Dear Ellice and everybody-
Ellice asked,
> why do you think math instruction is
> sometimes fact-oriented but history, English, etc. is not? Can't you
teach
> any subject as if it were about learning facts (grammatical rules, dates
> and places in history, arithmetic facts, scientific "truths") or teach it
> as if it were learning about problem solving, interpretation, concepts?
> Why decide that mathematics is the discipline that is most fact-oriented
> while history is not or vice versa?
No, this is not my position at all. However, it is a position of traditional
education. I think it is based on Christian fundamentalist attitude to a
text that has meaning that has to be uncoded and consumed (I refer to
"Christian fundamentalist attitude" because it was historically applied to
Bible). It has assumed only one correct reading of the text and this reading
is located in the text alone. The text was treated as a sign with rigidly
assigned meaning. Text is a container of meaning.
Currently, I see a trend in the mainstream practice of US public education
to get away from this fundamentalist approach in English and social studies.
For example, the Delaware Standards in Language Art focus teachers on
"activation of prior knowledge" is reading and discussing literary texts.
"Activation of prior knowledge" is "subjectivizing" of the objectivized text
and curricula in general (in Russian "razpedmechivanie" literally
disobjectivizing) as it shows how the text (the curricula) is rooted in the
students' prior, current, and future experiences, goals, relations, and
values. You can find somewhat similar approaches in teaching Social Studies
although less developed in my view (please correct me if I'm wrong).
However, in math I can't find this at all. I can't find analog of
"activation of prior knowledge" in educational approaches to math texts.
There is not much challenge to the statement in teacher education that the
meaning of 2+2=4 is located in the formula (i.e., math text) itself. For the
purpose of this discussion, I treat math facts as "math text."
My concern about constructivist reluctance of teaching math facts can be a
potential surrender "math text" to the fundamentalist traditional approach
to text. At least, this is how my preservice teachers see it. Since the
State requires teaching math facts, my students understand it as returning
back to a transmission of knowledge. They talk about "a balanced approach"
of eclectic mixture of constructivism for teaching problem solving and math
concepts and (fundamentalist) transmission of knowledge for teaching math
facts.
I see "activation of prior knowledge" approach, applied in Language Art for
reading and comprehension of literary text, as potentially useful for
teaching math text (math facts). I think in her 1988 book, Jean Lave
developed powerful methodology of investigating "prior math knowledge" of
Just Plain Folks that can be used in education by "activating" people's
everyday math practices (I see school use of math is also another "everyday
practice"). For example, it would useful to investigate how 2+2=4 is rooted
in kids' lives and role it plays or can play for their past, present, and
future lives. When 2+2 is not 4 in their lives (e.g., 2 friends plus 2
friends are not always 4 friends).
My Delaware colleague Tony Whitson designed a powerful lesson for preservice
teachers about how subjectivized (disobjectivized) the facts about state
capitals. He asked his students to list all state capitals that they can
remember and then together with the students analyzed the pattern of their
mistakes revealing their ideas of what state capitals are and what were the
criteria on which the states capitals were chosen (like the biggest city in
the state, proximity to water, military significance, the most famous city
in the state, and so on). After this lesson, not only the students better
understand what state capital is but they also started developing different
mnemotechniques for memorizing them (in case it is necessary for some reason
like a test or trivia).
I also think that subjectivization of math texts reveal the process of
building "math voices" in the students as it promotes a discourse on
personal biases in students' participation in math practices in and out the
school. By the way, I found Ellice's recent article on voices in math most
useful. I have it in PDF format for those who are interested :-)
Thanks, Ellice, for asking this clarifying question as it helped me to push
my thinking further.
What do you think?
Eugene
> -----Original Message-----
> From: Ellice Forman [mailto:ellice+ who-is-at pitt.edu]
> Sent: Saturday, July 26, 2003 3:10 PM
> To: ematusov@UDel.Edu; xmca (XMCA)
> Subject: RE: Space and time in chat
>
> Hello Eugene,
> I have a question for you Eugene--why do you think math instruction is
> sometimes fact-oriented but history, English, etc. is not? Can't you
teach
> any subject as if it were about learning facts (grammatical rules, dates
> and places in history, arithmetic facts, scientific "truths") or teach it
> as if it were learning about problem solving, interpretation, concepts?
> Why decide that mathematics is the discipline that is most fact-oriented
> while history is not or vice versa?
> Ellice Forman
> University of Pittsburgh
>
> --On Saturday, July 26, 2003 12:07 PM -0400 Eugene Matusov
> <ematusov@udel.edu> wrote:r
>
> >
> >
> > Hello Jay and everybody–
> >
> >
> >
> > Thanks, Jay, for your reply.
> >
> >
> >
> > -----Original Message-----
> > From: Jay Lemke [mailto:jaylemke@umich.edu]
> > Sent: Wednesday, July 23, 2003 10:19 PM
> > To: ematusov@UDel.Edu
> > Subject: RE: Space and time in chat
> >
> >
> >
> >
> > I was very happy to see Eugene's message about chronotopes and
> > educational ethnography. It is just one of the topics that I raised at
> > the recent Ethnography in Education research conference at the U of
> > Pennsylvania. (I was asked to do a keynote address.)
> >
> > Unfortunately I did not do a full paper, but my notes are linked from my
> > website at: http://www-personal.umich.edu/~jaylemke/new.htm
> >
> > Thanks, Jay, for the paper!
