Early in my career, I focused on being clear — as close to perfectly clear as I could manage. Class time was easy for students to follow. Eventually, I realized that my students were not learning very much and decided that I was part of the problem.
Since then, I have seen my role as “confusion manager”. In planning for what to do in class, I would look for a sequence of activities or problems that were likely to lead to some confusion. In a basic way, confusion is the brain’s assessment that there is a gap between existing knowledge and needed knowledge. Without confusion, learning new material is limited for most people.
There is a recent article in The Chronicle called “Confuse Students to Help Them Learn” by Steve Kolowich (http://chronicle.com/article/Confuse-Students-to-Help-Them/148385/?cid=cc&utm_source=cc&utm_medium=en) The initial part of the article covers the experience of another teacher noticing this ‘confusion to help’ property. Later, the article brings in some experts in psychology. Certainly, the points in this article are consistent with what I know as a teacher and as a reader of cognitive psychology.
So … here is what I think is so important about the concept of “confusion to help learning”: There is a great pressure to utilize digital resources, such as short videos. These videos are almost always created with an emphasis on BEING CLEAR and avoiding confusion. To check this out, just do a search for videos on your favorite math topics and watch.
Of course, it is possible to create short videos made with productive confusion in mind. The article listed above suggests that it is not possible; however, I believe that I could create a video that would confuse my students just enough to be helpful. The problem is that it is much easier to avoid confusion entirely OR to create a lot of confusion. Productive confusion videos would take the type of planing that goes in to commercial production or movies. Who has the resources to invest 20 hours in order to create a 5 minute video?
I think students who watch clear videos (or clear lectures) see the experience as validating their existing knowledge — even when their knowledge conflicts with what they just experienced. A little additional information might survive through short-term memorization, or limited amounts of disconnected long-term information. If all we are after is recall of facts or replication of simple procedures, clear videos might be sufficient.
As mathematicians, however, we are more interested in goals of reasoning … of application … and connecting knowledge. This type of learning needs deliberate effort by students, and that means that we need to create and manage confusion. Confusion, like anxiety, is a natural state for humans; too little of either leads to less learning just as too much of either impedes learning. Our professional judgment and connection to every student is needed to provide productive confusion.
Have you confused any students yet today? I hope so!
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