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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