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Subject:   RE: confused
Author: Alan Cooper
Date: Jan 4 2005
Actually, y=f(1) is the equation of a *line*, not a point.

But the wording of the instructions doesn't actually ask for that.

In fact the instructions are ambiguous in that they just ask for the blue dot in
the equation "f(1)=blue dot" to be dragged to the "correct position". Since f(1)
is just a number, it requires more information to identify a point in the plane
and there are several "natural" choices.

For example, the point (0,f(1)) on the y-axis may seem reasonable for the
location of a "y-value" with no x specified; and (f(1),0) on the x-axis also
might be reasonable since f(1) is just a number and when there is only one
number we usually call it x.

Even if the intended choice (namely the position (1,f(1))) is judged to be "more
natural" than these others, the wording is poor and does not model the kind of
discourse that we want to encourage in students.

That said, the tool does represent a nice type of exercise, and aside from the
easily corrected wording is quite nicely done. The only other thing I would
change is build in a larger set of examples (perhaps randomly generated).

On Jan  4 2005, proofpad wrote:
> On Jan  4 2005, satellite73j wrote:
> > my students are often
> > confused by this, and i can see why.  
> > f(1) is not a point in the plane. . .
> Unless I too am confused by the above, f(1) should be
> just a number and y = f(1) is a point . . .

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