An prescription for English beginners poor at using auxiliary verbs

For English beginners such as Japanese student in junior high school or high school, grammar is the very absolute things that they must follow in English compositions. So, they are poor at writing an English essay while they can solve problems in English-paper test.
On improving their English expressive skills, I feel, it is effective to learn a shade of meaning in case of using certain English expression. As writing on this article, there are many auxiliary verbs or modal verbs in English. Japanese students are good at making sure the number of the subject matches the number of the verb. But they has little chance to learn a shade of meaning, in particular the meanings of auxiliary verbs or modal verbs.
For example, a difference between “be going to”,”will”, “can” and “may” is one of the most typical sore spots. Japanese students can tell one from the others but can’t use them in appropriate contexts.
To overcome these weak points, what is effective? As my opinion, studying these meanings or definitions in English and using them in English conversations or compositions are nice method. Especially repeating trial and error and correction are powerful way in learning these meanings.
For not only Japanese student but also the whole English learner, I think, this is effective way. So we go to the language school or study English in English-speaker countries. Above all, I think that the environment to be able to learn with the student of various levels and various nationalities is the best. This is my recommendation: http://www.getitnyc.com/rookie-blog/