At LingQ we set the target for "known words" high. We will be introducing tests to measure whether the words that are claimed as "known words" are, in fact, known. However, we will make sure that we test the learner only against the words that he/she claims to know. The important thing is to have a vocabulary level of 8,000 or 12,500, which have been "earned" through listening and reading. If there are still many lower frequency words that the learner has not encountered in listening and reading often enough to know them, that is not a problem.
Remember that the native speaker might know 50,000 or more, and the learner cannot match that, but can focus on contexts which are relevant to him or her. There will always be holes.
2) What does knowing a word mean?
To me, knowing a word, just like knowing people, means recognition. There is such a large potential range of understanding of a word, its scope, how it is used with other words, when it is used most appropriately etc., that there is no clear point at which we can say that a learner has achieved total mastery of the word. Once we have recognition of a word, we are on our way to grasping more and more of the word, and this process might include forgetting it and relearning it. Hopefully we wil understand it when we meet it again and build on that.
I doubt that there is only a 20% difference between active and passive vocabulary in a non -native speaker. I think the difference is much larger. BE quotes a source which describes the vocabulary knowledge that Japanese students have of English as being "large, shallow and useless". This is unnecessarily harsh. The non-native speaker has had more limited exposure to the words he/she has learned and therefore his/her grasp of these words is necessarily shal ower. This is not unique to Japanese learners. Only continued exposure can gradual y deepen this understanding.
We will get better at using these words through use. We can build up our potential (passive) vocabulary, but ultimately to get good at using them we have to use them. As long as we have no need to use them we can happily continue building up our potential usable vocabulary, and our understanding of the scope of meaning and usage patterns of these words through meaningful input.
3) How do we best learn words?
Most people learning languages have limited opportunities to use the language. That would certainly be the case for Japanese learners. For that reason, although not only for that reason, I think the correct strategy in learning words is to focus on building up one's passive vocabulary.
This is also easier to do where there are not a lot of native speakers around. This means a great deal of emphasis on input, meaningful input. It means reading and listening to a lot content that is of interest and at an appropriate level of difficulty.
In my view, the first goal in language learning has to be a defensive one, to understand what is said and written in the language. The native speaker of English knows anywhere from 30-50,000 or more words. Even a 14 year old knows 14,000. With the native speaker, the difference between active and passive vocabulary is not as great as with the learner, so we have no idea which words the native speaker is going to use in communicating with us, oral y or in writing. We need to prepare ourselves in order to understand. There is no escaping lots of reading and listening.
We al want to learn to use words. We want more active vocabulary. However, I believe that having a large passive vocabulary is very important, and it can be 2 or 3 times or even ten times larger than the active vocabulary, it does not matter. Passive vocabulary will convert to active vocabulary over time.
I would guard against any attempt to be perfect in another language. Even people with a high level of fluency and a large vocabulary will stumble on the simplest words or structures.
This is not a problem.
BE says that not consolidating one's grasp of the first 2,000 words is like building on a foundation of sand, and that this is a bad thing. He points out that children use a very small number of words. However, children spend up to two years just listening, without speaking.
Learning vocabulary is not like building on sandy foundations, but rather like climbing up a sand dune. That is why you do not want to stand still , but rather need to keep going if you want to get to your destination.
I was asked in an email about learning idioms in a language. Maybe I am different from most people, but I do not bother with them. To me they are kind of the dessert of language learning. They come at the end of a meal. Once you have fil ed up on the solid fare, the key words and phrases that are used in a variety of situations, then you can add a few idioms to spice things up. And by that time you wil be able to pick them up natural y anyway.