I should start this post by saying that I work in a school with "inclusive classrooms." Students are in the same class based on grade level alone, no tracking by "ability level" or any other metric. I suppose I should also say that I am doing an action research project on mathematical agency. Agency is a slippery word to define, but for the sake of simplicity for now let's say mathematical agency is defined by a positive self-concept as a mathematician (as one who believes in their ability to make sense of mathematical tasks and situations and to judge the validity of those responses). Lately, I have been thinking most closely about how the set-up and discussion of tasks in the classroom can affect student agency and power - for good and bad.

This all came about the other day when some of Brian Lawler's credential students were in observing my 10th grade class working on "Consecutive Sums." Basically, the prompt is: "explore consecutive sums and see what you discover" (where equations such as 1+2+3=6 and 7+8=15 are considered consecutive sums). Eventually, the conversation turned into trying to figure out which numbers can (or cannot) be written as consecutive sums. I put a table up on the board with the numbers 1-25 on it and asked groups to send people up to fill in the chart once they had found one. What ended up happening is that about 5 students dominated this part of the lesson while others sat and watched. I know there are plenty of suggestions about better ways to handle this particular part of the lesson, but I think the implications are greater than that.

I have read several articles and books for my action research (a couple good ones if you are interested) that outline an amazing vision for a classroom community in which students present ideas, challenge each other, and construct meaning together. Most times when I try this, one of two things happens:
1. I select and sequence student share outs so that certain voices are heard that are usually silenced. Mostly, because I have created the conversation, there isn't much to talk about and students seem disinterested. They aren't debating anything; they aren't solving things collaboratively. OR...
2. I'll select one or two pieces of work to get a conversation started and then step out of the way. This usually gets students talking and debating. The only problem is, it's usually no more than 10 students out of a class of 20-30.

I'm not sure I have any answers to this yet, or even that an answer exists that will work for all groups of students. But, I am really interested by the intricacies of teaching...by the tasks we choose, by how we set up those tasks, by how we get students talking about those tasks, by how we conclude those tasks, and, especially, how ALL of those moves inevitably make a difference in what students are learning about themselves as capable mathematicians. This last bit, to me, is far more important than the "mathematics" that they learn.
 


Comments

09/06/2012 1:37pm

Hi Bryan,

I've been reading and enjoying your blog for a while. This post really resonated with me as an experience I've had in my own classroom and as a guest in others.

My colleague Suzanne who has taught middle-school math and computing for many years and has a really thoughtful approach to equity and access and inclusion and just plain valuing students just published an article about Unsilencing Student Voices.

http://mathforum.org/articles/communicator.article.sep.2012.pdf

(linked to on this Math Forum page: http://mathforum.org/pow/teacher/articles.html)

I hope you can find some pieces to help you keep thinking about this, and I look forward to hearing more about the choices and you make around this issue!

Max

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09/08/2012 12:49pm

Hi Max...

Thanks for your thoughts and for sharing the article you posted here. I read through it and there is certainly some valuable stuff there. Often, I just think complex instruction gets oversimplified. People think: give them a cool problem, let them work in groups, and then discuss it as a class. It is just so much more...uh...complex than that! :)

I have read articles that talk about the value of whole-class discussion and collaboration (such as the ones I have attached in the post). Lately, I have been thinking that whole-class discussion (at least in my setting...classes of about 30 high school students) is best used as a forum for making connections between different responses and, perhaps, exposing common misconceptions. To get ALL students active, I am beginning to think there is a delicate balance of individual time, partner time, group time, and whole-class time (usually vacillating back and forth between these). Of course, the tasks themselves also play a large role in what students are learning about "what is mathematics" and "who am I as a mathematician and thinker." I'll try to keep posting as this (which is closely linked to my action research) unfolds more for me. Thanks again!

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09/13/2012 8:23am

This is a neat conversation for me! One thing I do when I'm not thinking about math teaching, is work with social activist groups, and that includes learning how to do training and facilitation in that setting. I've taken workshops from groups like Training for Change (http://trainingforchange.org, which actually has a historical connection with the Math Forum, through the group Educators for Social Responsibility).

I'm starting to learn a lot about how different formats (individual, partner, group, whole-group, oral, written, standing up, sitting down, etc. etc.) can really shift how students work with the materials -- and it seems like that's something teachers, especially high school teachers, don't get a lot of exposure to or chances to play around with.

I wonder how you got started exploring the grouping formats, paying attention to how they engaged different students differently, etc. I'm really excited to keep following this blog to learn more about it and have different examples to share with the teachers I work with!

Max

09/17/2012 10:16pm

Thanks Max...I'm happy to have someone to exchange ideas with. I think my interest in all this was first sparked in my credential program at CSUSM (which was great) and I am now exploring it in depth through my graduate work and action research project. I am exploring student agency and how different classroom factors play in role in how students come to realize themselves as mathematicians and thinkers. I'll definitely keep you posted...I imagine my writing will naturally take me that way.

Michael Reitemeyer
10/09/2012 8:37pm

Bryan, great piece. I often grow frustrated with the struggle between a teacher-led full-access discussion and a student-led restricted-access one. I have spent the last several months thinking about and trying to promote student efficacy, but after reading your piece I think that I'm often fighting the wrong battle. And that if I can win the agency piece then the efficacy piece will follow. Last year I heard Dan Meyer say that he feels, "Math is magic," (like you can do seemingly supernatural things with it) and that he wants his students to feel the same way too. I've tried pushing that idea at the end of last year and this year and feel that it has helped promote general student agency a little, but after reading your blog I think I need to focus it more. Perhaps I need to add something to the unit portfolio (IMP curriculum), that might help address and even promote student agency. Any thoughts or suggestions?

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Bryan Meyer
10/10/2012 7:36pm

Hi Michael...

Interesting questions! I would agree that agency comes before efficacy. I wonder if pushing efficacy gets in the way of helping students realize authority? I would be interested to hear about your experience pushing the "math is magic" idea and how it has preserved student agency. It is interesting to me because I think of it rather differently. I take mathematical thinking and sense making as a natural function of being human. In other words, when put into a state of disequilibrium we respond mathematically by sorting things out and making sense. In this way, mathematical agency and authority is something that I feel is already a part of each of us. Somehow, "teaching math" seems to rob people of that because we never actually give students a chance to sort anything out for themselves...we end up just telling them what to think or how things are.

I'm working a lot on agency this year....so I'll keep you posted about how things are coming along. My main idea has been to put mathematical habits of mind (things we all do as part of being human) at the center of our classroom. As we work on things, I ask students to meta-cognate (is that a word?) about where they see those habits in their work. I am hoping to help them notice more moments where they are "doing mathematics" and, consequently, to realize that they are mathematicians.

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