I have said this before: middle schoolers are extremely concrete thinkers. This is why I find it so helpful to have a clear and concrete rubric I can use to help them to understand assessment of their work as specifically as possible. I'm reasonably happy with the rubric I've revised over the years for problem-solving, as it seems to help students diagnose and understand what went wrong in their individual work and where they need to head. But I've realized I also needed a new rubric — one for what I've been calling "collaboration literacy" in this blog. My students need help naming and understanding the various component skills that make up being a healthy and valuable collaborator.
My draft of this rubric for collaboration, which is grounded in restorative practices, can be found on the MS Math Teacher's wiki. I would very much value your input and feedback on this tool and its ideas.
I don't want to spend a lot of time talking about how and why Complex Instruction does not work for me. Suffice it to say that the rigid assignment of individual roles is a deal breaker. If CI works for you, please accept that I am happy that you have something that works well for you in your teaching practice.
This rubric incorporates a lot of great ideas from a lot of sources I admire deeply, including the restorative practices people everywhere, Dr. Fred Joseph Orr, Max Ray and The Math Forum, Malcolm Swan, Judy Kysh/CPM, Brian R. Lawler, Dan Pink's book Drive, Sam J. Shah, Kate Nowak, Jason Buell, Megan Hayes-Golding, Ashli Black, Grace A. Chen, Breedeen Murray, Avery Pickford, "Sophie Germain," and yes, also the Complex Instruction folks. I hope it is worthy of all that they have taught me.
It is an amazing rubric. I wonder if it possible to include something which reflects "critique the reasoning of others" as stated in the CCSS Mathematical Practices. But as Sam said, it is a thing of beauty.
ReplyDeleteThanks so much, Mermaid of Brooklyn! I am sure you could include something about doing a critique of the reasoning of others in the rubric, though I find that this is not a skill that most of my students have trouble with. How would you envision that working?
Delete- Elizabeth (@cheesemonkeysf)
I think it would come under your "Exploratory Talk" category. I also think it would require significant modeling, so that students learn how to be constructive when critiquing, yet still be able to question someone else's ideas. Many adults have trouble with this as well. (!) But it seems to me that it comes under the umbrella of "I Wonder.."
DeletePerhaps an activity or problem which doesn't have one solution, but is rather subject to different interpretations could be used to work on this kind of skill. I actually work on a team of teachers who review Common Core aligned tasks for the NYC Department of Education, and we find that this is one of the most difficult practices to elicit. Clearly I have some thinking to do about how to get my students to do this as well!
BTW, this is from Wendy Menard (@wmukluk); I usually sign in with my Wordpress ID - hermathness.wordpress.com - but Blogger wasn't allowing me to do this.
Thank you. I updated my version, which has no grading component. I also had trouble with the enforced roles, but thought maybe it was a difference between high school and college.
ReplyDeleteThank you, Sue. I posted editable versions on the wiki, so you could easily delete the point scores.
Delete- E.
Elizabeth, these are terrific works of genius! Would you be adverse to posting the word versions instead of just the pdf? I would love to be able to edit and make it my own for use in class, as well as repost the modified versions.
ReplyDeletethank you very much for these!
Thanks, Glenn! I have good news and bad news. The good news: I have put my editable files up on the Math Teacher Wiki along with the PDF versions. The bad news: these are all Mac-based documents, created using either Apple's Pages software or a terrific drawing program called Omni Graffle. My experience has been that the rubrics are almost impossible to format in Word. In Omni Graffle or in Pages I can just bang them out (except for writing all the content, of course).
Delete- Elizabeth (@cheesemonkeysf)
I don't have Omni Graggle, but I do have a mac. I may have to copy and paste the items out into word and I will send them to you so you have all the formats for others.
DeleteThank you for all you do!
Glenn — You could download a 30-day time-expiring copy of Omni Graffle from the Omni Group so you can mess with my file and copy/paste what you want from it: http://www.omnigroup.com/products/omnigraffle/
DeleteAn educational license is $59.99 (you just need the regular, not the Pro version). I'm a huge fan of the company; I've known those kids since they first started out!
