Jay Warner wrote:
> I find these references very interesting from like, a 'pedagogical' 
> viewpoint.  My typical Business & MBA students, who are by no means 
> mathematically / analytically / statistically inclined, frequently 
> insist on seeing and using the equations, as a means of 'understanding' 
> what they are doing.  I can go along with the gag once, but after that, 
> let's have the machines do the work, OK?
> 
> As a means of 'understanding,' I think grinding through some examples 
> 'by hand' is a good thing.  Whether it really helps those who are 
> seriously math impaired, could be debatable.  But I'm willing to try it. 
> Does anyone have experience with a strictly 'pull down menu' approach?
> 
> Jay

Hi Jay.  As anyone who teaches introductory stats knows, 
textbooks have indeed been moving away from presentation 
computational formulae, and instead tend to concentrate more 
on the concepts.  I don't have a problem with that.

However, when I stand back and look at what actually happens 
in introductory stats classes today, it seems to me that 
things are not really all that different than they were when 
I was taking stats (for a psychology degree) in the 80s.  In 
classes I took, a textbook author or lecturer would proceed 
roughly as follows:

1) Present the conceptual formula for some statistic (e.g., 
the conceptual formula for the variance).

2) Point out that if you used the conceptual formula to 
calculate the statistic in question, you would often end up 
with an inaccurate answer due to rounding area.

3) Give you a computational formula for the same statistic 
that allowed you to avoid the rounding error, but provided 
little or no conceputal insight into the statistic.

PCs with stats packages were not available to us, so we did 
all the calcuations on hand calculators, using computational 
formulae.  It should come as no surprise, therefore, that we 
knew the computational formulae inside out and backwards, 
but could hardly recognize some of the conceptual formulae.

Fast forward to today's stats classes, with their emphasis 
on presentation of conceputal formulae, and "letting the 
computer do the computations".  This sounds like a great 
idea.  But, it seems to me that all we have done to the old 
sequence of events is replace use a computational formula on 
a hand calculator with use of a computer.  The point is that 
/neither/ of these activities provides any great conceputal 
insight into the statistic you are calculating.

What lecturers and textbook authors /ought/ to be doing 
instead, it seems to me, is this:

1) Ask students to perform the calculations using the 
conceptual formula, not with a hand calculator, but on the 
computer, where they can carry enough decimal places to 
avoid rounding error.  (I sometimes refer to this as using 
the computer to do the calcuations "by hand".)

2) Then, after students have had some practice with the 
conceputal formula (which should promote conceptual 
understanding), show them how to obtain the same results 
using the standard functions and procedures provided in the 
stats package of choice.

Point number 1 has obvious limitations (i.e., it works for 
something simple like variance, but perhaps not for multiple 
regression).  But the principle can be extended--i.e., use 
the building blocks you have already learned to compute 
something in a conceputal fashion BEFORE you click on a 
button that does it all for you.  For example, ask students 
generate all of the sums of squares needed for a one-way 
ANCOVA model by running the appropriate series of linear 
regresion models BEFORE they are allowed to click on an 
ANCOVA button in the stats package.  (Dave Howell's book 
Statistical Methods for Psychology gives a good example of 
this approach.)

As one regular in these groups often says...

FWIW,
Bruce
-- 
Bruce Weaver
[EMAIL PROTECTED]
www.angelfire.com/wv/bwhomedir/

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