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*To*: <xmca@weber.ucsd.edu>*Subject*: Re: education, technology & chat (The Mathematics of it)*From*: "Peg Griffin" <Peg.Griffin@worldnet.att.net>*Date*: Wed, 10 Nov 2004 14:28:21 -0600*Delivered-to*: xmca@weber.ucsd.edu*Old-return-path*: <owner-xmca@weber.ucsd.edu>*References*: <s1921f59.018@MORPHEUS.PPS> <5BF3553C-3353-11D9-9CF4-000A957B2E66@portlandschools.org>*Reply-to*: xmca@weber.ucsd.edu*Resent-date*: Wed, 10 Nov 2004 12:25:04 -0800 (PST)*Resent-from*: xmca@weber.ucsd.edu*Resent-message-id*: <ufouYC.A._PF.gknkBB@weber>*Resent-sender*: xmca-request@weber.ucsd.edu

Clarification, please, for a phrase I think I don't understand: "in a chat-like way." ----- Original Message ----- From: "Peter Moxhay" <moxhap@portlandschools.org> To: <xmca@weber.ucsd.edu> Sent: Wednesday, November 10, 2004 2:01 PM Subject: Re: education, technology & chat (The Mathematics of it) > 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/ > >>> > >>> > >>> > >>> > >> > >> > > > > > > > >

**References**:**Re: education, technology & chat (The Mathematics of it)***From:*Peter Moxhay <moxhap@portlandschools.org>

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