I think it's pretty hard to tell the differences between these three words, and here's the dialogue:
A: 你现在在干什么？ B: 我正在做作业。 A: 你怎么还在做作业呀！
Can you help me to understand and remember these words? Thanks a lot!
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A: 你现在在干什么？: What are you doing now?
B: 我正在做作业。: I am doing homework.
正在is this sentence can be translated to doing something at this particular moment, in English you just add ing at the end for currently doing something, but in Chinese you don't have this, so you use 正在 to express doing something now. 我正在做...becomes "I am doing...", or 我正在读...becomes "I am reading..."
A: 你怎么还在做作业呀!: You are still doing homework?
还pronounced "hai" instead of "huan" in this sentence means still doing something.
还在看书：Still reading, 还在这里: Still here...
Also to mention, 还 can also be pronounced "huan", as in 还钱: Pay debt, 还给我: Give it back, it means to return something, but that's a different context itself.
I guess to make it clearer, sometimes you don't really need to add 现在 or 正在，you just say "你在干什么？What are you doing?", or "我在做作业。I am doing homework.", it sounds more friendly like when you are talking to a friend. 你现在在干什么？sounds more like when your boss or teacher would ask haha.
Generally, “现在” means NOW; "正在" means NOW DOING SOMETHING; "还在" means STILL BE DOING SOMETHING;
Here's a technique in understanding those words:
The key in understanding the words is "在":
The "在" AFTER “现在” in the first sentence and that IN the words “正在” and "还在" is equal to the progressive tense in English. "现在"(NOW), “正”(NOW/CURRENTLY), “还”(STILL) are all adverbs for modifying "在".
"我在做作业" is equal to “I'm doing my homework”. "正" is a WEAK emphasis. It lays emphasis on NOW DOING. In fact, "我正在做作业" can also be translated as "I'm doing my homework" since the emphasis is weak.
A1: 你现在在干什么？ B: 我正在做作业。 A2: 你怎么还在做作业呀！
I think Frank is correct to say, the 2nd 在 A1 and the 在 in B and A2 has become a particle equivalent to 'ing', except, of course, it sits in front and not behind the word it acts upon. '在干' and '在做'
If you know any Spanish, it is easier to understand. There are 2 verbs for 'be' in Spanish, namely 'ser = be' and 'estar = be in'. 'estar' gets used like '在'. However Spanish has a gerund comparative to the English 'ing', usually formed by adding a 'd' to the verb stem, whereas Chinese does not.
A: ¿tu ahora estás(zai) haciendo que?
¿you now be-in making/doing what?