Re: [Phys-L] effective teaching of scaling/ratio use

[Richard Heckathorn <geepaw@wowway.com>]

Greetings, I have been told that a two-year-old, when an adult, has increased by an approximate scale value of two.  If one takes this as a starting point, then all areas increase by two squared or four times, and all volumes and weight increases by two cubed or eight times.

Have a Great Day

Website rheckathorn.weebly.com



> On Dec 20, 2014, at 1:25 AM, John Clement <clement@hal-pc.org> wrote:
>
> Explicit teaching of ratio techniques does not really change their attitudes
> about proportional reasoning.  What they really need is a dose of "Thinking
> Science" by Shayer, Adey, Yates. If you look at what they do, you might be
> able to do some of it in class.  The method uses exploration first where the
> inapplicability of their existing math paradigm is insufficient to make
> sense of the situation.  Then they have the students do bridging to other
> very different situations.  This is the application phase.  At no time are
> they told the explicit technique to use for the application phase.  However,
> there is supposed to be a class discussion about the exploration.
>
> The idea of teaching scaling is nonsense if the student has no
> "understanding" of proportional reasoning.  It will just be another
> memorized thing to be used in the specific problems in which it is
> presented.  Actually half is about the right number.  25% of advanced
> students and 75% of regular students do not use proportional reasoning.  You
> can find out the ratio by giving the Lawson test.
>
> I always recommend reading "Really Raising Standards" by Shayer & Adey.
>
> John M. Clement
> Houston, TX  
>
> > As John Denker routinely points out, using scaling laws (or 
> > ratio and proportion) is extremely valuable and powerful.  
> > This tool has great value beyond physics, reaching into 
> > carpentry, economics, and even flying airplanes :).  
> >
> > My quandry is how to get students to actually use it.  I 
> > demonstrate it in class, I give exercises and show solutions, 
> > but when it comes time for a test or quiz, about half my 
> > students act like they have never seen the technique, even 
> > when I tell them "use ratio and proportion like you did on 
> > the homework and classwork."
> >
> > The other half can't seem to grasp how to use the general 
> > concept on a new law. For example, after using the technique 
> > on the electric field of a point charge I then tell them (and 
> > show them) the far-field distance behavior of the dipole 
> > E-field.  This isn't the only situation. It seems they don't 
> > really understand the concept of scaling.
> >
> > What methods have any of you found which are effective in 
> > having students grasp the concept of scaling and apply it to 
> > a "new" relationship they haven't been drilled on before?
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