I was chatting with a Taiwanese student the other day and asked him what language they speak there. He just answered "Chinese" and didn't know about a dialect or variant of Mandarin. Even the words Mandarin or Cantonese didn't ring a bell. The answer I got was "Chinese, the same as in Beijing".
I'm curious to know if that's a widespread conception of the language in Taiwan or just him who skipped that part of the lesson at grade school :) If not from lack of knowledge, are there other cultural or political reasons why making the distinction is not encouraged there?