Learn Hardcore Chinese: Wǒ yǐwéi tā shì lǎoshī, yuánlái tā shì lái cānguān de xuéshēng. - I thought she was a teacher; it turns out she is a visiting student.

以为 specifically means “to think/assume something, but it turns out to be wrong or different from reality.”
It almost always carries the idea: “I thought X, but X was not true.”

我以为她是老师 = “I thought she was a teacher (but she isn’t / but that was mistaken).”
我想她是老师 = “I think she is a teacher” (a guess; may or may not be wrong).
我觉得她是老师 = “I feel / I have the impression she is a teacher” (opinion, not necessarily wrong).

So 以为 is perfect here because the second half of the sentence shows the earlier assumption was wrong.

There is no past tense in 我以为她是老师. How does Chinese show that this happened in the past?

Chinese verbs do not change form for past/present/future like English. Tense is shown by:

Time words: 昨天 (yesterday), 以前 (before), 刚才 (just now), etc.
Aspect particles: 了, 过, 着, etc.
Context and certain verbs: some verbs inherently imply past assumptions, like 以为.

In 我以为她是老师, 以为 itself strongly suggests a past mistaken thought. The verb 是 does not change, but because we know this is a mistaken belief, we naturally understand it as “I thought (before) she was a teacher.”

What exactly does 原来 (yuánlái) mean here? Is it “originally” or “it turns out that”?

In this sentence, 原来 means “it turns out (that)… / actually (in fact)…” and signals a new realization that corrects a previous misunderstanding.

我以为她是老师，原来她是来参观的学生。
= “I thought she was a teacher; it turns out she’s a student who came to visit.”

So here 原来 doesn’t mean “originally” in the sense of “at first she was X, later she became Y.”
It marks a discovery like: “Oh, so that’s how it is!”

In other sentences, 原来 can mean “original / former”:

原来的老师 = “the original/former teacher”.

Context tells you which meaning is intended. Here, because of the contrast with 我以为, it clearly means “it turns out that...”

What is the function of 来 (lái) in 来参观? Could you just say 参观?

参观 (cānguān) means “to visit (a place) / tour / inspect.”
来 (lái) adds the idea of “come (here) to do something.”

参观 = visit / tour
来参观 = come (to this place) in order to visit/tour

In 她是来参观的学生, 来 emphasizes the direction: she came (to this place) to visit.
You could say just 参观的学生 and people would still understand, but 来参观的学生 is more natural when the student has come from elsewhere to visit your school, company, museum, etc.

How does 来参观的学生 work grammatically? What is 的 (de) doing here?

来参观的学生 is a relative clause:

来参观的 = “who came to visit”
学生 = “student”

So 来参观的学生 literally = “student who came to visit.”
Here 的 is the marker that turns the verb phrase 来参观 into a modifier of the noun 学生.

Pattern:
[Verb phrase] + 的 + [Noun]
= [Noun] who/that [verb phrase]

Examples:

昨天来的学生 = “the student who came yesterday”
喜欢看书的人 = “people who like reading”
穿红衣服的老师 = “the teacher who is wearing red clothes”

So 来参观的学生 fits this pattern exactly.

Why do we say 她是老师 and 她是来参观的学生, but there is no 的 after 老师?

In 她是老师, 老师 is just a predicate noun (“teacher”). It’s part of the A 是 B pattern:

她是老师 = “She is a teacher.”

We don’t need 的 after a simple noun used as a predicate in this pattern.

In 她是来参观的学生, we have:

来参观的: a verb phrase turned into an adjective/relative clause by 的
学生: the noun being modified.

Here 的 is not attached to 是; it attaches to 来参观, creating 来参观的学生 (“a student who came to visit”).
So:

老师: simple noun, predicate → no 的
来参观的学生: [verb phrase + 的] + noun → 的 is required before 学生

Is 她是来参观的学生 an example of the 是…的 structure?

No. It looks a bit similar but it’s not the classic 是…的 emphasis pattern.

In the 是…的 pattern, 是 and 的 are a pair that wrap around information we want to emphasize, usually about a past action:
- 我是昨天来的。 = “It was yesterday that I came.”
- 他是坐火车来的。 = “He came by train (that’s how he came).”

In 她是来参观的学生:

是 is just the copula (“to be”).
来参观的学生 is a noun phrase: “a student who came to visit.”
The 的 belongs to 来参观的学生, not to a 是…的 frame.

So the structure is:
她 (subject) + 是 (copula) + [来参观的学生] (predicate noun phrase)

Can we drop the second 她 and just say: 我以为她是老师，原来是来参观的学生。?

Yes, that’s perfectly natural and actually very common:

我以为她是老师，原来是来参观的学生。

The subject 她 is understood from context, so it can be omitted in the second clause.
Both versions are correct:

With repetition: 我以为她是老师，原来她是来参观的学生。
Without repetition: 我以为她是老师，原来是来参观的学生。

Leaving it out sounds slightly more concise and more typical of spoken Chinese.

Could you add 一个 and say 她是来参观的一个学生? Does that change the meaning?

You can say:

她是来参观的一个学生。

This is also correct. The difference is:

她是来参观的学生。
= “She is the student who came to visit” / “She’s a visiting student.”
(Neutral about whether she’s one of many.)
她是来参观的一个学生。
= “She is one student who came to visit.”
This subtly highlights that she is one among several visiting students.

So 一个 adds the sense of “one (of them)” or “a certain.”

Why is there a comma (，) instead of 但是 (“but”) between the two parts?

Chinese often uses just a comma to show a turn or contrast between two clauses, especially when the relationship is obvious:

我以为她是老师，原来她是来参观的学生。

The contrast is clear from 以为 + 原来, so adding 但是 (“but”) is usually unnecessary. You could say:

我以为她是老师，但是原来她是来参观的学生。

but it sounds a bit heavier. The simple comma is more natural and fluent here; the “but” is implied by 原来 itself.

Why is 是 used before both 老师 and 来参观的学生? Could we say 我以为她老师?

In Chinese, when linking two nouns (or a noun and a noun phrase) in an equational sentence, you almost always use 是:

她是老师。 = “She is a teacher.”
她是来参观的学生。 = “She is a student who came to visit.”

Leaving out 是 here (她老师) is ungrammatical in modern standard Mandarin.

是 can sometimes be omitted in special patterns (e.g. 他老师呢？ = “Where is his teacher?” or in some very casual speech), but 我以为她老师 does not work as a normal sentence. For A is B, use A 是 B.

What is the difference between 原来 and 其实 (qíshí)? Could we say 其实她是来参观的学生 instead?

Both can be translated as “actually,” but the nuances differ:

原来 → “it turns out that…”
Emphasizes a new realization that corrects a previous misunderstanding.
Fits very well with 我以为… (“I thought (wrongly) that…”).
其实 → “actually / in fact…”
Emphasizes a fact that may contrast with what someone thinks, but it doesn’t inherently carry the feeling of “Oh, now I realize I was wrong.”

Compare:

我以为她是老师，原来她是来参观的学生。
= “I thought she was a teacher; it turns out she is a visiting student.”
(Strong sense of discovery.)
我以为她是老师，其实她是来参观的学生。
= “I thought she was a teacher; actually she is a visiting student.”
(Also correct, but more neutral; less “Ohhh, so that’s how it is!”)

In your sentence, 原来 is especially natural because it matches the “I thought…but I was wrong” feeling created by 以为.