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Discussion: Understanding Distance, Speed, and Time Relationships Using Simulation Software tool
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: Jeff L
Date: Apr 18 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.

Obviously, KT8 is correct about pacing vs step size. This particular applet
coincides with a CMP lesson as a lead in to linear functions. (grade 7)

One of the problems with introducing concepts is that one must build on
experiences. Most children are familiar with the concept of taking big steps and
taking small or 'baby' steps. It is not axiomatic that they would understand
that you could take a different amount of time to execute each step.  I'm sure
the applet designers gave some though on how to introduce rate change in a
manner that would be easy to comprehend.  In their own materials, they refer to
the size of the step as 'speed.' Most children would make an assumption that
taking bigger steps would get you there faster. Once they can see the results of
their 'guess,' the teacher can then expand on the concept of rate (depending on
the age of the student), and make the the connections between step length and
step frequency.

The times that I have used this applet, the question of step frequency has never
come up and does not seem relevant for the age group in this application.
If we are talking about older children, there are better applets...

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