I propose a new addition to this group: pseudointeraction, which is a classroom where it appears that students are interacting, but they are interacting trivially or only very few are doing the interacting. A good example is to check “USA Lesson 2, Part 2” on this webpage by Oliver Knill.
I thought about this because I have heard a lot of mathematics professors say, “My classes are interactive lectures” (I have said the same thing myself). What this typically means is that it is a lecture, but students are encouraged to ask questions at any time and the professor will frequently ask students during class. Having observed many college mathematics classrooms by many different teachers (it used to be my job to view other classes), I think that I can safely say this:
- Giving the students opportunity to interact is not the same as students interacting. Worse yet, if only a couple of students interact but interact frequently, it can give the illusion that the whole class is participating. In fact, I would estimate that a very good “interactive lecture” would have at most 25% of the students interacting at any point during class. So three times as many students never say anything as those who do, and those who do say something will often just say 1-2 sentences during the course of a lecture. So it looks like an interactive class from the professor’s point of view, but the average student basically does not participate.
- The interactions in an “interactive lecture” are not the kind that we really want. The questions tend to be fact recall (What is 2+8? What is the derivative of ?) or speculation as to what the professor is thinking (What is the next step in the proof?). These may have value, but the students are not really interacting with the mathematics—at best, “what is the next step in the proof?”-type questions are an attempt to see which students are already interacting with the mathematics on their own. Of course, since the professor moves on once he/she hears one student answer, the only information gained is “one student was following the proof.”
Finally, note that I am not talking about people who lecture, but then break for a think-pair-share-type exercise (I am sure there are a lot of some people who say that they do an “interactive lecture” and really do get. And I am not trying to say that “interactive lectures” lack value, and that we should stop doing them (I have not stopped completely). But I think that we should stop calling them “interactive,” since the level of interaction per student is ridiculously small, and I don’t think that this is the right type of interaction. Perhaps we should just call them “lecture” and not delude ourselves into thinking that the average student is interacting with the material in any serious way.