Tag Archives: communication

A First Plank Across The Feedback Swamp

Much of my geometry class is built around a series of what I call Investigations. My students just wrapped up their work on the second one of the year.  This Investigation explores different kinds of geometric properties through a set of problems–position, size, shape, connection, and dimension.  For the Investigation, students can try their hand at several of the problems, but after initial forays they choose one problem to dig into and then do a write-up about their results.  You can view the collection of problems here: Investigation #2.

On Wednesday, my students turned in their write-ups and we had time for most of them to do a short presentation about their work.  On their warm-up for the day were a couple of  housekeeping questions, as well as the following:

What kind of feedback do you want on your first two Investigation write-ups? Are there parts of your work for which you are especially interested in my feedback?

Over the summer, I wrote about a minor epiphany that hit me about my struggles with giving useful and timely feedback to my students about their work.  In short, I always end up feeling swamped and overwhelmed by wanting to “do right” by my students–to give them the individualized attention that I know they deserve. To help to get me around this sinkhole, I realized that I should be asking my students about the kind of feedback they want.  I figured that this would make the task of giving feedback feel less like an infinite task where I needed to be all-seeing and say the “right” things and more like a conversation where the goal is to be relevant and helpful.

In teaching, of course, nice theories need to be borne out in practice.  What would my students say when I asked them what kind of feedback they wanted?

Here are a few:

“I would like some pointers on how to write a clearer math paper.”

“I would actually like very harsh feedback.  No sparing of feelings please.”

“Things I could have done more precisely.”

“I would like feedback about how clear I am in explaining and if my calculations are correct.”

“I don’t know.”

These are all great first stabs, including the last one.  These responses will each help to focus my reader’s eye and will shape the comments I give to individual students.

By asking and continuing to ask my students about what feedback they want on their assignments, I hope–and dare even expect–that they will become more reflective about their work, both upon its completion and during its progress.  I can already see it making me feel more comfortable and confident in giving feedback.  And I know that it will help me to better serve them and to let them know that I care about them and that I want to help them to meet their goals and to flourish.

Flying Blind: Teaching Without the Answer Key

David Coffey wrote a post about teachers giving students problems that they themselves don’t know the answers to–doing this deliberately, as a pedagogical strategy.  I’d like to share an example from my own classroom, as well as some reasons why I’ve pursued this path.

Before I begin, allow me to say that what follows is a “sometimes” occurrence in my classes.  Most times when I share open-ended explorations with my students, I’ve already investigated the problem pretty thoroughly–either with a previous class, or on my own in preparation.  And of course, there are plenty of times when my classes are more closed-ended.  But on a few occasions I’ve purposefully held myself back from thinking about a problem before sharing it with students.

I think the first time I did this with serious malice and forethought–teaching in the first degree–was at the beginning of last year with my sixth and seventh graders.  In addition to beginning our diagnostic and review work with arithmetical topics, I gave out this first sheet of problems that were inspired by / stolen from James Tanton’s Math Without Words:

Not a free-form task–plenty of specificity here–but at the same time, no instructions.  I hadn’t done these problems before I handed them out.  What I mean is that I had played around with them a little, but hadn’t convinced myself that any were impossible, and certainly didn’t have any kind of general theory.  I recognized that there was some mathematical depth here and felt that there were likely many connections and extensions to be made.  I wanted to open the year by modeling problem definition, problem creation, and problem solving in a live, off-the-cuff way, and this starting problem seemed like a great way to do it.

The kids dove in–faster, slower, with frustration and accomplishment and bits of insight.  The variations they composed on the back were fabulous–different sized grids, different shaped grids, obstacles, fixed end points, three-dimensional versions, and on and on.  They shared these with each other and critiqued each other’s work, and we discussed the gradations of variation that had sprung up in these new problems.

Here’s what came next:

Here I was pushing for clear language and problem definition, as well as another go-round at creating variations to the original problem.

For the next assignment, I asked my students to explore the nearby space of the original problem–looking for insight into it by looking at variations, and especially at simpler variations.  That’s a problem-solving strategy that worth of the name.  I gave them graph paper and asked them to try out this kind of grid-path problem on some smaller and perhaps bigger boards.  I did the same.

