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Topic: Does step size really equal speed?
Related Item: http://mathforum.org/mathtools/tool/13171/


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Subject:   RE: Does step size really equal speed?
Author: Craig
Date: Apr 17 2007
On Apr 10 2007, KT8 wrote:
> There is an assumption being made in this simulation that I don't
> agree with. (If this has been addressed in other discussions, I
> apologize). I can take loooong steps very slowly or short steps very
> quickly, so I don't like the assumption that increasing step size
> will cause the "runner" to get there faster. If the x-axis scale
> were in "number of steps" instead of "time," this would make sense.
> One of the sessions I attended at NCTM in ATL was about the
> shortcomings of some electronic manipulatives and how these could
> lead to misunderstandings about the mathematical concepts. Distance
> = RATE * time, not LENGTH OF STEP * time.

You have made very valid points.  Even "teachable" points... the applet isn't
perfect for all uses.  For example, clicking on a runner changes the runner's
direction, but the "speed" remains positive: a "missed opportunity" to  talk
about negative slope (or negative rate of change).  This is where the art of
teaching comes in: as a teacher, you know where your students are, and what
their capabilities are.  You design questions that students can use a variety of
tools to answer, and if the tool isn't quite ideal (but still possibly useful)
you discuss the tool's shortcomings with the class.  Maybe ask students whether
the horizontal axis should be labeled something other than "time," or whether it
might make sense to use some label other than "step size" for the parameter
boxes.  The electronic manipulatives can, indeed, have shortcomings; we as
educators must decide how and whether we can overcome them, use them for
teaching, ignore the shortcomings, or even ignore the tool.

This very forum has provided a vehicle, in some instances, for the manipulative
developer to modify and improve the manipulative based on user suggestions.
Perhaps the developer of this tool might respond?

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