Not all my geometry students bombed the trig quiz. Some students knew exactly what they were doing:
A lot of my students, however, multiplied the tangent ratio by the height of their triangle:
In essence, it’s a corresponding parts mistake — the ’20’ corresponds to the ‘0.574’. The situation calls for division.
Half my class made this mistake on the quiz. What to do?
Pretty much everyone agrees that feedback is important for learning, but pretty much nobody is sure what effective feedback looks like. Sure, you can find articles that promise 5 Research-Based Tips for great feedback, but there’s less there than meets the eye. You get guidelines like ‘be as specific as possible,’ which is the sort of goldilocks non-advice that education seems deeply committed to providing. Other advice is too vague to serve as anything but a gentle reminder of what we already know: ‘present feedback carefully,’ etc. You’ve heard this from me before.
As far as I can tell, this vagueness and confusion accurately reflects the state of research on feedback. The best, most current review of feedback research (Valerie Schute’s) begins by observing that psychologists have been studying this stuff for over 50 years. And yet: “Within this large body of feedback research, there are many conflicting findings and no consistent pattern of results.”
Should feedback be immediate or delayed? Should you give lots of info, or not very much at all? Written or oral? Hints or explanations? If you’re hoping for guidance, you won’t find it here. (And let’s not forget that the vast majority of this research takes place in environments that are quite different from where we teach.)
Here’s how bad things are: Dylan Wilam, the guy who wrote the book on formative assessment, has suggested that the entire concept of feedback might be unhelpful in education.
It’s not looking like I’m going to get any clarity from research on what to do with this trig quiz.
I’m usually the guy in the room who says that reductionist models are bad. I like messy models of reality. I get annoyed by overly-simplistic ideas about what science is or does. I don’t like simple models of teaching — it’s all about discovery — because I rarely find that things are simple. Messy, messy, (Messi!), messy.
Here’s the deal, though: a reductionist model of learning has been really clarifying for me.
The most helpful things I’ve read about feedback have been coldly reductive. Feedback doesn’t cause learning . Paying attention, thinking about new things — that leads to learning. Feedback either gets someone to think about something valuable, or it does nothing at all. (Meaning: it’s affecting either motivation or attention.)
Dylan Wiliam was helpful for me here too. He writes,
“If I had to reduce all of the research on feedback into one simple overarching idea, at least for academic subjects in school, it would be this: feedback should cause thinking.”
When is a reductive theory helpful, and when is it bad to reduce complexity? I wonder if reductive theories are maybe especially useful in teaching because the work has so much surface-level stuff to keep track of: the planning, the meetings, all those names. It’s hard to hold on to any sort of guideline during the flurry of a teaching day. Simple, powerful guidelines (heuristics?) might be especially useful to us.
Maybe, if the research on feedback was less of a random assortment of inconsistent results it would be possible to scrap together a non-reductive theory of it.
Anyway this is getting pretty far afield. What happened to those trig students?
I’m a believer that the easiest way to understand why something is wrong is usually to understand why something else is right. (It’s another of the little overly-reductive theories I use in my teaching.)
The natural thing to do, I felt, would be to mark my students’ papers and offer some sort of explanation — written, verbal, whatever — about why what they did was incorrect, why they should have done 20/tan(30) rather than 20*tan(30). This seems to me the most feedbacky feedback possible.
But would that help kids learn how to accurately solve this problem? And would it get them to think about the difference between cases that call for each of these oh-so-similar calculations? I didn’t think it would.
So I didn’t bother marking their quizzes, at least right away. Instead I made a little example-based activity. I assigned the activity to my students in class the next day.
I’m not saying ‘here’s this great resource that you can use.’ This is an incredibly sloppy version of what I’m trying to describe — count the typos, if you can. And the explanation in my example is kind of…mushy. Could’ve been better.
What excites me is that this activity is replacing what was for me a far worse activity. Handing back these quizzes focuses their attention completely on what they did and what they could done to get the question right. There’s a time for that too, but this wasn’t a time for tinkering, it was a time for thinking about an important distinction between two different problem types. This activity focused attention (more or less) where it belonged.
So I think, for now, this is what feedback comes down to. Trying to figure out, as specifically as possible, what kids could learn, and then trying to figure out how to help them learn it.
It can be a whole-class activity; it can be an explanation; it can be practice; it can be an example; it can be a new lesson. It doesn’t need to be a comment. It doesn’t need to be personalized for every student. It just needs to do that one thing, the only thing feedback ever can do, which is help kids think about something.
The term ‘feedback’ comes with some unhelpful associations — comments, personalization, a conversation. It’s best, I think, to ignore these associations. Sometimes, it’s helpful to ignore complexity.