Re: education, technology & chat (The Mathematics of it)

[Mike Cole <lchcmike@gmail.com>]

Peg's article,  mentioned in her note, with Belyaeva, Soldatova
and others in the book edited by Forman, Minnick and ? (Contexts of
LEarning) might be a good starting point, Peter.

We could scan it and post it if this is a topic people want to go
for....... but rumor has it that a new poll for MCA articles also
of relevance may appear soon. 

Whose for what in what order?
mike


On Wed, 10 Nov 2004 15:01:50 -0500, Peter Moxhay
<moxhap@portlandschools.org> wrote:
> Very interesting discussion, Mike, Peg, Bill, and all!
> 
> Following up Mike's comment, I would be interested to hear your
> opinions of how,
> when technology (say, software), is used, one incorporates the
> curriculum *content*
> in a chat-like way.
> 
> In particular, in a given content area, might there not be software
> that enables the
> children's  assimilation of the "germ cell" of the subject? If so, what
> would this look like
> in different school subjects?
> 
> In our use of Davydov's math curriculum, we have played with creating
> software
> within which the children assimilate the action of
> measuring/constructing a quantity
> (area, length, etc.) using a unit, where the action of
> measuring/constructing is
> mediated by one of Davydov's "models" (a diagram or formula).
> 
> In the case of written language acquisition, I suppose one might create
> software
> based on Elkonin's boxes and other diagrammatic supports for the
> concepts of
> word, phoneme, syllable, etc.
> 
> What should the content of the technology/software be like, in a given
> subject area,
>   to help the children "get" the germ cell so they can ascend from the
> abstract to the concrete?
> 
> Peter
> 
> 
> 
> 
> > I hope people will pay attention to Peg's emphasis on conceptual
> > content of the domain in question when talking about obuchenia
> > (teaching/learning). I and many others all too easily overlook the
> > centrality of content so key to Devydov's
> > thinking, in my case, in part, because 5th Dimensions are
> > chock a block with all different kinds of content, partly because my
> > grad training was 100% process.
> >
> > With respect to another comment: yes, I believe technology is
> > a very broad term, the sub-parts of which are very interesting
> > to consider, but a term which is badly underextended in discussions of
> > technology and human affairs.
> >
> > Work is progressing on fortifying and improving xmca, glad to see that
> > there is life despite the spam.
> > mike
> >
> >
> >
> > On Wed, 10 Nov 2004 10:47:40 -0600, Peg Griffin
> > <peg.griffin@worldnet.att.net> wrote:
> >> Thanks, Bill, for such a prompt answer.
> >> I'm afraid I don't know the "TERC Geometry 1 Topic" to unpack "
> >> learning
> >> about polygons -- describing and making shapes."
> >> (Just to set some background: I was a co-author of "The construction
> >> zone"
> >> with Denis Newman and Mike Cole and I worked with mathematics
> >> software in
> >> the early fifth dimensions and in work on mathematics genetically
> >> primary
> >> examples [germ cells] written about with Belyaeva and Soldatova.  I
> >> have
> >> recently been
> >> looking at very early mathematics education content.  One of the
> >> recent
> >> things that has intrigued me is Deborah Ball's thesis that teaching
> >> mathematics is one among other branches of mathematics.  And in that
> >> line is
> >> the work of  Ma, Liping.  1999.  Knowing and Teaching Elementary
> >> Mathematics: Teachers' Understanding of Fundamental Mathematics in
> >> China and
> >> the United States [Studies in Mathematical Thinking and Learning].
> >> Mahwah,
> >> NJ: Erlbaum.)
> >>
> >> We undoubtedly agree that what to tally and whether more or less of
> >> something tallied can be interpreted as helpful for development,
> >> depends on
> >> the underlying mathematical concepts.  I say this because you wrote
> >> "The
> >> buddies are talking math shapes to each other more often than the
> >> ones who
> >> are working individually, although when one child noisily discovers
> >> something new, he draws the attention of many others in his vicinity,
> >> "  and
> >> "When she picks partners she is thinking in an integrated way of the
> >> children's social and cognitive development and what sort of mutual
> >> zoped
> >> will emerge between the two partners.  The zoped is highly
> >> multidimensional
> >> as well as bidrectional."  To me, those two statements suggest you
> >> (and the
> >> teacher) rely on analyses of mathematics concepts, the ways they are
> >> represented in talk and act, and the ways that representations are
> >> involved
> >> in children's planning, guiding, monitoring, and checking moves in the
> >> sometimes long and winding road of development of the concepts and of
> >> mathematics proficiency in a more global sense.
> >>
> >> So, I want to know more about the mathematics.  The click and drag
> >> part
> >> sounds like a kind of tangram activity, so children might be getting
> >> at
> >> compositionality and analyzable units within apparent units as well as
> >> stability under transformations (rotate/flip).  So, I wonder how the
> >> work is
> >> capitalized on -- for topology, projective geometry, Euclidian
> >> concepts,
> >> other domains of mathematics?  How are the acts and talk
> >> mathematized?  In
