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%UNITS OF MEASUREMENT 731215
Measurement is one of the most characteristic aspects
of the work of the natural-scientist. Measurements are
implicit in virtually all the work. The equations relate
various different historical and/or possible measurements.
Theories interrelate constellations of equations which
refer implicitly to measurements. Sophisticated equipment
is often thrust at students, and they are instructed as to
what operations to perform to obtain certain measurements.
However only rarely are students systematic-ally
introduced to basic concepts of measurement and the
developments of units in terms of which the results of
measurements are communicated and inter-compared.
Systematic measurement is not part of the typical
student's life. It is true that students are trained to
perform operations that yield conventional measurements to
facilitate the functioning of the technocratic society:
reading clocks, reading speedometers, reading
tachometers, using a ruler, stepping on a set of scales
and reading a dial, and a few other such processes. Yet,
in none of these does the person really participate in the
process of measurement in an experiment designed by self.
Before a student can understand the equations of
physics, the student must have internalized the process of
measurement, the representation of the results of
measurement and the symbolic manipulation of the results
of measurement. Developmental stages are skipped only to
fall in confusion or to regress. It is futile to ask
students to abstractly manipulate generalized statements
regarding the results of possible symbolic manipulation of
the results of measurement --- without their first having
actually designed, carried out, and concretely
manipulated specific measurements which are specific
instances of the types to which the generalized state-
ments point. The equations of physics are statements
regarding the approximate equality of the results of
possible theoretically related measurements --and--
computation procedures. Unless students have participated
in such theoretically related measurement--and--
computation procedures with insight, student consideration
of abstract equations will be without insight.
The rather universal confusion within the physics
profession regarding units of measurement Points to the
inadequate preparation which characterizes early training
in physics and science in general. There is too little
insight into the essential nature of scientific
measurement and theoretical generalization.
(c) 1999 by Paul A. Smith in
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