- Elizabeth
Fantastic. I like @mermaid's idea also.
ReplyDeleteI'd like to talk to you more about CI. What I think is the core of CI is working at changing the myth of mathematical ability and who is smart. It is the 2 practices of (1) Multiple Ability treatments and (2) Status treatments that define CI, as I see it. Other things group stuff I've heard all over the place. For the novice implementer, the 2 CI practices I identified are usually awkward and stilted at first. But as the teacher begins to own and believe the message for themselves, it becomes very natural.
Brian — I am in complete agreement with you about the treatment of multiple abilities and status issues in CI. I value those practices very deeply, and I implement them with fidelity.
DeleteWhere I have problems with CI is in its rigid and limiting assignment of artificial "roles" to each learner in a group. I have experienced the disastrous consequences of this practices both as a teacher/facilitator and as a learner. At the most basic level, I have seen learners too often self-censor or be censored by others in the group whenever their question or contribution seems to step outside their assigned "role." By the same token, many learners use the roles (or not-my-role role) as an excuse for opting out of full participation.
I feel guilty saying this in public, but the notion of roles seems really "beneath" the best aspects of CI. And I have found no compelling justification for their continued use. That is why I've been working on developing the ideas in this rubric.
If I am going to value EQUAL participation by all learners, then I cannot endorse or enforce a system that encourages a form of self-limitation I have seen to be damaging to many different kinds of learners' self-concepts. The system of artificial assigned roles in CI is also at odds with all the forms of collaboration I have experienced in my own 20+ years as an entrepreneur, as a meditation practitioner, and as a person deeply committed to social justice. When you are on a team in the real world, there is no "them." There is only us. No recorder, no resource manager. Just learners all learning equally together. In effective entrepreneurial teams, whoever has a good idea and the courage to put it forward simply does so — according to norms of what is appropriate in the given situation. That is the kind of spirit I want to encourage in my learners as well.
I believe that the goals and practices to which you refer could be easily transferred to a system without the artificial limiting roles that CI demands. I also believe this would free both teachers and learners to better deal with the authentic situations and social and emotional learnings that arise.
As for the point values, they could be used or discarded as a teacher sees fit. I teach in an environment/community where the use of points raises the "status" of this dimension of learning. But if I were still teaching in the inner city, I would probably NOT use points. Instead, I would use a highlighter on the copy of the rubric to reflect back what I witnessed in a learner's collaborative work.
Does this make any sense?
- Elizabeth (@cheesemonkeysf)
Instead of strict roles, I've always liked the "hats" idea. It's a way of talking about roles in a much more flexible way. That website has more of a corporate focus, but I just took the core idea and ran with it.
DeleteElizabeth--
ReplyDeleteYou already know how much I appreciate you sharing; the thought that went into the rubrics is apparent. For my purposes I added levels of proficiency using a scale of 4=distinguished, 3=proficient, 2=developing, 1=emerging. That way I can have the students monitor their own progress and when I'm ready to start "taking it for a grade" I'll convert it into a percentage.
I know we previously talked about CI and roles. Here you make a strong argument. I think your rubric may settle any dispute. The rubric holds everyone accountable to the same expectations as well as informs students of the criteria for success.
With regards to Mermaid’s inquiry a while ago I blogged about a RUBRIC for assessing the mathematical practices. It is something our district’s director of assessment created. I might use it as is or revise it.
Again, your thoughtful and thorough work is clearly evident. Great job!
P.S. I goofed by posting this comment on your 7/27/2013 post. You may want to delete it:)
Sending my MS Word copy of these (without the rubric part), which I made on a MAc, to both cheesemonkey and Glenn, in case htey're of use.
ReplyDeleteI didn't read the other comments yet -- sorry -- but I wanted to chime in to say that I thought it was interested that your problem-solving rubric defines excellence in problem solving as excellent in conceptual understanding. And your collaboration rubric targets the signs of a good collaborator. (Which, you know, makes sense and all.)
