XMCA Mail 2003_07: RE: personalizing voice

> -----Original Message-----
> From: David H Kirshner [mailto:dkirsh@lsu.edu]
> Sent: Sunday, July 27, 2003 6:26 PM
> To: ematusov@UDel.Edu
> Subject: RE: personalizing voice
>
>
>
>
>
> Eugene, said:
> Although have students' own representations and notations is not exactly
> what I want and meant, I'd love to have references.
> _______
>
> Hi Eugene.
>
> Much of this work is being conducted in the "early algebra" movement,
> conceived not as a way to bring algebraic symbols in early, but as a way
to
> prepare the conceptual path for algebra by focused arithmetic explorations
> at the elementary school level. You can find many references if you go to
> the JRME web site:
> http://my.nctm.org/eresources/journal_home.asp?journal_id=1
> and do an advanced search for "invented notations" as a key word.
>
> Regarding your point that mathematics education falls behind other subject
> areas in the implementation of nonobjectivist curricula, I can't say. I do
> know there are tremendous problems in moving away from the standard
> textbooks to more open ended pedagogies. Perhaps this has to do more with
> the math-avoident tendencies of many elementary school teachers than with
> the subject area itself.
>
> I enjoyed your account of the Zimbabwean class. There also is excellent
> critical pedagogy going on in mathematics classes in the U.S. See, for
> example,
> Gutstein, E. (2003). Teaching and learning mathematics for social justice
> in an urban Latino school. Journal for Research in Mathematics
> Education, 34(1), 37-73.
>
> Best regards.
> David
>
>
>
>
>
> "Eugene Matusov"
> <ematusov who-is-at udel.e To:
<xmca@weber.ucsd.edu>
> du> cc: (bcc: David H
Kirshner/dkirsh/LSU)
> Subject: RE: personalizing
voice
> 07/27/2003 03:48
> PM
> Please respond
> to ematusov
>
>
>
>
>
>
> Dear David and everybody-
>
> David wrote,
> > This characterization of mathematics education as the dinosaur of
subject
> > areas with respect to outmoded ontologies surprises me a bit, because my
> > experience of the field is so contrary to that. Firstly, the radical
> > constructivist movement that has motivated the field since the 1970s is
> > very clear that mathematical competence is about viable knowledge,
> > individually conceived, not about "objective" knowledge, deemed to be
> > impossible. The teacher's role coming from that kind of epistemology
> > consists of trying to formulate models of the student's understanding as
> a
> > tentative purchase from which to design tasks that will problematize
> their
> > experience as a vehicle for conceptual restructuring.
>
> I agree and disagree with David. It is fair to characterize the
> fundamentalist approach as dinosaur but this dinosaur is very alive and it
> is not OUTMODED. At least not in school practice. It is true that a
> wonderful constructivist approach has been developed and there are
> innovative schools where it is used. But these innovative constructivist
> approaches in math are often out of reach for teachers working in
> traditional public schools (which is not true for Language Art curricula).
> Innovative math instruction often moves away from math text into math
> projects. Of course, these projects use math texts, but it is not driven
by
> math texts. Math texts seem not to be emphasized by new math approaches. I
> have heard from many math constructivists, "We are not interested in
> teaching facts."
>
> I'm not a math educator but talking with many math educators working in a
> sociocultural approach, I came to a conclusion that there does not seem to
> be much done in terms of empirical deconstruction of math texts.
>
> David wrote,
> > The more recent focus
> > on social constructivist, sociocultural, and situated notions of
learning
> > has pushed the field toward collaborative meaning making, as evidenced,
> for
> > instance, in the current interest in having students develop their own
> > representations and notations--a long way from Eugene's sense that in
> > mathematics education "the meaning of 2+2=4 is located in the formula
> > (i.e., math text) itself."
>
> Although have students' own representations and notations is not exactly
> what I want and meant, I'd love to have references.
>
> When I was in South Africa last January, I videotaped lessons by a
> wonderful
> Zimbabwean teacher of science, economics, and workshop. He created great
> discussions among 48 7-grade African kids from a Black township next to
> Pretoria about carpenter tools, safety in chemical lab, and about the
> notion
> of economic value. The kids looked around the workshop and guessed how and
> what for each carpenter tool can be used. In another lesson, the discussed
> people's economic needs. They had heated discussions of whether love, or
> air, or money, or God, or education are economic needs or not. Listening
to
> the kids, I could learn about their communities and lives. For example,
one
> issue that became especially hot for the kids was whether living without
> earning money on welfare is moral or not. This focus on welfare came out
of
> split among the kids on those who argued that money are economic needs
> necessary for people's survival in modern society and those who argued
that
> money are not necessary (there were those also who argued that money are
> means and not ends for survival and well-being). Although, the kids
> participate in big ideas, their unique personalities and voices were
> developing through this participation.
