In regards to ‘concrete proof’, there is no concrete proof of its effectiveness in language learning. I did a review of literature in this area looking at all the scholarly journals I can find on the topic and found lots of contradictions. To be fair, there is little ‘concrete proof’ in Educational Psychology and Intelligence. Differences in methods and operational definitions, failed replications, and political implications all make it quite difficult to be certain about a lot of the issues revolving intelligence.
I find that the problem with Gardner’s Multiple Intelligences model is that the conventional public schooling doesn’t create an environment where implementing this model is very easy or efficient. In a class of 20-40 students, most of them have learned to learn in the same way. There will be a few who would learn better in different ways, but practically speaking, can you afford to change your teaching style to meet the needs of a few students over the rest?
Personally, I believe that students are malleable and just as capable of learning how to learn through verbal and written instruction, as they are capable of learning a new language at a young age. More important than learning styles, I believe, is engagement – think about when a teacher gets their class to learn ‘kinesthetically’ through movement, ‘interpersonally’ through peer discussion, or ‘visually’ through pictures and spatial understanding – what may be driving improvement in learning more than appealing to a specific learning style is the engagement of the student who is tired of doing it in the same boring way.