ReplyDeleteTo me, what's missing is a rubric that assesses problem solving ability independent of content. Or is there such a thing at all? Is good problem-solving just about providing evidence of understanding the underlying content?
I often encounter problems where the difficulty is in applying and making connections between the content that I know. Now, we could say that this means that I'm really encountering new content, but that strikes me as false. What's hard is grounding yourself, discovering patterns, finding a simpler problem, doing all that Polyaish stuff.
Is there a way to assess this?
I've noticed that I've needed to learn to assess problem-solving skills (methods is my shorthand, as in concept-method-procedure) in order to give kids quality feedback.
DeleteOften if I see a student struggling to solve a problem, I'm quick to assess accuracy and understanding, and slower to notice that the highest leverage point may be that they didn't have a robust process for checking their work, or they didn't do a good job of finding and organizing known and unknown quantities, or their [lack of] organization got in the way of them finding and leveraging patterns, or they didn't have any strategies for understanding what was happening in the story behind reading it (i.e. didn't think to draw a picture, act it out, etc.).
Almost every time I start to write a question for a kid and think, "wow, that really sounds leading" or "I'm trying to get them to notice/think this thing," I find there's a problem-solving habit of mind related to the act of noticing that I could be requesting instead. So instead of, "did you notice that the small rectangles matter too, what do you notice about the ones on the top vs. the ones on the bottom" it's "did you try an answer you're pretty sure is wrong -- and can you show why it's wrong?" or "can you think of something you could guess for? What calculations would you do? Do you know how you would check that guess?"
I don't have a rubric yet, but I'm narrowing in on a set of things I want to see evidence of kids being good at:
* Careful noticing
* Being able to see the "big picture" and represent it in multiple ways
* Identifying key quantities
* Describing relationships among quantities
* Exploring & using good ways of recording and organizing data
* Working at multiple levels of abstract representation
* Being metacognitive -- monitoring progress, trying different things purposefully
* Checking work robustly in multiple ways, as needed
* Making tools out of what you have done already, to create a more robust repertoire of things to try & a library of "types" of problems and representations that work well for different types
* Persevering
* Extending, wondering, asking good questions
11 things is too many for a rubric probably, but not a bad set of standards for a problem-solving strand in a year long course, right?
I can't wait to see/hear examples of this lovely rubric in practice. Please do keep us updated, everyone.
ReplyDeleteMy math nerd says it seems like this rubric spans and partitions the space of Collaboration Literacy very nicely -- it's comprehensive and the categories fill the space without overlapping. :)
I love your rubric. I decided for my purposes, I didn't actually want a rubric, but I have been needing to do a better job of communicating my groupwork expectations to my college students, so I modified it, and posted the result here (it's at the bottom of the page).
ReplyDeleteAnd I decided to put it in a blog post, too. http://mathdancing.wordpress.com/2013/08/23/my-new-explicit-mathematical-collaboration-expectations/
DeleteBlogging might be turning into a procrastination technique.
I love your improvements to the rubric! I hope it's OK that I'm going to incorporate them into my next revision. :)
Delete- Elizabeth (@cheesemonkeysf)
Love the rubric...thanks!
ReplyDeleteYou're welcome! Thanks for stopping by!
DeleteFrom my biased perspective as someone who works primarily with novice teachers, I think what I initially find most lovely about this (among all the beautiful things, some of which previous commenters have already identified) is that it can remind teachers what they should be doing as they interact with students as well-- noticing others' contributions, insights, and learnings; allowing others adequate time; making eye contact; paraphrasing; etc., rather than standing at the front of the room delivering information to an array of sponges.
ReplyDeleteIt also just reads like you :)
Grace,
DeleteThanks for your kind words — and thanks even more for this reminder that the rubric also applies to me too!
Elizabeth (@cheesemonkeysf)
Thanks so much for sharing your rubric - it's jam packed with good stuff. My teaching partner and I would like to take it and modify it for a more general use in all of our core grade 6 classes- break it into chunks until we can use the whole thing. Will share back. Linda
ReplyDelete