The Chinese word "以为" means "thought", as in "I thought it was Tuesday today" (我以为今天是星期二). There's only one little detail some Chinese speakers often overlook: the verb in the subordinate clause should be in the past tense. "I thought it is Tuesday today" is not right.
If you think about it, though, the past tense in the subordinate clause doesn't meaningfully indicate a past behavior; only the verb "thought" in the main clause is clearly in the past. The past tense of "was" in the example sentence is required by the grammatical agreement between the main and subordinate clauses. Probably due to lack of this semantic implication in the subordinate clause, a Chinese student often takes the easier word "is" and forgets the correct one, "was".
Interestingly, I found this sentence in a German learning CD: "Und ich dachte es ist Dienstag." (literally: "And I thought it is Tuesday") That means in German, it's acceptable to use the simple present tense in the subordinate clause even if its main clause uses the past tense. But I'm sure using the past tense is fine too ("Ich dachte, es war Dienstag.").