>
> I would like to hear similar discussion among kids about 2+2=4. Where are
> these discussions? Why do we have them about carpenter tools, safety
rules,
> and economic values and not about 2+2=4?
>
> What do you think?
>
> Eugene
>
> > -----Original Message-----
> > From: David H Kirshner [mailto:dkirsh@lsu.edu]
> > Sent: Sunday, July 27, 2003 2:17 PM
> > To: xmca@weber.ucsd.edu
> > Subject: RE: personalizing voice
> >
> >
> > This characterization of mathematics education as the dinosaur of
subject
> > areas with respect to outmoded ontologies surprises me a bit, because my
> > experience of the field is so contrary to that. Firstly, the radical
> > constructivist movement that has motivated the field since the 1970s is
> > very clear that mathematical competence is about viable knowledge,
> > individually conceived, not about "objective" knowledge, deemed to be
> > impossible. The teacher's role coming from that kind of epistemology
> > consists of trying to formulate models of the student's understanding as
> a
> > tentative purchase from which to design tasks that will problematize
> their
> > experience as a vehicle for conceptual restructuring. The more recent
> focus
> > on social constructivist, sociocultural, and situated notions of
learning
> > has pushed the field toward collaborative meaning making, as evidenced,
> for
> > instance, in the current interest in having students develop their own
> > representations and notations--a long way from Eugene's sense that in
> > mathematics education "the meaning of 2+2=4 is located in the formula
> > (i.e., math text) itself."
> > ...Perhaps I missed the beginning of the conversation.
> > David
> >
> > _____________________
> > David Kirshner
> > Department of Curriculum & Instruction
> > Louisiana State University
> > Baton Rouge LA 70803-4728
> > (225) 578-2332 (225) 578-9135 (fax)
> > dkirsh@lsu.edu
> >
> >
> >
> >
> > "Eugene Matusov"
> > <ematusov who-is-at udel.e To:
> <xmca@weber.ucsd.edu>
> > du> cc: (bcc: David H
> Kirshner/dkirsh/LSU)
> > Subject: RE:
personalizing
> voice
> > 07/27/2003 12:38
> > PM
> > Please respond
> > to ematusov
> >
> >
> >
> >
> >
> >
> > Dear Jay and everybody-
> >
> > I find Jay's juxtaposition of "social voice" and "personal voice" very
> > useful and intriguing. I did not think about that before (thanks, Jay!).
> >
> > In my view, Jim Gee's notions of Discourse (with capital D) and
discourse
> > (small d) can be useful. Of course personal voice is defined by social
> > relations and participation in practices and discourses. But it has
> rather
> > UNIQUE embodied properties. While I see social voice as replicable and
> > replaceable. Bakhtin wrote about personal voice as being unique.
> Repeating
> > the same phrase or utterance by another person changes its meaning. But
> > apparently it is not recognized in math (or in math education)! It
claims
> > that it does not matter who said that 2+2=4! It means the same! The
> meaning
> > of the formula is the same and rooted in the math text (i.e., formula)
> > itself! Yes, Latour showed that in making math (actually biological
> > science, but it does not matter for my point), who is saying a statement
> is
> > actually important (you have to have reputation and personal stake in
the
> > statement to be heard in academic community) but for ready-made math, it
> is
> > not.
> >
> > Thus, we should either acknowledge that Bakhtin and Gee and many other
> > sociocultural folks (including Jay and myself) are wrong about math (OK,
> it
> > is ready-made math to be exact) that personal voice is important or we
> must
> > reveal in our empirical research where is a personal voice in one's
> > statement 2+2=4 that is crucial for the math practice itself.
> >
> > What do you think?
