Transformation Feedback that Worked, I Think

I felt good about how I handled feedback today in class. The class has been studying transformations in 8th Grade, and I wanted kids to practice visualizing different transformations. The task was to match shapes with transformations.


The above work is something I saw a lot. My kids had a pretty good sense of the different motions that translations, rotations and reflections were describing, and overall were pretty accurate.

Rotations around centers besides (0,0), though? Kids didn’t seem to know how to handle that. Some treated a rotation around (2,0) as just another rotation around the origin. Others seemed to get the quadrant of the image correct, but the coordinates weren’t right.

I decided that this would be what I’d focus the start of my next lesson on. I’d start with a pre-feedback activity, give some quick comments on the work, and then ask kids to revise their work.

This was the diagram I started class with:


I was trying to figure out what prompt to start with. I thought about just asking kids, “Where would the image be?” but this idea had problems. First, I wanted to know a bit more about how they thought because I wasn’t sure exactly where the problem was with their thinking about this. Second, I knew that kids would have trouble with this based on their previous work.

Instead, I posted the image and asked kids to figure out as much as they could about the diagram. I figured that this vaguer prompt would be more revealing while also giving me a chance to respond to ideas and help kids learn how to think about this sort of rotation.

(I also thought about just telling kids, here’s how you do this. I think that would have been plenty effective in this case, but I also like giving kids chances to have interesting mathematical ideas, and this seemed like a chance for that.)

Here was the annotated picture from under the document camera.


The three ideas on the top were from kids. After hearing them I pointed out that some of these were correct, assuming that the transformation was around the origin.

Then I said, this is why I brought this image into class, because I noticed from your classwork that rotations not around the origin are hard. I have something that I think will help, I call it drawing a tether. And then I connected points A and B. Does this help you figure anything else out?

Very quickly a kid said, yeah, now I’ve got this and there was a lot of chatter about where the other points would go. I annotated those, and summarized that adding the tether would help. I also said that you might figure out where the other points are relative to B, and this led to more mathematical chatter and more asserting of where the points are. (Is that the sort of evidence I can use to know if a class is working out? Mathematical chatter?)

Then I said, I want you to try out these ideas while revising your classwork. I highlighted ones that could be revised, and I’d like you to draw a revision on the page. From past experience, I wanted to keep the timing of this quick, so I said you’ve got 5-10 minutes, and if you don’t start quickly then you probably won’t get a chance to learn much now.

Here was some of the revised work.


Not everyone got feedback about rotation around (2,0). These kids get feedback about reflections around y = x and y = -x (which is good, because we need to know those for the next activity we’re working on).


The questions that I’m left with are about how sure I can be that this lesson went as well as I felt it could be. What’s my evidence? Is it the way the kids were acting? Was it their engagement? Or their resulting work? Should I have done a quick exit assessment — would that have supported my claim that this worked?

And does “this lesson worked” mean that it just worked in the classroom? Or can it mean that the planning worked, that I made moves on purpose and with confidence?

How do you really know if a lesson worked?

Is Feedback A Chore?

But Wiliam offers two pieces of guidance that I think can create an effective, practical framework for using comments-only feedback.

  1. Students should do something with the feedback — and if it’s important to us, we should prioritize instructional time for them to do so.
  2. Opportunities for feedback should be structured such that the feedback is transferable beyond the task itself.

This framework suggests that much of the feedback I give is ineffective. If I don’t prioritize instructional time for students to respond to it, students who most need that feedback are unlikely to make effective use of it. And many tasks that I give feedback on are unlikely to lead to transferable learning, instead focusing student attention on concrete features of the task that will not support their learning in the future.

This is from Dylan Kane, who is one of the best classroom bloggers out there.

I’ve been grappling with the same issues Dylan brings up. I’ve recently written three pieces that try to get at my current approach. They also are my attempt to grapple with the limitations of research on feedback.

Feedback – We Still Don’t Know What Works

We Still Don’t Know What Works: Bonus Track

Beyond “Better-Luck-Next-Time” Feedback

Dylan’s post captures the idea that giving feedback is a chore, a regiment like dieting that we can discipline ourselves to keep. This attitude makes a lot of sense if feedback is an instructional “add-on,” something that goes over and above teaching. It’s extra, unnecessary, but (somehow) crucial.

My view is that it’s far more helpful to think about teaching routines that more naturally feature feedback, but are something more than “giving feedback.” This year I’ve nailed down one such routine in which written comments are just one helpful component: I give feedback to the class via an activity, and then use comments to connect that general, transferable lesson to my kids’ specific work.

It’s also my view that current research on feedback treats it like an “add-on.” I might be wrong, but I think that this is partly due to the lineage of “feedback.” It entered our lexicon through research on learning that did not grapple with classroom contexts. We teachers need to get better at expressing a view of the work that is truer to the work. When feedback is just slapped on to our teaching, it feels like a chore because it is a chore, because it’s sole purpose is to justify our judgement.

Is feedback good for learning? Are pencils good for learning? Feedback is the wrong thing to focus on. The right thing to focus on are the patterns of our teaching that we keep coming back to. Some of these involve written comments, others don’t.

Ultimately, we might need to stop thinking in terms of feedback. Meanwhile, we should look for routines that don’t make writing comments feel like a burden.

