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[Xmca-l] Re: Article on Positioning Theory
The impressions I thought about were:
1. The difficult task of establishing a collaboration so that everyone is
committed voluntarily and that allows for re-appraisal of the commitments.
That is, to establish a task in which "positions" are not a big deal.
2. Problematic aspects of the activity: the priming of a competitive schema
in the positioning questionaire and the operational nature of much of the
work. It seems to me that the collaborative conjuction of the various
operations (cutting shapes etc) is in the ongoing planning and directives,
but that the emphasis is on the making.
3. The relations of "posiitioning" to inferential perspectives (Brandom)
and methods to show its "genesis".
So this seems, to me, to be all about the difficulty children have with
planning and thinking about their tasks: how they need to be doing them in
order to help them think about the planning but also the potential
amplification of the problem if they are doing it in a "scrum".
I think what you are reporting serves to elucidate the complexity (for the
children) in this task and how the difficulties in coming up against this
complexity may obscure the intended mathematical content (i.e. reduce the
salience of the mathematical concepts).
Perhaps, one basic activity theoretic contribution would be to seek to
calibrate the complexity of the collaboration to the point whereby the
mathematical concepts themselves become the issues that dominate the
Thank you for presenting the paper!
On 27 March 2014 12:22, Donna Kotsopoulos <firstname.lastname@example.org> wrote:
> Interesting your use of the word "rereading" the videos. All I could see
> was the positioning - despite not having that theoretical orientation prior
> to the viewing of the videos. My initial focus on was on Gee's little "d"
> discourse. Remarkably, I was asked to go back and reread the videos and
> "just" attend to the mathematics which I could not do. There was an ethical
> obligation that made the actual mathematics seem secondary.
> Almost parallel in time and design, another mathematics education
> researcher studied older students' collaborations. Our videos were
> remarkably, remarkably similar. The dystopic view of productive was
> undeniable in videos from each of the studies. Yet, one of us read the
> mathematics and, as you see from my work, I read something different.
> 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
> DISCLAIMER: This e-mail and any file(s) transmitted with it, is intended
> for the exclusive use by the person(s) mentioned above as recipient(s). Any
> unauthorized distribution, copying or other use is strictly prohibited.
> >>> On 3/26/2014 at 7:44 PM, in message <
> Larry Purss <email@example.com> wrote:
> Your reflection,
> "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?"
> Is a profound question exploring what we are actually attending to when we
> are *consciously* attending. Your further insights that,
> 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.
> Donna, this *concealment* may indicate that what we as teachers are
> *attending to* always includes *concealment* as our *attending*
> presents partial ASPECTS of our *lived experience* with each other while
> other ASPECTS remain *concealed*.
> Also you mention you initially PLANNED on attending to the emerging
> cognitive development of math concepts, but on *re-reading* the video
> sequences, the positioning sequences were so compelling, that your initial
> *intention* had to be re-adjusted..
> What teacher's are actually *seeing* may be as *constrained* and
> *concealed* as what they are *saying* and *hearing* and *doing*. It may be
> that the relational flow BETWEEN *revealing* and *concealing* may be very
> complex and the conceptual understanding of *discursive* may need to EXTEND
> further the notion of *voice* to include *felt tendency* in our
> understanding of positioning.
> The phrase that we need to *hear each other into voice* speaks to the
> vitality of Jennifer's insight that until we EXPLICITLY attend to the
> quality of *hearing each other into voice* in contrast to the more
> traditional educational goal of helping each student *find their own
> voice* [as a possession which they need to locate and claim] we may be
> attending to [REVEALING] the more individualistic aspects of *voice* AS
> positioning, while the intersubjective dialogical aspect of our
> responsibility to HEAR the other INTO voice remains concealed [and
> On Wed, Mar 26, 2014 at 3:25 PM, Donna Kotsopoulos <firstname.lastname@example.org>
> > 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
> > 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
> > the videos contained. That was totally unanticipated given how carefully
> > 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
> > 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
> > 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
> > looking or thinking they are attending? Gee (1999) claim that
> > 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,
> > is often very clear to me who is suddenly participating when I approach
> > 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
> > www.wlu.ca/education/dkotsopoulos
> > www.wlu.ca/mathbrains
> > DISCLAIMER: This e-mail and any file(s) transmitted with it, is intended
> > for the exclusive use by the person(s) mentioned above as recipient(s).
> > unauthorized distribution, copying or other use is strictly prohibited.
> > >>> 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
> > 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
> > 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
> > 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"
> > 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
> > 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
> > 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
> > 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
> > 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
> > great deal more than the suggestions that "for educators is to keep in
> > 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
> > 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
> > Phillip White, PhD
> > Urban Community Teacher Education Program
> > Site Coordinator
> > Montview Elementary, Aurora, CO
> > email@example.com
> > or
> > firstname.lastname@example.org
> > ________________________________________
> > From: email@example.com [firstname.lastname@example.org]
> > On Behalf Of Ed Wall [email@example.com]
> > 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
> > 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
> > knowledge of the class. Is this necessary or desirable? It depends on
> > 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
> > to see this, perhaps incorrectly, a misfire of the very idea of
> > collaborative). What I find quite interesting in this regard is Donna's
> > 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
> > are to be cherished (all this is an opinion) for their potential.
> > 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
> > 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)
> > 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
> > What I don't know is how people position themselves, if they do,
> > (including the teacher) in the light of the ensuing dialogue. Very
> > interesting!!
> > Thanks
> > Ed Wall