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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