This is from the perspective of the U.S. education system, to which my experience is limited.  Of course, a cross-cultural perspective would be more interesting.  My question comes at the end if you wish to skip the definitions :)  However, I suspect that even with all the (provisional) definitions, the question might still not be precise enough.

Let me start by defining the term "NITT" (Non-intelligent technological tool):

NITTdef : A technological teaching tool that would not pass the Turing Test.

Clear examples of NITT would be animations, videos, recorded lectures etc. that populate the teaching space of many current courses.  ELIZA would also be a NITT if it were adapted as a teaching tool (is this controversial?).  If Data of the classical TV series Star-Trek Next Generation were actualized, it could be adapted to be a non-NITT (ITT?)  I assume that Data as presented in the series would pass standard implementations of the Turing Test.

Here are some definitions that are essential to understand the foregoing definition, and what is to come.  They might still be imprecise and in need of refinement--please feel free to criticize:

technologicaldef: in this context, the correct application of this adjective is limited to items that are not part of the traditional teaching tools, such as textbooks, chalk, teachers etc. So a first definitional attempt would be "IT and/or A/V based tools"

normal studentdef: A college student who comes from a normal highschool, and whose highschool gpa and test (SAT/ACT) scores are within one (two? anything in between?) standard deviation of the student-body gpa/test score distributions.

normal highschooldef: a highschool for which the average test/scores (SAT/ACT) of graduating seniors is within one standard deviation of the national distribution.

normal higher-education institutiondef: a higher-education institution for which the average test/scores (GRE/LASAT/MCAT, etc.) of graduating seniors is within one standard deviation of the national distribution. (AFAIK, these scores are not currently available.  If anyone knows how to obtain them, please share)

engaging in a learning activitydef: performing a set of actions (including mental actions like listening, thinking, but certainly including physical actions like sanding a piece of wood) with the intention and active attention direction necessary (but not necessarily sufficient) for learning from the activity. As defined, carefully listening to a lecture delivered by an instructor, carefully reading a passage in a textbook, reflectively responding to an interactive quiz embedded in an instructional video all qualify as engaging in a learning activity. 

active attention directiondef: the state of mind that is exemplified when watching a cooking program with "pen in hand" mode, vs. watching it while thinking about what to do about the latest shenanigans of your offspring(s).  I am sure that psychologists have a lot more to say about this mind-state than I do, so I will leave it to them :)

using a NITTdef: performing a set of NITT-directed actions to the whole NITT with the intention of learning.  Notice that as defined, using a NITT does not presuppose active attention direction.  A clear example of not using a NITT would be watching only a portion of it.  A borderline(?) case might be taking a training quiz by guessing or answering the questions randomly.

Now we define two kinds of NITTs:

NITTFTdef : A NITT that can be used only if a normal student engages in learning activities outside of the context provided by the current NITT. So, consider an instructional video with n embedded quizzes, Vq1-n.  Sometimes, the information provided in Vq1-n is sufficient for the student to answer questions posed in some qi.  Sometimes, it is not.  The student has to ask the instructor questions, re-read a passage from the textbook, or engage with a portion of another previously used NITT before coming up with an adequate answer. 

NITTWTdef : A NITT that is not a NITTFT.

NITT-densitydef : The ratio of the sum of NITTs in a course to the sum of non-technological teaching tools. The measure can be extended easily to NITTFT-density and NITTWT-density.

Interaction-densitydef: This is supposed to be a measure of how often students interact with an instructor.  It can be measured in a number of ways, one of the most basic of which would be "the number of content-related questions directed to the instructor".  Other relevant quantities might be "number of announcements read", "number of content-related questions students ask each other", "number of students studying together", and so on.  Obviously, some of these are extremely difficult to track down and quantify.

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Hypothesis: Among normal students in a normal higher education institution, NITTWT-density is negatively correlated with interaction-density.

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Has anyone tested this or a similar hypothesis, or is engaged in the process of developing a test?

Thanks and regards