[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

*To*: xmca@weber.ucsd.edu*Subject*: Re: education, technology & chat (The Mathematics of it)*From*: Peter Moxhay <moxhap@portlandschools.org>*Date*: Wed, 10 Nov 2004 15:01:50 -0500*Delivered-to*: xmca@weber.ucsd.edu*In-reply-to*: <s1921f59.018@MORPHEUS.PPS>*Old-return-path*: <owner-xmca@weber.ucsd.edu>*References*: <s1921f59.018@MORPHEUS.PPS>*Reply-to*: xmca@weber.ucsd.edu*Resent-date*: Wed, 10 Nov 2004 12:01:56 -0800 (PST)*Resent-from*: xmca@weber.ucsd.edu*Resent-message-id*: <3Kf-7D.A.TxD.0OnkBB@weber>*Resent-sender*: xmca-request@weber.ucsd.edu

Very interesting discussion, Mike, Peg, Bill, and all!

in a chat-like way.

in different school subjects?

mediated by one of Davydov's "models" (a diagram or formula).

word, phoneme, syllable, etc.

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 "learningabout polygons -- describing and making shapes."(Just to set some background: I was a co-author of "The constructionzone"with Denis Newman and Mike Cole and I worked with mathematicssoftware inthe early fifth dimensions and in work on mathematics geneticallyprimaryexamples [germ cells] written about with Belyaeva and Soldatova. Ihaverecently beenlooking at very early mathematics education content. One of therecentthings that has intrigued me is Deborah Ball's thesis that teachingmathematics is one among other branches of mathematics. And in thatline isthe work of Ma, Liping. 1999. Knowing and Teaching ElementaryMathematics: Teachers' Understanding of Fundamental Mathematics inChina andthe United States [Studies in Mathematical Thinking and Learning].Mahwah,NJ: Erlbaum.) We undoubtedly agree that what to tally and whether more or less ofsomething tallied can be interpreted as helpful for development,depends onthe underlying mathematical concepts. I say this because you wrote"Thebuddies are talking math shapes to each other more often than theones whoare working individually, although when one child noisily discoverssomething new, he draws the attention of many others in his vicinity," and"When she picks partners she is thinking in an integrated way of thechildren's social and cognitive development and what sort of mutualzopedwill emerge between the two partners. The zoped is highlymultidimensionalas well as bidrectional." To me, those two statements suggest you(and theteacher) rely on analyses of mathematics concepts, the ways they arerepresented in talk and act, and the ways that representations areinvolvedin 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 dragpartsounds like a kind of tangram activity, so children might be gettingatcompositionality and analyzable units within apparent units as well asstability under transformations (rotate/flip). So, I wonder how thework iscapitalized on -- for topology, projective geometry, Euclidianconcepts,other domains of mathematics? How are the acts and talkmathematized? Inthe hands-on blocks and computer versions is the chance taken to getat thesimilar (enclosed forms) and the different (3D faces, edges, andcorners butjust sides and angles in the 2D)? (Tangrams mask the 3D-2D contrast;doesthe 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 ElenaBodorovahave done in Colorado and New Jersey with pre-K and K children usingexternal mediators to promote powerful "buddy" work? They have bigears andlips, for example that help self- and other-regulation early on in apair'swork together (andeventually get lost). I mention it to think about times when theteachersees a pairing as desirable on cognitive grounds and wants toengineer/scaffold the social aspects of their development so they canprofitfrom 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 & chatOn 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 makingshapes-- following the TERC Geometry 1 topic. One part of the mathsoftwarethatthe children were using allows the children to click and dragpolygonsfrom atool palette to fill in a line-drawing outline. There is a similar "hands-on" activity ("activity" with a little "a", not the big "A" ofCHAT)with plastic polygons to fill in an outline line drawing on paperworksheets-- copied from the TERC curriculum folder. One thing I've observed,onthesame day, is that the children are more facile with the hands-onbuildingthan with the computer, even though the computer constrains thepossiblewaysthat a shape can be rotated or flipped. Hands-on there are endless possibilities, but the computer transformations require clicking on atransformation icon in the tool palette and then clicking on theshape totransform it. If one gets it wrong, (s)he must select anothertransformationand reapply, whereas manually making transformations with the plasticblocksare done in split seconds.Another part of the math software shows a shape made of polygonswhen aniconresembling a set of eyeballs is clicked. Then the children try tomaketheshape that they saw. Jane does a similar activity with the wholeclassusingan overhead projector (it's one of the TERC lessons) showing a shapemadeofpolygons for a few seconds, then hiding it and asking the childrento drawwhat they see. I've observed that the children are often tempted todrawwhile the shape is being shown, against the rules of the activity.Janeasksthem to put their pencils back down on the table until she hides theshapeand then they can draw it.An "affordance" of minor interest in the software is that thechildrencannotbe tempted as they can when sitting at tables looking at the overheadprojection. Since they are using the mouse, and the shape onlyappearswhenthey click on the eyeballs, they cannot simultaneously see the shapetheyaretrying to remember, while building their copy. They can stop andpeek,however, and then resume building. An affordance more widelyunderstoodisthat individuals working at computers can choose their own pace. The computer activity does not require the pulsing out of rhythm by theteacher,which, with the overhead projector, often proceeds when the lastchild isready. I'm left with the impression that, over all, more studentworkgetsdone on this kind of activity at the computer. I'd need to do someclosetallying to support this claim, but it's not a claim that has anyrealsignificance, except perhaps for Jane's practice. The flip side isthattheteacher-directed overhead activity often results in minor butcollectiveebullitions across the tables as the teacher reveals the shape asecondtimeso children can check their drawings. There is a more salientemotionalelement involved with the teacher-directed activity than with thecomputeractivity.The TERC curriculum has been and continues to be hotly debated.Here's alocal 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/

**Follow-Ups**:**Re: education, technology & chat (The Mathematics of it)***From:*Mike Cole <lchcmike@gmail.com>

**Re: education, technology & chat (The Mathematics of it)***From:*"Peg Griffin" <Peg.Griffin@worldnet.att.net>

- Prev by Date:
**another job** - Next by Date:
**Re: education, technology & chat (The Mathematics of it)** - Previous by thread:
**another job** - Next by thread:
**Re: education, technology & chat (The Mathematics of it)** - Index(es):