Discussion:  All Topics 
Topic:  Does step size really equal speed? 
Related Item:  http://mathforum.org/mathtools/tool/13171/ 
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Subject:  step size or time? 
Author:  Seth 
Date:  Apr 17 2007 
I looked in on your post about step size and it caused me to stop and think.
And since it did, I thought it appropriate that I respond. So here goes 
I just spent a little bit of time looking at the applet. The xaxis is
labeled "time" and the yaxis is labeled "position." Thinking about those
labels, you seem to be absolutely correct  a big assumption is being made 
that the step size equals time. As you point out, this is not necessarily the
case.
I had to think about it, though. "What if one runner stepped more slowly but
had the same length of stride?" I thought. Both runners could begin at the same
time and end the same distance away (their position) but it would take different
amounts of time for them to complete their journey. KT8 is correct, I thought.
The graph would be inaccurate if that were the case.
But then I considered your last comment
"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."
I'm thinking that this "shortcoming" might not be a shortcoming at all. You
studied the applet and it made you think about what was really occuring in the
simulation as well as on the graph. You connected what you know about rates and
graphs and real world situations and you commented on it. I read your comment
and it caused me to think more deeply about the situation. Do I agree or
disagree? Why? How can I support my opinion?
Then I thought about my 8th graders. Most of them would probably accept the
applet at face value. But some might see what you saw. They would raise the
issue. We would discuss it. I would challenge my student to defend his/her
thoughts mathematically. We would bring other students into the conversation.
I think this sort of dialogue would encourage mathematical thought and
understanding.
Ultimately, this sort of deeper thinking is what I'd love to see in my
classroom. So was it a shortcoming? I'm thinking maybe not.
Seth Leavitt
Field Middle School
Minneapolis
 
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