That was actually a homework assignment.  When they came back in, I had them get into small groups to share and compile their findings:

What they uncovered was really awesome and–as best as I can remember–a surprise to me!  On the even boards, it seemed like the problem was possible no matter when the starting dot was located.  The odd boards, on the other hand, had a very suggestive checkerboard pattern.  Conjectures and excitement filled the room.

The following came next–I don’t know if the idea came from me or from a kid:

I won’t spell out the gory details, but there’s so much here–parity, induction, tiling, Hamiltonian circuits.  And I didn’t know it was all there when we started, except in my gut.  So much depends on having a stock of such problems.  Finding them is both hard and easy.  Maybe I’ll talk about that some other time.

At this point last year, some kids went on to explore their own variations during free-choice time.  (Geofix polyhedra laced with string, anyone?)  There were probably loose ends that never got resolved, but that’s not important.  What is important is that having this open-ended, let’s-figure-it-out-together exploration at the start of the year really helped to set the tone that I was hoping for.  So here’s to say that posing problems that you don’t know the answer to is entirely possible and potentially extraordinarily fruitful.  It can happen in large or small doses, but it belongs in the hands of every kid–not just the ones who are “good at math” in conventional ways.  Everyone needs the experience of a math classroom where there are no “haves” and “have-nots”–the teacher included.

Right now I’m in the midst of doing something similar with my fifth grade classes.  We’re working to figure out how many different combinations of pattern blocks can fit together to make a full turn at a point.  I have no idea of what the answer is, or what patterns will crop up.  I’ll let you know when we figure it out!

I hope you find something worth chewing on in the above.  Wow–it feels so great to finally share some math!

PS  With respect to all of this business about problem creation and variations, extensions, and generalizations, let me say that I owe so much Avery Pickford.  I had the great fortune of cutting my teeth on this crazy profession while sitting next to Avery in our math department office at Saint Ann’s.  Louder voices than mine have sung his praises, but I know firsthand how thoughtful and awesome he is.  Just a for-instance: check out this sweet description of the problem cycle and variations, extensions, and generalizations that he wrote and I tweaked.  For this and so much–thank you, Avery!

A (Partial) Solution to the Feedback Swamp

October is when the quicksand hits.  I’m up to my knees in student work and am starting to feel serious pangs of conscience for not being able to give every scrap of paper the care and attention that children and young adults deserve.  So I hold onto the work, thinking that I’ll be able to properly process it soon enough.

There’s no way that’s going to happen.  There are how many of them and one of me?  They can produce far faster than I can respond.  I can try to expand the audience for their work–with peer review and even more daring ideas like student blogging that I haven’t tried out yet–but I still feel this intense obligation to give them personal, thoughtful feedback myself.  So their classwork and write-ups and reading logs pile up, and soon enough I’m in over my head.

Every year I struggle with this.  Every August I prepare a new plan to combat it.  I’ve racked my brain trying to find the solution.

Sometimes when you’re so deep into struggling with something, you have to hear a fresh perspective more than once for it to stick.

I read this post by Steve Miranda the other day about his experiences trying to give thoughtful feedback to his English students.  Amazing stuff.  I recognized myself in his frustration with students who do not seem to appreciate the labor of commenting, and I loved both his experiment and his ability to understand the logic of his students’ motivations.  But no lightbulb went off in my head just then.

The next day I was in the park re-reading The Open Classroom by Herbert R. Kohl.  I first read it after my first year of teaching, and it had been calling out to me from my shelf at the beginning of the summer.  I came across this passage toward the end, in a section entitled On Correcting:

“It is not a matter of whether one corrects a student’s paper so much as a question of when and how.  Students produce some papers that they care about and others that they would just as soon forget.  In school, teachers have a tendency to consider all the work of a student on the same level.  Everything a student does is supposed to be a finished product.  There is little allowance for hesitant beginnings, false starts, bad ideas, impossible dreams–all the explorations writers attempt before finding their own voices and the forms appropriate to expressing them.  They are expected to be perfect every time.  In my experience when students produce a work they care about they want it to be correct in every way–that is, to communicate as fully as possible.  They ask for corrections and want to get things right” (p. 111).

Whoa.  Students can decide what matters to them, and they can tell me about it.

