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Topic:  teaching about scale 
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Subject:  RE: teaching about scale 
Author:  Jeff L 
Date:  Jun 14 2005 
> In both some literature research and personal teaching experience, I
> found that students often have difficulty with the concept of
> scaling graphs. Do you directly address this issue with your
> students? I found this to be a particular problem when working with
> technology based graphing tools. It seems that the students need to
> have a good deal of experience in working with scales by hand ever
> before having them use a graphing tool.
What have you found that
> works best?
http://www.analyzemath.com/verticalscaling/verticalscaling.html  assuming this
is what you are referring to, I think the problem goes back to middle level and
perhaps earlier.
The earliest exposure for students might be map scales or it might be the notion
of scale factor. When working with scale factor in isolation, middle level
students seem to experience a disconnect between a linear measurement, an area
and a volume. They have a tendency to apply the scale factor to whatever measure
they are working with, i.e., they multiply the length by the scale factor, the
area by the scale factor, and the volume by the scale factor. Part of this is
language ("Make it twice as big.")
When working with graphs (1st quadrant  CMP Stretching and Shrinking, the Wump
family) they can follow the procedure for multiplying the xcoordinate by a
factor and multiplying the ycoordinate by a factor, but it doesn't
necessarily internalize. There is also the issue of 'the reason why'. "Scaling
the graph" may translate as "make it twice as big" which might not compute
internally.
Obviously this same process carries over into perimeter, area, volume and
surface area. I have often wondered if this is a developmental rather than an
instructional issue, or maybe kids just don't play with blocks enough.
http://mathforum.org/mathtools/tool/13433/ is a step in the right direction, but
more leadin or related activities are needed. There should be a
simultaneous process for scaling graphs with a clear explanation of the
difference.
 
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