed a completely different activity and now I want to apply for a teaching job again. So when describing my experience to a potential employer in a cover letter (or orally), I need to mention that I taught history at a certain time. Since I don't want to use a definite time reference I thought "in the past" would do the job. My question is whether using the Present Perfect with an indefinite time reference is acceptable or not, since I already know that a definite time reference requires the past tense and not PP.
In those circumstances, "I have taught history in the past" is probably a good choice and grammatically correct.

Thanks a lot, Grammar Geek.

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Hi

Your choice might also depend on just how much information you want to give to a prospective employer about when you taught history:

1. I am a Cambridge graduate and taught history ten/twenty/many years ago. (You taught it in the past, as stated, and you are not implying that your experience has any current relevance.)

2. I am a Cambridge graduate and have taught history recently. (Your previous teaching experience has current relevance and, although you are not teaching now, you did so in the recent past.)

3. I am a Cambridge graduate and have taught history in the past. (Again, this implies that your experience has current relevance, but the use of the word 'past' implies that your experience was gained some time ago - perhaps many years before - although you're not being specific about just when.)