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For context: my language partner wrote me back and she explained to me in
Japanese the use and grammar behind "て-form + いる" in the context of one's
personal past.

The sentence in question (including some pretext):

> 「 大学の勉強の間、移住者の子供にドイツ語を教えるアルバイトをしています」 について考えてみましょう。
>
> **アンドレアスさんが言っているのは、「経験・経歴を表すテイル形」のことだと思います。**

My attempt at translation of the bold part:

> "Concerning what Andreas said, I think it is 'experience/personal history
> revealing TAIL-FIGURE'".

This "Tail-figure" doesn't make much sense, at least to me since I have no
idea what it is supposed to tell me...^^

I would be happy if someone could elaborate :=)
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grammar
What is the meaning of this テイル形
テイル形 simply means “て form of verb plus いる”.

> テ + イル + 形
>
> て + いる + form
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> 「 大学の勉強の間、移住者{いじゅうしゃ}の子供{こども}にドイツ語{ご}を教{おし}えるアルバイトを **しています** 」
> について考えてみましょう。

↓

> 「しています」＝「している」 in meaning

Voilà, you have the ている-form of the verb 「する」 there!

And it certainly expresses one's " ** _experience/personal history_** " of
移住者の子供にドイツ語を教えるアルバイト ("working part-time teaching German to immigrant
children").

"Tail-figure" is just out of the question. Users here tend to "translate"
things too early, namely, before even understanding the words and phrases in
question.

As a Japanese learner, you must have encountered the terms such as マス形、テ形,
etc. テイル形 is just another one of those terms. Those are discussed all day
every day here.
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You're probably finding テイル形 is getting translated as "Tail Figure" because
it's written in katakana, but it's actually referring to the ている form, i.e.
the form of verbs ending in -te iru.
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