> >
> > Eugene
> >
> > -----Original Message-----
> > From: Jay Lemke [mailto:jaylemke@umich.edu]
> > Sent: Saturday, July 26, 2003 4:30 PM
> > To: XMCA LISTGROUP
> > Subject: personalizing voice
> >
> >
> > Eugene wrote in response to an earlier posting of mine on "space and
time
> > in CHAT":
> >
> > I think we need to unpack the notion of voice (any help can be highly
> > appreciated). My students, preservice teachers, become so excited when I
> > stated that, in my view, the purpose of teacher education is to develop
> > their teaching voices. That seems to liberate them from any standardized
> > judgment that does not take their personal agency into account in
> changing
> > their performance. However, they challenge me, as an educational
> > researcher, to develop the same voice-oriented approach to all academic
> > areas like math, science, English& They said that it is easy for them to
> > see open-ended voice- and person- oriented approach in teacher
education,
> > art education, even English education but it is more difficult to see it
> in
> > math or science education. What is a math voice as personal agency? What
> > can be personal in 2+2=4?
> >
> > So, I m on the mission from my students to find answers to their
> questions.
> > I d appreciate any help from XMCA community.
> >
> > So far, I contacted Paul Cobb and Ellice Forman, as great math educators
> > and researchers, whom I tremendously respect. From reading they
> suggested,
> > I ve come to a conclusion that constructivist folks avoid this question
> by
> > avoiding teaching facts (like 2+2=4). Although I understand that
> > educational priority can be on teaching concepts rather memorizing
facts,
> I
> > think we should not surrender teaching facts to educational
> > decontextualists. ...
> >
> > -----------------
> >
> > I think we use the Bakhtinian notion of "voice" most often in the sense
> of
> > "social voice" (as in the social voices of heteroglossia, which are the
> > discourse types circulating in a community whose diversity reflects and
> > helps constitute the social diversity of the community).
> >
> > But, as Eugene noted, of course for B. voice also meant "personal
> voice",
> > the authentic voice comprised of our appropriations from the discourses
> and
> > styles of others, but re-accentuated to make them our own. Or at least
> our
> > own for some particular time, place, and activity.
> >
> > I have recently read an interesting ms that quoted Voloshinov (a close
> > collaborator of Bakhtin, and perhaps in some cases a pseudonym for his
> > work) to the effect that we cannot always take an external voice and
make
> > it our own if that voice really conflicts with our individual being ...
> > perhaps we might say, with our habitus.
> >
> > I don't think people want to be, or are, indefinitely malleable with
> > respect to what cultural beliefs and practices we can identify with or
> > assimilate. We do reject some social voices and practices, rather
> > vehemently, as opposed to our nature or our desires. In the ms I was
> > reading, a student says this about the discourse of Chemistry, even
> though
> > she becomes quite fluent in it for the primary purpose of developing a
> > personal relationship with her tutor, whom she greatly likes. But she
> fails
> > her Chemistry tests regularly and will no doubt be relieved to be done
> with
> > Chemistry once and for all.
> >
> > We have to accept, I think, that some academic discourses, some middle
> > class discourses, some technological discourses, some religious
> discourses,
> > some political discourses, are just contrary to the convictions of many
> > people, even very young people, about who they are, what they want to
be,
> > what voices they want to speak with, what they like, what they believe.
I
> > can make a very good case against the humane value of much scientific
and
> > mathematical discourse. I can make a good case, I think, that they
> > epitomize certain pathological developments in European culture with
> > respect to the longterm human norm, that they are instruments of
> domination
> > and oppression, that they exist in large part to afford stroking of
> > masculinized male ego's, that they promote inhuman and inhumane forms of
> > abstraction and instrumental reasoning that are more compatible with
> > imperialism and exploitative economic orders than with the kinds of
lives
> > most people would like to lead and the kinds of communities most people
> > would like to live in. I would hardly be the first person to make such a
> > case.
> >
> > And it does not matter whether the case is "valid" or not. The key
> social
> > fact is that there is substantial value-diversity and value-conflict in
> the
> > world over these discourses and their associated practices and the
> > institutions that enable them to flourish. Some of us may be able to
> > articulate these conflicts in very precise terms. Many other people
> merely
> > feel the sense of conflict with their own values.
> >
> > Academic institutions, and especially public schools, are (as I've said
> > here often enough in the past) fundamentally coercive institutions. They
> > seek to impose a single set of values and they are not tolerant of the
> kind
> > of diversity I have just indicated. Educators are all very busy trying
to
> > persuade themselves, and students, that even if you hate a discourse,
you
> > should learn it because it will enable you to lead a better life. Even
if
> > you do not identify with it, you should maintain it as some sort of
> > additional cultural competence, or capital, like a second language that
> you
> > might find it distasteful to speak.
