Confusion is traditionally an unwelcome guest in the classroom. It is a problem that the conscientious instructor needs to root out with clear explanations, and if students harbor it we expect bad things to follow. Recently, however, its reputation has been changing.

In August, *The Chronicle* published an article titled “Confuse Students to Help Them Learn.” Among other things, it describes an experiment in which physics students watched one of two different educational videos: one video explained a basic physics concept straightforwardly in a clear and concise manner, while the other featured a confused student trying to wrap his head around the concept and, despite receiving only guided questions from a tutor, eventually got it right. The student viewers found the first video easy to understand, clear, and concise, while they found the second one confusing. But, the article notes, “the students who had watched the more confusing videos learned more. The students who had watched the more-straightforward videos learned less, yet walked away with more confidence in their comprehension.”

Psychologists are also conducting research on confusion and learning. Professors Sidney D’Mello and Arthur Graesser have worked on a number of studies investigating the relationship between confusion and learning. They, along with their collaborators, published an article this year entitled “Confusion Can Be Beneficial for Learning” (preprint here), in which they observe that “confusion is expected to be more the norm than the exception during complex learning tasks. Moreover, on these tasks, confusion is likely to promote learning at deeper levels of comprehension under appropriate conditions.” The article goes on to explore what these conditions are in a controlled experiment.

The role of confusion in the classroom, along with the phrase, “under appropriate conditions,” is something I have been thinking about lately (albeit in a less scientific manner). *The Chronicle* article states a similar sentiment with the section heading “Confusion works, except when it doesn’t.” But before the caveats that not all confusion is helpful, the big idea is that *confusion can be helpful*. Many of my students are conditioned to think that all confusion is bad, so the first thing I need to do in order to use it effectively in the classroom is help students see that confusion can be productive.

I find it helpful to make the following distinction. Confusion comes in two flavors: productive and unproductive. Confusion is productive if you have the skills and resources to work on and sort out your confusion; it is unproductive if you do not have these resources. And because constructing your own knowledge is much more effective than simply receiving knowledge from someone else, productive confusion is a valuable commodity in the learning process.

But just knowing that confusion can be productive is not always helpful in practice. The trouble is, you do not know immediately of what kind a particular confusion is—quite often, even productive confusion *feels* unproductive until you resolve it. Always try to see if you have the tools to address your own confusion! (And if not, try to figure out what tools you might need but don’t have—a major part of an education consists of converting previously unproductive confusion into productive confusion.)

It is much easier to talk about the relationship between confusion and learning than it is to harness its power, though, so here are some thoughts on how productive confusion has shown up recently in my classroom:

I am currently teaching an Inquiry Based Learning class for pre-service elementary school teachers. In fact, many of the course materials are developed to situate students in the “productively confused’’ category. For instance, we recently spent a week studying place value and how strongly it influences the way we think about numbers. We do this by working in *base-five*. What’s more, I change up the digits, so we write numbers with the symbols A, B, C, D, and 0. (This is post number AA on this blog…) *This is all done in the service of creating confusion.* In order to make this confusion productive, I consider how I set the context for our study, what tools and information I give the students to start with, and what questions I ask them to investigate (and in what order).

First, I think context is very important in order for students to recognize confusion as productive. In the class described above, I tell students that we are interested in studying the structures and patterns of the way we write numbers, and the change to base-five is in the service of distinguishing structures and patterns from things that just feel obvious to them in base-ten. Without this explicit objective, some students may lack motivation to apply themselves to the problems, and others may side-step a successful resolution of their confusion by employing simple procedural methods. In effect, I have described what is going to make this exercise “productive.” For the remainder of the class, we relate all of our progress in understanding base-five to the primary goal of understanding the structure of a base system.

Second, I need to tell students enough that they can start working on problems, but not so much that the problems become only applications of what I tell them. This can be a delicate balance (and is also influenced by what problems I pick to put on the worksheet). For our work in base-five, I tell the class what symbols we will use (A, B, C, D, and 0), and how to count in base-five (by listing the numerals A, B, C, D, A0, AA, AB, AC, AD, B0,…). At this point, I assume that students can continue counting (perhaps with the help of their group members), and thus can make some kind of progress on the worksheet. I leave them to discover patterns and structures in their groups.

Finally, I select problems and put them in a particular order. I want students to have success (confidence is very helpful for making confusion productive), but I also want them to learn something substantial. The problems are arranged to be increasingly difficult to solve just by counting (“figure out in base-five how many gummy bears you have in a package,” followed by “then figure out how many gummy bears you and the group next to you have all together”). Eventually, groups will need to utilize the structure of how a number is written in base-five in order to progress (“accurately place 0, AD, CDD, B000 and A0000 on a base-five number line”).

By the time students have (at least partially) resolved their confusion with writing numbers in base-five, they have discovered the use of grouping and ungrouping (by fives) as well as what the phrase “place value” means in a base system. These discoveries become things that they own, and that they will reference in future investigations. My students have encountered productive confusion, and converted it into knowledge and understanding.