> >
> > The html powerpoint may only work if you have a very recent version of
> > your web browser, but the ppt file itself should work fine.
> >
> > My major point was that ethnography increasingly has been emphasizing
the
> > multiple sites of people lives and how we move among them, while
> > educational ethnography, for practical reasons but also because of not
> > seeing schools as tightly integrated into the rest of students' lives,
> > has tended to stay within the classroom or within the school. I linked
> > this to my notion of traversals and timescales, more or less saying that
> > learning that matters has to be, and is, learning that extends along the
> > larger trajectories of our/students' lives, and that these are never
> > confined to classrooms or school.
> >
> > To add some flesh to the bones, it seemed to me that the notion of
> > chronotope can usefully unite the spatial traversals and the temporal
> > pacings, interruptions and resumptions, etc. of both activities-in-situ
> > and activities-across-places.Characterising the chronotopes of learning,
> > in schools and across home-school-elsewhere can be a rich project for
> > educational ethnography, and hopefully for formulating alternatives to
> > school-obsessed and classroom-myopic views of education.
> >
> > Eugene usefully reminds us that Bakhtin, especially in his earlier
> > essays, always added the value dimension to his characterisations of how
> > novelistic worlds portray our human lives. This is still strong in his
> > work on heteroglossia (ideational and axiological unite to define a
> > "social voice": what we say of the world and how we feel about it). We
> > lose something in social science when we attempt to make value-free or
> > value-neutral descriptions of how people live ... even the effort to say
> > simply what people do and when and where they do it is misguided if it
> > neglects to also say how people feel about what they are doing. This is
a
> > very deep insight in Bakhtin, and it is not surprising that it comes
from
> > his literary-humanistic sensibility, which we appropriate today into
> > social science.
> >
> > I just talked with Ana Marjanovic-Shane in “meatspace” (we
> > both live in Philadelphia) and she reminded me work by Stanislavskii
> > (famous Russian theater educator). Stanislavskii also focused on (at
> > least) three chronotopes for actor’s work that roughly correspond
> > to three chronotopes of schooling that I described. Actor chronotopes
> > are: 1) chronotope of play (“didactic chronotope” in
school);
> > 2) chronotope of scene (here-and-now) (cf. “local chronotope of
the
> > classroom”), and 3) chronotope of the actor’s past
> > experiences (cf. “ontological chronotope” although I think
> > that ontological chronotope is not only about past experiences, but it
is
> > also future oriented). Ana promised to bring references from
> > Stanislavkii…. (thanks, Ana!)
> >
> > Take this in its strong form: there is no valid characterization, or
even
> > description, of activity without a concern for evaluative orientations
or
> > how people feel about what they are doing (good/bad, bored/surprised,
> > proud/guilty, enthusiastic/reluctant, etc.).
> >
> > Yes. That is why is should be called “axiological
chronotope”
> > to include value. Although, the term becomes a bit too long and awkward.
> >
> > To some extent we also tend to lose sight of this key dimension of
> > activity when we abstract to the level of social-cultural activity
> > systems, which are of course very important to characterise. But it is
> > easy to wonder how at this level do the elements of feelings and
> > evaluations enter? For they are not the same for all participants, and
> > indeed there are not often general rules to assign value orientations to
> > particular participants roles. The distribution of value orientations
may
> > not be systematic when the activity as such is the unit of analysis.
> > Bakhtin's suggestion here is heteroglossia, as sociologically
> > re-interpreted to mean that the distribution of value orientations
> > becomes systematic in relation to participants social positions in a
> > larger system, across activities as well as in them. (Bourdieu makes
much
> > the same point about habitus.)
> >
> > 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…
> >
> > Of course activity theory wants very much to retain a humanistic
> > perspective, and at the level of the individual-in-activity, this is
> > done. But at the level of the activity system, we find ourselves with a
> > notion of social norms of activity, and that characterizes for us the
> > possible and typical attitudes and value orientations -- but not
> > necessarily how they are distributed among actual and possible subjects
> > engaged in the activity, especially differentially, or why the
> > distribution is as it is.
> >
> > Yes, and I think we should get away from mono-chronotopic view of an
> > activity system.
> >
> > What do you think?
> >
> > Eugene
> >
> > So the chronotope does I think offer us an important extension of our
> > ways of characterising activity systems at the collective and
> > social-historical level, not just in reminding us of the importance of
> > space as well as time, but also in defining a unit of analysis at this
> > level, in which we cannot say what sorts of things people typically do
> > without also saying what those actions mean, not just in relation to an
> > object or to typical social norms, but with respect to our value
> > orientations quite generally. Here again is an important case where we
> > need to think of feelings in this sense as fully a part of meanings. We
> > have all long ago agreed that we have to characterise actions and
> > activities in terms of what they mean for the participants ... and we
> > still need to remember that such a sense of meaning must include also
how
> > we are feeling about what we do. No meaning without feeling.
> >
> > JAY.
> >
> > PS. I think Kevin's article is faithful to this conception in the many
> > ways that it tells us how the students feel about activity that takes
> > place, or move them, from one place and space to another, which has a
> > different kind of meaning for them.
>
>
>
> Ellice Ann Forman
> Department of Psychology in Education
> University of Pittsburgh
> 5C01 WWPH
> Pittsburgh, PA 15260
> (412) 648-7022
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