Discussion:  Roundtable 
Topic:  Handheld Computing 
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Subject:  Thinking Required for Data Analysis 
Author:  Craig Russell 
Date:  Mar 19 2003 
true that graphing calculators and spreadsheets can give "basic" regressions
quickly and easily, and students can find a "good fit" without having any idea
about what they are doing. The same thing can be said about using a formula for
the surface area of a pyramid.
The approach to data analysis throughout COMAP's Mathematics: Modeling Our World
curriculum does much to encourage critical thinking. An example from Unit 5 of
Course 3: students are given (or collect, or find) data from damped
oscillations. They examine the "period" of the data and construct sinusoids,
then use spreadsheets to examine and fit curves to the residuals. The residuals
then yield a damping function. What critical thinking is involved? Well,
students need to understand the parameters (period, amplitude, phase shift, axis
of oscillation) in sinusoidal functions, and be able to "read" those parameters
from graphs. They need to diagnose discrepancies, interpret what a residual
graph says, think about what function shapes fit the residual graph, figure out
how to adjust their initial models using the refinements, and finally discuss
whether and how their models might be applicable for extrapolations or other
situations. Without technology, students are limited to such basic calculations
and graphs that the synthesis of several ideas doesn't have a chance of
happeningespecially if the student is not good at visualization.
 
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