Lisa Hiton, Professor of English and Arts, Poet, Filmmaker, Writer
There are a few ways to think about multiple styles of learning. The origins of this idea and phrasing does, indeed, come from Gardner's work. As an HGSE student, I will tell you, the reception and use of his theory of multiple intelligences has not been so simple.
Although, as Nedda Gilbert mentioned, the ideas are widely accepted, the use of them in classrooms sometimes went astray from the moral ideals at the center (rampant testing in each of these categories inherently defeats the purpose of the various styles). Gardner's current project is "GoodWork". It seeks to bring ideas about excellence, engagement, and ethics together--in journalism, politics, education, etc. It is, in that way, directly responding to some of the misuses of multiple intelligence that began happening during the rise of high-stakes testing.
Another source for multiple learning styles these days is Universal Design for Learning. This relates most directly to Gina Bidalatay's response. UDL is used most commonly for inclusion classrooms. As a member of the teaching team for UDL, I saw students develop apps, curriculum, websites, and more for all kinds of inclusion in classrooms (blindness, autism, bipolar disorder, and more). As many public and private schools have changed what inclusion classrooms can do, more of these small and large scale ideas have been put to the test.
Like many things in life, multiple learning styles demands more time of teachers. It requires inventing and facilitating lessons that make information accessible via multiple learning avenues (music learners, spatial learners, etc.). Some content areas have more flexibility in these constructionist approach to learning while others don't. I've rarely observed a math course that allowed a student to show their work in a means other than the logical, taught version. Whereas, in order to understand a science lesson, students who understand musical patterns may have a different way of figuring out a basic genetics strand and have that be a perfectly acceptable way to show their work. There are more and more case studies of different learners succeeding because of excellent lesson plans or workshop facilitations; hopefully the more we can model the equality of learning styles (which inherently cannot happen on a high stakes test), the more common it will be to have students learn through their own habits of mind.