> >
> > I think this view rather underestimates the price of even partially
> > assimilating discourses and practices which we reject on value or
> identity
> > grounds. Of course the price varies considerably across individuals.
> >
> > It is in this context that I would respond to Eugene's request ... what
> is
> > there about the discourses of science and mathematics that is more or
> less
> > personalizable than the discourses of literature, art, history, etc.?
> >
> > On the "less" side ... I would agree with Eugene's students insofar as
> the
> > discourses of science and mathematics are themselves highly intolerant
of
> > diversity ... they do present a single monolithic and monlogical
> discourse
> > about the way things are ... and a single view about how one should
> argue,
> > what counts as evidence, what values should be paramount in inquiry,
etc.
> > They do not invite other opinions, they do not play well with other
> > discourses (artistic, literary, narrative, humanistic, political,
> > religious, sociocultural, critical, dialectical, etc.). They are quite
> > snobby, exclusive, arrogant, and also very narrow-minded, and place a
> > premium on extreme specialization of knowledge. All these qualities, I
> > would argue, make them palatable, assimilable, and personalizable for
> only
> > a very small fraction of the population.
> >
> > On the "more" side ... of course the actual conduct of science as a
> social
> > and human enterprise includes a much wider range of kinds of social
> voices
> > than the official view of science that is enshrined in curriculum. And
> > equally important, even the factual formulations of science can be
> > appropriated in more personal ways. Real science ("in the making" as
> Latour
> > says) involves quite a bit of political drama, discovery, excitement,
> > frustration, uncertainty ... etc. A curriculum that was about how
science
> > is really done could provide more assimilable voices of science. But the
> > official version of science in the curriculum is not about science, it
is
> > about "nature" ... that is, it ventriloquates the voice of Nature
> herself,
> > speaking to us of how she really is. Among all the cultural voicings of
> > Nature, the euro-scientific remains one of the least broadly appealing,
> > unfortunately. One could personalize official science by assimilating it
> > creatively into some other view of Nature, but doing so would certainly
> be
> > ruled unacceptable by official science and its powerbrokers in the
> coercive
> > curriculum.
> >
> > This seems to leave one last option. The factual presentations of
> science,
> > what it says about the world, and what mathematics says about whatever
it
> > is that mathematics is "about" (if ever anything were a pure social
> > construction ...), are after all still "enunciations" in Foucault's
> sense,
> > and though they come to us embedded in larger discourses, they can be
> > disembedded. Few students ever do master the larger discursive
formations
> > around what they are taught to say in the language of science or
> > mathematics. Science fiction and science-based fantasy stories are one
> > strong example of the re-accentuation of scientific propositions.
> > Statements in mathematics can even be used as proverbs ("2 and 2 is
> four").
> > Popularized science, as in the writing of Stephen Jay Gould, or perhaps
> > moreso for those who take more licence, is a re-voicing of science in a
> > more humanistic vein. Students can "play" with the ideas and the
> > propositions of science, can embed them in very different discourses
> > (narratives, fantasies, word-play, insults) and practices (making
> > stinkbombs, experimenting with combinations of street drugs).
> >
> > Of course none of these options are acceptable to official science and
> the
> > official curriculum in science, because they are all contrary to its
> > purpose: convert or exclude. Lest anyone think I am particularly
> > anti-science in my attitudes, I should say for those who don't know,
that
> > my PhD is in theoretical physics and that I have worked my whole career
> at
> > least in part in the field of science education. Nor is the stance of
> > science in the curriculum really so different from that of other
> subjects;
> > it is just more extreme. All curriculum areas seek to impose a single
> view
> > and value system on students, and to penalize them or exclude them from
> > further academic and social opportunity if they do not conform. Schools
> are
> > above all "socializing" institutions, not institutions which aim to
> promote
> > genuinely creative or critical, i.e. culture-changing,
> ideology-challenging
> > discourses.
> >
> > So I would suggest that science and mathematics may be a little more
> > susceptible of re-accentuation into the personal voices of Eugene's
> > students than they imagine ... and that other subjects in the curriculum
> > may be a little less so than they imagine.
> >
> > JAY.
> >
> >
> >
> >
> > Jay Lemke
> > Professor
> > Educational Studies
> > University of Michigan
> > 610 East University
> > Ann Arbor, MI 48109-1259
> >
> > Ph: 734-763-9276
> > Fax: 734-936-1606
> > http://www.umich.edu/~jaylemke
> >
> >
>
>
>
>

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