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[Xmca-l] Re: Article on Positioning Theory

Thanks for your comments, Phillip.

The classroom teacher was textbook exemplary in terms of preparing students for collaborative learning and in terms his negotiation of the classroom culture and context. Exemplary. In fact, it was a key factor in terms of why I chose this class. My goal was to study mathematical learning and I did not want poor teaching to distract from that. The reality was that my focus was on social interactions more than mathematics, given what the videos contained. That was totally unanticipated given how carefully I selected the teacher. I was also a seasoned teacher when I conducted the research.

 I recall, with great clarity, my first viewing of one of the videos where the positioning resulting in productive silencing. Most disturbing was images of me circulating in the background, the teacher stopping in to check on and work with the group. We simply didn't notice - despite our skill level, engagement, and our attending. The masking behavior was so effective that we didn't notice - and this is precisely why the positioning was so powerful and resulted in productive silencing. Even to the trained and present eye, it went unnoticed. This has raised to me very important questions about what  is it that teachers actually see, even when they are looking or thinking they are attending? Gee (1999) claim that interactions have the potential of infecting future interactions was obvious in the videos and watching the broader classroom interactions. It could be that what we see is also infected. 

In my current post-secondary teaching, when I circulate amongst groups, it is often very clear to me who is suddenly participating when I approach the group. What I recognize from this research is that there is likely an underlying dynamic that I do not see, even if I try to see it. Consequently, assuming I can't see this underlying or subversive context, then there is a moral imperative for me to think actively about it when I think about teaching and learning.

Donna Kotsopoulos, Ph.D.
Associate Professor
Faculty of Education & Faculty of Science, Department of Mathematics
Wilfrid Laurier University
75 University Avenue West, BA313K
Waterloo, Ontario, N2L 3C5
(519) 884-0710 x 3953

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>>> On 3/26/2014 at 6:00 PM, in message <E23E629A42F087498471D39762DF7EB2DCA4221EBA@ESTES.ucdenver.pvt>, "White, Phillip" <Phillip.White@ucdenver.edu> wrote:

your comments resonated with me strongly, Ed.  as i read Donna's ethnography, i kept on wondering where the teacher was in all this.  in my experience as a classroom teacher, particularly when students are working collaboratively, is constantly moving from group to group observing and analyzing the social interactions that should be supporting the learning taking place.  i rove the room from group to group, jotting down monitoring notes (these days on an iPad), particularly noting the group interactions in order to make either immediate interventions on the spot, and for consideration the next day. i couldn't understand how it came to pass that the teacher never observed Mitchell's activity.
the richness of your descriptions, Donna, illustrated wonderfully the complexities of social interactions within a classroom.  i wondered, like Ed, what engagement expectations had the teacher presented - running a classroom of collaborative groups in demanding in paying attention to a multiplicity of details.  as you noted, Donna, "At the forefront of all pedagogical choices made by teachers should be explicit consideration of who is privileged and who is silenced and marginalized by such choices" (p. 50). regardless of pedagogical practices, it is more than possible, it is quite likely that positioning will be undetected.  i find myself unconvinced my your essentially cause and effect statement that, "Participation in collaborative learning may create roadblocks for some students in the mathematical learning ..., or in the way in which they come to see themselves as a mathematics learners or mathematically able" (p. 50).  Timothy J. Lensmire's research "When Children Write:
  Critical Re-Visions of the Writing Workshop" (1994) noted that third graders were petty, unkind prejudiced and selfish.  Lensmire understood these behaviors as a reflection of the difficulties, problems and tensions with adult American society.  Likewise, Karen Gallas' ethnography, "Sometimes I Can Be Anything: Power, Gender, and Identity in a Primary Classroom" (1997) demonstrates that, as Lensmire noted, students, in this case first and second graders, arrive in the classroom with a wide array of social practices that involve positioning of each other as well as themselves.
you noted Gee's statement that "interactions have the potential of infecting future interactions" (p. 50).  and indeed i wondered what history your participants Alice, Ella, Joanne, Mitchell and Will had brought to this particular activity.  my take on this ethnography is that it is exceedingly rich, and that there is data embedded there that can explain a great deal more than the suggestions that "for educators is to keep in mind that for some students, like Mitchell, working collaboratively may not be in their best interest" (p. 50).  another conclusion could be that students, like Mitchell, need additional resources and supports to work in a collaborative group.  in fact, the behaviors towards Mitchell of Alice, Ella and Joanne, suggests that they too fail to understand how to work collaboratively.


Phillip White, PhD
Urban Community Teacher Education Program
Site Coordinator
Montview Elementary, Aurora, CO
From: xmca-l-bounces@mailman.ucsd.edu [xmca-l-bounces@mailman.ucsd.edu] On Behalf Of Ed Wall [ewall@umich.edu]
Sent: Wednesday, March 26, 2014 12:48 PM
To: eXtended Mind, Culture, Activity
Subject: [Xmca-l]    Article on Positioning Theory

I always enjoy reading about the dynamics of mathematics classrooms so thanks to Donna.

Some somewhat random thoughts (and as I am not entirely familiar with the terminology of positioning I may use it quite incorrectly) as I've been thinking about related issues.

Teachers are placed in classrooms (positioned?) with certain toolsets and among these is something that, in its various forms, is called collaborative learning. This is, in a sense, neither good or bad; collaborative leaning is simply a tool. When difficulties do arise, it is, in a sense, because it becomes a one-size-fits-all method (positioning?) for inducing dialogue. When it works it is very very good, when it is bad it is horrid (smile). The question, one might say, it gives a sort of answer to  becomes in mathematics classrooms, at least, how to give students opportunities to learn use publicly established ideas, methods, and language so as to make, validate, improve, and extend the mathematical knowledge of the class. Is this necessary or desirable? It depends on your point of view I guess.

Teachers are placed in some quandaries if they get up from their desk or relinquish their place at the blackboard. Collaborative learning of some sort (and the group could be two) forces this issue somewhat. However, it also surfaces the need for some careful grouping and the possible need to publicize appropriately in the collective class. That is, 'positioning' yourself as a teacher that supports some sort of collaborative work is usefully discomforting (smile).

Along with this, if done thoughtfully, comes the ability to manufacture and juggle ruptures. Mitchell is a nice example of this although unfortunately his rupture does not seem to make it out of his group (I tend to see this, perhaps incorrectly, a misfire of the very idea of collaborative). What I find quite interesting in this regard is Donna's (I think I read this correctly) attempt to re-'position' Mitchell and the pronounced resistance from Mitchell's colleagues and, in a sense, from himself. Ruptures almost always arise with reasonable mathematics tasks and are to be cherished (all this is an opinion) for their potential. However, realizing that potential takes some serious teacherly skill and I'm not sure that re-positioning Mitchell is the solution (he may need to do this himself with, one might say, encouragement) although re-positioning his rupture may well be.

Finally, for some reason, I tend to read into the dynamics of Mitchell and his group Michel de Certeau's ideas of 'everyday' strategy and tactics. Mitchell (and I am, in part, reading myself into this) is engaged in tactical maneuvers (he says something to this regard) in the face of a somewhat strategic view of mathematics embodied by his colleagues (the omnipresent 'it'). He has also put something on the table that with a little teacherly push (although this needs some careful thought out) could usefully challenge that strategic view of mathematics.

I have seen this activity done a number of times and when it 'succeeds' (my opinion) it usually is because a rupture surfaces for the entire class. What I don't know is how people position themselves, if they do, afterwards (including the teacher) in the light of the ensuing dialogue. Very interesting!!


Ed Wall