Steve’s post warmed me up for this thought, and Herbert Kohl’s paragraph drove it home.  I’ve held the conscious belief for a few years now that it’s more important that my students do good work than it is for me to know about it.  I don’t think it has affected my behavior nearly enough.  What I need to know about my students’ work is whatever allows me to assemble good future tasks for them that will meet them where they are.  That, whatever information I need to be able to write fair and descriptive end-of-term reports.  If my attention to my students’ work isn’t serving those two purposes, and if my feedback isn’t particularly desired by a student on a particular piece of work, then I am wasting my attention and time.   If my efforts to interpret and respond aren’t shaping my lesson plans, giving me something to say about the kid come report time, or helping me to build up a relationship with the student around a piece of work, then it’s just ornamental–a mental game that I’m playing alone and with no real-world consequences.  I’m just writing comments for myself.

I don’t want to do that.

So I’m going to start asking my students what kind of feedback they want from me, and when.

I’m going to stop treating every slightly-mashed worksheet as though it’s an exotic flower with mysteries in the offing.  These products of student thinking and work are entirely secondary to the thinking process they engaged in.  Most of what was going to happen for them has happened already.  There’s no point to autopsies for worksheets.  The kid is still alive and kicking.  The question is less, “what happened here?” and more, “what can I do to shape what happens next?”

Finally, I’m going to trust my students more–trust that if I show my willingness to give them attention and advice, celebration and critique, that they’ll seek it out.

I’ll let you know what that looks like in practice.  Check back in October.

SBG: Affective Quizzing

When has a student mastered a skill?  Part of the purpose of Standards-Based Grading is to help us answer this question.  (I’d even say it helps us to articulate the question in the first place.)  Different teachers establish skills mastery in their versions of SBG in different ways–for instance, getting everything right on a skill quiz, or getting everything right on two skill quizzes in a row.  In these versions, once a student achieves a certain outcome, she is exempt from further quizzes on that skill.  For other teachers, a kid is never “done” with a skill until the year is over; skills continue to come up on new assessments, and the student’s grade for that skill is his most recent one.  On top of these, I’m sure there are many other awesome variations and hybrids that people have devised that work well for their classrooms.  I’d love to hear about your own twist.

This past year I was in the “one-and-done” camp, and I’m planning on staying there.  That said, I think I will be keeping a better eye out for occasions when a student is struggling with the mechanics of a skill that he has previously quizzed well on.  That may be a good time for a conversation and perhaps reviewing and requizzing.  (Without grades in the picture, there won’t be anything punitive about this–just an opportunity to learn.)  But I’m looking forward to including a new facet to my skills quizzes themselves this year.  Like so:

"How did that go for you?"

It’s that last bit.  I’m curious to see how asking students about their quizzing experiences affects the whole assessment process.  I can’t say exactly where the idea to do this came from, but I think it was at least partially inspired by a student of mine from last year.  She would often write notes to me on her quizzes explaining what she still felt fuzzy on.  This was on quizzes she was choosing to take, buffet-style.   I found that her notes both gave me a better sense for her understanding and provided a really natural way for us to start conversations about remediation.  While there were times that she struggled with our course material, her ability to self-evaluate helped to make her year a successful one.

I’m sure you’ve taught both over-confident and under-confident students.  I feel that by asking “How did that go for you?” on quizzes I may sometimes hear anxiety and doubts from under-confident students even when they get everything right.  In the past, I’ve just checked off their correct responses, said “good job” and moved on.  They were “done” with that skill, despite not feeling at home with it.  No doubt they were in the short-term relieved, but perhaps they were left feeling uneasy about this skill in the long run.  That isn’t what mastery should look like.  By putting that quick gut check at the bottom of each quiz, I’m trying to give my students a safe and immediate place to tell me about their relationship with the skill, right after they’ve shown me their attempts to apply it.  And if they’re telling me they don’t feel like they’ve mastered it yet–even with a perfect paper–then they haven’t.  More steps need to be taken.

I’m sure you can fill in the corresponding things that could transpire with an over-confident student.

Of course, it’s entirely possible that a kid will pose as more confident than he really is, or decide not to respond to the question at all.  To me, it’s not important that all of my students share their feelings toward their skills with me in this way.  If providing the occasion helps even a few of them to do so, the fruits of that will make me feel like it’s well worth asking.

To sum up, I’ve come to think that any answer to the question “When has a student mastered a skill?” needs to include, “when she feels like a master of it.”
I hope that finding room in my classroom for the affective aspect of learning skills will make for more effective assessment and feedback.

(Ah, there’s the punchline.  It turns out I’m not a spelling dummy after all.)