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Re: approaches to content

And, Nancy, about the students -- didn't you mention earlier that they were
identified as in need of remediation?
----- Original Message ----- 
From: "Ares, Nancy" <nancy.ares@rochester.edu>
To: <xmca@weber.ucsd.edu>
Sent: Thursday, November 11, 2004 12:52 PM
Subject: RE: approaches to content

> HI Peter,
> You asked:
> > Again, as with Peg's work, I'm wondering if the students "model" the
> > general
> > relation (between amount and rate, etc.) with some sort of special
> > diagrams, or formulas, or tables, or special algebraic notation, and
> > whether
> > this helps them assimilate the general concept.
> >
> the networked technology we work with (HubNet and Participatory
> developed by Uri Wilensky and Walter Stroup) includes a couple of
> activities that do have students moving from general to particular in the
> way you describe. The system involves a network of graphing calculators
> kind that many schools in the US have; Texas Instruments TI-83) connected
> hubs that communicate with a computer server. Using network technology
> a public display space, students can, for example, become agents in a
> population where a disease is introduced and be part of the system as the
> disease spreads. In another simulation they each can control a stoplight
> a simulated city's traffic grid and together work toward improving the
> traffic flow.  For both activities, graphs are included in the public
> display of the emerging system (e.g., traffic flow in the grid, icons
> representing individual agents in the population through which disease is
> spreading), so that the graphical representations emerge in real time as
> system is evolving. Students' and teachers' discussion and analysis of the
> graphs in relation to each other and to the motion in the display has them
> exploring relations (e.g., stopped cars over time, average speed, average
> wait time in Gridlock; number of sick individuals over time in Disease) in

> very qualitative instead of quantitative ways at first. What we see in our
> data is that students develop increasingly sophisticated and eventually
> quantified notions of relations (e.g., velocity), but those notions are
> built on strong conceptual understanding of general relations first.
> I will ask my colleagues more about assessing students' understanding...I
> have been concentrating on describing and understanding the patterns of
> participation we are witnessing. :)
> Nancy
> > I'd also be interested
> > if you have
> > methods for *assessing* whether students are actually solving problems
> > by moving
> > from the general to the particular, or just solving each particular
> > problem as a new
> > case.
> >
> > That is, how can you assess that:
> >
> > > , it is seen as a simpler case rather than a different
> > > phenomenon.
> >
> > Peter
> >
> >