> >> the hands-on blocks and computer versions is the chance taken to get
> >> at the
> >> similar (enclosed forms) and the different (3D faces, edges, and
> >> corners but
> >> just sides and angles in the 2D)?  (Tangrams mask the 3D-2D contrast;
> >> does
> >> the activity you are describing do that in the opposite way?)  Does
> >> discussion of a match in the eyeball activity bring in estimates and
> >> precision about mathematical attributes of mathematical entities (like
> >> number and size of sides and angles) compared to other nice but not
> >> mathematical ones?
> >>
> >> As a separate note, have you seen the work that Deb Leong and Elena
> >> Bodorova
> >> have done in Colorado and New Jersey with pre-K and K children using
> >> external mediators to promote powerful "buddy" work?  They have big
> >> ears and
> >> lips, for example that help self- and other-regulation early on in a
> >> pair's
> >> work together (and
> >> eventually get lost).  I mention it to think about times when the
> >> teacher
> >> sees a pairing as desirable on cognitive grounds and wants to
> >> engineer/scaffold the social aspects of their development so they can
> >> profit
> >> from the pairing.
> >>
> >> Peg
> >>
> >> ----- Original Message -----
> >> From: "Bill Barowy" <xmcageek@comcast.net>
> >> To: <xmca@weber.ucsd.edu>
> >> Sent: Tuesday, November 09, 2004 5:27 PM
> >> Subject: Re: education, technology & chat
> >>
> >>> On Tuesday 09 November 2004 3:27 pm, Peg Griffin wrote:
> >>>
> >>>> What is the mathematics learning goal for the kids?
> >>>
> >>> They were working on learning about polygons -- describing and making
> >> shapes
> >>> -- following the TERC Geometry 1 topic.  One part of the math
> >>> software
> >> that
> >>> the children were using allows the children to click and drag
> >>> polygons
> >> from a
> >>> tool palette to fill in a line-drawing outline.   There is a similar
> >>> "hands-on" activity ("activity" with a little "a", not the big "A" of
> >> CHAT)
> >>> with plastic polygons to fill in an outline line drawing on paper
> >> worksheets
> >>> -- copied from the TERC curriculum folder.  One thing I've observed,
> >>> on
> >> the
> >>> same day, is that the children are more facile with the hands-on
> >>> building
> >>> than with the computer, even though the computer constrains the
> >>> possible
> >> ways
> >>> that a shape can be rotated or flipped.  Hands-on there are endless
> >>> possibilities, but the computer transformations require clicking on a
> >>> transformation icon in the tool palette and then clicking on the
> >>> shape to
> >>> transform it.  If one gets it wrong, (s)he must select another
> >> transformation
> >>> and reapply, whereas manually making transformations with the plastic
> >> blocks
> >>> are done in split seconds.
> >>>
> >>> Another part of the math software shows a shape made of polygons
> >>> when an
> >> icon
> >>> resembling a set of eyeballs is clicked.  Then the children try to
> >>> make
> >> the
> >>> shape that they saw. Jane does a similar activity with the whole
> >>> class
> >> using
> >>> an overhead projector (it's one of the TERC lessons) showing a shape
> >>> made
> >> of
> >>> polygons for a few seconds, then hiding it and asking the children
> >>> to draw
> >>> what they see.  I've observed that the children are often tempted to
> >>> draw
> >>> while the shape is being shown, against the rules of the activity.
> >>> Jane
> >> asks
> >>> them to put their pencils back down on the table until she hides the
> >>> shape
> >>> and then they can draw it.
> >>>
> >>>  An "affordance" of minor interest in the software is that the
> >>> children
> >> cannot
> >>> be tempted as they can when sitting at tables looking at the overhead
> >>> projection.  Since they are using the mouse, and the shape only
> >>> appears
> >> when
> >>> they click on the eyeballs, they cannot simultaneously see the shape
> >>> they
> >> are
> >>> trying to remember, while building their copy.  They can stop and
> >>> peek,
> >>> however, and then resume building.  An affordance more widely
> >>> understood
> >> is
> >>> that individuals working at computers can choose their own pace.  The
> >>> computer activity does not require the pulsing out of rhythm by the
> >> teacher,
> >>> which, with the overhead projector, often proceeds when the last
> >>> child is
> >>> ready.  I'm left with the impression that, over all, more student
> >>> work
> >> gets
> >>> done on this kind of activity at the computer.  I'd need to do some
> >>> close
> >>> tallying to support this claim, but it's not a claim that has any
> >>> real
> >>> significance, except perhaps for Jane's practice.  The flip side is
> >>> that
> >> the
> >>> teacher-directed overhead activity often results in minor but
> >>> collective
> >>> ebullitions across the tables as the teacher reveals the shape a
> >>> second
> >> time
> >>> so children can check their drawings.  There is a more salient
> >>> emotional
> >>> element involved with the teacher-directed activity than with the
> >>> computer
> >>> activity.
> >>>
> >>> The TERC curriculum has been and continues to be hotly debated.
> >>> Here's a
> >>> local article that came out today concerning a nearby school system,
> >>> different from the one in which I'm observing,
> >>>
> >>>
> >> http://www.boston.com/news/education/k_12/articles/2004/11/08/
> >> mathematical_unknowns/
> >>>
> >>>
> >>>
> >>>
> >>
> >>
> >
> >
> >
> 
>