As a middle school teacher I know that it’s difficult to make time to individually connect with each of your students since you may be dealing with 130 to 180 students (depending on how many classes and how many in each class). Elementary teachers usually don’t have the volume of students that middle or high school teachers have but because mathematics is usually just one of the subjects they are responsible for delivering to their students, their time is similarly precious when considering adding yet another task to their never-ending list of things to do.

Often I ask teachers who think that using the Math Forum’s online feedback/mentoring functionality, what writing their students are already doing. For example,

* do you have students keep journals? How often do you collect them? How often do you comment on them?

* do you have students write responses to problem solving prompts on paper? as classwork? as homework? as projects? How often do you collect them? How often do you comment on them?

* do you have students reflect on feedback and revise?

Another thing I ask teachers who are contemplating this is, how organized are your students? If they start writing in your class on one day, do they have the paper with them the next day? Do you keep their papers in folders and they stay in the classroom? Do they keep their papers in their own notebooks?

The reason that I ask these questions is that it’s possible that using an online system just might save time in the long run.

My main tip, however, is in how you provide feedback. I recommend that teachers make only two comments per student following the format:

I notice ….

I wonder ….

The “I notice” statement notes one thing that you value in the student’s solution. In other words, a sentence of praise. The “I wonder” statement is a question with the intention that as a result the student will reflect on their draft, revisit it and add more. Along with this, I recommend that teachers check these two boxes in our system so that they bypass using the full rubric:

- Choose not to score this submission.

Hide the scoring grid from students.

I suggest this abbreviated method for several reasons, including

* it doesn’t take very long per student

* it reinforces problem solving as a process

* … but … most importantly, the student’s thinking and problem solving remain in THEIR possession and is not transferred to the teacher

Recently I’ve realized that when a teacher repeats everything a student says or when they give detailed feedback, in some way they are taking over the student’s thinking. If the student is to embrace the Mathematical Practices of …

1. Make** sense **of problems and **persevere** in solving them.

2. **Reason** abstractly and quantitatively.

3. **Construct viable arguments** and critique the reasoning of others.

… **they** have to continue to own their work. **They** have to reflect and revise!

Thoughts?

What does this really have to do with my blog post? Nothing! I just love the photo. This is a sea dragon that I saw at the Monterey Bay Aquarium. (Click on the small photo to view a larger version.) I just love dragons!

I like the idea of limiting comments to “I notice…” and “I wonder…” My students like that language, and it is great language for helping students focus on a mathematical idea. But (not trying to be corny) I wonder whether this approach is as useful in encouraging better writing quality. I have not spent much time in class discussing writing quality, so I suppose I shouldn’t have such high expectation.

When I give students (this year, they’re all seniors in first or second year Calculus) writing assignments, I look for quality of writing as well as quality of mathematics. When students do turn in excellent work, they (and I!) are very pleased. When their work fails to meet the “excellent” benchmark, they often already know why, and it’s often more to do with writing quality than with mathematical thinking. They always have an opportunity to revise, and some (but not as many as I’d like) take the opportunity seriously.

Your blog entries always make me think, and when “think” is followed by “act,” I notice that I become a better teacher… so thanks!

Craig, the rubric “template” that the Math Forum has developed also recognizes that the quality of writing is important since we focus on interpretation, strategy, and accuracy and also completeness, clarity, and reflection.

And, I think that both Mathematical Practice #3 [Construct viable arguments....] and Mathematical Practice #6 [Attend to precision.] address this, as well.

I wonder why those students who don’t take the opportunity to reflect and revise seriously, don’t? Is it a lack of motivation? Is it that they don’t get “credit” and they’re really only motivated if they get points/better grade? Is it that they don’t understand the feedback and can’t use it? Is it something else?

I have students keep portfolios, a collection of all their work and activities. We keep them organized into 5 sections, this has everything to do with ease of use for students and grading for me!

I must admit the marking of these is a daunting task!

I love the “I notice…” and “I wonder…” language! I try to use it consistently during lessons, group work and corrections made, and I even find myself using it with my own children on various occasions!

I wouldn’t hesitate to utilize the on-line mentoring within the system as you suggest, IF, my students all had access all the time. I think in our not too far off future, the issuing of textbooks, will be replaced with the issuing of i pads or tablets.

I like this idea a lot! and could see it saving lots of time….as well as allowing students to maintain ownership of their thinking and problem solving processes.

Writing about the mathematics and its processes is most valuable in helping students identify what they know and what they don’t know. I find the language “I notice…” and “I wonder…” as positive feedback,

“I wonder..” is much less threatening as a starting point for students to continue the process they started, whereas, this isn’t correct, followed by an explanation or guiding questions does the thinking for the student or shuts them down as you noted.

Thanks for the thoughts, insight, and the cool sea dragon!

Patty, I just remembered to add a note that if you click on the small photo of the sea dragon, a much larger one is revealed. They are such amazing creatures.

Your point about computer access is a good reminder! I currently have the luxury of working in classrooms that have regular computer access (at school since it can’t be assumed that all of the students have it at home) and but I know that’s not always the case. Thanks! It also sounds like you are organized and help your students keep all of their work organized. :)

I have found that student’s taking ownership is a slow process. Since many of my Grade six students have been taught by a traditional method, I find they are not comfortable with exploring and revising. I encourage them to keep a notebook with their thoughts on math pows. We do not have daily access to computers so once they have an answer and explanation they submit online.

When my students are mentored, but university students, they get excited that this person they do not know has responded to them. The amount of information provided can be too detailed for the student and they are not sure where to begin. If I provide one main wonder to push there thinking they are not as overwhelmed.

Lately I have been providing an option of the primary or Pre-algebra POWs for my students. Many of my weaker students are becoming much more engaged in the submission since they can reason it through. I think that the building of confidence is valuable.

My students are expected to submit in week one and complete a revision in week 2. I encourage my students to return to previous work and revise also.

Encouraging and nudging forward in understanding I believe to be the important elements of using Math Forum Pows.

Glenys, my guess is that only one or two of your students’ solutions are chosen by the university (pre-service) students when we offer free mentoring. If that’s the case (and not that all of your students receive mentoring at one time on a particular problem), have you turned this into a “class project”? Here’s my thinking:

* all of the students are working on the PoW

* all of the students submit

* Student X and Student Y receive a mentor reply from a university student working with us

* you ask Student X and Y if it’s okay to share their response and the mentor’s response with the class (the first time you could do this anonymously)

* you could project or make copies for groups or whatever routines you have developed with your students — the idea would be that all of the students would read the feedback (which I agree is often quite long and involved), they’d talk about it with each other to try to make sense of it and Student X and Student Y might get ideas of how they might revise

This could take place as a whole class activity but, as you might imagine, it could also just be one small group activity as you’re doing other activities.

Is that something you’ve tried? If, yes, how did it go? If, no, what are your thoughts on how this might help students decode feedback and use it to reflect and revise?

Thanks!

That is a great idea. With my smart board it would be very easy, however it might be more effective in paper and small groups. This dialogue could lead to deeper understanding of the problem that is being worked on. Questions regarding unclear comments could be discussed as a group and unresolved, therefore understandings could be shared with the entire class. I find that there is a fine balance between students feeling overwhelmed and engaged.