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Topic: Demise of Green Globs


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Subject:   RE: Demise of Green Globs
Author: Alan Cooper
Date: Aug 4 2005
On Aug  4 2005, Mathman wrote:

(re ExploreLearning's "ZapIt" and other similar games)

>  What is expected of the student besides guessing a possibly large > number of
possibilities?  

1. Imagine various parabolas and try to find one that passes through more than 3
of the displayed points
2. First use trial and error to discover or reinforce prior knowledge of the
effects of changing the parameters (actually, I prefer my own java version for
this because the graph changes in real time as the sliders are moved)
3. Later use known or discovered facts to develop a strategy for producing the
equation, eg as follows:
(i) Identify axis and vertex (or intercept and apparent slope at x=0)
(ii) Use direction and magnitude of curvature (determined eg by vertical change
in one horizontal unit from vertex)to get the a-value

> If there is work to be done on paper to determine
> maximum effect of one graph, before actually drawing the graph, then
> what is the advantage of the game please?  
The game provides an effectively infinite set of sample problems. Which, with a
bit more programming, could be arranged to provide exactly the right level of
challenge for each student (as determined by success history of prior
attempts).
And the slider versions shortcut some of the tedium of a trial-and-error
approach when that is being used.

> That is, what exactly is being taught/learned?
> The likely parameters [3] of a general
> quadratic to pass through some given points?  
Yes, exactly. And also the less "computational" but still useful skill of being
able to visualize an imagined (in this case parabolic) curve through the given
points.(Useful for math modelling of experimental data and shooting hoops in
basketball among other things)

> What is the likelihood of being correct in one's choices?
This depends on what one has learned/discovered so far.

> What type of work/study precedes
> and specifically perpares for success in the game?
I would think that the game could be used before learning as a way of developing
motivation for what is to be learned (I think the Ed-Biz people call this an
"advance organizer"), but it could also be used as a reinforcing activity after
learning about the theory.
(I'd prefer to think of the game as serving the learning by providing some
additional motivation or reinforcement than thinking of the learning as
"preparing for success in the game".)

cheers,
    Alan

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