So you need data to determine if teachers add value to the educational complex?  lol.  Obviously, the question is how much value not if there is value.  What would you chose: teacher-directed or self-directed learning.  Keep in mind, you chose the former by allegedly studying at UH.

You need data?  Our test scores are average compared to our mainland counterparts.  Considering our diverse immigrant population, that is an impressive feat.  My wife (an 8th grade public school teacher) has three Micronesian kids that cannot speak or read English and barely have a grasp of basic arithmetic.  They will be taking the standardized test this year after the one year grace period.  The difficulty in our state is our ESL kids come from all over the world.  Unlike Cali, Arizona, Nevada,  North Dakota, etc., a bi-lingual teacher in Hawaii doesn't guarantee effective communication.

When the test scores are stable or go up, critics like you always try to find another metric to demean teachers.