"My parents thought that you were our teacher."

Translation: Мои родители думали, что вы наш учитель.

[Shane_Carrol_Ray]

why does it not "мои родители думали что ты был нашем учителем"?

[daughterofAlbion]

Here the English is ambiguous. "My parents thought that you were our teacher" could mean
a) they thought you were currently our teacher
b) they thought you are the teacher that we used to have. i.e. they thought they recognised you but got it wrong**

Am I right in thinking that Russian does distinguish between the two interpretations, and would use был(а) in the latter case?

[CHN2142]

Yes, it would be <Мои родители Думали что вы Были нашим учителем.> But it would not imply that your parents were wrong or right. Just that they thought the person was the teacher we used to have.

[AsvatRa]

"Мои родители думали, что ты наш учитель" is fine too.

[jlabuda]

Yes, but if you are speaking to someone older, in a position of authority, or a stranger, then you should probably use вы

[Imnuts7]

Normally you wouldn't call a teacher ты

[billi65]

were прошедшее время are настоящее это к модерам хватит спать

[Oberoth-SGA]

Тут всё абсолютно правильно. Просто в английском необходимо согласовывать времена, а в русском нет. Поэтому английское предложение:
I thought he knew переводиться как Я думал он знает т.е. знает на тот момент когда я думал. Так как действие происходит в одно и тоже время.
А предложение Я думал он знал будет переводиться так: I thought he had known.
https://www.native-english.ru/grammar/sequence-of-tenses

[BorisGrins]

мои родители думали что ты был нашем учетелям

"Were" refers to past tense. This answer should be also accepted don't you think?

[MarekHavli2]

i think you are my teacher= i think you were my teacher =》never learn math in english