We Still Don’t Know What Feedback Works: Bonus Track

I wrote a piece about research on feedback — how it’s helped me, how it hasn’t — for the Learning Scientists blog. I worked hard on the piece, you should go read it. I also had a great time working with Megan and Yana — both learning science researchers — who run the Learning Scientists blog, and you should check out their work too.

Over at their blog, I make an argument that research on feedback has not, so far, been able to make real recommendations for the classroom. This is inherent in the way the work has been done — mostly in lab settings. Laboratory work usually simulates classroom environments where feedback is occasional, spotty, and easy to identify. Most k-12 classrooms — even ones with mediocre teaching — are knotty webs of interaction. Our classrooms are rich with feedback.

Our question isn’t whether or how to give feedback. After all, we’re going to give lots of verbal feedback, and every teacher ends up giving written feedback too. Sometimes we give immediate feedback; other times its delayed. We respond to so many ideas and actions that, in teaching, we end up giving a little bit of everything, when it comes to feedback. The question is: how do we structure all this feedback so that it actually helps learning? What form should it take, and what routines can help us give feedback that advances learning?

Go read the piece! It’s not long.

There was something else I had to say about this, but it didn’t belong in the piece. It’s about whether “feedback” is the right thing for us all to be talking about in the first place.

After all, there was a time before people talked about giving or receiving feedback. It’s a relatively recent development, actually. Check out the term’s frequency in the Google database:

Screenshot 2016-03-29 at 3.12.11 PM

The term originated in engineering contexts, and was only brought into education (and wider usage) later. Here’s Dylan Wiliam on the early history of the term:

Screenshot 2016-03-29 at 2.53.01 PM.png

Jumping ahead a bit, Wiliam argues that the move from engineering to education was not an entirely smooth one:

Screenshot 2016-03-29 at 2.55.26 PM.png

It’s been a while since I revisited this, there was a time when I was able to convince myself (mostly through Google Book searches, admittedly) that it was Skinner and the Behaviorists (solid band name) that helped shepherd the term into wider usage. Skinner’s version of feedback functioned a great deal as feedback does in engineering.  Feedback, for Skinner involved a bit of pain, a bit of pleasure, slowly conditioning a rat or person towards some greater truth. In these sorts of settings, yes, it makes some sense to talk about feedback all on its own. Learning has been immensely simplified into a positive or a negative association, so talk of feedback is clear and distinct. There is not major ambiguity as to what we are talking about.

In a classroom, though? If a teacher tells me that he “gave students some feedback” that could mean they did any of the following things: graded and returned their work; had a conversation one-on-one about an assignment; yelled at a kid for crossing a line; explained in a whole-class setting why a certain common answer was wrong; wrote a comment on a paper, without a grade; praised an answer; praised a person; sent a report card. And then we ask, “What’s the most effective way to give feedback?”

This is insane, and ultimately untenable. We can’t talk about how to give effective feedback for the same reason we can’t talk about how to effectively build a table.

What I’m putting my hopes into — and I said this at the end of my Learning Scientists piece — is in expanding the lens through which we look at feedback. If we are interested in creating opportunities for rich interactions between teacher and student that help learning, we need to describe whole routines of instruction that create these moments. The moment of feedback is a part of these routines, but the only way to make sense of them is to consider them as bits in entire movements of teaching. (Feedback is just an aria.)

Am I the only person to point this out? Hardly. I’ve borrowed this rant from others. Check out Kluger and DenisiValerie Shute, or Dylan Wiliam. They all call for expanding the scope of what we study — formative assessment, or feedback for learning, or formative feedback or whatever, but we have to study something more substantial than just feedback.

This is all pretty theoretical (see why it got cut?) but practically, here’s what it means: if someone tells you how to give effective feedback, do not believe them. Instead, try to find the larger routine where that effective feedback might thrive.

Essay: On Visual Patterns and Feedback

can you find a pattern in every direction?

Last summer I wrote an essay about how feedback and the math that visual pattern problems can help students learn.

Looking back, I don’t think this essay ever worked entirely, as a piece of writing.As my initial excitement about the piece soured, I never got around to giving it the big edit that it needed. Still, there are some good ideas in there that it helped me to figure out.

Here’s the essay: On Visual Patterns and Feedback

Here’s an excerpt:

I knew what I wanted to help Toni see. She was looking for a pattern in the growth, but she was having trouble getting specific about it. I wanted to ask a question that would draw Toni’s attention to helpful features of the pattern’s growth and help her get specific about precisely how this shape is changing.

This would involve a bit of guessing on my part, though, since I didn’t really know what question would work!

My first question was a promising dud: “Can you see the previous step in the following step?”

To which Toni responded, “no.”

I tried again, this time directing her attention more directly: “Do you see the second picture in the third? Imagine that you were building the third picture from the second. Where would you put the extra bricks?”

Bingo. She grabbed her pencil and started sketching.

Why did that question work? I think it’s because it encouraged Toni to see the static picture on the page as a changing thing. Toni had lots of experience playing with blocks and adding on parts to existing doodles. By asking her to think of one picture in the next, I helped direct her thinking to this analogy, and she was able to see the pattern’s growth in a useful way that related to things she had lots of experience with.

Like I said, an interesting failure. Enjoy! Let me know if you find parts of this useful.