What feedback would you write on this kid’s paper? Why?

(Thanks, KN!)

We chatted on twitter about this question for a bit. What predictions can you make about the predictions that were made? Click through to check your answers!

It's #mathmistake time! What percent of kids got this right? What was the most common wrong answer? Percent on that? pic.twitter.com/lNbaDxUeXx

— Michael Pershan (@mpershan) August 18, 2014

Here are the results from the 59 students who answered this question on an exam:

How would you give feedback to the students who wrote “infinity”?

Imagine that you were to give feedback to the students who wrote “-3/7.” What feedback would you give?

In a previous post, lots of commenters said that they didn’t feel that you could give helpful, written feedback because there wasn’t enough evidence of student thinking on the quiz. Given that complaint, it might be interested to see how those same teachers would give written feedback on a quiz that gives significantly more evidence of how a student is thinking.

Here’s another quiz: what sort of written feedback would you give? (The checkmarks are from the student, who was provided with an answer key and checked her own work, ala this.)

As before, imagine that you don’t have to write a grade on this paper. Some things I’m wondering about:

- Would you give comments on every solution, or only some of them?
- Will you ask kids to “explain why you said _______”? When is it helpful to ask for an explanation? When isn’t it?
- Will you give your kids specific next steps, or will you mostly point out the good and the bad of their work?
- Will you throw up your hands and say “You really need to have a conversation with the kid!” for this sort of quiz also?

In a lot of ways, it’s much easier for me to come up with helpful feedback to give on rich, juicy problems (see here) than it is for your typical quiz or test. I find it much harder to think about how to give feedback that helps a kid’s learning when (a) the quiz is full of non-open questions and (b) the kid’s solutions don’t show a lot of thinking. But a lot of classroom assessments end up like that, and it’s important to figure out how to deal with those tough situations effectively.

So: What would you write as feedback on this quiz?

Some constraints/notes, that you should feel free to reject or challenge:

- Assume that we’re dealing with
*written*feedback here. Not a conversation. - Assume that we
*don’t*have to write a grade on this piece of work. (If we wrote a grade on here, some research indicates that would ruin any feedback we gave.) - You might decide to give feedback on every question of this quiz, you might not.

I’ll jump in with my thoughts in the comments. Here are some questions about your choices that I’m wondering about:

- Would you choose to mark the questions as right/wrong?
- Would you try to find something to value about this kid’s work in your comments, or will you be all hardass instead?
- Would you ask questions or give suggestions?
- Would you write one, several, or many comments?
- Would you reject the constraints in some way?
- Would you ask the kid to explain himself?

Excited to read your thoughts!

What mistakes would you expect to see in the proofs of the problem below? Take a moment and make some predictions. You might find it helpful to know that this was part of an end-of-the-year exam, and that kids were able to use whatever proof representation they wanted. In other words, they could write two-column proofs, paragraph proofs or flowchart.

Here are the mistakes, pulled from the class set. Or maybe you feel uncomfy describing these proofs as “mistakes”? Maybe it’s better to say that they contain mistakes? Or that they are proofs that aren’t where we probably want them to be?

Do you feel comfy calling these “mistakes”? What would you call them?

What are the next steps for these kids? What would you recommend that their teacher do?

A note from the submitter:

Along the lines of one I sent you awhile back. This is one of my best students, and several other students gave answers with similar misconceptions. I pretty much ignored it last time it came up, thinking that it was an anomaly, but I think it’s a significant hole in my students’ understanding. Students were using calculators today.

What’s going on here in the student work? What’s the connection to the earlier post?

What you need to know is that the student work is the stuff typed in red, and that this came on a take-home quiz:

Why does this student think that ln(e) = x^1. Or did I get that wrong? Are there ideas that “feel similar” that he’s confusing, or is it something else?

(Thanks Taylor!)