Epistemic Status: Casual thoughts on small ways to improve teaching flows.
In the lectures for my current classes, things don't always make sense. Sometimes the not making sense comes from a feeling of incompleteness. The definition seems incomplete. I notice that I don't have enough info to fully explain the concept.
Generally I've noticed two reasons for this. This first is that there was some assumed prior knowledge. Sometimes that can be explicit. Maybe I was supposed to know multivariate calculus for this course, yet there was some concept I missed that is being used here. Other times the assumption of prior knowledge is implicit. This is when the professor didn't realize that there was something to explain (i.e unaware of inferential distance).
In these cases, the best route is to ask a question.
In other cases, the professor purposefully gave an incomplete explanation, which they proceed to expand on in the following slide.
In this case, the best route is to put a mental astericks next to new concept and hold tight.
A problem arises from the fact that almost all of the professors I've had (and most people just trying to casually teach me something) talk in a way where I can't distinguish what is assumped prior knowledge and what is a placeholder to be filled in later. This leads to wasted movement. I might ask a lot of questions that get "Hold on for two minutes" as a reply, or I might never explore an idea myself because I figure it will be explained at some point. I think that being explicit can make it much easier for one trying to learn.
In conversation, I can imagine a simple habit of tagging a word or concept with a mental astericks and making clear that you currently are presenting a "working explanation". Something like "A linear seperator divides n-dimensional space in to two region. We'll circle back to how it does that in a sec."
If you teach in any sort of formal setting and use visual aids, it could be worthwhile to introduce a convention like, "Things I'm going to explain later will be highlighted in blue, things that you are expected to know are highlighted in green."
If anyone tries this out in a formal setting, let me know if it had any effect.
Personally I really dislike it when concepts are used that you're only supposed to understand later (the most common example is a textbook which gives an equation with several new variables and explains below what those variables mean). It makes me backtrack through my notes the moment I run into the equation, and by the time we get to the explanation my study flow is completely interrupted.
In my experience as lecturer/while giving presentations this can be easily avoided by giving short summaries before making complicated claims. Something along the lines of 'I am now going to tell you X, which requires concept Y that you haven't heard of yet. We need this to ultimately do Z. So bear with me.' I've had a lot of positive feedback on this (and it has the additional benefit of slowing the presentation down and forcing you to make the structure of the talk explicit).
I also get a bit annoyed by it. I imagine I'd be far less annoyed if I trusted that the source to ensure I had all the relevant info to make whatever inferntial leap I was on.
I agree on "short summary" + "bear with me". The core seems to involve being explicit that you're introducing a new blackbox and giving the essential input/output, along with a promise to circle back and unpack it.
I really like this, and I'm going to be trying this in an upcoming training at work, with the implict rule of "stop me if you don't understand anything in green" made explicit.
Thinking about how to decide whether or not to highlight a given statement; I think I'm going to try go through and look for things that are the "end" of a line of thought, and those are the greens. So once we get to a green, that's the end of a line, and a good spot for listeners to stop and ask questions before continuing.
On the other hand, some lines are "length zero" and are just a dangling green presented on their own, with the assumption being that you've already encountered the lines leading up to it somewhere else in your life.
Did trying it out in your training pan out?
Moved to frontpage.