Up until recently (even in the early days of electronic calculators)
the nearly-exclusive focus of computation was on computation with
scalars -- numbers taken one at a time, leading to a single result. With
contemporary graphing calculators (and corresponding computer-based
tools) there is the capability to store and calculate with _arrays_ of
numbers, either in parallel (e.g. adding two lists element by element)
or by reductive operations (e.g. finding row sums, products or maxima
for a given matrix). In addition to obvious efficiencies that can be
achieved by parallel computation, there are new issues that come up
that provide additional insight into algebraic properties of computation,
for example the fact that the mean of a set of data is not affected by
sorting the data. And room for new thoughts: is the sum of the means
of two data sets of equal length the same as the mean of the sum of
these two sets of data? What if we replace the word "sum" here by "product"?
Or what if we replace "mean" by "median"?
There are also important issues of notation (really the heart of
much of the teaching in introductory algebra, anyway). As far as I
know there still does not exist standard, universally-agreed-on
notation to document computations with lists, vectors, matrices, etc.
but learning _any_ formal notation to describe, document, and discuss
algebraic manipulations with arrays of numbers would be an important
plus for a student facing the need for further practical work. Arrays of
data are really what come up in applications today, and not just in
statistics. I would think that operations with arrays of numbers (including
simple work with matrices) really ought to be part of the content of any
technology-assisted experience of mathematics teaching today.
RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623
>>>> The plural of mongoose begins with p. <<<<
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